1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
Copyright © June 2005, The Aluminum Association, Inc. All rights reserved
No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form, or by any means,
electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of
The Aluminum Association, Inc.
TABLE OF
CONTENTS
Aluminum Design Manual
Table of Contents
PART
TITLE
IA
Specification for Aluminum Structures –
Allowable Stress Design
IB
Specification for Aluminum Structures –
Building Load and Resistance Factor Design
IIA
Commentary on Specification for Aluminum Structures –
Allowable Stress Design
IIB
Commentary on Specification for Aluminum Structures –
Building Load and Resistance Factor Design
III
Design Guide
IV
Materials
V
Material Properties
VI
Section Properties
VII
Design Aids
VIII
Illustrative Examples of Design
IX
Guidelines for Aluminum Sheet Metal Work in Building Construction
Appendix 1
Metric Guide for Aluminum Structural Design
Index
FOREWORD
FOREWORD
The Aluminum Design Manual includes aluminum structural design specifications and accompanying commentary, a
supplemental design guide, material properties, section properties, design aid tables and graphs, illustrative design examples
and guidelines for aluminum sheet metal work in building construction.
This edition of the Aluminum Design Manual is the product of the efforts of the Aluminum Association Engineering and Design
Task Force, whose members are listed below.
The Aluminum Association Engineering and Design Task Force
Steve Sunday, Alcoa Inc., chair
Frank Armao, Lincoln Electric Co.
Randy Killian, Conservatek Industries, Inc.
Randy Kissell, The TGB Partnership
Greg McKenna, Kawneer Company, Inc.
Craig C. Menzemer, University of Akron
George Olive, Larson Engineering of Missouri
Gerald Orrison, Temcor
Teoman Peköz, Cornell University
Frank Shoup, Alcoa Inc.
Mike Skillingberg, The Aluminum Association, Inc.
Check www.aluminum.org for ADM 2005 updates.
Aluminum Design Manual
PART I-A
Specification for
Aluminum Structures–
Allowable Stress Design
The Aluminum Association, Inc.
1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
Eighth Edition, January 2005
FOREWORD
The first edition of the Specification for Aluminum Structures was published in November, 1967, followed by subsequent editions in 1971, 1976, 1982, 1986, 1994, and 2000. This eighth edition of the allowable stress design Specification, developed as
a consensus document, includes new or revised provisions concerning
• shear yield strengths
• welded strengths
• adding 6063-T52, 6351-T6, and 7005-T53
• materials for screws used to connect aluminum parts
• factors on welded tensile ultimate strength and compressive yield strength
• welded connections (groove, fillet, plug and slot, and stud welds)
• screw pull-over
• revision of Section 1.2, Materials
• revision of Section 5, Mechanical Connections
• revision of Section 6, Fabrication and Erection
• a new Section 8, Castings
• weighted average strengths
• design stresses for wind loads
• fatigue strength for welds with permanent backing
• net effective areas for channels, I beams, zees, angles, and tees
• single angles in flexure
• tapered thickness element strength
• web crippling of extrusions
• compressive strength of complex cross sections
• strength of elements in bending in their own plane
• unbraced length in bending
These improvements and additions are the result of studies sponsored by the Aluminum Association and others. The Aluminum
Association gratefully acknowledges the efforts of the Engineering and Design Task Force in drafting this Specification and the
Engineering Advisory Committee in reviewing it.
The Aluminum Association Engineering and Design Task Force
Steve Sunday, Alcoa Inc., chair
Frank Armao, Lincoln Electric Co.
Randy Killian, Conservatek Industries, Inc.
Randy Kissell, The TGB Partnership
Greg McKenna, Kawneer Company, Inc.
Craig C. Menzemer, University of Akron
George Olive, Larson Engineering of Missouri
Gerald Orrison, Temcor
Teoman Peköz, Cornell University
Frank Shoup, Alcoa Inc.
Mike Skillingberg, The Aluminum Association, Inc.
The Aluminum Association Engineering Advisory Committee
Includes the members of the Engineering and Design Task force and the following persons:
Robert E. Abendroth, Iowa State University
Francisco Castano, Geometrica, Inc.
Terence Cavanagh, Terrapin Testing, Inc.
Karen C. Chou, Minnesota State University, Mankato
Cynthia Ebert, Larson Engineering of Missouri
January 2005
I-A-3
Andrew J. Hinkle, S & K Technologies
Dimitris Kosteas, Technical University of Munich
LeRoy Lutz, Computerized Structural Design
Brian Malloy, Alcoa Engineered Products
Ray Minor, Hapco American Flag
Carl Wagus, American Architectural Manufacturers Association
Robert W. Walton, Texas Wall Systems
Guidelines for the Preparation of Technical Inquiries on the Specification for Aluminum Structures
Technical inquiries to obtain an interpretation or request a revision to the Specification for Aluminum Structures should be
directed to:
VP, Technology
The Aluminum Association
1525 Wilson Blvd. Suite 600
Arlington, VA 22209
Fax: 703-358-2961
email: mhskilli@aluminum.org
Comments on other parts of the Aluminum Design Manual are also welcome.
Inquiries should be typewritten and include the inquirer’s name, affiliation, and address. Each inquiry should address a single
section of the Specification unless the inquiry involves two or more interrelated sections. The section and edition of the Specification should be identified.
Requests for interpretations should be phrased, where possible, to permit a “yes” or “no” answer and include the necessary
background information, including sketches where appropriate.
Requests for revisions should include proposed wording for the revision and technical justification.
Inquiries are considered at the first meeting of the Engineering and Design Task Force following receipt of the inquiry.
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November 2005
IA
Specification for Aluminum Structures—Allowable Stress Design
TABLE OF CONTENTS
Section 1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Safety Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Building Type Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Bridge Type Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.3 Other Type Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Section 2. Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1 Section Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Section 3. General Design Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 Tables Relating to Mechanical Properties and Buckling Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 Allowable Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4.1 Tension, Axial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.2 Tension in Extreme Fibers of Beams—Flat Elements In Uniform Tension . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.3 Tension in Extreme Fibers of Beams—Round or Oval Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.4 Tension in Extreme Fibers of Beams—Flat Elements In Bending in Their Own Plane . . . . . . . . . . . . . . . 26
3.4.5 Bearing on Rivets and Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.6 Bearing on Flat Surfaces and Pins and on Bolts in Slotted Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.7 Compression in Columns, Axial, Gross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.7.1 Sections Not Subject to Torsional or Torsional-Flexural Buckling . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.7.2 Doubly or Singly Symmetric Sections Subject to Torsional or Torsional-Flexural Buckling. . . . 26
3.4.7.3 Nonsymmetric Sections Subject to Torsional or Torsional-Flexural Buckling . . . . . . . . . . . . . . . 27
3.4.8 Uniform Compression in Elements of Columns Whose Buckling Axis is an Axis of Symmetry—
Flat Elements Supported On One Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4.8.1 Uniform Compression in Elements of Columns Whose Buckling Axis is not an Axis of
Symmetry—Flat Elements Supported On One Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4.9 Uniform Compression in Elements of Columns—Flat Elements Supported on Both Edges . . . . . . . . . . . 28
3.4.9.1 Uniform Compression in Elements of Columns—Flat Elements Supported on
One Edge and With Stiffener on Other Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4.9.2 Uniform Compression in Elements of Columns—Flat Elements Supported on
Both Edges and With an Intermediate Stiffener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4.10 Uniform Compression in Elements of Columns—Curved Elements Supported on Both Edges . . . . . . . . . 32
3.4.11 Compression in Beams, Extreme Fiber, Gross Section—Single Web Shapes . . . . . . . . . . . . . . . . . . . . . . 32
3.4.12 Compression in Beams, Extreme Fiber, Gross Section—Round or Oval Tubes . . . . . . . . . . . . . . . . . . . . . 32
3.4.13 Compression in Beams, Extreme Fiber, Gross Section—Solid Rectangular and Round Sections . . . . . . . 32
3.4.14 Compression in Beams, Extreme Fiber, Gross Section—Tubular Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.15 Uniform Compression in Elements of Beams—Flat Elements Supported on One Edge. . . . . . . . . . . . . . . 33
3.4.16 Uniform Compression in Elements of Beams—Flat Elements Supported on Both Edges . . . . . . . . . . . . . 34
3.4.16.1 Uniform Compression in Elements of Beams—Curved Elements Supported on Both Edges . . 34
3.4.16.2 Uniform Compression in Elements of Beams—Flat Elements Supported on
One Edge and With Stiffener on Other Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
3.4.16.3 Uniform Compression in Elements of Beams—Flat Elements Supported on
Both Edges and With an Intermediate Stiffener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.17 Compression in Elements of Beams (Element in Bending in Own Plane)—Flat Elements Supported on
Tension Edge, Compression Edge Free . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
January 2005
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3.4.18
Compression in Elements of Beams (Element in Bending in Own Plane)—
Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4.19 Compression in Elements of Beams (Element in Bending in Own Plane)—
Flat Elements Supported on Both Edges and With a Longitudinal Stiffener . . . . . . . . . . . . . . . . . . . . . . . 35
3.4.20 Shear in Elements—Unstiffened Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.21 Shear in Elements—Stiffened Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Section 4. Special Design Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
4.1 Combined Axial Load and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1.1 Combined Compression and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1.2 Combined Tension and Bending. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Torsion and Shear in Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 Torsion and Bending in Open Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.4 Combined Shear, Compression, and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.5 Longitudinal Stiffeners for Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.6 Transverse Stiffeners for Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.6.1 Stiffeners for Web Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.6.2 Bearing Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.7 Effects of Local Buckling on Member Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.7.1 Local Buckling Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.7.2 Weighted Average Axial Compressive Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.7.3 Weighted Average Bending Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.7.4 Effect of Local Buckling on Column Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.7.5 Effect of Local Buckling on Beam Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.7.6 Effective Width for Calculation of Bending Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.7.7 Web Crippling of Flat Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.7.8 Combined Web Crippling and Bending for Flat Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.8 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.8.1 Constant Amplitude Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.8.2 Variable Amplitude Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.9 Compression in Single Web Beams Including Single Web Beams With Tubular Portions . . . . . . . . . . . . . . . . . . . 47
4.9.1 Doubly Symmetric Sections and Sections Symmetric About the Bending Axis . . . . . . . . . . . . . . . . . . . . . 47
4.9.2 Singly Symmetric Sections Unsymmetric about the Bending Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.9.3 Singly Symmetric Sections Symmetric or Unsymmetric about the Bending Axis,
Doubly Symmetric Sections and Sections Without an Axis of Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.9.4 Lateral Buckling Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.9.4.1 Doubly Symmetric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.9.4.2 Singly Symmetric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.9.4.3 Special Cases—Doubly or Singly Symmetric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.9.4.4 Cantilever Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.10 Compression in Elastically Supported Flanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.11 Single Angles in Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.11.1 Bending About Geometric Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.11.2 Bending About Principal Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.12 Tapered Thickness Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.13 Compressive Strength of Beam Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.13.1 Compressive Strength of Beam Elements—Flat Elements in Uniform Compression . . . . . . . . . . . . . . . . . 51
4.13.2 Compressive Strength of Beam Elements—Flat Elements in Bending In Their Own Plane . . . . . . . . . . . . 51
Section 5. Mechanical Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52
5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.1.1 Minimum Edge Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.1.2 Maximum Spacing of Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.1.3 Block Shear Rupture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.1.4 Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.1.5 Effective Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.1.6 Long Grips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
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January 2005
5.2
5.3
5.4
5.5
5.1.7 Strength and Arrangement of Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1.8 Countersunk Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.1 Bolt Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.2 Holes and Slots for Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.3 Bolt Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.4 Bolt Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.5 Bolt Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.6 Minimum Spacing of Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.7 Lockbolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.8 Slip-Critical Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.8.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.8.2 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.8.3 Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.8.4 Design for Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.8.5 Design for Slip Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.8.6 Washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.8.7 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Riveted Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3.1 Rivet Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3.2 Holes for Cold-Driven Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3.3 Rivet Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3.4 Rivet Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3.5 Rivet Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.6 Minimum Spacing of Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.7 Blind Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.8 Hollow-End (Semi-tubular) Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Tapping Screw Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.4.1 Screw Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.4.2 Screw Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.4.2.1 Pull-Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.4.2.2 Pull-Over . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.4.3 Screw Shear and Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.4.4 Minimum Spacing of Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Building Sheathing Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.5.1 Endlaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.5.2 Sidelaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.5.3 Fasteners in Laps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.5.4 Flashing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Section 6. Fabrication and Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
6.1 Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.1.1 Punch and Scribe Marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.1.2 Temperature Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2 Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2.2 Edge Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2.3 Re-entrant Corners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2.4 Oxygen Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.3 Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.4 Holes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4.1 Fabrication Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4.2 Hole Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.5 Riveting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.5.1 Driven Head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.5.1.1 Flat Heads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.5.1.2 Cone-Point Heads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
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I-A-7
6.5.2 Hole Filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.5.3 Defective Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.6 Finishes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.6.1 Where Painting Is Required . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.6.2 Surface Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.7 Contact with Dissimilar Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.7.1 Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.7.2 Wood, Fiberboard, or Other Porous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.7.3 Concrete or Masonry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.7.4 Runoff From Heavy Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.8 Mechanical Finishes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.9 Fabrication Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.10 Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.11 Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.11.1 Erection Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.11.2 Bolt Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Section 7. Welded Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62
7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.2 Welded Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.2.2 Members with Part of the Cross Section Weld-Affected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.2.3 Columns or Beams with Transverse Welds Away from Supports and Cantilevers with
Transverse Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.3 Welded Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.3.1 Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.3.1.1 Complete Penetration and Partial Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.3.1.2 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.3.1.3 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.3.2 Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.3.2.1 Effective Throat and Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.3.2.2 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.3.3 Plug and Slot Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.3.3.1 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.3.3.2 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.3.4 Stud Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.4 Post-Weld Heat Treating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Section 8. Castings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
8.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
8.2 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
8.3 Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
8.4 Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Section 9. Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
9.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
9.2 Test Loading and Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
9.3 Number of Tests and the Evaluation of Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
9.3.1 Tests for Determining Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
9.3.2 Tests for Determining Structural Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
9.4 Testing Roofing and Siding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
9.4.1 Test Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
9.4.2 Different Thicknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
9.4.3 Allowable Loads from Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
9.4.4 Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
I-A-8
January 2005
Section 1. General
1.1 Scope
This Specification shall apply to the design of aluminum
alloy load-carrying members.
This Specification also applies to castings that meet the
requirements of Section 8.1.
1.3 Safety Factors
1.2 Materials
1.3.1 Building Type Structures
This Specification applies to the aluminum alloys listed
in Tables 3.3-1, 5.2.3-1, and 5.3.4-1 and produced to the
following ASTM specifications:
Basic allowable tensile stresses for buildings, structural
supports for highway signs, luminaires, traffic signals, and
similar structures shall be the lesser of the minimum yield
strength divided by a factor of safety of 1.65, or the minimum ultimate tensile strength divided by a factor of safety
of 1.95. Other allowable stresses for buildings and similar
structures shall be based upon the factors of safety shown
in Table 3.4-1.
B 209 Aluminum and Aluminum-Alloy Sheet and Plate
B 210 Aluminum and Aluminum-Alloy Drawn Seamless Tubes
B 211 Aluminum and Aluminum-Alloy Bar, Rod,
and Wire
B 221 Aluminum and Aluminum-Alloy Extruded Bars,
Rods, Wire, Profiles, and Tubes
B 241 Aluminum and Aluminum-Alloy Seamless Pipe
and Seamless Extruded Tube
B 247 Aluminum and Aluminum-Alloy Die Forgings,
Hand Forgings, and Rolled Ring Forgings
B 308 Aluminum-Alloy 6061-T6 Standard Structural
Profiles
B 316 Aluminum and Aluminum-Alloy Rivet and
Cold-Heading Wire and Rods
B 429 Aluminum Alloy Extruded Structural Pipe
and Tube
B 632 Aluminum Alloy Rolled Tread Plate
B 928 High Magnesium Aluminum-Alloy Sheet and
Plate for Marine Service
F 468 Nonferrous Bolts, Hex Cap Screws, and Studs
for General Use
January 2005
1.3.2 Bridge Type Structures
Basic allowable tensile stresses for bridge type structures
shall be the lesser of the minimum yield strength divided by
a factor of safety of 1.85, or the minimum ultimate tensile
strength divided by a factor of safety of 2.2. Other allowable stresses for bridge and similar structures shall be based
upon the factors of safety shown in Table 3.4-1.
1.3.3 Other Type Structures
Where it is customary or standard practice to use factors
of safety other than those given in Sections 1.3.1 or 1.3.2,
the general formulas in Table 3.4-3 shall be permitted to
be used with the desired factors of safety substituted for
nu , ny , or na .
I-A-9
Section 2. Design Procedure
2.1 Section Properties
2.3 Loads
Section properties such as cross-sectional area, moment
of inertia, section modulus, radius of gyration, and torsion
and warping constants shall be determined using nominal
dimensions. Cross section dimensions shall not vary by more
than the tolerances given in Aluminum Standards and Data.
Building-type structures shall be designed for the nominal loads given in the applicable building code or performance specification. Nominal loads shall be factored and
combined in accordance with the applicable building code
or performance specification. In the absence of a code or
performance specification, ASCE 7-02, Minimum Design
Loads for Buildings and Other Structures, shall be used.
Bridge-type structures shall be designed for the loads
given in AASHTO’s Standard Specifications for Highway
Bridges.
Other structures shall be designed for the loads given in
the performance specification.
2.2 Procedure
Computations of forces, moments, stresses, and deflections shall be in accordance with accepted methods of elastic structural analysis and engineering design. The formulas and methods for determining allowable stresses in this
Specification have been simplified in many cases for ease
of computation but are not intended to preclude the use of
more rigorous analysis.
I-A-10
January 2005
Section 3. General Design Rules
3.1 Material Properties
Minimum mechanical properties used for non-welded
material shall be as listed in Table 3.3-1.
Minimum mechanical properties used for welded material
shall be as listed in Table 3.3-2.
The following properties shall be used unless more precise values are specified:
Coefficient of
13 × 10-6/oF
thermal expansion
Density
0.1 lb/in3
Poisson’s ratio
(23 × 10-6/oC)
(2.7 × 103 kg/m3)
0.33
3.2 Nomenclature
A consistent set of units shall be used throughout this
Specification.
a = detail dimension parallel to the direction of stress
ae = equivalent width of rectangular panel
al = shorter dimension of rectangular panel
a2 = longer dimension of rectangular panel
A = cross sectional area
Ac = area of compression element (compression flange
plus 1/3 of area of web between compression
flange and neutral axis)
Ah = gross area of cross section of longitudinal
stiffener
As = area of the stiffener
Asn = thread stripping area of internal thread per unit
length of engagement
Aw = the portion of area of cross section A lying within
1.0 in. (25 mm) of a weld
b = width of section or element
be = effective width of flat element to be used in
deflection calculations
bo = width of element with an intermediate stiffener
as shown in Fig. 3.4.9.2-1
b/t = width to thickness ratio of a flat element of a
cross section
B = buckling formula intercept with the following
subscripts:
c-compression in columns
p-compression in flat elements
t-compression in curved elements
tb-bending in curved elements
br-bending in flat elements
s-shear in flat elements
c = distance from neutral axis to extreme fiber
C = buckling formula intersection (see B for
subscripts)
C = coefficient which depends on screw
location
Cb = coefficient which depends on moment gradient
January 2005
Cf = constant to be determined from Table 4.8.1-1 and
Figure 4.8.1-1
Cm = 0.6 - 0.4(M1/M2) for members whose ends are
prevented from sway
= 0.85 for members whose ends are not prevented
from swaying
CP = correction factor
Cw = torsional warping constant
of the cross section
____
Cwa = t2 sin θ (0.46Fcy + 0.02√EFcy )
Cwb = Cw3 + Ri (1– cosθ)
Cw1 = 5.4 in. (140 mm)
Cw2 = 1.3 in. (33 mm)
Cw3 = 0.4 in. or 10 mm consistent with other units used
C1 = coefficient defined in Section 4.9.4
C2 = coefficient defined in Section 4.9.4
d = depth of section or beam
df = distance between flange centroids
ds = flat width of lip stiffener shown in Fig. 3.4.9.1-1
d1 = clear distance from the neutral axis to the
compression flange
D = buckling formula slope (see B for subscripts)
D = diameter
Dh = nominal hole diameter
Dn = nominal dead load
Ds = defined in Fig. 3.4.9.1-1
Dw = nominal washer diameter
Dws = larger of the nominal washer diameter and the
screw head
e = base for natural logarithms ≈2.72
E = compressive modulus of elasticity
(See Table 3.3-1)
f = calculated stress
fa = average stress on cross section produced by axial
load
fb = maximum bending stress produced by transverse
loads and/or bending moment
fs = shear stress caused by torsion or transverse shear
loads
F = allowable stress
Fa = allowable compressive stress for a member considered as an axially loaded column according
to Sections 3.4.7 through 3.4.10
Fao = allowable compressive stress of axially loaded
member considered as a short column according
to Section 4.7.2.
Fb = allowable bending stress for members subjected
to bending only
Fc = allowable compressive stress
Fcr = local buckling stress for element from
Section 4.7.1
Fcy = compressive yield strength
Fcyw = compressive yield strength across a groove weld
(0.2% offset in 2 in. (50 mm) gage length)
π2E
Fe = elastic buckling stress divided by nu = _______
nu(kL/r)2
I-A-11
Feb = elastic lateral buckling stress of beam calculated
using Eq. 3.4.11-3 or Section 4.9 with ny = 1.0
Fec = elastic critical stress
Fec = allowable elastic lateral buckling stress of beam
calculated assuming that the elements are not
buckled
Fef = elastic torsional-flexural buckling stress
Fet = elastic torsional buckling stress
π2ECw
1 GJ + ______
Fet = ____
2
2
(K
Ar
tLt)
2
πE
Fex = ______
kxLb 2
____
rx
Fm = mean value of the fabrication factor
Fn = allowable stress for cross section 1.0 in. (25 mm)
or more from weld
Fpw = allowable stress on cross section, part of whose
area lies within 1.0 in. (25 mm) of a weld
Frb = allowable stress for beam with buckled elements
Frc = allowable stress for column with buckled
elements
Fs = allowable shear stress for members
subjected only to torsion or shear
FST = allowable stress according to Section 3.4.9.1 or
3.4.16.2
Fsu = shear ultimate strength
Fsuw = shear ultimate strength within 1.0 in.
(25 mm) of a weld
Ft = allowable tensile stress for the member loaded
only axially according to Section 3.4.1
Ftu = tensile ultimate strength
Ftuw = tensile ultimate strength across a groove weld
Ftul = tensile ultimate strength of member in contact
with the screw head
Ftu2 = tensile ultimate strength of member not in
contact with the screw head
Fty = tensile yield strength
Ftyw = tensile yield strength across a groove weld
(0.2% offset in 2 in. (50 mm) gage length)
FUT = allowable stress according to Section 3.4.9.1
or 3.4.16.2
Fw = allowable stress on cross section if entire area
were to lie within 1.0 in. (25 mm) of a weld
Fy = either Fty or Fcy, whichever is smaller
g = spacing of rivet or bolt holes perpendicular to
direction of load
go = distance from shear center to the point of
application of load
G = shear modulus
Gf = grip of rivet or bolt
h = clear height of shear web
I = moment of inertia
Ib = required moment of inertia of bearing stiffener
Icy = moment of inertia of compression flange
about web
Ih = moment of inertia of longitudinal stiffener
O
(
( )
I-A-12
)
Io = moment of inertia of the stiffener about the centroidal axis of the stiffener parallel to the flat
element that is stiffened
Is = moment of inertia of transverse stiffener to resist
shear buckling
Ix = moment of inertia of a beam about axis
perpendicular to web
Iy = moment of inertia of a beam about axis parallel
to web
Iyc = moment of inertia of compression element about
axis parallel to vertical web
j = parameter defined by Eq. 4.9.3-5 or -6
J = torsion constant
k = the effective length factor. k shall be taken larger
than or equal to unity unless rational analysis
justifies a smaller value
kt = coefficient for tension members
kx = effective length coefficient for buckling about the
x-axis
ky = effective length coefficient for buckling about the
y-axis
kl = coefficient for determining slenderness limit S2
for sections for which the allowable compressive
stress is based on ultimate strength
k2 = coefficient for determining allowable compressive stress in sections with slenderness ratio
above S2 for which the allowable compressive
stress is based on ultimate strength
Ks = coefficient in Section 5.4.2.1
Kt = effective length coefficient for torsional buckling.
Kt shall be taken larger than or equal to unity
unless rational analysis justifies a smaller value
L = unsupported length in the plane of bending
Lb = unbraced length for bending
Ln = nominal live load
Ls = length of tube between circumferential stiffeners
Lt = unbraced length for twisting
m = constant to be determined from Table 4.8.1-1
M = bending moment applied to the member
Ma = allowable bending moment for the member if
bending moment alone is applied to the member
MA = absolute value of moment at quarter-point of the
unbraced beam segment
MB = absolute value of moment at mid-point of the
unbraced beam segment
MC = absolute value of moment at three-quarter point
of the unbraced beam segment
Me = elastic critical moment
Mi = bending strength of member with intermediate
thickness
Mm = mean value of the material factor
MMAX = absolute value of maximum moment in the
unbraced beam segment
M1 = bending strength of member of thinnest material
M2 = bending strength of member of thickest material
January 2005
M1/M2 = ratio of end moments where M2 is the larger of
the two end moments and M1/M2 is positive when
the member is bent in reverse curvature, negative
when bent in single curvature
n = number of tests
n = number of threads per unit length for a screw
na = factor of safety on appearance of buckling
ns = factor of safety for screw connections
nu = factor of safety on ultimate strength
ny = factor of safety on yield strength
N = length of bearing at reaction or concentrated load
N = number of cycles to failure
Ns = number of stress ranges in the spectrum
P = applied interior reaction or concentrated load per
web for flat webs
Pas = allowable shear force per screw
Pat = allowable tensile force per screw
Pbs = concentrated load on bearing stiffener
Pc = allowable reaction or concentrated load per web
Pnot = nominal pull-out strength per screw
Pnov = nominal pull-over strength per screw
Pns = nominal shear strength per screw
Pnt = nominal tensile strength per screw
q = uniform design load
r = radius
of gyration
_______________
2
ro = √r x + r y2 + x o2 + y o2
rs = radius of gyration of the stiffener
rx , ry = radii of gyration of the cross-section about the centroidal principal axes (see Section 4.9.2 for rye of
singly symmetric sections unsymmetric about the
bending axis)
rye = effective radius of gyration
R = transition radius, the radius of an attachment of
the weld detail
Rb = mid-thickness radius of a round element or maximum mid-thickness radius of an oval element
Ri = bend radius at juncture of flange and web
measured to inside surface of bend
Rs = stress ratio, the ratio of minimum stress to
maximum stress
s = spacing of transverse stiffeners (clear distance
between stiffeners for stiffeners consisting of a
pair of members, one on each side of the web,
center-to-center distance between stiffeners consisting of a member on one side of the web only);
spacing of rivet or bolt holes parallel to direction
of load___
E
S = 1.28 ___
Fcy
Sc = section modulus of a beam, compression side
Sra = the applied stress range
Srd = allowable stress range
Sre = equivalent stress range
Sri = the ith stress range in the spectrum
St = section modulus of a beam, tension side
Sw = size of a weld
Sx = standard deviation of the test results
S1, S2 = slenderness limits
t = thickness of element
tavg = the average thickness of the element
tc = depth of full thread engagement of screw into t2
not including tapping or drilling point
ti = thickness of the intermediate thickness material
tested
tmax = thickness of thickest material tested
tmax = greater thickness of a tapered thickness element
tmin = thickness of thinnest material tested
tmin = lesser thickness of a tapered thickness element
t1 = thickness of member in contact with the screw
head
t2 = thickness of member not in contact with the
screw head
U = parameter defined by Eq. 4.9.3-8
V = shear force on web at stiffener location
VF = coefficient of variation of the fabrication factor
VM = coefficient of variation of the material factor
VP = coefficient of variation of the ratio of the observed
failure loads divided by the average value of all the
observed failure loads
VQ = coefficient of variation of the loads
xo = x - coordinate of the shear center
Xa = strength at which 99% of the material is expected
to conform at a confidence level of 95%
Xi = failure load of ith test
Xm = mean of the test results
yo = y - coordinate of the shear center
α = Dn /Ln
αi = number of cycles in the spectrum of the ith stress
range divided by the total
number of cycles
αs = a factor equal to unity for a stiffener consisting
of equal members on both sides of the web and
equal to 3.5 for a stiffener consisting of a member on one side only
β = 1 – (xo /ro)2
βo = the target reliability index
βs = spring constant (transverse force applied to the
compression flange of the member of unit length
divided by the deflection due to the force)
(tmax – tmin)
δ = _________
for tapered thickness elements
t
min
√
λs = equivalent slenderness ratio for an
intermediate stiffener
ρst = ratio defined in Section 3.4.9.1 and 3.4.16.2
θ = angle between plane of web and plane of bearing
surface (θ ≤ 90°)
January 2005
I-A-13
3.3 Tables Relating to Mechanical
Properties and Buckling Constants
This Section consists of the following tables concerning
formulas for determining allowable stresses and constants
and coefficients needed for these formulas:
3.3-1
Minimum Mechanical Properties for Aluminum Alloys
3.3-1M Minimum Mechanical Properties for Aluminum Alloys
I-A-14
3.3-2
Minimum Mechanical Properties for Welded
Aluminum Alloys
3.3-2M Minimum Mechanical Properties for Welded
Aluminum Alloys
3.3-3
Formulas for Buckling Constants for Products Whose Temper Designation Begins
With -O, -H, -T1, -T2, T3, or -T4
3.3-4
Formulas for Buckling Constants for Products Whose Temper Designation Begins
With -T5, -T6, -T7, -T8, or -T9
January 2005
Table 3.3-1
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
1100-H12
-H14
2014-T6
-T651
-T6, T6510, T6511
-T6, T651
Alclad
2014-T6
-T6
-T651
3003-H12
-H14
-H16
-H18
-H12
-H14
-H16
-H18
Alclad
3003-H12
-H14
-H16
-H18
-H14
-H18
3004-H32
-H34
-H36
-H38
-H34
-H36
Alclad
3004-H32
-H34
-H36
-H38
-H131, H241, H341
-H151, H261, H361
3005-H25
-H28
3105-H25
5005-H12
-H14
-H16
-H32
-H34
-H36
5050-H32
-H34
-H32
-H34
THICKNESS
RANGE
in.
Ftu
ksi
Fty
ksi
Fcy
ksi
Fsu
ksi
All
All
0.040 to 0.249
0.250 to 2.000
All
All
14
16
66
67
60
65
11
14
58
59
53
55
10
13
59
58
52
53
9
10
40
40
35
38
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (ksi)
10,100
10,100
10,900
10,900
10,900
10,900
Sheet
Sheet
Plate
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Drawn Tube
Drawn Tube
0.025 to 0.039
0.040 to 0.249
0.250 to 0.499
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.006 to 0.128
All
All
All
All
63
64
64
17
20
24
27
17
20
24
27
55
57
57
12
17
21
24
12
17
21
24
56
58
56
10
14
18
20
11
16
19
21
38
39
39
11
12
14
15
11
12
14
15
10,800
10,800
10,800
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.006 to 0.128
0.025 to 0.259
0.010 to 0.500
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.006 to 0.128
0.018 to 0.450
0.018 to 0.450
16
19
23
26
19
26
28
32
35
38
32
35
11
16
20
23
16
23
21
25
28
31
25
28
9
13
17
19
15
20
18
22
25
29
24
27
10
12
14
15
12
15
17
19
20
21
19
20
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Sheet
Cold Fin. Rod & Bar
Drawn Tube
Cold Fin. Rod & Bar
Drawn Tube
0.017 to 0.249
0.009 to 0.249
0.006 to 0.162
0.006 to 0.128
0.024 to 0.050
0.024 to 0.050
0.013 to 0.050
0.006 to 0.080
0.013 to 0.080
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.017 to 2.000
0.009 to 0.249
All
27
31
34
37
31
34
26
31
23
18
21
24
17
20
23
22
25
22
20
24
27
30
26
30
22
27
19
14
17
20
12
15
18
16
20
16
17
21
24
28
22
28
20
25
17
13
15
18
11
14
16
14
18
15
16
18
19
21
18
19
15
17
14
11
12
14
11
12
13
14
15
13
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
All
25
20
19
15
10,100
PRODUCT
Plate, Drawn Tube,
)
( Sheet,
Rolled Rod & Bar
Sheet
Plate
Extrusions
Cold Finished Rod & Bar,
Drawn Tube
For all footnotes, see last page of this Table.
January 2005
I-A-15
Table 3.3-1
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
5052-O
-H32
-H34
-H36
5083-O
-H111
-H111
-O
-H116
-H32, H321
-H116
-H32, H321
5086-O
-H111
-H111
-O
-H112
-H112
-H112
-H112
-H116
-H32
-H34
5154-H38
5454-O
-H111
-H111
-H112
-O
-H32
-H34
5456-O
-H116
-H32, H321
-H116
-H32, H321
-H116
-H32, H321
6005-T5
6061-T6, T651
-T6, T6510, T6511
-T6, T651
-T6
-T6
6063-T5,
-T52
-T5
-T6
6066-T6, T6510, T6511
6070-T6, T62
6105-T5
6351 -T5
6351 -T6
6463-T6
7005-T53
PRODUCT
Sheet & Plate
Sheet & Plate
Cold Fin. Rod & Bar
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Extrusions
Extrusions
Extrusions
Sheet & Plate
Plate
Plate
Plate
Plate
Sheet & Plate
Sheet & Plate
Drawn Tube
Sheet & Plate
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Plate
Plate
Extrusions
Sheet & Plate
Extrusions
Cold Fin. Rod & Bar
Drawn Tube
Pipe
Extrusions
Extrusions
Extrusions
Extrusions & Pipe
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
(
)
THICKNESS
RANGE
in.
Ftu
ksi
Fty
ksi
Fcy
ksi
Fsu
ksi
0.006 to 3.000
All
All
25
31
34
9.5
23
26
9.5
21
24
16
19
20
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (ksi)
10,200
10,200
10,200
0.006 to 0.162
up thru 5.000
up thru 0.500
0.501 to 5.000
0.051 to 1.500
0.188 to 1.500
0.188 to 1.500
1.501 to 3.000
1.501 to 3.000
up thru 5.000
up thru 0.500
0.501 to 5.000
0.020 to 2.000
0.025 to 0.499
0.500 to 1.000
1.001 to 2.000
2.001 to 3.000
All
All
37
39
40
40
40
44
44
41
41
35
36
36
35
36
35
35
34
40
40
29
16
24
24
18
31
31
29
29
14
21
21
14
18
16
14
14
28
28
26
16
21
21
18
26
26
24
24
14
18
18
14
17
16
15
15
26
26
22
24
24
23
25
26
26
24
24
21
21
21
21
22
21
21
21
24
24
10,200
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
All
44
34
32
26
10,400
0.006 to 0.128
up thru 5.000
up thru 0.500
0.501 to 5.000
up thru 5.000
0.020 to 3.000
0.020 to 2.000
0.020 to 1.000
0.051 to 1.500
0.188 to 1.250
0.188 to 1.250
1.251 to 1.500
1.251 to 1.500
1.501 to 3.000
1.501 to 3.000
up thru 1.000
0.010 to 4.000
All
up thru 8.000
0.025 to 0.500
All
up thru 0.500
up thru 1.000
0.500 to 1.000
All
All
up thru 2.999
up thru 0.500
up thru 1.000
up thru 0.750
up thru 0.500
up thru 0.750
45
31
33
33
31
31
36
39
42
46
46
44
44
41
41
38
42
38
42
42
38
22
22
21
30
50
48
38
38
42
30
50
35
12
19
19
12
12
26
29
19
33
33
31
31
29
29
35
35
35
35
35
35
16
16
15
25
45
45
35
35
37
25
44
33
12
16
16
13
12
24
27
19
27
27
25
25
25
25
35
35
35
35
35
35
16
16
15
25
45
45
35
35
37
25
43
24
19
20
19
19
19
21
23
26
27
27
25
25
25
25
24
27
24
25
27
24
13
13
12
19
27
29
24
24
27
19
28
10,300
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,500
1. Ftu and Fty are minimum specified values (except Fty for 1100-H12, H14 Cold Finished Rod and Bar and Drawn Tube, Alclad 3003-H18 Sheet and
5050-H32, H34 Cold Finished Rod and Bar which are minimum expected values); other strength properties are corresponding minimum expected
values.
2. Typical values. For deflection calculations an average modulus of elasticity is used; this is 100 ksi lower than values in this column.
I-A-16
May 2005
Table 3.3-1M
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
1100-H12
-H14
2014-T6
-T651
-T6, T6510, T6511
-T6, T651
Alclad
2014-T6
-T6
-T651
3003-H12
-H14
-H16
-H18
-H12
-H14
-H16
-H18
Alclad
3003-H12
-H14
-H16
-H18
-H14
-H18
3004-H32
-H34
-H36
-H38
-H34
-H36
Alclad
3004-H32
-H34
-H36
-H38
-H131, H241, H341
-H151, H261, H361
3005-H25
-H28
3105-H25
5005-H12
-H14
-H16
-H32
-H34
-H36
5050-H32
-H34
-H32
-H34
THICKNESS
RANGE
mm
Ftu
MPa
Fty
MPa
Fcy
MPa
Fsu
MPa
All
All
1.00 to 6.30
6.30 to 50.00
All
All
95
110
455
460
415
450
75
95
400
405
365
380
70
90
405
400
360
365
62
70
275
275
240
260
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (MPa)
69,600
69,600
75,200
75,200
75,200
75,200
Sheet
Sheet
Plate
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Drawn Tube
Drawn Tube
0.63 to 1.00
1.00 to 6.30
6.30 to 12.50
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.15 to 3.20
All
All
All
All
435
440
440
120
140
165
185
120
140
165
185
380
395
395
85
115
145
165
85
115
145
165
385
400
385
70
95
125
140
75
110
130
145
260
270
270
75
85
95
105
75
85
95
105
74,500
74,500
74,500
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.15 to 3.20
0.63 to 6.30
0.25 to 12.50
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.15 to 3.20
0.45 to 11.50
0.45 to 11.50
115
135
160
180
135
180
190
220
240
260
220
240
80
110
140
160
110
160
145
170
190
215
170
190
62
90
115
130
105
140
125
150
170
200
165
185
70
85
95
105
85
105
115
130
140
145
130
140
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Sheet
Cold Fin. Rod & Bar
Drawn Tube
Cold Fin. Rod & Bar
Drawn Tube
0.40 to 6.30
0.20 to 6.30
0.15 to 4.00
0.15 to 3.20
0.60 to 1.20
0.60 to 1.20
0.32 to 1.20
0.15 to 2.00
0.32 to 2.00
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.40 to 6.30
0.20 to 6.30
All
185
215
235
255
215
235
180
215
160
125
145
165
120
140
160
150
170
150
140
165
185
205
180
205
150
185
130
95
115
135
85
105
125
110
140
110
115
145
165
195
150
195
140
170
115
90
105
125
75
95
110
95
125
105
110
125
130
145
125
130
105
115
95
75
85
95
75
85
90
95
105
90
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
All
170
140
130
105
69,600
PRODUCT
Plate, Drawn Tube,
)
( Sheet,
Rolled Rod & Bar
Sheet
Plate
Extrusions
Cold Finished Rod & Bar,
Drawn Tube
For all footnotes, see last page of this Table.
January 2005
I-A-17
Table 3.3-1M
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
5052-O
-H32
-H34
-H36
5083-O
-H111
-H111
-O
-H116
-H32, H321
-H116
-H32, H321
5086-O
-H111
-H111
-O
-H112
-H112
-H112
-H116
-H32
-H34
5154 -H38
5454-O
-H111
-H111
-H112
-O
-H32
-H34
5456-O
-H116
-H32, H321
-H116
-H32, H321
-H116
-H32, H321
6005-T5
6061-T6, T651
-T6, T6510, T6511
-T6, T651
-T6
-T6
6063-T5,
-T52
-T5
-T6
6066-T6, T6510, T6511
6070-T6, T62
6105 -T5
6351-T5
6351-T6
6463-T6
7005-T53
PRODUCT
Sheet & Plate
Sheet & Plate
Cold Fin. Rod & Bar
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Plate
Plate
Sheet & Plate
Sheet & Plate
Drawn Tube
Sheet & Plate
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Plate
Plate
Extrusions
Sheet & Plate
Extrusions
Cold Fin. Rod & Bar
Drawn Tube
Pipe
Extrusions
Extrusions
Extrusions
Extrusions & Pipe
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
(
)
THICKNESS
RANGE
mm
Ftu
MPa
Fty
MPa
Fcy
MPa
Fsu
MPa
0.15 to 80.00
All
All
170
215
235
65
160
180
66
145
165
110
130
140
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (MPa)
70,300
70,300
70,300
0.15 to 4.00
up thru 13.00
up thru 12.70
12.70 to 130.00
1.20 to 6.30
4.00 to 40.00
4.00 to 40.00
40.00 to 80.00
40.00 to 80.00
up thru 130.00
up thru 12.70
12.70 to 130.00
0.50 to 50.00
4.00 to 12.50
12.50 to 40.00
40.00 to 80.00
1.60 to 50.00
All
255
270
275
275
275
305
305
285
285
240
250
250
240
250
240
235
275
275
200
110
165
165
125
215
215
200
200
95
145
145
95
125
105
95
195
195
180
110
145
145
125
180
180
165
165
95
125
125
95
115
110
105
180
180
150
165
165
160
170
180
180
165
165
145
145
145
145
150
145
145
165
165
70,300
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
All
300
235
220
180
71,700
0.15 to 3.20
up thru 130.00
up thru 12.70
12.70 to 130.00
up thru 130.00
0.50 to 80.00
0.50 to 50.00
0.50 to 25.00
1.20 to 6.30
4.00 to 12.50
4.00 to 12.50
12.50 to 40.00
12.50 to 40.00
40.00 to 80.00
40.00 to 80.00
up thru 25
0.25 to 100.00
All
up thru 200
0.63 to 12.50
All
up thru 12.50
up thru 25.00
12.50 to 25.00
All
All
up thru 80.00
up thru 12.50
up thru 25.00
up thru 20.00
up thru 12.50
up thru 20.00
310
215
230
230
215
215
250
270
290
315
315
305
305
285
285
260
290
260
290
290
260
150
150
145
205
345
330
260
260
290
205
345
240
85
130
130
85
85
180
200
130
230
230
215
215
200
200
240
240
240
240
240
240
110
110
105
170
310
310
240
240
255
170
305
230
85
110
110
90
85
165
185
130
185
185
170
170
170
170
240
240
240
240
240
240
110
110
105
170
310
310
240
240
255
170
295
165
130
140
130
130
130
145
160
180
185
185
170
170
170
170
165
185
165
170
185
165
90
90
85
130
185
200
165
165
185
130
195
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
72,400
1. Ftu and Fty are minimum specified values (except Fty for 1100-H12, H14 Cold Finished Rod and Bar and Drawn Tube, Alclad 3003-H18 Sheet and
5050-H32, H34 Cold Finished Rod and Bar which are minimum expected values); other strength properties are corresponding minimum expected
values.
2. Typical values. For deflection calculations an average modulus of elasticity is used; this is 700 MPa lower than values in this column.
I-A-18
January 2005
Table 3.3-2
MINIMUM MECHANICAL PROPERTIES FOR WELDED ALUMINUM ALLOYS
All
All
TENSION
Ftuw1
Ftyw2
ksi
ksi
11
3.5
14
5
All
All
13
22
4.5
4.5
8.5
8.5
All
Sheet
All
All
All
Extrusions
Sheet & Plate
Plate
Extrusions
Plate
Sheet & Plate
Sheet
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Plate
Extrusions
All
All
All
Extrusions
Extrusions
Extrusions
Extrusions
21
17
15
18
25
39
40
39
35
35
35
30
31
31
31
42
41
24
24
24
17
24
24
17
40
8
6.5
5
6
9.5
16
18
17
14
14
14
11
12
12
12
19
18
13
15
11
8
15
11
8
24
8
6.5
5
6
9.5
15
18
17
13
14
14
11
11
12
12
18
17
13
15
11
8
15
11
8
24
ALLOY AND TEMPER
1100-H12, H14
3003-H12, H14, H16, H18
Alclad
3003-H12, H14, H16, H18
3004-H32, H34, H36, H38
Alclad
3004-H32, H34, H36, H38
3005-H25
5005-H12, H14, H32, H34
5050-H32, H34
5052-O, H32, H34
5083-O, H111
5083-O, H116, H32, H321
5083-O, H116, H32, H321
5086-O, H111
5086-H112
5086-O, H32, H34, H116
5154-H38
5454-O, H111
5454-H112
5454-O, H32, H34
5456-O, H116, H32, H321
5456-O, H116, H32, H321
6005-T5
6061-T6, T651, T6510, T65113
6061-T6, T651, T6510, T65114
6063-T5, T52, T6
6351-T5, T63
6351-T5, T64
6463-T6
7005-T53
PRODUCT
THICKNESS
RANGE
in.
0.188-1.500
1.501-3.000
0.250-2.000
0.188-1.500
1.501-3.000
up thru 0.250
over 0.375
over 0.375
0.125-0.500
up thru 0.750
COMPRESSION
Fcyw2
ksi
SHEAR
Fsuw
ksi
3.5
5
8
10
10
14
13
12
9
12
16
23
24
24
21
21
21
19
19
19
19
25
25
15
15
15
11
15
15
11
22
1. Filler wires are listed in Table 7.1-1. Values of Ftuw are AWS D1.2 weld qualification values.
2. 0.2% offset in 2 in. gage length across a groove weld.
3. Values when welded with 5183, 5356, or 5556 alloy filler wire, regardless of thickness. Values also apply to thicknesses less than or equal
to 0.375 in. when welded with 4043, 5554, or 5654 alloy filler wire.
4. Values when welded with 4043, 5554, or 5654 alloy filler wire.
January 2005
I-A-19
Table 3.3-2M
MINIMUM MECHANICAL PROPERTIES FOR WELDED ALUMINUM ALLOYS
All
All
TENSION
Ftuw1
Ftyw2
MPa
MPa
75
25
95
35
All
All
90
150
30
60
30
60
70
95
All
Sheet
All
All
All
Extrusions
Sheet & Plate
Plate
Extrusions
Plate
Sheet & Plate
Sheet
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Plate
Extrusions
All
All
All
Extrusions
Extrusions
Extrusions
Extrusions
145
115
105
125
170
270
270
270
240
240
240
205
215
215
215
285
285
165
165
165
115
165
165
115
275
55
45
35
40
65
110
115
115
95
95
95
75
85
85
85
125
125
90
105
80
55
105
80
55
165
55
45
35
40
65
110
115
115
85
95
95
75
85
85
85
125
120
90
105
80
55
105
80
55
165
90
85
62
85
110
160
165
165
145
145
145
130
130
130
130
170
170
105
105
105
75
105
105
75
155
ALLOY AND TEMPER
1100-H12, H14
3003-H12, H14, H16, H18
Alclad
3003-H12, H14, H16, H18
3004-H32, H34, H36, H38
Alclad
3004-H32, H34, H36, H38
3005-H25
5005-H12, H14, H32, H34
5050-H32, H34
5052-O, H32, H34
5083-O, H111
5083-O, H116, H32, H321
5083-O, H116, H32, H321
5086-O, H111
5086-H112
5086-O, H32, H34, H116
5154-H38
5454-O, H111
5454-H112
5454-O, H32, H34
5456-O, H116, H32, H321
5456-O, H116, H32, H321
6005-T5
6061-T6, T651, T6510, T65113
6061-T6, T651, T6510, T65114
6063-T5, T52, T6
6351-T5, T63
6351-T5, T64
6463-T6
7005-T53
PRODUCT
THICKNESS
RANGE
mm
6.30-38.00
38.00-80.00
6.30-50.00
6.30-38.00
38.00-80.00
up thru 12.50
over 9.50
over 9.50
3.20-12.50
up thru 20.00
COMPRESSION
Fcyw2
MPa
SHEAR
Fsuw
MPa
25
35
55
70
1. Filler wires are listed in Table 7.1-1. Values of Ftuw are AWS D1.2 weld qualification values.
2. 0.2% offset in 50 mm gage length across a groove weld.
3. Values when welded with 5183, 5356, or 5556 alloy filler wire, regardless of thickness. Values also apply to thicknesses less than or equal
to 9.5 mm when welded with 4043, 5554, or 5654 alloy filler wire.
4. Values when welded with 4043, 5554, or 5654 alloy filler wire.
I-A-20
January 2005
Table 3.3-3
FORMULAS FOR BUCKLING CONSTANTS FOR PRODUCTS WHOSE TEMPER
DESIGNATION BEGINS WITH -O, -H, -T1, -T2, -T3, OR -T4
Intercept
ksi
Type of Member and Stress
Intercept
MPa
[ ( )]
[ ( )]
[ ( )]
[ ( )]
[ ( )]
Slope
[ ( )]
[ ( ) ]
[ ( )]
[ ( )]
[ ( ) ]
Intersection
Compression in Columns
and Beam Flanges
Fcy 1/2
Bc = Fcy 1 + _____
1000
Fcy 1/2
Bc = Fcy 1 + _____
6900
B 6B 1/2
Dc = ___c ___c
20 E
( )
2B
Cc = ____c
3Dc
Axial Compression
in Flat Elements
Fcy 1/3
Bp = Fcy 1 + ______
7.6
Fcy 1/3
Bp = Fcy 1 + ______
14.5
Bp 6Bp 1/2
Dp = ___ ___
20 E
( )
2Bp
Cp = ____
3Dp
Axial Compression
in Curved Elements
Fcy 1/5
Bt = Fcy 1 + ______
5.8
Bending Compression
in Flat Elements
Bending Compression
in Curved Elements
( )
F
F
B 6B
B = 1.3F 1 +
B = 1.3F 1 +
D =
7
13.3
20 ( E )
F
F
B B
B = 1.5F 1 +
B = 1.5F 1 +
D =
2.7 ( E )
5.8
8.5
F
F
( F /√3 )
( F /√ 3 )
B 6B
B =
1+
B =
1+
D =
[
]
(E)
[
]
11.8
20
6.2
√3
√3
1/3
br
cy
cy
______
y
y
______
Ultimate Strength of Flat
Elements in Compression
or Bending
cy
ty
_________
k1 = 0.50,
k2 = 2.04
cy
_____
br
1/5
tb
y
y
_____
__
1/3
ty
___
__
s
B B 1/3
Dt = ___t __t
3.7 E
1/3
br
1/5
tb
__
Shear
in Flat Elements
Fcy 1/5
Bt = Fcy 1 + ______
8.5
s
ty
___
__
tb
1/3
ty
_________
s
br ____
br
___
tb ___
tb
___
___s ___s
1/2
Ct*
2Bbr
Cbr = ____
3Dbr
(
)
1/3
Btb – Bt 2
Ctb = _______
Dtb – Dt
1/2
2B
Cs = ____s
3Ds
*Ct shall be determined using a plot of curves of limit state stress based on elastic and inelastic buckling or by trial and error solution.
January 2005
I-A-21
Table 3.3-4
FORMULAS FOR BUCKLING CONSTANTS FOR PRODUCTS WHOSE TEMPER
DESIGNATION BEGINS WITH -T5, -T6, -T7, -T8, OR -T9
Intercept
ksi
Type of Member and Stress
Intercept
MPa
[ ( )]
Compression in Columns
and Beam Flanges
Fcy 1/2
Bc = Fcy 1 + _____
2250
Axial Compression
in Flat Elements
( Fcy )1/3
Bp = Fcy 1 + ______
11.4
Axial Compression
in Curved Elements
( Fcy )1/5
Bt = Fcy 1 + ______
8.7
Bending Compression
in Flat Elements
( Fcy )1/3
Bbr = 1.3Fcy 1 + _____
7
Bending Compression
in Curved Elements
( Fy )1/5
Btb = 1.5Fy 1 + _____
8.7
Shear
in Flat Elements
Fty /√ 3 1/3
Fty
__ 1 + _________
Bs = ___
9.3
√3
Ultimate Strength of Flat
Elements in Compression
k1 = 0.35,
k2 = 2.27
Ultimate Strength of Flat
Elements in Bending
k1 = 0.50,
k2 = 2.04
Slope
[ (
)]
B B 1/2
Dc = ___c __c
10 E
[
]
Bp Bp 1/2
Dp = ___ __
10 E
[
]
B B 1/3
Dt = ___t __t
4.5 E
Fcy 1/2
Bc = Fcy 1 + ______
15510
[
]
( Fcy )1/3
Bp = Fcy 1 + ______
21.7
[
]
( Fcy )1/5
Bt = Fcy 1 + ______
12.8
[
[
[
(
__
]
]
)
[
( Fcy )1/3
Bbr = 1.3Fcy 1 + _____
13.3
[
( Fy )1/5
Btb = 1.5Fy 1 + _____
12.8
]
[
(
__
)
]
]
Fty /√ 3 1/3
Fty
__ 1 + _________
Bs = ___
17.7
√3
( )
B
Cc = 0.41___c
Dc
( )
Bp
Cp = 0.41___
Dp
( )
Ct*
( )
2Bbr
Cbr = ____
3Dbr
( )
Btb – Bt 2
Ctb = _______
Dtb – Dt
( )
B
Cs = 0.41___s
Ds
Bbr ____
6Bbr 1/2
Dbr = ___
20 E
Btb ___
Btb 1/3
Dtb = ___
2.7 E
]
Intersection
B B 1/2
Ds = ___s __s
10 E
(
)
*Ct shall be determined using a plot of curves of limit state stress based on elastic and inelastic buckling or by trial and error solution.
I-A-22
January 2005
3.4 Allowable Stresses
• Values of k1 and k2 shall be taken from Tables 3.3-3
and 3.3-4.
The formulas of this Section are also listed in Table 3.4-3.
Allowable stresses shall be determined in accordance
with provisions of this Specification.
In the following subsections:
• The factors nu, ny, and na shall be taken from Table 3.4-1.
• Values of coefficient kt shall be taken from Table 3.4-2.
Table 3.4-1
SAFETY FACTORS
Building and similar type
structures
Bridge and similar type
structures
nu
1.95
2.20
ny
1.65
1.85
na
1.20
1.35
Other safety factors are given throughout this Specification.
Table 3.4-2
COEFFICIENT kt
Alloy and Temper
Non-welded or Regions
Farther than 1.0 in.
(25 mm) from a Weld
Regions Within 1.0 in.
(25 mm) of a Weld
2014-T6, -T651, -T6510, -T6511
Alclad 2014-T6, -T651
1.25
–
6066-T6, -T6510, -T6511
1.1
–
6070-T6, -T62
1.1
–
All Others Listed in Table 3.3-1
1.0
1.0
kt is used in Sections 3.4.1, 3.4.2, 3.4.3, and 3.4.4.
January 2005
I-A-23
I-A-24
March 2005
5
On rivets and bolts
b
4
Flat elements in bending in
their own plane (webs)
9.2
10
Curved elements
supported on both
edges
bo
9.1
9
ny
Fcy
___
ny
t
(
)
Dt
nuFcy 2
Bt – _____
ny
1.6Dp
Rb _________
__
=
t
b = ________
__
nu
p
p
p
t
t
)
)
)
(
√t )
___
Rb
1 Bt – Dt __
__
See Section 3.4.9.2
See Section 3.4.9.1
nu (
p
1 B – 1.6D __
b
__
nu (
nuFcy
Bp – _____
ny
ny
5.1 Dp
Fcy
___
t
)
1 B – 5.1D __
b
__
p
r
nuFcy
Bp – _____
ny
b
________
__ =
t
5.1Dp
c
Fcy
___
8.1
p
c
nu (
nu (
t
8
nuFcy
Bp – _____
ny
Dc
b = ________
__
Fcy
___
r
kL = ________
___
1 B – D ___
kL
__
Allowable Stress
S1 < Slenderness < S2
ny
ny
nuFcy
Bc – _____
ny
Slenderness
Limit S1
t
t
t
t
Rb
__
=C
1.6Dp
5.1
k1Bp
b = _____
__
t
Cp
b = ___
__
5.1Dp
c
k1Bp
b = _____
__
r
kL = C
___
Slenderness
Limit S2
( )(
)
2
Rb 1 + √ R___
b/t
16nu __
t
35
π2E ____
_________________
nu(1.6b/t)
____
k2√BpE
________
nu(5.1b/t)2
π2E
_________
nu(5.1b/t)
____
k2√BpE
________
(r)
π2E
______
kL 2
nu ___
Allowable Stress
Slenderness ≥ S2
For tubes with circumferential welds, equations of Sections 3.4.10,
3.4.12, and 3.4.16.1 apply for Rb /t ≤ 20.
Table 3.4-3
GENERAL FORMULAS FOR
DETERMINING ALLOWABLE STRESS
FROM SECTION 3.4
1 B – 5.1D __
b
__
Fcy
___
Slenderness ≤ S1
Allowable
Stress
2Ftu /(1.5nu)
2Ftu /nu
for unsymmetric shapes
see Section 3.4.4
1.3Fty
1.42Ftu
______
F = _____
ny or F = kt nu
7
SubSec.
Flat elements
supported on both
edges and with an
intermediate stiffener
Flat elements supported
COMPRESSION on both edges
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
bo
Type of Member or Element
6
1.17Fty
1.24Ftu
______
F = ______
ny or F = kt nu
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted
holes
Fty
Ftu
____
F = ___
ny or F = kt nu
2
Flat elements in uniform tension (flanges)
for symmetric shapes:
Fty /ny
Ftu /(ktnu)
Allowable Stress
1
SubSec.
Any tension member
gross section
net section
Type of Member or Element
COMPRESSION
IN COLUMNS,
All columns
axial, gross
section
Flat elements supported
on one edge—columns
buckling about a symmetry
axis
Flat elements supported
on one edge—columns
not buckling about a
symmetry axis
Type of Stress
BEARING
TENSION IN
BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
I-A-25
Single web shapes
SHEAR IN
ELEMENTS,
gross section
bo
b
21
19
Stiffened flat elements
supported on both edges
1.3Fcy
_____
20
ny
18
Fty
____
__
√3 ny
Fty
____
__
√3 ny
ny
1.3Fcy
_____
1.17Fcy
______
ny
ny
(
1.6Dp
t
t
t
√ )
___
p
t
]
]
[
t
t
1.25Ds
(
1.25Ds
Bs – naFty / ny√3
ae ______________
__
=
t
__
t
a
[
[
t
t
ae
1
__
__
n Bs – 1.25Ds
y
]
t
]
t
t
1.25
1.25
C
ae ____
__
= s
t
Cs
h = ____
__
0.29Dbr
k1Bbr
h = _____
__
mDbr
]
3.5
Cbr
b = ___
__
Rb
__
t = Ct
1.6Dp
k1Bbr
h = _____
__
t
5.1Dp
k1Bp
b = _____
__
t
2
2
)]
( 1.6)
Cc
___
2.3
y
k1Bp
b = _____
__
0.5Cb√IyJ
t
)
)(
LbSc___
________
=
t Cbd
_____
y
nu
nu
__
__
n Btb-Bt / n Dtb-Dt
Cbr
Lb
d ____
__
= ___
[(
]
]
[
y
[
h
1
__
__
n Bbr – mDbr
y
b
1
__
__
n Bbr – 3.5Dbr
See Section 3.4.16.3
h
1
__
__
n Bs – 1.25Ds
)
p
p
See Section 3.4.16.2
(
[
p
Rb
1
__
__
ny Bt – Dt t
ny
[
1 B – 1.6D __
__
b
ny
1 B – 5.1D __
__
b
Bs – Fty /√3
h = __________
__
__
√
t
Rb
__
=
L___
b
_____
= 1.2Cc
ry√Cb
Slenderness
Limit S2
] √
_________
LbSc
________
ny Bc – 1.6Dc 0.5Cb√___
IyJ
1
__
t Cbd
y
0.29Dbr
√
____
h
1
__
__
n Bbr – 0.29Dbr
t
[
√t )
Bbr – 1.3Fcy
h = __________
__
mDbr
3.5Dbr
Bbr – 1.3Fcy
b = __________
__
br –1.3Fcy
h = B_________
__
t
)
2
y
(
b
)
Lb
d ____
1
__
__
n Bbr – 2.3Dbr
y
___
y
Rb
1
__
___
n Btb – Dtb
(
Dc Lb
1
__
_________
ny Bc – 1.2 r √___
C
Allowable Stress
S1 < Slenderness < S2
) (
Bt – 1.17Fcy 2
Rb __________
__
=
t
Dt
t
5.1Dp
(
Bp – Fcy
b = _______
__
t
0.5Cb√IyJ
B –F
1.6Dc
c
cy
LbSc___ _______
_________
=
Fcy
___
ny
Unstiffened flat elements
supported on both edges
2.3Dbr
Bp – Fcy
b = _______
__
ny
1.3Fcy
_____
16.3
Flat elements
supported on both
edges and with an
intermediate stiffener
√
t Cbd
Fcy
___
ny
Fcy
___
17
16.2
Flat elements supported on
one edge and with stiffener
on other edge
16.1
16
Flat elements supported on
both edges
Curved elements supported
on both edges
15
Flat elements
supported on one edge
Flat elements supported on
tension edge, compression
COMPRESSION
edge free
IN BEAM
ELEMENTS,
Flat elements supported on
(element in
both edges
bending in own
plane), gross
Flat elements supported on
section
both edges and with a
longitudinal stiffener
COMPRESSION
IN BEAM
ELEMENTS,
(element in
uniform
compression),
gross section
14
ny
13
_____
Bbr – 1.3Fcy
Lb __________
d ____
__
=
2
1.3Fcy
_____
Rb ___________
tb
cy
___
=
)
ny
12
B – 1.17F
Dtb
1.17Fcy
______
11
(
Fcy
___
ny
t
1.2(Bc – Fcy)
L___
b
_____
= __________
Dc
ry√Cb
Slenderness ≤ S1
Allowable
Stress
Slenderness
Limit S1
SubSec.
Tubular shapes
bo
Type of Member or Element
COMPRESSION Round or oval tubes
IN BEAMS,
extreme fiber,
Solid rectangular and
gross section
round sections
Type of Stress
2
()
(
)
na( 1.25ae /t )2
π2E
___________
ny ( 1.25h/t )2
π2E
__________
ny(0.29h/t)
k2√BbrE
_________
_____
nymh / t
k2√BbrE
_______
____
ny(3.5b/t)2
π2E
_________
( )(
√Rb/t
Rb 1 + _____
16ny __
t
35
)
π2E ____
________________
ny(1.6b/t)
k2√BpE
________
____
ny(5.1b/t)
k2√BpE
________
____
LbSc___
2.56ny _________
0.5Cb√IyJ
2
πE
________________
d Lb/d
5.29ny __
t
2
π ECb
_____________
Same as
Secion 3.4.10
( )
Lb 2
ny ____
1.2ry
π2ECb
________
Allowable Stress
Slenderness ≥ S2
2
3.4.1 Tension, Axial
direction of the applied load and shall not be less than 1.5
times the fastener diameter to extruded, sheared, sawed,
rolled, or planed edges.
Axial tensile stress shall not exceed
F = Fty /ny
(Eq. 3.4.1-1)
on the gross area and
F = Ftu /( kt ) ( nu )
(Eq. 3.4.1-2)
on the effective net area (see Section 5.1.5).
Values of nu and ny are listed in Table 3.4-1. Values of kt
are listed in Table 3.4-2.
Block shear rupture strength provisions for the end connections of tension members are given in Section 5.1.3.
3.4.2 Tension in Extreme Fibers of Beams—
Flat Elements In Uniform Tension
The allowable stress is the lesser of:
Fty
Ftu
___
F = ___
ny and F = ktnu
The allowable stress is the lesser of:
1.17Fty
F = ______
ny
and
(Eq. 3.4.3-1)
1.24F
F = ______tu
kt nu
(Eq. 3.4.3-2)
3.4.4 Tension in Extreme Fibers of Beams—
Flat Elements In Bending in Their
Own Plane
a. For elements symmetric about the bending axis, the
allowable stress is the lesser of:
1.3Fty
F = _____
(Eq. 3.4.4-1)
ny
and
(Eq. 3.4.4-2)
b. For elements unsymmetric about the bending axis, the
extreme fiber stress of the element shall not exceed the
limiting value from a. and the stress at midheight of
the element shall not exceed the stress given in Section 3.4.2.
3.4.5 Bearing on Rivets and Bolts
F = 2Ftu /nu
(Eq. 3.4.5-1)
This value shall be used for a ratio of edge distance to fastener diameter of 2 or greater. For smaller ratios this allowable stress shall be multiplied by the ratio: (edge distance)/
(2 × fastener diameter). Edge distance is the distance from
the center of the fastener to the edge of the material in the
I-A-26
F = 2Ftu /( 1.5nu )
(Eq. 3.4.6-1)
(See Section 5.2.2 for limits on slot lengths.)
3.4.7 Compression in Columns, Axial,
Gross Section
For members in axial compression, the allowable stress
is the lesser of that determined from this Section and Sections 3.4.8 through 3.4.10.
Fcy
a. Fc = ___
(Eq. 3.4.7-1)
ny
kL
___
for r ≤ S1
Dc kL
Bc – _____
r
__________
b. Fc =
(Eq. 3.4.7-2)
nu
kL
for S1 < ___
r < S2
π2E
c. Fc = _______
(Eq. 3.4.7-3)
kL 2
nu ___
r
(
3.4.3 Tension in Extreme Fibers of Beams—
Round or Oval Tubes
1.42F
F = ______tu
kt nu
3.4.6 Bearing on Flat Surfaces and Pins and on
Bolts in Slotted Holes
)
( )
kL ≥ S
for ___
2
r
where
nuFcy
Bc – _____
ny
________
S1 =
(Eq. 3.4.7-4)
S2 = Cc
(Eq. 3.4.7-5)
Dc
k = the effective length factor by rational analysis.
k shall be taken larger than or equal to unity
unless rational analysis justifies a smaller value.
L = the unsupported length
r = radius of gyration of the column about the axis
of buckling
3.4.7.1 Sections Not Subject to Torsional or
Torsional-Flexural Buckling
For closed sections and other sections that are not subkL shall be
ject to torsional or torsional-flexural buckling, ___
r
the largest slenderness ratio for flexural buckling of the
column.
3.4.7.2 Doubly or Singly Symmetric Sections
Subject to Torsional or TorsionalFlexural Buckling
For doubly or singly symmetric sections subject to torkL shall be the larger
sional or torsional-flexural buckling ___
r
of the largest slenderness ratio for flexural buckling and the
equivalent slenderness ratio determined for torsional-flexural
buckling as follows:
January 2005
___
kL ) = π __
( ___
r
√ FE
e
(Eq. 3.4.7.2-1)
e
where Fe is the elastic critical stress determined as follows:
For torsional buckling:
Fe = Fet
(Eq. 3.4.7.2-2)
For torsional-flexural buckling:
__________________
1 [ ( F + F ) – √( F + F )2 – 4βF F ]
Fe = Fef = ___
ex
et
ex
et
ex et
2β
(Eq. 3.4.7.2-3)
Alternatively, for torsional-flexural buckling, a conservative
estimate of Fe shall be permitted to be obtained as follows:
FexFet
Fe = Fef = _______
Fex + Fet
(Eq. 3.4.7.2-4)
A
= cross-sectional area
Cw
= torsional warping constant of the cross-section
E
= compressive modulus of elasticity
(See Table 3.3-1)
(Eq. 3.4.7.2-5)
( )
)
(Eq. 3.4.7.2-6)
G
= shear modulus = 3E/8
(Eq. 3.4.7.2-7)
J
= torsion constant
kx
= effective length coefficient for buckling about the
x-axis
Fet
(
π2ECw
1 GJ + ______
= ____
2
(KtLt)2
Ar
O
Kt
= effective length coefficient for torsional buckling.
Kt shall be taken larger than or equal to unity
unless rational analysis justifies a smaller value.
Lt
= unbraced length for twisting
Lb
= unbraced length for bending about the x-axis
ro
=
___________
√r x2 + r y2 + x o2
(Eq. 3.4.7.2-8)
polar radius of gyration of the cross-section
about the shear center.
rx, ry = radii of gyration of the cross-section about the
centroidal principal axes
xo
= x - coordinate of the shear center
β
= 1 – ( xo /ro )
2
(Eq. 3.4.7.2-9)
3.4.7.3 Nonsymmetric Sections Subject to
Torsional or Torsional-Flexural Buckling
For nonsymmetric sections subject to torsional or
kL shall be determined by
torsional-flexural buckling ___
r
rational analysis.
January 2005
(Eq. 3.4.8-1)
for b/t ≤ S1
1
b
__
b. Fc = __
nu Bp – 5.1Dp t
for S1 < b/t < S2
[
]
(Eq. 3.4.8-2)
____
k2√BpE
c. F =________
(Eq. 3.4.8-3)
c
nu( 5.1b/t )
for b/t ≥ S2
where
(Eq. 3.4.8-4)
5.1Dp
x-axis is the centroidal symmetry axis
π2E
= ______
k____
xLb 2
rx
Fcy
a. Fc = ___
ny
nu
Bp – __
ny Fcy
_________
S1 =
In the above equations
Fex
3.4.8 Uniform Compression in Elements of
Columns Whose Buckling Axis is an Axis of
Symmetry—Flat Elements Supported On
One Edge
k1Bp
S2 = _____
5.1Dp
(Eq. 3.4.8-5)
b = distance from unsupported edge of element to toe
of the fillet or bend, except if the inside corner
radius exceeds 4 times the thickness; then the
inside radius shall be assumed equal to 4 times
the thickness in calculating b. Element width b is
illustrated in Figure 3.4.8-1.
3.4.8.1 Uniform Compression in Elements of
Columns Whose Buckling Axis is not an
Axis of Symmetry—Flat Elements
Supported On One Edge
Fcy
a. Fc = ___
ny
(Eq. 3.4.8.1-1)
for b/t ≤ S1
[
1
b
__
b. Fc = __
nu Bp – 5.1Dp t
for S1 < b/t < S2
πE
c. Fc = _________
nu( 5.1b/t )2
2
]
(Eq. 3.4.8.1-2)
(Eq. 3.4.8.1-3)
for b/t ≥ S2
where
nu
Bp – __
ny Fcy
_________
S1 =
5.1Dp
(Eq. 3.4.8.1-4)
Cp
S2 = ___
(Eq. 3.4.8.1-5)
5.1
b = distance from unsupported edge of element to toe
of the fillet or bend, except if the inside corner
radius exceeds 4 times the thickness; then the
inside radius shall be assumed equal to 4 times
the thickness in calculating b. Element width b is
illustrated in Figure 3.4.8-1.
I-A-27
Figure 3.4.8-1
FLAT ELEMENTS SUPPORTED ON ONE EDGE
If r > 4t, then use r = 4t to calculate b.
3.4.9 Uniform Compression in Elements of
Columns—Flat Elements Supported
on Both Edges
Fcy
a. Fc = ___
ny
(Eq. 3.4.9-1)
for b/t ≤ S1
1
b
__
b. Fc = __
nu Bp – 1.6Dp t
for S1 < b/t < S2
[
]
(Eq. 3.4.9-2)
____
k2√ BpE
c. F = ________
c
nu( 1.6b/t )
for b/t ≥ S2
(Eq. 3.4.9-3)
1.6Dp
k1Bp
S2 = _____
1.6Dp
I-A-28
3.4.9.1 Uniform Compression in Elements of
Columns—Flat Elements Supported
on One Edge and With Stiffener on
Other Edge
The provisions of this Section apply when Ds /b ≤ 0.8.
The allowable stress is the lesser of
where
nu
Bp – __
ny Fcy
_________
S1 =
b = distance from unsupported edge of element to toe
of the fillet or bend, except if the inside corner
radius exceeds 4 times the thickness; then the
inside radius shall be assumed equal to 4 times
the thickness in calculating b. Element width b is
illustrated in Figure 3.4.9-1.
(Eq. 3.4.9-4)
Fcy
Fc = ___
ny
(Eq. 3.4.9-5)
Fc = FUT + ( FST – FUT )ρST ≤ FST
(Eq. 3.4.9.1-1)
and
(Eq. 3.4.9.1-2)
January 2005
Figure 3.4.9-1
FLAT ELEMENTS SUPPORTED ON BOTH EDGES
If r > 4t, then use r = 4t to calculate b.
For a simple straight lip edge stiffener of constant thickness, Fc shall not exceed the allowable stress for the
stiffener according to Section 3.4.8.
rs
In the above equations
Ds = defined in Figure 3.4.9.1-1 and -2
FUT = allowable stress according to Section 3.4.8
neglecting the stiffener
FST = allowable stress according to Section 3.4.9
ρST = ratio to be determined as follows:
ρST = 1.0
ds
for b/t ≤ S/3
(Eq. 3.4.9.1-3)
rs
ρST = _________
≤ 1.0
b/t
1
9t ___ – __
S
for S/3 < b/t ≤ S
(Eq. 3.4.9.1-4)
b
rs
ρST = ___________
≤ 1.0
b/
1.5t ___t + 3
S
for 2S > b/t > S
(Eq. 3.4.9.1-5)
( S 3)
(
January 2005
)
= radius of gyration of the stiffener determined
as follows:
- For simple straight lip stiffeners of constant thickness similar to that shown in
Figure 3.4.9.1-1, rs shall be calculated as:
ds sin
θ
__
rs = ______
√3
- for other stiffeners, rs shall be calculated
about the mid-thickness of the element
being stiffened
= flat width of lip stiffener shown in Figure
3.4.9.1-1
___
E
= 1.28 ___
Fcy
√
= distance from unsupported edge of element to
toe of fillet or bend, except if the inside corner
radius exceeds 4 times the thickness; then the
inside radius shall be assumed to equal 4 times
the thickness in calculating b. Element width b
is illustrated in Figures 3.4.9.1-1. and 3.4.9.1-2
I-A-29
Figure 3.4.9.1-1
EDGE STIFFENED ELEMENTS
If r > 4t, then use r = 4t to calculate b.
Figure 3.4.9.1-2
EDGE STIFFENED ELEMENTS
If r > 4t, then use r = 4t to calculate b.
3.4.9.2 Uniform Compression in Elements of
Columns—Flat Elements Supported
on Both Edges and With an
Intermediate Stiffener
Fcy
a. Fc = ___
ny
(Eq. 3.4.9.2-1)
for λs ≤ S1
(Bc – Dcλs)
b. Fc = _________
nu
(Eq. 3.4.9.2-2)
πE
c. Fc = ____
nuλs2
for λs ≥ S2
2
(Eq. 3.4.9.2-3)
The allowable stress Fc obtained above shall not be more
than the allowable stress according to Section 3.4.9 for the
sub-elements of the intermediately stiffened element.
The allowable stress Fc obtained above shall not be less
than that determined according to Section 3.4.9 ignoring
the intermediate stiffener.
for S1 < λs < S2
I-A-30
January 2005
In the above equations:
As = area of the stiffener
Io = moment of inertia of a section comprising the stiffener and one half of the width of the adjacent subelements and the transition corners between them
taken about the centroidal axis of the section parallel
to the element that is stiffened (Figure 3.4.9.2-1).
nuFcy
_____
ny
S1 = Bc ‒ _____
(Eq. 3.4.9.2-4)
S2 = Cc
(Eq. 3.4.9.2-5)
Dc
()
_______________
√ √
1 __________
+ As / bt
b _______________
λs = 4.62 __
t
10.67Io
1 + 1 + _______
bt3
(Eq. 3.4.9.2-6)
Figure 3.4.9.2-1
FLAT ELEMENTS WITH AN INTERMEDIATE STIFFENER
Line o-o is the neutral axis of the stiffener and plate of width b/2 on each side of the stiffener. Io is the moment of inertia of the
portion shown in the partial section.
If r > 4t, then use r = 4t to calculate b.
January 2005
I-A-31
3.4.10 Uniform Compression in Elements of
Columns—Curved Elements
Supported on Both Edges
Fcy
a. Fc = ___
ny
(Eq. 3.4.10-1)
for Rb/t ≤ S1
___
√ ]
[
Rb
1
__
b. Fc = __
nu Bt – Dt t
(Eq. 3.4.10-2)
for S1 < Rb/t < S2
π E ____
c. Fc = __________________
2
√Rb /t
R
16nu __b 1 + _____
t
35
for Rb/t ≥ S2
( )(
where
(
2
)
)
nu F 2
Bt – __
n cy
y
S1 = ________
Dt
S2 = Ct
(Eq. 3.4.10-3)
(Eq. 3.4.10-4)
(Eq. 3.4.10-5)
For tubes with circumferential welds, the equations of
this Section apply for Rb /t ≤ 20.
3.4.11 Compression in Beams, Extreme Fiber,
Gross Section—Single Web Shapes
For single web shapes not subject to lateral buckling
(bent about the strong axis with continuous lateral support
or bent about the weak axis), determine the compressive
allowable stress Fc from Sections 3.4.15 through 3.4.19 as
applicable.
For single web shapes subject to lateral buckling (bent
about the strong axis without continuous lateral support),
the compressive allowable stress Fc is the lesser of that
determined from Sections 3.4.15 through 3.4.19 as applicable and the following:
Fcy
a. Fc = ___
ny
(Eq. 3.4.11-1)
L___
b
for _____
≤ S1
ry√Cb
Dc Lb___
Bc – ________
1.2ry√Cb
b. Fc = ____________
ny
L___
b
for S1 < _____
< S2
ry√ Cb
(
)
Cbπ2E
c. Fc = ________
Lb 2
ny ____
1.2ry
L___
b
for _____
≥ S2
ry√Cb
( )
Lb = length of the beam between bracing points or
between a brace point and the free end of a
cantilever beam. Bracing points are the points
at which the compression flange is restrained
against lateral movement or the cross section
is restrained against twisting.
Cb = coefficient that depends on moment variation
over the unbraced length. Cb shall be as given
in Section 4.9.4 or taken as 1.
Alternatively, Fc may be calculated by replacing ry by rye
given in Section 4.9.
3.4.12 Compression in Beams, Extreme Fiber,
Gross Section—Round or Oval Tubes
1.17Fcy
a. Fc = ______
ny
(Eq. 3.4.11-2)
(Eq. 3.4.11-3)
1.2 ( Bc – Fcy )
S1 = ___________
Dc
(Eq. 3.4.11-4)
S2 = 1.2Cc
(Eq. 3.4.11-5)
(Eq. 3.4.12-1)
for Rb /t ≤ S1
___
Rb
1
__
b. Fc = ny Btb – Dtb __
t
for S1 < Rb /t < S2
(
√ )
(Eq. 3.4.12-2)
c. For Rb /t ≥ S2, the allowable bending stress shall be
determined from the formulas for tubes in compression in Section 3.4.10 using the formula that is appropriate for the particular value of Rb /t.
In the above equations
Rb = mid-thickness radius of a round element or maximum mid-thickness radius of an oval element
(
)
Btb – 1.17Fcy 2
S1 = __________
Dtb
n
__u B – B 2
ny tb t
_________
S2 = nu
__ D – D
t
ny tb
(
where
I-A-32
ry = radius of gyration of the shape (about an axis
parallel to the web) (For beams that are unsymmetrical about the horizontal axis, ry shall be
calculated as though both flanges were the same
as the compression flange).
)
(Eq. 3.4.12-3)
(Eq. 3.4.12-4)
For tubes with circumferential welds, the equations of
this Section apply for Rb /t ≤ 20.
3.4.13 Compression in Beams, Extreme Fiber,
Gross Section—Solid Rectangular and
Round Sections
For rectangular sections bent about the weak axis, rod,
1.3Fcy
and square bar: Fc = _____
ny
For rectangular sections bent about the strong axis:
1.3Fcy
a. Fc = _____
(Eq. 3.4.13-1)
ny
____
Lb
d ____
for __
t Cb d ≤ S1
√
March 2006
(
____
√ )
Lb
d ____
1
__
b. Fc = __
ny Bbr – 2.3Dbr t Cb d
____
Lb
d ____
for S1 < __
t Cb d < S2
√
(Eq. 3.4.13-2)
πE
c. Fc = ____________
Lb
d 2____
5.29ny __
t
C
bd
____
Lb
d ____
for __
t Cb d ≥ S2
2
(Eq. 3.4.13-3)
()
√
where
Bbr – 1.3Fcy
S1 = _________
2.3Dbr
(Eq. 3.4.13-4)
Cbr
S2 = ___
2.3
(Eq. 3.4.13-5)
d = depth of section
Lb = length of the beam between bracing points or
between a brace point and the free end of a
cantilever beam. Bracing points are the points
at which the compression flange is restrained
against lateral movement or the cross section
is restrained against twisting.
Cb = coefficient that depends on moment variation
over the unbraced length. Cb shall be as given
in Section 4.9.4 or taken as 1.
3.4.14 Compression in Beams, Extreme Fiber,
Gross Section—Tubular Shapes
For the purposes of this Specification, tubular shapes are
defined as closed sections.
For tubular shapes not subject to lateral buckling (bent
about the strong axis with continuous lateral support or
bent about the weak axis) and round, square, hexagonal,
and octagonal tubes, determine the compressive allowable
stress Fc from Sections 3.4.12 and 3.4.15 through 3.4.19 as
applicable.
For tubular shapes subject to lateral buckling (bent about
the strong axis without continuous lateral support), the
compressive allowable stress Fc is the lesser of that determined from Sections 3.4.12 and 3.4.15 through 3.4.19 as
applicable and the following:
Fcy
a. Fc = ___
(Eq. 3.4.14-1)
ny
L___
bSc
for __________
≤ S1
Cb( √Iy J / 2 )
___________
(
√ (√
L___
bSc
1
___________
b. Fc = __
n Bc – 1.6Dc
y
Cb
L___
bSc
for S1 < ________
< S2
Cb√IyJ / 2
Iy J / 2 )
π2E
c. Fc = _________________
L___
bSc
2.56ny __________
Cb( √Iy J / 2 )
(
)
)
(Eq. 3.4.14-2)
(Eq. 3.4.14-3)
where
(
)
Bc – Fcy 2
S1 = ______
1.6Dc
(Eq. 3.4.14-4)
( )
C 2
S2 = ___c
(Eq. 3.4.14-5)
1.6
Iy = moment of inertia of the beam about the minor
axis
J = torsion constant
Lb = length of the beam between bracing points or
between a brace point and the free end of a
cantilever beam. Bracing points are the points
at which the compression flange is restrained
against lateral movement or the cross section
is restrained against twisting.
Cb = coefficient that depends on moment variation
over the unbraced length. Cb shall be as given
in Section 4.9.4 or taken as 1.
Alternatively, Fc may be calculated by using the equations in Section 3.4.11 and replacing ry by rye given in Section 4.9.
For narrow rectangular tubes bent about the strong axis
with a ___
depth-to-width ratio greater than or equal to 6, the
term √Iy J /2 may be replaced by Iy
3.4.15 Uniform Compression in Elements of
Beams—Flat Elements Supported on
One Edge
Fcy
a. Fc = ___
ny
(Eq. 3.4.15-1)
for b/t ≤ S1
[
1
b
__
b. Fc = __
ny Bp – 5.1Dp t
for S1 < b /t < S2
]
(Eq. 3.4.15-2)
____
k2√ BpE
c. F = _________
c
ny( 5.1b / t )
for b/t ≥ S2
(Eq. 3.4.15-3)
where
Bp – Fcy
S1 = ______
5.1Dp
(Eq. 3.4.15-4)
k1Bp
S2 = _____
(Eq. 3.4.15-5)
5.1Dp
b = distance from unsupported edge of element to
toe of the fillet or bend, except if the inside corner radius exceeds 4 times the thickness; then the
inside radius shall be assumed equal to 4 times
the thickness in calculating b. Element width b is
illustrated in Figure 3.4.8-1.
L___
bSc
for _________
≥ S2
Cb√ Iy J / 2
January 2005
I-A-33
3.4.16 Uniform Compression in Elements of
Beams—Flat Elements Supported on
Both Edges
Fcy
a. Fc = ___
ny
for b/t ≤ S1
1
b
__
b. Fc = __
ny Bp – 1.6Dp t
for S1 < b/t < S2
[
(Eq. 3.4.16-1)
]
(Eq. 3.4.16-2)
(Eq. 3.4.16-3)
c
ny( 1.6b / t )
for b/t ≥ S2
where
Bp – Fcy
S1 = _______
1.6Dp
k1Bp
S2 = _____
1.6Dp
(Eq. 3.4.16-4)
(Eq. 3.4.16-5)
b = distance from unsupported edge of element to
toe of the fillet or bend, except if the inside corner radius exceeds 4 times the thickness; then the
inside radius shall be assumed equal to 4 times
the thickness in calculating b. Element width b is
illustrated in Figure 3.4.9-1.
3.4.16.1 Uniform Compression in Elements of
Beams—Curved Elements Supported
on Both Edges
1.17Fcy
a. Fc = ______
ny
(Eq. 3.4.16.1-1)
for Rb/t ≤ S1
___
Rb
1
__
b. Fc = ny Bt – Dt __
t
for S1 < Rb/t < S2
π2E _____
c. Fc = ___________________
√Rb / t 2
Rb
______
16ny __
1
+
t
35
for Rb/t ≥ S2
√ ]
( )(
where
(
)
)
Bt – 1.17Fcy 2
S1 = __________
Dt
S2 = Ct
(Eq. 3.4.16.1-2)
(Eq. 3.4.16.1-3)
(Eq. 3.4.16.1-4)
(Eq. 3.4.16.1-5)
Ct shall be determined using a plot of the curves of
allowable stress for values of Rb /t less than and greater than
S2 or by a trial and error solution.
For tubes with circumferential welds, the equations of
this Section apply for Rb /t ≤ 20.
3.4.16.2 Uniform Compression in Elements of
Beams—Flat Elements Supported on
One Edge and With Stiffener on
Other Edge
The provisions of this Section apply when Ds /b ≤ 0.8.
The allowable stress is the lesser of
I-A-34
(Eq. 3.4.16.2-1)
and
Fc = FUT + ( FST -FUT ) ρST ≤ FST
(Eq. 3.4.16.2-2)
For a straight stiffener of constant thickness, Fc shall
not exceed the allowable stress for the stiffener according
to Section 3.4.8.
In the above equations
____
k2√BpE
c. F = _________
[
Fcy
Fc = ___
ny
Ds = defined in Figure 3.4.9.1-1 and -2
FUT = allowable stress according to Section 3.4.15
neglecting the stiffener
FST = allowable stress according to Section 3.4.16
ρST = ratio to be determined as follows:
ρST = 1.0
for b/t ≤ S/3
r
s
ρST = __________ ≤ 1.0 for S/3 < b/t ≤ S
b / t – __
1
9t ____
S
3
rs
ρST = _____________
≤ 1.0 for 2S > b/t > S
b/t+3
1.5t ____
S
rs = radius of gyration of the stiffener determined
as follows:
- For simple straight lip stiffeners of constant thickness similar to that shown in
Figure 3.4.9.1-1, rs shall be calculated as:
ds sin
θ
__
rs = ______
√3
- for other type stiffeners, rs shall be calculated
about the mid-thickness of the element being
stiffened
ds = flat width
of stiffener shown in Figure 3.4.9.1-1
___
E
S = 1.28 ___
Fcy
b = distance from unsupported edge of element to
toe of fillet or bend, unless the inside corner
radius exceeds 4t; then the inside radius shall
be assumed to be 4t to calculate b. Element
width b is illustrated in Figure 3.4.9.1-1.
(
)
(
)
√
3.4.16.3 Uniform Compression in Elements of
Beams—Flat Elements Supported on
Both Edges and With an Intermediate
Stiffener
Fcy
a. Fc = ___
ny
(Eq. 3.4.16.3-1)
for λs ≤ S1
( Bc – Dcλs )
b. Fc = _________
ny
(Eq. 3.4.16.3-2)
for S1 < λs < S2
ππ22EE
c. Fc = ____
nyλs2
for λs ≥ S2
(Eq. 3.4.16.3-3)
March 2006
The allowable stress Fc obtained above shall not be more
than the allowable stress according to Section 3.4.16 for
the sub-elements of the intermediately stiffened element.
The allowable stress Fc obtained above shall not be less
than that determined according to Section 3.4.16 ignoring
the intermediate stiffener.
In the above equations:
Bc – Fcy
S1 = _______
Dc
(Eq. 3.4.16.3-4)
S2 = Cc
(Eq. 3.4.16.3-5)
______________
1+
A / bt
__________
( ) ______________
10.67I
______
s
1+ 1+
(Eq. 3.4.16.3-6)
o
bt3
3.4.17 Compression in Elements of Beams
(Element in Bending in Own Plane)—
Flat Elements Supported on Tension
Edge, Compression Edge Free
1.3Fcy
a. Fc = _____
ny
for b/t ≤ S1
b
1
__
b. Fc = __
ny Bbr – 3.5Dbr t
for S1 < b/t < S2
π2E
c. Fc = _________
ny( 3.5b/t )2
for b/t ≥ S2
[
(Eq. 3.4.17-1)
]
(Eq. 3.4.17-3)
(Eq. 3.4.17-4)
(Eq. 3.4.17-5)
Figure 3.4.18-1
DIMENSIONAL NOTATION
January 2005
]
(Eq. 3.4.18-2)
for S1 < h/t < S2
____
k2√BbrE
c. F = _________
c
ny ( mh / t )
for h/t ≥ S2
(Eq. 3.4.18-3)
where
Bbr−1.3Fcy
S1 = _________
mDbr
k1Bbr
_____
S2 =
mDbr
(Eq. 3.4.18-4)
(Eq. 3.4.18-5)
m = 1.15 + co /(2cc)
for –1 < co /cc < 1
m = 1.3/(1 – co /cc)
for co /cc ≤ –1
cc = distance from neutral axis to extreme fiber of the
element with the greatest compressive stress
co = distance from neutral axis to other extreme fiber
of the element
Distances to compressive fibers are negative and distances to tensile fibers are positive.
h = clear height of web (illustrated in Figure 3.4.18-1)
(Eq. 3.4.17-2)
where
Bbr – 1.3Fcy
S1 = _________
3.5Dbr
C
br
S2 = ___
3.5
(Eq. 3.4.18-1)
for h/t ≤ S1
[
Io = moment of inertia of a section comprising the stiffener and one half of the width of the adjacent subelements and the transition corners between them
taken about the centroidal axis of the section parallel
to the element that is stiffened (Figure 3.4.9.2-1).
√ √
1.3Fcy
a. Fc = _____
ny
h
1
__
b. Fc = __
ny Bbr – mDbr t
As = area of the stiffener
b
λs = 4.62 __
t
3.4.18 Compression in Elements of Beams
(Element in Bending in Own Plane)—
Flat Elements Supported on Both Edges
3.4.19 Compression in Elements of Beams
(Element in Bending in Own Plane)—
Flat Elements Supported on Both Edges
and With a Longitudinal Stiffener
The provisions of this Section apply for stiffeners located
at 0.4d1 from the flange as shown in Figure 3.4.19-1.
1.3Fcy
a. Fc = _____
(Eq. 3.4.19-1)
ny
for h/t < S1
Figure 3.4.19-1
DIMENSIONS h AND d1
I-A-35
[
h
1
__
b. Fc = __
ny Bbr – 0.29Dbr t
]
(Eq. 3.4.19-2)
__
for S1 < h/t < S2
____
k2√BbrE
c. Fc = ___________
ny ( 0.29h / t )
(Eq. 3.4.19-3)
for h/t ≥ S2
where
Bbr – 1.3Fcy
S1 = _________
0.29Dbr
(Eq. 3.4.19-4)
k1Bbr
S2 = _______
0.29Dbr
(Eq. 3.4.19-5)
h = clear web height (see Figure 3.4.19-1)
d1 = clear distance from the neutral axis to the compression flange (see Figure 3.4.19-1)
3.4.20 Shear in Elements—Unstiffened Flat
Elements Supported on Both Edges
__
Fty / √3
a. Fs = ______
ny
for h/t ≤ S1
[
h
1
__
b. Fs = __
ny Bs –1.25Ds t
(Eq. 3.4.20-1)
]
(Eq. 3.4.20-2)
for S1 < h/t < S2
π2E
c. Fs = __________
ny( 1.25h/t )2
for h/t ≥ S2
I-A-36
where
h = clear web height (see Figure 3.4.18-1)
(Eq. 3.4.20-3)
Bs – Fty / √3
S1 = __________
1.25Ds
C
s
S2 = ____
1.25
(Eq. 3.4.20-4)
(Eq. 3.4.20-5)
3.4.21 Shear in Elements—Stiffened Flat
Elements Supported on Both Edges
__
Fty / √ 3
a. Fs = ______
ny
for ae /t ≤ S1
(Eq. 3.4.21-1)
[
ae
1
__
b. Fs = __
na Bs – 1.25Ds t
]
(Eq. 3.4.21-2)
for S1 < ae /t < S2
πE
c. Fs = ___________
na( 1.25ae / t )2
2
(Eq. 3.4.21-3)
for ae /t ≥ S2
where
a1
___________
ae = ____________
a1 2
1 + 0.7 __
a2
√
( )
a1 = shorter dimension of rectangular panel
a2 = longer dimension of rectangular panel
naFty
__
Bs – _____
ny√3
_________
S1 =
(Eq. 3.4.21-4)
1.25Ds
Cs
S2 = ____
(Eq. 3.4.21-5)
1.25
January 2005
Section 4. Special Design Rules
4.1 Combined Axial Load and Bending
4.1.2 Combined Tension and Bending
4.1.1 Combined Compression and Bending
A member subjected to axial tension and bending shall
be proportioned in accordance with the formula:
A member subjected to axial compression and bending
moment loads shall be proportioned in accordance with the
following two formulas (both equations must be checked):
Cmy fby
fa ____________
Cmx fbx
__
+
+ ____________ ≤ 1.0
Fa Fbx( 1 – fa /Fex ) Fby ( 1 – fa /Fey )
(Eq. 4.1.1-1)
fby
fa ___
f
___
+ bx + ___ ≤ 1.0
Fao
Fbx
Fby
(Eq. 4.1.1-2)
When fa /Fa < 0.15, the following Equation 4.1.1-3 shall
be permitted to be used in lieu of Equations 4.1.1-1 and
4.1.1-2:
fby
fa ___
f
__
+ bx + ___ ≤ 1.0
Fa
Fbx
Fby
(Eq. 4.1.1-3)
In Equations 4.1.1-1, 4.1.1-2, and 4.1.1-3, the subscripts
x and y, combined with subscripts b, m, and e indicate the
axis of bending about which a particular stress or design
parameter applies and
fa
= average compressive stress on cross section
produced by the compressive load
fb
= maximum compressive bending stress produced
by the transverse loads and/or end moments
Fa
= allowable compressive stress for member considered as axially loaded column according
either to Sections 3.4.7 through 3.4.10 or 4.7.2
Fb
= allowable compressive stress for member considered as a beam according to either Sections
3.4.11 through 3.4.19 or 4.7.2
Cm
= 0.6 – 0.4(M1/M2) for members whose ends are
prevented from sway
= 0.85 for members whose ends are not prevented
from swaying
M1/M2 = ratio of end moments where M2 is the larger
of the two end moments and M1/M2 is positive
when the member is bent in reverse curvature,
negative when bent in single curvature
Fao
= allowable compressive stress of an axially loaded
member considered as a short column according
to Section 4.7.2 without consideration of Section 3.4.7
r
= elastic buckling stress divided by nu
π2E
= ________
nu( kL /r )2
= radius of gyration about the bending axis
L
= unsupported length in the plane of bending
k
= effective length factor in the plane of bending
Fe
January 2005
fby
fa ___
f
__
+ bx + ___ ≤ 1.0
Ft
Fbx
Fby
(Eq. 4.1.2-1)
In Equation 4.1.2-1, the subscripts x and y, combined
with the subscript b indicate the axis of bending about which
a particular stress or design parameter applies and where
fa = average tensile stress on cross section produced by
the tensile load
fb = maximum tensile bending stress produced by the
transverse loads and/or end moments
Fb = allowable tensile stress for the member as a beam
according to Section 3.4.2 through 3.4.4 and 4.7.3
Ft = allowable tensile stress for the member loaded only
axially according to Section 3.4.1
4.2 Torsion and Shear in Tubes
Allowable shear stresses in round or oval tubes subjected to torsion or shear loads shall be determined from
Section 3.4.20 with the ratio h/t given by
( t ) ( __RL )
Rb
h = 2.9 __
__
5/8
s
1/4
(Eq. 4.2-1)
t
b
where
Rb = mid-thickness radius of a round tube or maximum
mid-thickness radius of an oval tube
t = thickness of tube
Ls = length of tube between circumferential stiffeners,
or overall length if no circumferential stiffeners are
present
4.3 Torsion and Bending in Open Shapes
The stresses in open sections caused by torsion due to twisting
moments applied directly or due to lateral loads or supports
not in the plane of the shear center of open sections shall
include shear, flexural and warping stresses. The stresses
thus computed plus those due to bending shall not exceed
the appropriate allowable stress for the type of stress in the
element considered.
4.4 Combined Shear, Compression,
and Bending
Allowable combinations of shear, compression, and bending shall be determined from either of the following formulas:
a. For walls of curved surfaces or round tubular members:
( F ) ≤ 1.0
F F
fa __
f
f
__
+ b + __s
a
b
s
2
(Eq. 4.4-1)
I-A-37
b. For webs of rectilinear shapes, plates of built-up girders or
similar members:
f
+
≤ 1.0
F (F ) (F)
fa
f
__
+ __b
a
2
s
__
b
2
(Eq. 4.4-2)
s
where
fa = average compressive stress produced by axial compressive load
Fa = allowable compressive stress for members subjected to compression only
fb = maximum bending stress (compression) produced by
applied bending moment
Fb = allowable bending stress (compression) for members subjected to bending only
fs = shear stress caused by torsion or transverse shear
loads
Fs = allowable shear stress for members subjected only to
torsion or shear
4.5 Longitudinal Stiffeners for Webs
If a longitudinal stiffener is used on a beam web, it shall
be located so that the distance from the toe of the compression flange to the centroid of the stiffener is 0.4 of the distance from the toe of the compression flange to the neutral
axis of the beam. The longitudinal stiffener shall have a
moment of inertia, about the web of the beam, not less than
that given by the expression:
0.02αs fth
I = _________
3
h
E
[(
)( h )
6A
1 + ___h __s 2 + 0.4
ht
]
(Eq. 4.5-1)
where
Ah = gross cross sectional area of longitudinal stiffener
f = compressive stress at toe of flange
h = clear height of web between flanges
Ih = moment of inertia of the longitudinal stiffener. For a
stiffener consisting of equal members on both sides
of the web, the moment of inertia Ih shall be the sum
of the moments of inertia about the centerline of the
web. For a stiffener consisting of a member on one
side only, the moment of inertia shall be taken about
the face of the web in contact with the stiffener.
s = distance between transverse stiffeners
t = thickness of the web
αs = 1, for stiffener consisting of equal members on both
sides of web
αs = 3.5, for stiffener consisting of member on only one
side of web
4.6 Transverse Stiffeners for Webs
When a stiffener is composed of a pair of members, one
on each side of the web, the stiffener spacing s shall be
the clear distance between the pairs of stiffeners. When a
I-A-38
stiffener is composed of a member on one side only of the
web, the stiffener spacing s shall be the distance between
rivet lines or other connecting lines.
For a stiffener composed of members of equal size on
each side of the web, the moment of inertia of the stiffener
shall be computed about the centerline of the web. For a stiffener composed of a member on one side only of the web, the
moment of inertia of the stiffener shall be computed about
the face of the web in contact with the stiffener.
In the determination of the required moment of inertia
of stiffeners, the distance h shall be taken as the full clear
height of the web regardless of whether or not a longitudinal stiffener is present.
Unless the outer edge of a stiffener is continuously stiffened, its thickness shall not be less than 1/12th the clear width
of the outstanding leg.
4.6.1 Stiffeners for Web Shear
Stiffeners applied to beam webs to resist shear buckling
shall have a moment of inertia not less than the value given
by the following expression:
0.46naVh __s
s ≤ 0.4, I = _________
__
s
(h)
(Eq. 4.6.1-1)
( )
(Eq. 4.6.1-2)
2
h
E
s > 0.4, I = 0.073n
h
aVh
__
_________
__
s
s
2
EE
h
where
h = clear height of web
Is = moment of inertia of stiffener
na = factor of safety on appearance of buckling from
Table 3.4-1
s = stiffener spacing
V = shear force on web at stiffener location
Stiffeners shall extend from flange to flange but need
not be connected to either flange.
4.6.2 Bearing Stiffeners
Bearing stiffeners at points of support of concentrated
loads shall be connected to the web by enough rivets, or
other means, to transmit the load. Such stiffeners shall be
fitted to form a tight and uniform bearing against the loaded
flanges, unless welds, designed to transmit the full reaction
or load, are provided between flange and stiffener.
Only that part of a stiffener cross section which lies outside the fillet of the flange angle shall be considered as effective in bearing.
The moment of inertia of the bearing stiffener shall not
be less than that given by the following expression:
Pbsh2nu
Ib = Is + ______
π2E
where
E = compressive modulus of elasticity
(Eq. 4.6.2-1)
h = clear height of web between flanges
January 2005
Ib = required moment of inertia of bearing stiffener
Is = moment of inertia required to resist shear buckling
nu = factor of safety
Pbs = concentrated load on stiffener
4.7 Effects of Local Buckling on
Member Performance
Mac = Fcf If /ccf + Fcw Iw /ccw
4.7.1 Local Buckling Stresses
Where local buckling stress values are required to be
calculated, the critical stresses, Fcr, given in Table 4.7.1-1
shall be used. For cases not covered in Table 4.7.1-1, the
value of Fcr shall be determined using the expression for Fc
in the appropriate subsection of Section 3.4 for the case b/t
> S2 with nu or ny taken as 1.0.
Table 4.7.1-1
Section
Local Buckling Stress, Fcr
3.4.8 and 3.4.15
π2E
_______
3.4.9 and 3.4.16
π2E
_______
3.4.9.1 and 3.4.16.2
( nyFc )2
______
Fcy
( 5.1b/t )2
( 1.6b/t )2
( mh/t )2
π E for y
________
( 0.65h/t )2
3.4.19
NA
= h/2
π2E
________
( 0.29h/t )2
4.7.2 Weighted Average Axial Compressive Stress
As an alternative to using the least of the allowable compressive stresses of a section’s elements for the allowable
axial compressive stress of the section, the weighted average allowable axial compressive stress shall be determined
in accordance with this Section.
The weighted average allowable axial compressive stress
of a section is the average allowable stress of the section’s
elements, where the allowable stress for each element is
weighted by the ratio of the area of the element to the total
area of the section.
The allowable stress in elements with stiffeners shall not
exceed the allowable stress in an intermediate stiffener or an
edge stiffener.
The allowable axial compressive stress of the section
shall not exceed that given by Section 3.4.7.
4.7.3 Weighted Average Bending Strength
As an alternative to using the least of the strengths of a
section’s elements for the bending strength of the section, the
strength shall be determined in accordance with this Section.
January 2005
where
Fcf = the allowable compressive stress for the flat elements
in uniform compression
Fcw = the allowable compressive stress for the flat elements in bending in their own plane
If = the moment of inertia of the flange group about the
neutral axis of the entire section. The flange group
consists of the flat elements in uniform compression and the flat elements in uniform tension and
their edge or intermediate stiffeners.
Iw = the moment of inertia of the web group about the
neutral axis of the entire section. The web group
consists of the flat elements in bending in their own
plane and their intermediate stiffeners.
ccw = the distance from the web group’s extreme compression fiber to the neutral axis of the entire crosssection
πE
______
2
(Eq. 4.7.3-1)
ccf = the distance from the centerline of the compression
flange to the neutral axis of the entire cross-section
2
3.4.18
The allowable stress in elements with stiffeners shall
not exceed the allowable stress in an intermediate stiffener
or an edge stiffener.
For shapes not subject to lateral buckling, the allowable
bending moment Ma is the lesser of the allowable compressive
bending moment and the allowable tensile bending moment.
The allowable compressive bending moment is
(See Figure 4.7.3-1).
If there are stiffeners located farther than the compression
flange from the neutral axis of the entire cross-section, the
allowable compressive bending moment shall not exceed
Fcy If /(ny ccs) + Fcw Iw /ccw
(Eq. 4.7.3-2)
where
ccs = the distance from the neutral axis of the entire crosssection to the extreme fiber of compression flange
stiffeners
The allowable tensile bending moment is
Mat = Ftf If /ctf + Ftw Iw/ctw
(Eq. 4.7.3-3)
where
Ftf = the allowable tensile stress for the flat elements
in uniform tension
Ftw = the allowable tensile stress for the flat elements
in bending in their own plane
If , Iw = the same as above
ctf
= the distance from the extreme tension fiber to the
neutral axis of the entire cross-section
ctw = the distance from the web group’s extreme tension fiber to the neutral axis of the entire crosssection
I-A-39
Figure 4.7.3-1
For shapes subject to lateral buckling, the allowable
bending moment Ma is the least of the allowable compressive bending moment Mac, the allowable tensile bending
moment Mat, and Fb S where
Fb = allowable compression bending stress given by
Section 3.4.11 or 3.4.14
S = section modulus of the entire cross-section
An additional limitation shall be placed on the allowable stress for columns in which local buckling of the cross
section occurs at a stress that is less than the calculated
flexural buckling stress of the column, assuming that the
elements are not buckled. The allowable stress shall not
exceed the value given by
For Fcr /nu < Fc
(Eq. 4.7.4-1)
(Eq. 4.7.5-1)
For Fcr /ny < Fc
(Eq. 4.7.5-2)
Fcr = element local buckling stress given in Section 4.7.1
Feb = elastic lateral buckling stress of beam calculated
using Equation 3.4.11-3 and Section 4.9 with
ny = 1.0
Frb = allowable stress for beam with buckled elements
The allowable stress also shall not exceed the allowable
stress for the section given in Section 4.7.2.
(Eq. 4.7.4-2)
where
Fc = allowable stress for column given in Section 3.4.7
Fcr = element local buckling stress given in Section 4.7.1
π2E
Fec = ______
(Eq. 4.7.4-3)
( kL /r )2
Frc = allowable stress for column with buckled elements
The allowable stress also shall not exceed the allowable
stress given in Section 4.7.2.
4.7.5 Effect of Local Buckling on Beam Strength
The allowable compressive bending stress shall be reduced
for single web beams whose flanges consist of thin, flat elements supported on one edge and in which local buckling
I-A-40
Feb1/3Fcr2 /3
Frb = ________
ny
where
Fc = allowable stress for beam given in Section 3.4.11
or Section 4.9
4.7.4 Effect of Local Buckling
on Column Strength
Fec1/3Fcr2 /3
Frc = ________
nu
of the cross section occurs at a stress that is less than the
lateral buckling stress of the beam, calculated assuming that
the elements are not buckled. The allowable stress shall not
exceed the value given by
4.7.6 Effective Width for Calculation
of Bending Deflection
The effective width concept shall be used to determine
an effective section for the moment of inertia used to calculate deflections.
For sections containing elements covered in Sections
3.4.15, 3.4.16, 3.4.18, or 3.4.19 with b/t or h/t values exceeding 1.65S2 and elements covered in Sections 3.4.16.2 or
3.4.16.3 with Fcr < fa, the effective width be of a thin element
subjected to direct compression stresses is:
If fa ≤ Fcr , be = b
_____
If fa > Fcr , be = b√Fcr /fa
(Eq. 4.7.6-1)
(Eq. 4.7.6-2)
January 2005
where
be = effective width of flat element to be used in deflection calculations
b = width of element as defined in Sections referred to
above
Fcr = local buckling stress for element from Section 4.7.1
fa = compressive stress for element due to applied loads
The same expression is used to calculate the effective width
on the compression side of a web in bending, with the maximum compressive bending stress due to the applied loads,
fb, replacing fa. In this case the effective web area is to be
placed next to the compression flange.
4.7.7 Web Crippling of Flat Webs
For interior reactions and concentrated loads:
Cwa ( N + Cw1 )
Pc = ____________
(Eq. 4.7.7-1)
nyCwb
For end reactions and concentrated loads:
1.2Cwa ( N + Cw2 )
Pc = ______________
nyCwb
(Eq. 4.7.7-2)
where
____
Cwa = t 2 sin θ ( 0.46Fcy + 0.02√EFcy )
(Eq. 4.7.7-3)
Cwb = Cw3 + Ri( 1 – cos θ )
(Eq. 4.7.7-4)
Cw1 = 5.4 in. (140 mm)
Cw2 = 1.3 in. (33 mm)
Cw3 = 0.4 in. (10 mm)
E = compressive modulus of elasticity of the web
Fcy = compressive yield strength of the web
Pc = allowable transverse force per web for flat webs
N = length of bearing at the reaction or concentrated
load
Ri : for shapes made by bending, Ri = bend radius at
juncture of the flange and web measured to the inside of
the bend; for extruded shapes, Ri = 0
= web thickness
= angle between the plane of web and the plane of
the bearing surface (θ ≤ 90 degrees)
t
θ
P = applied interior reaction or concentrated load per
web for flat webs
Pc = allowable interior reaction or concentrated load
per web for flat webs calculated according to Section 4.7.7.
4.8 Fatigue
Welded details, mechanically fastened joints and base
material of aluminum alloys subjected to repeated fluctuations of stress shall meet all the static requirements of this
Specification as well as the fatigue requirements of this
Section. Fatigue design of castings and associated details
shall be made by testing in accordance with Section 9.
Categories of details for fatigue design parameters shall
be chosen from Figure 4.8-1 and Table 4.8-1.
The maximum and minimum stresses used to calculate
the stress range are nominal stresses determined by standard
elastic methods. Stresses perpendicular to the expected plane
of cracking shall be used.
4.8.1 Constant Amplitude Loading
For constant amplitude loading
Sra ≤ Srd
where
Sra
(Eq. 4.8.1-1)
= applied stress range, the algebraic difference between
the minimum and maximum calculated stress in the
member or detail
Srd
= the allowable stress range
Srd
= Cf N –1/m
(Eq. 4.8.1-2)
Cf , m = constants from Table 4.8.1-1 and shown in
Figure 4.8.1-1
N
= the number of cycles to failure
If the applied stress range, Sra, is less than the constant
amplitude fatigue limit as given in Table 4.8.1-1, then no
further fatigue consideration shall be needed. The allowable stress range, Srd shall not be less than the value from
Equation 4.8.1-2 when N = 5 × 106 cycles and shall not be
greater than the value from Equation 4.8.1-2 when N = 105
cycles.
4.7.8 Combined Web Crippling and Bending
for Flat Webs
4.8.2 Variable Amplitude Loading
Allowable combinations of interior reactions and concentrated loads and bending shall be determined from the
following formula:
If the maximum stress range in the spectrum is less than
the fatigue limit, then no further fatigue assessment shall
be needed.
For variable amplitude loading:
( MM ) + ( PP ) ≤ 1.0
___
a
1.5
__
c
1.5
(Eq. 4.7.8-1)
where
M = bending moment applied to the member
Ma = allowable bending moment for the member if bending moment alone is applied to the member
January 2005
Sre ≤ Srd
where
Sre
(Eq. 4.8.2-1)
= equivalent stress range
(∑ )
Ns
Sre
=
αi S
i=1
m
ri
1/m
(Eq. 4.8.2-2)
I-A-41
Srd
= the allowable stress range
Srd
= Cf N–1/m
αi
= number of cycles in the spectrum of the ith stress
range divided by the total number of cycles
Sri
= the ith stress range in the spectrum
(Eq. 4.8.2-3)
Cf , m = constants from Table 4.8.1-1 and shown in
Figure 4.8.1-1
NS
= the number of stress ranges in the spectrum
N
= the number of cycles to failure
The allowable stress range Srd shall not be greater than
the value from Equation 4.8.2-3 when N = 105 cycles.
Table 4.8-1
STRESS CATEGORY
Detail
Category(1)
A
General Condition
Detail
Plain Material
Base metal with rolled, extruded, drawn, or cold finished surfaces; cut
or sheared surfaces with ANSI/ASME B46.1 surface roughness of
1000μ in. (25μm) or less.
Base metal and weld metal in members, without attachments, built-up B
of plates or shapes connected by continuous full- or partial-penetration
groove welds or continuous fillet welds parallel to the direction of
applied stress.
Built Up Members
Mechanically Fastened
Fillet Welds
Fatigue Design
Details(2)
1, 2
3, 4, 5
Calculated flexural stress, fb, in base metal at toe of welds on girder
webs or flanges adjacent to welded transverse stiffeners.
C
6, 21
Base metal at end of partial-length welded cover plates having square
or tapered ends, with or without welds across the ends.
Base metal at the gross section of slip-critical connections and at the
net section of bearing connections, where the joint configuration does
not result in out-of-plane bending in the connected material and the
stress ratio (the ratio of minimum stress to maximum stress)3 Rs is
Rs ≤ 0
0 < Rs < 0.5
0.5 ≤ Rs
E
5
B
D
E
7
7
7
Base metal at the gross section of slip-critical connections and at
the net section of bearing connections, where the joint configuration
results in out-of-plane bending in connected material.
Base metal at intermittent fillet welds.
E
8
E
Base metal at junction of axially loaded members with fillet welded end E
connections. Welds shall be disposed about the axis of the members
so as to balance weld stresses.
Weld metal of continuous or intermittent longitudinal or transverse fillet
welds.
F
15, 17
5, 15,18
See last page of this table for footnotes.
I-A-42
January 2005
Table 4.8-1
STRESS CATEGORY
(Continued)
Detail
Category1
B
Fatigue Design
Details2
9, 10
Base metal and weld metal at full-penetration groove welded splices
at transitions in width or thickness, with welds ground to slopes no
steeper than 1 to 2.5, with grinding in the direction of applied stress,
and with weld soundness established by radiographic or ultrasonic
inspection.
B
11, 12
Base metal and weld metal at full-penetration groove welded splices,
with or without transitions having slopes no greater than 1 to 2.5,
when reinforcement is not removed and/or weld soundness is not
established by radiographic or ultrasonic inspection.
C
9, 10, 11, 12
Base metal and weld metal at full-penetration groove welds with permanent backing
Base metal detail of any length attached by groove welds subject
to transverse and/or longitudinal loading, when the detail embodies
a transition radius, R, not less than 2 in. (50 mm) and with the weld
termination ground smooth:
R ≥ 24 in. (610 mm)
24 in. > R ≥ 6 in. (150 mm)
6 in. > R ≥ 2 in. (50 mm)
E
22
B
C
D
13
13
13
Base metal at a detail attached by groove welds or fillet welds, where
the detail dimension parallel to the direction of stress, a, is less than
2 in. (50 mm)
C
19
D
E
14
14, 19, 20
B
C
D
16
16
16
General Condition
Detail
Groove Welds
Base metal and weld metal at full-penetration groove welded splices
of parts of similar cross section ground flush, with grinding in the
direction of applied stress and with weld soundness established by
radiographic or ultrasonic inspection.
Attachments
Base metal at detail attached by groove welds or fillet welds subject
to longitudinal loading, with transition radius, if any, less than 2 in.
(50 mm):
2 in. (50 mm ) ≤ a ≤ 12b or 4 in. (100 mm)
a > 12b or 4 in. (100 mm)
where
a = detail dimension parallel to the direction of stress
b = detail dimension normal to the direction of stress and the surface of the base metal
Base metal at a detail of any length attached by fillet welds or
partial-penetration groove welds in the direction parallel to the stress,
when the detail embodies a transition radius, R, not less than 2 in.
(50 mm) and weld termination ground smooth:
R ≥ 24 in. (610 mm)
24 in. (610 mm) > R ≥ 6 in. (150 mm)
6 in. (150 mm) > R ≥ 2 in. (50 mm)
1. See Table 4.8.1-1. All stresses are T and Rev., where “T” signifies range in tensile stress only; “Rev.” signifies a range involving reversal of
tensile or compressive stress; except Category F where stress range is in shear including shear stress reversal.
2. See Figure 4.8-1. These examples are provided as guidelines and are not intended to exclude other reasonably similar situations.
3. Tensile stresses are considered to be positive and compressive stresses are considered to be negative.
January 2005
I-A-43
Figure 4.8-1
FATIGUE DESIGN DETAILS
I-A-44
January 2005
Figure 4.8-1
FATIGUE DESIGN DETAILS
(Continued)
January 2005
I-A-45
Table 4.8.1-1
CONSTANTS FOR S-N CURVES1
Cf
Detail Category3
ksi
MPa
A
96.5
665
B
130
C
m
Fatigue Limit2
ksi
MPa
6.85
10.2
70
900
4.84
5.4
37
278
1920
3.64
4.0
28
D
157
1080
3.73
2.5
17
E
160
1100
3.45
1.8
13
F
174
1200
3.42
1.9
13
1. Different constants are to be used for calculations in ksi and MPa
2. Fatigue limit is based on N = 5x106
3. See Table 4.8-1
Figure 4.8.1-1
SCHEMATIC FATIGUE CURVE
I-A-46
January 2005
4.9 Compression in Single Web Beams
Including Single Web Beams With
Tubular Portions
For compression in single web beams including single
web beams with tubular portions, analysis shall be conducted using either the provisions of Section 3.4.11 or by
replacing ry in Section 3.4.11 with rye determined in accordance with Sections 4.9.1 through 4.9.3. Sections with the
tension flange partially or fully braced and with the compression flange laterally unbraced shall be designed using
Section 4.9 without consideration of tensile flange restraint
or another rational method of analysis.
4.9.1 Doubly Symmetric Sections and Sections
Symmetric About the Bending Axis
For checking beam sections at brace or support points or
between brace or support points of beam spans subjected
to end moment only or to transverse loads applied at the
neutral axis of the beam:
____________________
________________
( )
√ √
Iy d
kyLb 2
J ____
1 ___
rye = ___
1 + 0.152 __
Iy d
1.7 Sc
(Eq. 4.9.1-1)
For checking beam spans between brace or support
points of beams subjected to transverse loads applied on
the top or bottom flange (where the load is free to move
laterally with the beam if the beam buckles):
_______________________________
__________________
√ [
√
( )]
Iy d
kyLb 2
J ____
1 ___
rye = ___
± 0.5 + 1.25 + 0.152 __
Iy d
1.7 Sc
(Eq. 4.9.1-2)
The minus sign in front of the term ‘0.5’ shall be used
when the load is on a flange acting towards the shear center; the plus sign shall be used when the load is on a flange
acting away from the shear center.
In the above equations
Lb = length of the beam between bracing points or between
a brace point and the free end of a cantilever beam.
Bracing points are the points at which the compression flange is restrained against lateral movement or
the cross section is restrained against twisting
d = depth of beam.
4.9.2 Singly Symmetric Sections Unsymmetric
about the Bending Axis
For a beam that is unsymmetric about the bending axis,
the rye in Section 4.9.1 is calculated by taking Iy, Sc, and J
as though both flanges were the same as the compression
flange with the overall depth remaining the same.
4.9.3 Singly Symmetric Sections Symmetric or
Unsymmetric about the Bending Axis,
Doubly Symmetric Sections and Sections
Without an Axis of Symmetry
For a loading that does not cause torsion or lateral bending a more accurate value of rye is determined according to
this section. If the loading causes torsion and/or lateral bending, warping stress and/or lateral bending flexural stress, the
provisions of Section 4.3 shall apply.
√
____
Lb ___
Me
rye = ____
(Eq. 4.9.3-1)
1.2π ESc
where
Me = the elastic critical moment determined as follows:
___________
( )]
[ √
Fet
Me = AFey U + U2 + r o2 ___
Fey
(Eq. 4.9.3-2)
Me for cantilever beams shall be determined by rational
analysis unless the free end is braced or if the beam loading is covered in Section 4.9.4. References for rational
analysis are given in the Commentary.
In the above equations
y-axis is the centroidal symmetry or principal axis such
that the tension flange has a positive y coordinate and
bending is about the x-axis
y-axis is the centroidal symmetry or principal axis such
that the tension flange has a positive y coordinate and
bending is about the x-axis
rye = effective radius of gyration
Iy = moment of inertia of beam about axis parallel to web
Sc = section modulus of beam, compression side
J = torsion constant of beam. For non-tubular open sections an approximate value of J shall be calculated by
assuming the section to be composed of rectangles
and letting J equal the sum of the terms bt3/3 for each
rectangle where b is the larger dimension. The term
for each rectangle whose b/t ratio is less than 10 shall
be computed by the expression (1/3 – 0.2t/b) bt3.
For sections containing open parts and tubular portions, J shall be taken as the sum of J for the open
parts and the tubular parts.
ky = effective length coefficient for compression flange
about the y-axis. ky shall not be taken less than 1.
A = cross-sectional area
January 2005
C1 and C2 = coefficients to be taken from Section 4.9.4, or,
for cases not covered in Section 4.9.4,determined by rational analysis
Cw = torsional warping constant of the cross section
E = compressive modulus of elasticity (see Table 3.3-1)
πE
Fey = ______
kyLb 2
____
ry
2
( )
π EC
F = 1 ( GJ +
KL) )
(
Ar
et
____
2
o
2
w
______
t
t
2
(Eq. 4.9.3-3)
(Eq. 4.9.3-4)
G = shear modulus = 3E/8
I-A-47
g0 = distance from the shear center to the point of application of the load; taken as + when the load is applied
directed away from the shear center and – when the
load is directed towards the shear center. When there
is no transverse load (pure moment cases) g0 = 0.
where
MMAX = absolute value of maximum moment in the
unbraced beam segment
Iy = moment of inertia of the section about the y axis
MB = absolute value of moment at mid-point of the
unbraced beam segment
MA = absolute value of moment at quarter point of
the unbraced beam segment
J = torsion constant (See definition in Section 4.9.1)
(
)
(Eq. 4.9.3-5)
MC = absolute value of moment at three-quarter point
of the unbraced beam segment
For doubly symmetric I sections, j = 0
For singly symmetric I sections, as an alternative to equation 4.9.3.-5,
Cb values for doubly symmetric section cantilever beams
unbraced at the free end are given in Section 4.9.4.4. Cb
values for cantilever beams braced at the free end can
be evaluated using Eq. 4.9.4.1-1.
j
1
= ___
2Ix
∫y dA + ∫ yx dA – y
2
3
A
(
A
o
)[ ( ) ]
2Icy
Iy 2
j = 0.45df ___ – 1 1 – __
Iy
Ix
(Eq. 4.9.3-6)
where Icy is the moment of inertia of the compression flange
taken about the web, Ix and Iy are the moments of inertia
of the entire section about the x- and y-axes and df is the
distance between the flange centroids or for T-sections df
is the distance between the flange centroid and the tip of
the stem.
For singly symmetric I sections where the smaller flange
is not less than 80 percent of the area of the larger flange j
shall be permitted to be taken as – yo.
ky
= effective length coefficient for compression
flange about the y-axis. ky shall not be taken less
than 1.0.
Lt
= unbraced length for twisting.
ro
= √r x2 + r y2 + x o2 + y o2
C1:
When the moments vary linearly between the ends
of the unbraced segment C1 = 0. For some special
cases the values of C1 are given in Section 4.9.4.3.
For other variations, unless more accurate values are
available, C1 shall be taken as 0.5.
C2:
Since j = 0, a value of C2 is not needed.
4.9.4.2 Singly Symmetric Sections
Cb:
For sections with Icy /Iy greater than 0.1 and less than
0.9, the value of Cb shall be determined according to
Eq. 4.9.4.1-1.
When MMAX produces compression on the larger flange
and the smaller flange is also subjected to compression in the unbraced length, then the member shall
be checked at the location of MMAX as well as at the
location where the smaller flange is subjected to its
maximum compression. Cb at the location of MMAX
shall be calculated using Eq. 4.9.4.1-1. Cb for the
location where the smaller flange is subjected to its
maximum compression shall be taken as 1.67.
________________
(Eq. 4.9.3-7)
Polar radius of gyration of the cross-section
about the shear center.
rx , ry = actual radii of gyration of the cross-section about
the centroidal principal axes
Sc
= section modulus for the extreme compression
fiber for bending about the x-axis
U
= C1g0 – C2 j
xo
= x - coordinate of the shear center
yo
= y - coordinate of the shear center
For sections with Icy /Iy less than or equal to 0.1 or
greater than or equal to 0.9, Cb = 1.0
(Eq. 4.9.3-8)
C1:
When the moments vary linearly between the ends of
the unbraced segment C1 = 0. For some special cases
the values of C1 are given in Section 4.9.4.3. For other
cases C1 shall be determined by rational analysis.
The origin of the coordinate system is the intersection
of the principal axes.
C2:
When the moments vary linearly between the ends
of the unbraced segment C2 = 1. For some special
cases the values of C2 are given in Section 4.9.4.3.
For other cases C2 shall be determined by rational
analysis.
4.9.4 Lateral Buckling Coefficients
For cases not covered in Sections 4.9.4.3 and 4.9.4.4,
coefficients Cb, C1 and C2 shall be determined as specified
in Section 4.9.4.1 or 4.9.4.2.
4.9.4.1 Doubly Symmetric Sections
Cb:
I-A-48
12.5MMAX
Cb = _________________________
2.5MMAX + 3MA + 4MB + 3MC
(Eq. 4.9.4.1-1)
4.9.4.3 Special Cases—Doubly or Singly
Symmetric Sections
For simply supported beams with loadings listed below,
the following Cb, C1 and C2 values shall be used, except for
sections with Icy /Iy less than or equal to 0.1 or greater than
or equal to 0.9 where Cb shall be taken as 1.0:
January 2005
a. Uniformly distributed load over the entire span
Cb = 1.13, C1 = 0.41Cb, C2 = 0.47Cb
b. One concentrated load placed at a distance aL from one
of the ends of span
Cb = 1.75 – 1.6a( 1 – a )
a. For local buckling:
1) If a leg tip is a point of maximum compression
(Figure 4.11-1):
(Eq. 4.9.4.3-1)
Cb
C1 = _______
sin2πa
(Eq. 4.9.4.3-2)
a( 1-a )π2
Cb – C1
C2 = ______
(Eq. 4.9.4.3-3)
2
c. Two concentrated loads placed symmetrically at a distance aL from each end of span
Figure 4.11-1
Mn = 1.3Fcy Sc
for b/t ≤ S1
(Eq. 4.11-1)
Cb = 1 + 2.8a3
(Eq. 4.9.4.3-4)
Mn = [Bbr – 4Dbr(b/t)]Sc
for S1 < b/t < S2
(Eq. 4.11-2)
2C
C1 = ____2b sin2πa
aπ
(Eq. 4.9.4.3-5)
(Eq. 4.11-3)
C
C2 = ( 1 – a )Cb – ___1
2
Mn = π2ESc /(4(b/t))2
for b/t ≥ S2
(Eq. 4.9.4.3-6)
where
S1 = (Bbr – 1.3Fcy)/(4Dbr)
(Eq. 4.11-4)
S2 = Cbr /4
(Eq. 4.11-5)
4.9.4.4 Cantilever Beams
For cantilever beams braced at the support and unbraced
at the free end Cb shall be taken as follows:
Concentrated load at free end
applied at the centroid
Cb = 1.28, ky = 1.0
Uniform transverse load
applied at the centroid
Cb = 2.08, ky = 1.0
Uniform bending moment
Cb = 0.50, ky = 2.1
4.10 Compression in Elastically
Supported Flanges
Allowable compressive stresses in elastically supported
flanges, such as the compression flange of a standing seam
roof or of a hat-shaped beam loaded with the two flanges
in compression, shall be determined from Section 3.4.11
with the following effective value of Lb /ry, substituted in
the formulas for allowable stress.
( )
EA c2 1/4
Lb
____
Effective __
ry = 2.7 βsIyc
(Eq. 4.10-1)
2) If a leg is in uniform compression (Figure 4.11-2)
Figure 4.11-2
Mn = Fcy Sc
for b/t ≤ S1
(Eq. 4.11-6)
Mn = [Bp – 5.1Dp(b/t)]Sc
for S1 < b/t < S2
(Eq. 4.11-7)
Mn = π2ESc /(5.1(b/t))2
for b/t ≥ S2
(Eq. 4.11-8)
where:
S1 = (Bp – Fcy)/(5.1Dp)
(Eq. 4.11-9)
S2 = Cp /5.1
(Eq. 4.11-10)
b. For yielding (Figure 4.11-3):
where
Ac = area of compression element (compression flange
plus 1/3 of the area of the web between the compression flange and the neutral axis
E = compressive modulus of elasticity
Iyc = moment of inertia of compression element about an
axis parallel to the vertical web
βs = spring constant (transverse force applied to the compression flange of the member of unit length divided
by the deflection due to the force)
4.11 Single Angles in Flexure
Figure 4.11-3
Mn = 1.3My
(Eq. 4.11-11)
where My = yield moment about the axis of bending.
c. For lateral-torsional buckling:
for Me ≤ My, Mn = (0.92 – 0.17Me /My)Me
(Eq. 4.11-12)
The strength of a single angle in flexure (Mn) is given in
this Section. The design strength is Mn /ny.
January 2005
I-A-49
______
for Me > My , Mn = ( 1.92 – 1.17√ My /Me ) My ≤ 1.3My
(Eq. 4.11-13)
where Me = elastic lateral-torsional buckling moment
from Section 4.11.1 or 4.11.2 as applicable.
Cb shall be determined in accordance with Section 4.9.4.1
but shall not exceed 1.5.
4.11.1 Bending About Geometric Axes
Bending about a geometric axis is shown in Figure
4.11.1-1.
Subsections a.
and b.
Subsection c.
Figure 4.11.1-1
a. Angles with continuous lateral-torsional restraint: Mn is
the lesser of:
1) local buckling strength determined by Section 4.11a.
2) yield strength determined by Section 4.11b.
b. Equal leg angles with lateral-torsional restraint only at
the point of maximum moment: Strengths shall be calculated with Sc being the geometric section modulus. Mn
is the least of:
1) local buckling strength determined by Section 4.11a.
2) yield strength determined by Section 4.11b.
3) If the leg tip is in compression, lateral-torsional buckling strength determined by Section 4.11c with
______________
0.82Eb tC
M = _________b [ √1 + 0.78 ( L t / b2 )2 – 1 ]
4
e
L
2
b
b
(Eq. 4.11.1-1)
If the leg tip is in tension, lateral-torsional buckling
strength determined by Section 4.11c with
______________
0.82Eb4tCb
[ √1 + 0.78 ( Lbt / b2 )2 + 1 ]
Me = _________
L2b
(Eq. 4.11.1-2)
c. Equal leg angles without lateral-torsional restraint:
Strengths shall be calculated with Sc being 0.80 of the
geometric section modulus.
If the leg tip is in compression, Mn is the lesser of:
1) local buckling strength determined by Section 4.11a(1)
2) lateral-torsional buckling determined by Section 4.11c
with
______________
0.66Eb4tCb
[ √1 + 0.78 ( Lbt / b2 )2 – 1 ]
Me = _________
L2b
(Eq. 4.11.1-3)
If the leg tip is in tension, Mn is the lesser of:
1) yield strength determined by Section 4.11b
2) lateral-torsional buckling determined by Section 4.11c
with
I-A-50
0.66Eb4tCb ______________
[ √1 + 0.78 ( Lbt / b2 )2 + 1 ]
Me = _________
L2b
(Eq. 4.11.1-4)
d. Unequal leg angles without lateral-torsional restraint:
moments about the geometric axes shall be resolved
into moments about the principal axes and the angle
shall be designed as an angle bent about a principal axis
(Section 4.11.2).
4.11.2 Bending About Principal Axes
Bending about principal axes is shown in Figure 4.11.2-1.
Minor Axis
Bending
Major Axis
Bending
Figure 4.11.2-1
a. Equal leg angles, major axis bending: Mn is the lesser of:
1) local buckling strength determined by Section 4.11a
2) lateral-torsional buckling strength determined by
Section 4.11c, with
0.46Eb2t2
Me = Cb ________
(Eq. 4.11.2-1)
Lb
b. Unequal leg angles, major axis bending: Mn is the lesser of:
1) local buckling strength determined by Section 4.11a
for the leg with its tip in compression
2) lateral-torsional strength determined by Section 4.11c,
with
[
]
________________
I
Me = 4.9E __z2 Cb √βw2 + 0.052( Lbt / rz )2 + βw
Lb
(Eq. 4.11.2-2)
Iz = minor principal axis moment of inertia
rz = minor principal axis radius of gyration
1 ∫z( w2 + z2 )dA – 2z ,
βw = __
(Eq. 4.11.2-3)
o
Iw
[
]
βw is a section property for unequal leg angles and
is positive when the short leg is in compression and
negative when the long leg is in compression. (See
the Commentary for values for common angle sizes
and equations for determining βw.) If the long leg is in
compression anywhere along the unbraced length of
the angle, βw is negative.
zo = coordinate along the z-axis of the shear center
with respect to the centroid
Iw = major principal axis moment of inertia
c. Equal and unequal leg angles, minor axis bending:
1) If the leg tips are in compression, Mn is the lesser
of the local buckling strength determined by Section
4.11a(1) and the yield strength determined by Section 4.11b.
January 2005
2) If the leg tips are in tension, Mn is the yield strength
determined by Section 4.11b.
(Eq. 4.13.1-2)
for S1 < λeq < S2
4.12 Tapered Thickness Elements
____
For uniform compression on elements with linearly varying thickness where δ ≤ 2.0:
a. For tapered thickness elements with the thick edge supported and the thin edge free, the slenderness ratio is
b
(1 – 0.12δ) ___
t
( )
avg
b. For tapered thickness elements with the thin edge supported and the thick edge free, the slenderness ratio is
b
___
tavg
( )
c. For tapered thickness elements supported on both edges,
b
the slenderness ratio is ___
t
( )
avg
where
b = width of the element
tmax + tmin
tavg = ________
2
= the average thickness of the element
tmin = lesser thickness
k2√ BpE
c. Fc = ______
nyλeq
(Eq. 4.13.1-3)
for λeq ≥ S2
where
Bp – Fcy
S1 = ______
Dp
(Eq. 4.13.1-4)
k1Bp
S2 = ____
Dp
(Eq. 4.13.1-5)
___
√
E
λeq = π ___
Fcr
(Eq. 4.13.1-6)
Fcr = Mcr /Sc
where Mcr is the elastic buckling moment of the beam
under pure bending with continuous lateral support determined by linear elastic analysis and Sc is the compressive
section modulus of the entire cross section.
4.13.2 Compressive Strength of Beam Elements—
Flat Elements in Bending In Their
Own Plane
tmax = greater thickness
δ
Bp –Dpλeq
b. Fc = ________
ny
(tmax – tmin)
= ________
tmin
1.3Fcy
a. Fc = _____
ny
(Eq. 4.13.2-1)
for λeq ≤ S1
Bbr – Dbrλeq
b. Fc = _________
ny
(Eq. 4.13.2-2)
for S1 < λeq < S2
____
k2√ Bbr E
c. Fc = _______
nyλeq
for λeq ≥ S2
(Eq. 4.13.2-3)
where
Figure 4.12-1
4.13 Compressive Strength of Beam Elements
As an alternative to Section 3, the compressive strength of
elements of beams composed entirely of flat elements addressed
by Sections 3.4.15, 3.4.16, 3.4.16.2, 3.4.16.3, or 3.4.18 shall
be determined as follows in Sections 4.13.1 and 4.13.2. The
allowable stress for the shape shall then be determined using
Section 4.7.3, except that the strength of any stiffened element
need not be limited to the strength of the stiffener.
4.13.1 Compressive Strength of Beam Elements—
Flat Elements in Uniform Compression
Fcy
a. Fc = ___
ny
Bbr – 1.3Fcy
S1 = _________
Dbr
(Eq. 4.13.2-4)
k1Bbr
S2 = ____
Dbr
(Eq. 4.13.2-5)
___
√
E
λeq = π ___
Fcr
(Eq. 4.13.2-6)
Fcr = Mcr /Sc
where Mcr is the elastic buckling moment of the beam
under pure bending with continuous lateral support determined by linear elastic analysis and Sc is the compressive
section modulus of the entire cross section.
(Eq. 4.13.1-1)
for λeq ≤ S1
January 2005
I-A-51
Section 5. Mechanical Connections
5.1 General
5.1.4 Net Area
5.1.1 Minimum Edge Distance
The net area An of a member is the sum of the products
of the thickness and the least net width of each element
computed as follows:
The width of holes shall be taken as the nominal hole
diameter for drilled or reamed holes and the nominal hole
diameter plus 1/32 in. (0.8 mm) for punched holes.
For a chain of holes extending across a part in any
diagonal or zigzag line, the net width of the part shall be
obtained by deducting from the gross width the sum of the
hole widths of all holes in the chain, and adding, for each
gage space in the chain, the quantity s2/4g where
If the distance from the center of a fastener to the edge
of the connected part in the direction of the force on the fastener is less than 2D, the allowable bearing strength of the
connected part shall be factored by this distance divided by
2D, where D is the nominal diameter of the fastener. (See
Sections 3.4.5 and 3.4.6).
The distance from the center of a fastener to an edge of
a part shall not be less than 1.5D.
5.1.2 Maximum Spacing of Fasteners
The pitch and gage of fasteners joining components of
tension members shall not exceed (3 + 20t) in. [(75 + 20t)
mm] where t is the thickness of the outside component.
In outside components of compression members:
1) the pitch of fasteners in the direction of stress shall be
based on the allowable stress from Section 3.4.7 with
an effective length kL = s/2, where s is the pitch, and
2) the gage of fasteners perpendicular to the direction
of stress shall be based on the allowable stress from
Section 3.4.9 with a width b = 0.8g where g is the
gage. If only one line of fasteners is used, the allowable stress shall be based on Section 3.4.8.1 with a
width b = the edge distance of the fastener.
5.1.3 Block Shear Rupture
The block shear rupture allowable force Psr of bolted
connections on a failure path with shear on some segments
and tension on the other segments is:
For Ftu Ant ≥ Fsu__Anv
Psr = ( ( Fty /√3 )Agv + Ftu Ant )/nu
(Eq. 5.1.3-1)
Otherwise
Psr = ( Fsu Anv + Fty Agt )/nu
(Eq. 5.1.3-2)
The block shear rupture allowable force Psr of welded
connections on a failure path with shear on some segments
and tension on the other segments is:
For Ftu Agt ≥ Fsu Agv
__
Psr = ( ( Fty /√3 )Agv + Ftu Agt )/nu
(Eq. 5.1.3-3)
Otherwise
Psr = ( Fsu Agv + Fty Agt )/nu
(Eq. 5.1.3-4)
where
Agv = gross area in shear
Agt = gross area in tension
Anv = net area in shear
Ant = net area in tension
I-A-52
s = longitudinal center-to-center spacing (pitch) of any
two consecutive holes
g = transverse center-to-center spacing (gage) between
fastener gage lines
For angles, the gage for holes in opposite legs shall be
the sum of the gages from the back of the angles less the
thickness.
Weld metal in plug or slot welds shall not be included
in the net area.
5.1.5 Effective Net Area
The effective net area for angles, channels, tees, zees,
and I-shaped sections shall be determined as follows:
1) If tension is transmitted directly to each of the crosssectional elements of the member by fasteners or
welds, the effective net area Ae is the net area.
2) If tension is transmitted by fasteners or welds through
some but not all of the cross-sectional elements of
the member, the effective net area Ae is:
_
_
y
x 1 – __
Ae = An 1 – __
(Eq. 5.1.5-1)
L
L
where
An = net area of the member at the connection
(
)(
)
L = length of the connection in the direction of load, measured from the center of fasteners or the end of welds
_
x = eccentricity of the connection in the x axis direction
_
y = eccentricity of the connection in the y axis direction
If the length of the connection L is zero, the net effective
area is the net area of the connected elements.
5.1.6 Long Grips
If the grip (total thickness of parts being fastened) of an
aluminum fastener exceeds 4.5D, the fastener’s nominal shear
strength shall be reduced by dividing by [½+Gf /(9D)] where
Gf is the grip and D is the fastener’s nominal diameter.
January 2005
5.1.7 Strength and Arrangement of Connections
5.2.2 Holes and Slots for Bolts
If the center of resistance of a connection does not coincide with the resultant line of action of the load, members
and connections shall be proportioned to account for load
eccentricities at the connection.
The nominal diameter of holes for bolts shall not be
more than 1/16 in. (2 mm) greater than the nominal diameter
of the bolt unless slip-critical connections are used.
The nominal width of slots for bolts shall not be more
than 1/16 in. (2 mm) greater than the nominal diameter of
the bolt. If the nominal length of the slot exceeds 2.5D or
the edge distance is less than 2D, where D is the nominal
bolt diameter, the edge distance perpendicular to the slot
length and slot length shall be sized to avoid overstressing the material along the slot. Unless slip-critical connections are used, the length shall be normal to the direction
of load.
5.1.8 Countersunk Holes
The bearing length for countersunk holes shall be the
part thickness less one-half the depth of the countersink.
5.2 Bolted Connections
5.2.1 Bolt Material
Bolt fastener material shall be one of the following:
5.2.3 Bolt Tension
a. Aluminum: Bolts shall meet ASTM F468 and be 2024-T4,
6061-T6, or 7075-T73. When 2024 bolts will be exposed
to contact with liquid water or humidity near the dew
point in the intended service, they shall have a minimum
0.0002 in. (0.005 mm) thick anodic coating. Nuts shall
meet ASTM F467. Nuts for ¼ in. (M6) bolts and smaller
shall be 2024-T4; larger nuts shall be 6061-T6 or 6262-T9.
Flat washers shall be Alclad 2024-T4. Spring lock washers shall be 7075-T6.
b. Carbon steel: Carbon steel bolts, nuts, and washers
shall be hot-dip galvanized to ASTM A153 or electrogalvanized to ASTM B633. Galvanizing thickness shall be
adequate to provide corrosion protection for the anticipated service. Hot-dipped galvanized A490 bolts shall
not be used. Galvanized steel fasteners shall be lubricated
to eliminate galling and assure adequate preload. When
other platings and/or coatings are used, evidence shall be
submitted to substantiate their corrosion resistance when
in contact in aluminum. Bolt hardness shall be less than
Rockwell C35.
c. Stainless steel: Stainless steel bolts, nuts and washers shall be 300 series stainless steel. Bolts shall meet
ASTM F593. Nuts shall meet ASTM F594.
The allowable tension load on an aluminum bolt is the
root area of the bolt (π/4[D − 1.191/n]2) times its allowable
tensile stress, which is Ftu /(1.2nu), where n = number of
threads/in.. (See Table 5.2.3-1 or Table 5.2.3-1M).
5.2.4 Bolt Shear
The allowable shear load on an aluminum bolt is its
effective shear area times its allowable shear stress, which
is Fsu /(1.2nu). (See Table 5.2.3-1 or Table 5.2.3-1M). The
effective shear area for bolts with no threads in the shear
plane shall be based on the nominal diameter. The effective
shear area for bolts with threads in the shear plane shall be
based on the root diameter (D − 1.191/n).
5.2.5 Bolt Bearing
The allowable bearing load applied by a bolt to an aluminum part is the part’s allowable bearing stress (see Sections
3.4.5 and 3.4.6) times the effective bearing area of the bolt.
The bolt’s effective bearing area is its nominal diameter multiplied by the bearing length (see Section 5.1.8 for countersunk
holes). This applies to threaded and unthreaded surfaces.
Table 5.2.3-1
DESIGN STRESSES FOR BOLTS
Building Type Structures
Bridge Type Structures
Alloy and
Temper
Minimum
Shear Ultimate
Strength1
Fsu
(ksi)
Minimum
Tensile Ultimate
Strength1
Ftu
(ksi)
Design Shear
Stress on
Effective Area2
(ksi)
Design Tensile
Stress on
Root Area 2
(ksi)
Design Shear
Stress on
Effective Area3
(ksi)
Design Tensile
Stress on
Root Area 3
(ksi)
2024-T4
37
62
16
26
14
23
6061-T6
25
42
10.5
18
9.5
16
7075-T73
41
68
18
29
16
26
1. From ASTM B316/B316M and F468
2. SF = 2.34
3. SF = 2.64
January 2005
I-A-53
Table 5.2.3-1M
DESIGN STRESSES FOR BOLTS
Building Type Structures
Bridge Type Structures
Alloy and
Temper
Minimum
Shear Ultimate
Strength1
Fsu
(MPa)
Minimum
Tensile Ultimate
Strength1
Ftu
(MPa)
Design Shear
Stress on
Effective Area2
(MPa)
Design Tensile
Stress on
Root Area 2
(MPa)
Design Shear
Stress on
Effective Area3
(MPa)
Design Tensile
Stress on
Root Area 3
(MPa)
2024-T4
255
425
110
180
95
160
6061-T6
170
290
75
125
65
110
7075-T73
280
470
120
200
105
180
1. From ASTM B316/B316M
2. SF = 2.34
3. SF = 2.64
5.2.6 Minimum Spacing of Bolts
The minimum distance between bolt centers shall be 2.5
times the nominal bolt diameter.
5.2.7 Lockbolts
Lockbolts shall meet the requirements in this Specification for conventional bolts and be installed in conformance
with the lockbolt manufacturer’s specifications. The bearing areas under the head and collar shall not be less than
those of a conventional bolt and nut.
5.2.8 Slip-Critical Bolted Connections
5.2.8.1 General
Slip-critical connections between aluminum members or
between aluminum and steel members shall comply with the
Research Council on Structural Connections (RCSC) Specification for Structural Joints Using ASTM A325 or A490
Bolts, Allowable Stress Design, except as modified here. The
shear on a bolt in a slip-critical connection shall not exceed
the allowable shear for the bolt (Section 5.2.8.4), the allowable bearing for the connected members (Section 3.4.5), or
the allowable slip load (Section 5.2.8.5).
5.2.8.2 Material
Aluminum used in slip-critical connections shall have
a tensile yield strength of at least 15 ksi (105 MPa). Bolts
shall comply with ASTM A325, nuts shall comply with
ASTM A563 Grade DH or ASTM A194 Grade 2H, and
washers shall comply with ASTM F436. Bolts, nuts, and
washers shall be zinc coated by the hot-dip or mechanically
deposited processes as specified in ASTM A325.
5.2.8.3 Holes
Holes shall be standard holes, oversize holes, short slotted holes, or long slotted holes. The nominal dimensions for
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each hole type shall not exceed those shown in the RCSC
Specification Table 1.
5.2.8.4 Design for Strength
The shear stress on a bolt shall not exceed 21 ksi (145 MPa)
for bolts with threads in the shear plane and 30 ksi (205 MPa)
for bolts without threads in the shear plane. Bolt shear stresses
are based on the nominal cross sectional area (unthreaded
body area) of a bolt. The bearing stress on the connected
parts shall not exceed the allowable bearing stress specified
in Section 3.4.5.
5.2.8.5 Design for Slip Resistance
Aluminum surfaces abrasion blasted with coal slag to
SSPC SP-5 to an average substrate profile of 2.0 mils (0.05
mm) in contact with similar aluminum surfaces or zinc
painted steel surfaces with a maximum dry film thickness
of 4 mils (0.1 mm) are Class B surfaces. Slip coefficients
for other surfaces shall be determined in accordance with
the RCSC Specification Appendix A.
In addition to the requirements of Section 5.2.8.4, bolts
shall be proportioned so that the allowable slip load per
unit of bolt area determined from the following table is not
exceeded. The nominal diameter of the bolt shall be used
to calculate its area.
Bolts shall be installed to develop the minimum bolt
tension specified in Section 5.2.8.7.
The effect on slip resistance of temperature changes
from the installation temperature and the difference in
coefficients of thermal expansion of aluminum and steel
shall be addressed.
5.2.8.6 Washers
a. Washers shall be used under bolt heads and under nuts.
b. At a long slotted hole in an outer ply, a galvanized steel
plate washer or bar at least 5/16 in. (8 mm) thick with
January 2005
Hole Type and Direction of Load
Any Direction
Transverse Parallel
Contact Surface
Oversize
&
Long
of Bolted Parts Standard
Long Slots
Short Slots
Slots
Class B (Slip
Coefficient 0.50)
ksi MPa
ksi
MPa
ksi MPa ksi MPa
28
24
165
20
195
140
17
115
standard holes, shall be used. The plate washer or bar
shall completely cover the slot but need not be hardened.
c. Where the outer face of the bolted parts has a slope
greater than 1:20 with respect to a plane normal to the
bolt axis, a beveled washer shall be used.
a. Aluminum: Aluminum shall meet ASTM B 316.
b. Carbon steel: Carbon steel shall not be used unless the
aluminum is joined to carbon steel (see Section 6.7.1), or
corrosion resistance of the structure is not required, or the
structure is protected against corrosion.
c. Stainless steel: Stainless steel shall be 300 series.
5.3.2 Holes for Cold-Driven Rivets
The finished diameter of holes for cold-driven rivets shall
not be more than 4% greater than the nominal diameter of
the rivet.
5.3.3 Rivet Tension
Rivets shall not be used to carry tensile loads.
5.2.8.7 Installation
Bolts shall be tightened in accordance with the RCSC
Specification.
5.3 Riveted Connections
5.3.1 Rivet Material
Rivet material shall be one of the following:
5.3.4 Rivet Shear
The allowable shear load on an aluminum rivet is its
effective shear area times its allowable shear stress, which
is Fsu /(1.2nu). (See Table 5.3.4-1 or Table 5.3.4-1M). The
effective shear area of solid rivets shall be based on the
nominal hole diameter. (See Section 5.3.2 for hole size limits and Section 5.3.8 for hollow-end rivets).
Table 5.3.4-1
DESIGN STRESSES FOR RIVETS
Minimum Shear Ultimate
Strength1
Fsu
(ksi)
Building Type Structures
Bridge Type Structures
Design Shear Stress on
Effective Area2
(ksi)
Design Shear Stress on
Effective Area3
(ksi)
2017-T4
33
14
12.5
2024-T42
37
16
14
2117-T4
26
11
10
2219-T6
30
13
11.5
6053-T61
20
8.5
7.5
6061-T6
25
10.5
9.5
7050-T7
39
17
15
7075-T6
42
18
16
7075-T73
41
18
16
7178-T6
46
20
17
Designation Before
Driving
1. From ASTM B316/B316M for heat treated alloys.
2. SF = 2.34
3. SF = 2.64
January 2005
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Table 5.3.4-1M
DESIGN STRESSES FOR RIVETS
Minimum Shear Ultimate
Strength1
Fsu
(MPa)
Building Type Structures
Bridge Type Structures
Design Shear Stress on
Effective Area2
(MPa)
Design Shear Stress on
Effective Area3
(MPa)
2017-T4
225
95
85
2024-T42
255
110
95
2117-T4
180
75
70
2219-T6
205
90
80
6053-T61
135
60
50
6061-T6
170
75
65
7050-T7
270
115
100
7075-T6
290
125
110
7075-T73
280
120
105
7178-T6
315
135
120
Designation Before
Driving
1. From ASTM B316/B316M for heat treated alloys.
2. SF = 2.34
3. SF = 2.64
5.3.5 Rivet Bearing
The allowable bearing load applied by a rivet to an aluminum part is the part’s allowable bearing stress (see Section 3.4.5) times the effective bearing area of the rivet. The
rivet’s effective bearing area is the nominal hole diameter
multiplied by the bearing length (see Section 5.1.8 for countersunk holes).
5.3.6 Minimum Spacing of Rivets
diameter from 0.164 in. (4.2 mm) through 0.25 in. (6.3 mm).
Screws shall be thread-forming or thread-cutting, with or
without a self-drilling point. As an alternate to Sections 5.4.1
and 5.4.2, strengths shall be based on tests according to Section 9.
Screws shall be installed and tightened in accordance
with the manufacturer’s specifications.
The following nomenclature applies to this Section:
Asn = thread stripping area of internal thread per unit
length of engagement
The minimum distance between rivet centers shall be 3
times the nominal rivet diameter.
C
5.3.7 Blind Rivets
Dh = nominal hole diameter
Grip lengths and hole sizes for blind rivets shall comply
with the rivet manufacturer’s specifications.
Dw = nominal washer diameter
5.3.8 Hollow-End (Semi-tubular) Rivets
Ftu1 = tensile ultimate strength of member in contact
with the screw head
The shear strength of hollow-end rivets with solid cross
sections for a portion of the length shall be taken equal to
the strength of solid rivets of the same material if the bottom
of the cavity is at least 25% of the rivet diameter from the
plane of shear.
5.4 Tapping Screw Connections
This Section applies to tapping screws with a nominal
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= coefficient that depends on screw location
D = nominal screw diameter
Dws = larger of the nominal washer diameter and the
screw head
Ftu2 = tensile ultimate strength of member not in contact
with the screw head
Fty1 = tensile yield strength of member in contact with
the screw head
Fty2 = tensile yield strength of member not in contact
with the screw head
Ks = coefficient that depends on member thickness
January 2005
n
= number of threads per unit length for a screw
ns = safety factor = 3.0
Ks = 1.20 for 0.080 in. ≤ tc ≤ 0.125 in.
(2 mm ≤ tc ≤ 3 mm)
Pnt = nominal tensile strength of a screw
b. for 0.125 in. < tc < 0.25 in. (3 mm < tc < 6.3 mm)
Pnot = nominal pull-out strength of a screw
Pnot = 1.2DFty2(0.25 – tc) + 1.16AsnFtu2(tc – 0.125)
(Eq. 5.4.2.1-2)
Pnov = nominal pull-over strength of a screw
c. for 0.25 in. ≤ tc ≤ 0.375 in. (6.3 mm ≤ tc ≤ 10 mm)
Pns = nominal shear strength of a screw
t1
= thickness of member in contact with the screw head
t2
= thickness of member not in contact with the screw
head
tc
= depth of full thread engagement of screw into t2
not including tapping or drilling point
5.4.1 Screw Material
Screws shall be:
a. aluminum,
b. austenitic stainless steel, or
c. if the screw will not be exposed to contact with liquid
water or humidity near the dew point in its intended service:
1) non-austenitic stainless steel with a minimum nominal
composition of 16% chromium and a Rockwell hardness less than C35 in the load bearing portion of the
shank, or
2) coated or plated carbon steel with a Rockwell hardness less than C35 in the load bearing portion of the
shank. Screws shall be zinc coated per ASTM A123,
A641, or B633 or nickel/chromium plated per ASTM
B456, Type SC. When other platings and/or coatings
are to be used, evidence shall be submitted to substantiate the corrosion resistance of these products.
For screws that carry tensile loads, the head of the screw
or washer, if a washer is provided, shall have a diameter Dw
not less than 5/16 in. (8 mm). Washers shall be at least 0.050 in.
(1.3 mm) thick.
The allowable tension force on a screw is the least of:
(see Section 5.4.2.1)
(see Section 5.4.2.2)
The nominal pull-out strength, Pnot, for pulling a screw
out of a threaded part, is:
1) For UNC threads (screw thread types C, D, F, G, and T)
a. for 0.060 in. ≤ tc ≤ 0.125 in. (1.5 mm ≤ tc ≤ 3 mm)
Pnot = Ks D tc Fty2
(Eq. 5.4.2.1-1)
where
Ks = 1.01 for 0.060 in. ≤ tc < 0.080 in.
(1.5 mm ≤ tc < 2 mm)
January 2005
Pnot = Ks D tc Fty2
(Eq. 5.4.2.1-4)
where
Ks = 1.01 for 0.038 in. ≤ tc < 0.080 in.
(1 mm ≤ tc < 2 mm)
Ks = 1.20 for 0.080 in. ≤ tc < 2/n
(2 mm ≤ tc < 2/n)
b. for 2/n < tc < 4/n
Pnot = 1.2D Fty2 (4/n – tc) + 3.26D Ftu2 (tc – 2/n)
(Eq. 5.4.2.1-5)
c. for 4/n ≤ tc ≤ 0.375 in. (4/n ≤ tc ≤ 8 mm)
Pnot = 1.63D tc Ftu2
(Eq. 5.4.2.1-6)
5.4.2.2 Pull-Over
The nominal pull-over strength, Pnov, for pulling connected material over the head of a screw or washer, if present, is:
(Eq. 5.4.2.2-1)
where C is a coefficient that depends on screw location (1.0
for valley fastening and 0.7 for crown fastening), and Dws is
the larger of the screw head diameter or the washer diameter, but no greater than 5/8 in. (16 mm). (See Section 5.4.2
for the washer thickness requirement.) The nominal pullover strength need not be less than the pull-over strength
computed from equation 5.4.2.2-2 for countersunk screws.
For countersunk screws with an 82o nominal angle head,
the nominal pull-over strength is:
Pnov = (0.27 + 1.45t1/D) D t1Fty1
5.4.2.1 Pull-Out
(Eq. 5.4.2.1-3)
2) For spaced threads (screw thread types AB, B, BP,
BF, and BT)
a. for 0.038 in. ≤ tc ≤ 2/n (1 mm < tc < 2/n)
Pnov = C t1 Ftu1 (Dws – Dh)
5.4.2 Screw Tension
1) Pnot /ns
2) Pnov /ns
3) Pnt /(1.25ns)
Pnot = 0.58 Asn tc Ftu2
(Eq. 5.4.2.2-2)
for 0.06 in. ≤ t1 < 0.19 in. (1.5 mm ≤ t1 < 5 mm) and t1/D ≤
1.1. If t1/D > 1.1, use t1/D = 1.1
5.4.3 Screw Shear and Bearing
The shear force on a screw shall not exceed the least of:
1) 2 Ftu1 D t1/nu.
(Eq. 5.4.3-1)
If the screw is countersunk, one-half the depth of the
countersink shall be deducted from t1.
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2) 2Ftu2 Dt2 /nu
(Eq. 5.4.3-2)
3) 4.2(t23D)1/2 Ftu2 /ns , for t2 ≤ t1
(Eq. 5.4.3-3)
4) Pns /(1.25 ns)
(Eq. 5.4.3-4)
5.4.4 Minimum Spacing of Screws
rugations, and the minimum sidelap for siding shall have a
width equal to half the pitch.
For a trapezoidal sheet of a depth greater than 1 in. (25
mm) the minimum sidelap for both roofing and siding shall
have a developed width equal to the width of the narrowest
flat plus 2 in. (50 mm). A trapezoidal sheet with a depth of 1
in. (25 mm) or less shall have an overlap of proven design
including an anti-siphoning feature.
The minimum distance between screw centers shall be
2.5 times the nominal screw diameter.
5.5.3 Fasteners in Laps
Minimum endlaps shall be those expressed in Table
5.5.1-1.
The minimum size of fasteners used in end laps and side
laps shall be #12 (5.5 mm) for screws and 3/16 in. (5 mm)
diameter for rivets. The maximum spacing for sidelap fasteners shall be 12 in. (300 mm). Endlap fasteners shall be
located no more than 2 in. (50 mm) from the end of the
overlapping sheet.
5.5.2 Sidelaps
5.5.4 Flashing
5.5 Building Sheathing Connections
5.5.1 Endlaps
For a sinusoidal corrugated sheet, the minimum sidelap
for roofing shall have a width equal to the pitch of the cor-
Flashing shall be formed from aluminum sheet.
Table 5.5.1-1
MINIMUM END LAPS
Minimum End Laps
Depth of section
1 in. or less
(25 mm or less)
Greater than 1 in., less than 2 in.
(Greater than 25 mm, less than 50 mm)
2 in. or more (50 mm or more)
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Roofing, slope greater than 2
on 12, less than 3 on 12
–
9 in.
(230 mm)
9 in.
(230 mm)
Roofing, slope 3 on 12
or more
6 in.
(150 mm)
6 in.
(150 mm)
6 in.
(150 mm)
Siding
4 in.
(100 mm)
4 in.
(100 mm)
6 in.
(150 mm)
October 2005
Section 6. Fabrication and Erection
6.1 Layout
6.1.1 Punch and Scribe Marks
Punched or scribed layout marks shall not remain on
fabricated material designed for fatigue.
Table 6.3-1
TEMPERATURE EXPOSURE LIMITS
FOR ARTIFICIALLY AGED TEMPERS OF
6005, 6061, AND 6063
Temperature1
6.1.2 Temperature Correction
A temperature correction shall be applied where necessary in the layout of dimensions. The coefficient of expansion used shall be 13 × 10-6 per oF (23 × 10-6 per oC).
6.2 Cutting
6.2.1 Methods
Time
o
F
o
C
450
230
5 min
425
220
15 min
400
205
30 min
375
190
2 hr
Cutting shall be by shearing, sawing, nibbling, routing,
arc cutting, laser or abrasive water jet. Edges which have
been arc or laser cut shall be planed to remove edge cracks.
350
175
10 hr
325
165
100 hr
6.2.2 Edge Quality
300
150
1,000 hr
Cut edges shall be true, smooth, and free from excessive
burrs or ragged breaks.
212
100
100,000 hr
6.2.3 Re-entrant Corners
Re-entrant corners shall be filleted.
6.2.4 Oxygen Cutting
Oxygen cutting is prohibited.
6.3 Heating
1) Interpolate time (t) for other temperatures (T) using
log( T2 /T )
logt = logt2 + __________( log t1/t2 )
log( T2 /T1 )
where
T1 = next lower temperature in Table 6.3-1 than T
T2 = next higher temperature in Table 6.3-1 than T
t1 = time corresponding to T1
t2 = time corresponding to T2
Aluminum heated above 150oF (66oC) during fabrication
other than welding is subject to the following requirements:
a. Temperature controls and supervision shall be provided to
ensure that time-temperature limits are met, and time and
temperature exposure shall be documented.
b. When heating reduces metal strengths, design stresses
shall be reduced consistent with the mechanical properties of the aluminum after the heating process. Reduced
design stresses need not be used for the alloys and tempers
in Table 6.3-1 if the cumulative time at the elevated temperature does not exceed the limits given.
January 2005
c. 5083, 5086, 5154, and 5456 shall not be held at temperatures from 150oF (66oC) to 450oF (230oC). To hot
form such alloys, they shall be
1) rapidly heated to a temperature not to exceed 550oF
(290oC)
2) formed before the metal cools below 450oF (230oC),
and
3) rapidly cooled from 450oF (230oC) to 150oF (66oC).
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6.4 Holes
6.4.1 Fabrication Methods
Holes shall be punched or drilled. Punching shall not be
used for castings or if the metal thickness is greater than
the diameter of the hole. The amount by which the diameter of a sub-punched hole is less than that of the finished
hole shall be at least ¼ the thickness of the piece but not
less than 1/32 in. (0.8 mm).
6.4.2 Hole Alignment
If holes must be enlarged to admit fasteners, they shall
be reamed. Poor matching holes shall be rejected. Holes
shall not be drifted in a manner that distorts the metal. All
chips and foreign matter between contacting surfaces shall
be removed before assembly.
6.5 Riveting
6.5.1 Driven Head
The driven head of aluminum rivets shall be flat or conepoint, with dimensions as follows:
6.5.1.1 Flat Heads
Flat heads shall have a diameter at least 1.4 times the
nominal diameter of the rivet and a height at least 0.4 times
the nominal diameter of the rivet.
6.5.1.2 Cone-Point Heads
Cone-point heads shall have a diameter at least 1.4 times
the nominal diameter of the rivet and a height to the apex
of the cone at least 0.65 times the nominal diameter of the
rivet. The nominal included angle at the apex of the cone
shall be 127o.
6.5.2 Hole Filling
Rivets shall fill holes completely. Rivet heads shall be
concentric with the rivet holes and shall be in continuous
contact with the surface of the part joined.
6.5.3 Defective Rivets
Defective rivets shall be removed by drilling. The drill
bit diameter shall not exceed the diameter of the replacement rivet.
6.6 Finishes
6.6.1 Where Painting Is Required
Aluminum shall be painted where:
a. 2014 is in the presence of moisture,
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b. aluminum would otherwise be in contact with or fastened to
dissimilar materials as described in Section 6.7,
c. aluminum is exposed to corrosive conditions.
6.6.2 Surface Preparation
Surfaces to be painted shall be prepared immediately
before painting by:
a. a chemical cleaner (such as a solution of phosphoric
acid and organic solvents)
b. abrasion blasting
c. unsealed anodizing
d. chemical conversion coating, or
e. using the procedure specified by the coating supplier.
6.7 Contact with Dissimilar Materials
Where aluminum is in contact with or fastened to the
materials specified in Sections 6.7.1 through 6.7.3, direct
contact between the aluminum and the other material shall
be prevented as specified in those sections or by placing a
compatible, nonporous isolator between the aluminum and
the other material.
6.7.1 Steel
Steel surfaces to be placed in contact with uncoated aluminum shall be painted with a coating suitable for the service. Where very corrosive conditions are expected, additional protection can be obtained by applying a sealant that
excludes moisture from the joint during service. Aluminized,
hot-dip galvanized or electro-galvanized steel in contact with
aluminum need not be painted. Stainless steel (300 series) in
contact with aluminum need not be painted except in high
chloride environments.
6.7.2 Wood, Fiberboard, or
Other Porous Materials
Aluminum surfaces to be placed in contact with wood,
fiberboard, or other porous material that absorbs water shall
be factory painted or given a heavy coat of alkali resistant
bituminous paint or other coating providing the equivalent
protection before installation.
6.7.3 Concrete or Masonry
Aluminum shall not be embedded in concrete with corrosive additives such as chlorides if the aluminum will be
electrically connected to steel.
Unless the concrete or masonry will remain dry after
curing and no corrosive additives such as chlorides are
used, aluminum surfaces to be placed next to or embedded
in concrete or masonry shall be:
a. given one coat of suitable paint, such as zinc molybdate
primer conforming to Federal Specification TT-P-645B
or equivalent, or
January 2005
b. given a heavy coating of alkali resistant bituminous
paint, or
c. isolated with a suitable plastic tape or other isolation
material.
6.10 Bending
6.7.4 Runoff From Heavy Metals
6.11.1 Erection Tolerances
Aluminum shall not be exposed to water that has come
in contact with a heavy metal such as copper. The heavy
metal shall be painted or coated or the drainage from the
metal diverted away from the aluminum or painted aluminum shall be used.
Tolerances on erected dimensions shall be suitable for
the intended service.
6.8 Mechanical Finishes
Abrasion blasting shall not be used if it distorts, perforates, or significantly reduces the thickness of the material
blasted.
Bend radii shall be large enough to avoid cracking.
6.11 Erection
6.11.2 Bolt Installation
Unless the joint is a slip-critical connection, bolts shall
be installed snug tight, defined as the tightness that exists
when all plies in a joint are in firm but not necessarily continuous contact. Slip-critical connections shall be tightened
in accordance with Section 5.2.8.7.
6.9 Fabrication Tolerances
A fabricated member shall not vary from straight or from
its intended curvature by more than its length divided by 960.
January 2005
I-A-61
Section 7. Welded Construction
7.1 General
Welding shall comply with the American Welding Society’s D1.2 Structural Welding Code—Aluminum. Filler alloys
shall meet AWS A5.10 and be selected from Table 7.1-1.
7.2 Welded Members
7.2.1 General
The weld-affected zone shall be taken to extend 1 in.
(25 mm) to each side of the centerline of a weld. Mechanical properties for weld-affected metal shall be taken from
Table 3.3-2. The modulus of elasticity for weld-affected
metal is the same as for non-welded metal.
Allowable stresses calculated in accordance with Section 7.2.1 apply to:
1) Members in axial tension with transverse welds affecting their entire cross section,
2) Bearing stresses at weld-affected metal,
3) Columns or beams supported at both ends with transverse welds affecting their entire cross-section and no
farther than 0.05L from the ends,
4) Columns or beams of tubes or curved elements with
transverse welds affecting their entire cross section, and
5) Flat elements of columns or beams with welds at the
supported edges only.
Allowable stresses for these welded members shall be calculated from the same formulas as for non-welded members with the following adjustments.
1) Allowable stresses for axial or flexural tension (Sections 3.4.1 through 3.4.4), bearing (Sections 3.4.5 and
3.4.6), and axial or flexural compression or shear (Sections 3.4.7 through 3.4.21) with slenderness less than S1
shall be calculated using welded mechanical properties
from Table 3.3-2.
2) Allowable stresses for tubes and curved elements in
axial or flexural compression or shear (Section 3.4.10,
3.4.12, and 3.4.16.1) with slenderness greater than S1
shall be calculated using welded mechanical properties
from Table 3.3-2 and buckling constants from Table
3.3-3 regardless of temper before welding.
3) Allowable stresses for all other members and elements
in axial or flexural compression or shear (Sections 3.4.7
through 3.4.21) with slenderness greater than S1 shall be
calculated using non-welded mechanical properties from
Table 3.3-1 and buckling constants from Table 3.3-3 or
3.3-4 as appropriate for the temper before welding.
7.2.2 Members with Part of the Cross Section
Weld-Affected
For members with part of the cross section weld-affected,
the allowable stress is
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A
Fpw = Fn – ___w ( Fn – Fw )
A
where
(Eq. 7.2.2-1)
Fpw = allowable stress on the cross section, part of which
is weld-affected.
Fn = allowable stress if no part of the cross section were
weld-affected. Use buckling constants for unwelded
metal from Table 3.3-3 or 3.3-4 and mechanical
properties from Table 3.3-1.
Fw = allowable stress if the entire cross sectional area
were weld-affected. Use buckling constants for
annealed material (Table 3.3-3) regardless of the
temper before welding, and mechanical properties
from Table 3.3-2.
A = net cross sectional area of a tension member or
tension flange of a beam; gross cross sectional
area of a column or compression flange of a beam.
A beam flange shall consist of the portion of the
section farther than 2c/3 from the neutral axis,
where c is the distance from the neutral axis to the
extreme fiber.
Aw = weld-affected cross sectional area. If Aw < 0.15A,
Aw shall be taken as zero.
7.2.3 Columns or Beams with Transverse Welds
Away from Supports and Cantilevers with
Transverse Welds
For columns or beams supported at both ends with transverse welds farther than 0.05L from the member ends and
cantilever beams with transverse welds, allowable stresses
shall be calculated in accordance with Section 7.2.2 as if
the entire cross sectional area were weld-affected.
7.3 Welded Connections
7.3.1 Groove Welds
7.3.1.1 Complete Penetration and Partial
Penetration Groove Welds
The following types of groove welds are complete penetration welds:
1) Welds welded from both sides with the root of the first
weld backgouged to sound metal before welding the
second side.
2) Welds welded from one side using permanent or temporary backing.
3) Welds welded from one side using AC-GTAW root pass
without backing
4) Welds welded from one side using PAW-VP in the keyhole mode.
All other groove welds are partial penetration welds.
January 2005
January 2005
I-A-63
4043
(4047)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
4043
(1100, 4047)
4043 (4047,
5183,5356,5556)
4145
4043
(1100, 4047)
6005, 6061,
6063, 6105,
6351, 6463
5454
5154
5086
5083, 5456
5052
5005, 5050
3004,
Alclad 3004
2219
1060, 1100,
3003,
Alclad 3003
2319
(4145)
DNW
DNW
DNW
DNW
DNW
DNW
DNW
4145
DNW
2219
5356
(5183, 5556)
5356
(4043, 4047,
5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183,5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(4043, 4047,
5183, 5556)
5356
(5183, 5556)
3004
Alclad 3004
5356
(4043, 4047,
5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5005
5050
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5052
5356
(5183, 5556)
5086
5556
(5183)
5356
5356
(5183, 5556) (5183, 5556)
5356
5356
(5183, 5556) (5183, 5556)
5356
5356
(5183, 5556) (5183, 5556)
5356
5356
(5183, 5556) (5183, 5556)
5556
(5183)
5083
5456
Notes:
1) This table is for structural applications subjected to normal atmospheric conditions using GTAW or GMAW.
2) DNW = Do Not Weld
5356
(5183, 5556)
1060
1100
3003
Alclad 3003
7005
Base Metal
Base Metal
Table 7.1-1
WELD FILLERS FOR WROUGHT ALLOYS
5654
(5183, 5356,
5556)
5654
(5183, 5356,
5556)
5356
(5183, 5556)
5356
(5183, 5556)
5154
5554
(5183, 5356,
5556)
5356
(5183, 5556)
5356
(5183, 5556)
5454
7005
5356
(4043, 4047,
5183, 5556)
5356
5556
(5183, 5556) (5183, 5356)
6005
6061
6063
6105
6351
6463
Table 7.3-1
FILLER STRENGTHS
7.3.1.2 Effective Area
1) Size: The weld size of a complete joint penetration
groove weld is the thickness of the thinner part joined.
The weld size of a partial joint penetration groove weld
is the depth of preparation Sw (see Figure 7.3-1) for
all V and bevel groove welds with an included angle
greater than 45o, and the depth of preparation of all J
and U groove welds.
2) Length: The effective weld length for tension and compression is the length of the weld perpendicular to the
direction of tensile or compressive stress. The effective
weld length for shear is the length of the weld parallel
to the direction of shear stress.
3) Area: The effective area of a groove weld is the effective weld length times the weld size.
Filler
1100
2319
4043
Minimum Tensile
Ultimate Strength
(ksi)
11
35
24
Minimum Shear
Ultimate Strength
(ksi)
7.5
16
11.5
4047
4643
5183
5356
5554
5556
5654
–
–
40
35
31
42
30
13
13.5
21
17
17
20
12
Table 7.3-1M
FILLER STRENGTHS
Filler
Figure 7.3-1
PARTIAL JOINT PENETRATION GROOVE
WELD DEPTH OF PREPARATION Sw
7.3.1.3 Design Strength
The allowable tensile or compressive strength of a groove
weld (Pgw) is
Ftuw Awe
Pgw = ______
nu
(Eq. 7.3.1.3-1)
1100
2319
4043
4047
4643
5183
5356
5554
5556
5654
Minimum Tensile
Ultimate Strength
(MPa)
75
240
165
–
–
275
240
215
290
205
Minimum Shear
Ultimate Strength
(MPa)
50
110
80
90
95
145
115
115
140
85
7.3.2 Fillet Welds
7.3.2.1 Effective Throat and Effective Length
The effective throat is the shortest distance from the joint
root to the face of the diagrammatic weld (see Figure 7.3-2).
where
Ftuw = least of the welded tensile ultimate strengths of
the base metals and the filler. Welded tensile ultimate strengths of base metals shall be taken from
Table 3.3-2 and tensile ultimate strengths of fillers from Table 7.3-1.
Awe = weld effective area
nu = 1.95
The allowable shear strength of a groove weld (Vgw) is
Fsuw Awe
Vgw = ______
nu
(Eq. 7.3.1.3-2)
where
Fsuw = least of the welded shear ultimate strengths of the base
metals and the filler. Welded shear ultimate strengths
of base metals shall be taken from Table 3.3-2 and
shear ultimate strengths of fillers from Table 7.3-1
Awe = weld effective area.
I-A-64
Figure 7.3-2
EFFECTIVE THROAT OF A FILLET WELD
January 2005
The weld effective length Lwe is the overall length of the
weld, including boxing. If the effective length of a fillet weld
is less than 4 times its nominal size Sw (see Figure 7.3-2) the
effective weld size shall be considered to be 25% of its effective length. The minimum length of segments of an intermittent fillet weld shall be 1½ in. (40 mm). The maximum
effective length of a longitudinal fillet weld is 100 times its
nominal size.
7.3.2.2 Design Strength
Stress on a fillet weld shall be considered to be shear for
any direction of applied load. The allowable shear strength
of a fillet weld (Vw) is
Fsw Lwe
Vw = ______
nu
(Eq. 7.3.2.2-1)
where
Fsw = least of:
1) the product of the filler’s shear ultimate
strength and the effective throat.
2) for base metal in shear at the weld-base
metal joint, the product of the base metal’s welded shear ultimate strength and
the fillet size Sw at the joint;
3) for base metal in tension at the weld-base
metal joint, the product of the base metal’s welded tensile ultimate strength and
the fillet size Sw at the joint.
Welded shear and tensile ultimate strengths
of base metals shall be taken from Table 3.3-2
and shear ultimate strengths of fillers from
Table 7.3-1.
Lwe = weld effective length
7.3.3.2 Design Strength
The allowable shear strength of a plug or slot weld (Vw) is
Fsw Awe
Vw = ______
nu
(Eq. 7.3.3.2-1)
where
Fsw = lesser of the welded shear ultimate strengths
of the filler and the base metal under the weld.
Welded shear ultimate strengths of base metals
shall be taken from Table 3.3-2 and shear ultimate
strengths of fillers from Table 7.3-1.
Awe = weld effective area
7.3.4 Stud Welds
The allowable tensile strength of a stud weld (Tw) is
Tuw
Tw = ___
(Eq. 7.3.4-1)
nu
where
Tuw = minimum tensile strength of the stud in Table 7.3-2
Table 7.3-2
MINIMUM TENSILE STRENGTHS FOR
5183, 5356, AND 5556 STUDS
Stud Size
Arc
(lb)
Capacitor Discharge
(lb)
6-32
–
375
8-32
–
635
10-24
770
770
/4-20
1360
1360
/16-18
2300
2300
1
7.3.3 Plug and Slot Welds
5
7.3.3.1 Effective Area
3
/8-16
3250
–
/16-14
4400
–
/2-13
5950
–
The effective area of plug or slot welds is the nominal
area of the hole or slot in the plane of the faying surface
(see Figure 7.3-3). Slot lengths shall not exceed 10 times
the slotted material’s thickness.
7
1
Figure 7.3-3
SLOT WELD PLAN VIEW
January 2005
I-A-65
Table 7.3-2M
MINIMUM TENSILE STRENGTHS FOR
5183, 5356, AND 5556 STUDS
Stud Size
Arc
(N)
Capacitor Discharge
(N)
6-32
–
1670
8-32
–
2820
10-24
3420
3420
1
/4-20
6050
6050
/16-18
10,200
10,200
3
/8-16
14,500
–
/16-14
19,600
–
/2-13
26,500
–
5
7
1
I-A-66
7.4 Post-Weld Heat Treating
For alloy 6005 lighting pole assemblies, up through
0.250 in. (6 mm) thick which are welded in the –T1 temper
with filler alloy 4043 and precipitation heat treated (artificially aged) to the –T5 temper by an approved method after
welding, the allowable stresses within 1.0 in. (25 mm) of
the weld shall be 85% of the values for non-welded alloy
6005-T5.
For alloy 6063 lighting pole assemblies, up through
0.375 in. (10 mm) thick which are welded in the –T4 temper
with filler alloy 4043 and precipitation heat treated (artificially aged) to the –T6 temper by an approved method after
welding, the allowable stresses within 1.0 in. (25 mm) of
the weld shall be 85% of the values for non-welded alloy
6063-T6.
January 2005
Section 8. Castings
8.1 Materials
Section 8 of this Specification applies to castings listed
in Table 8.2-1 and produced to the following ASTM Specifications:
Radiographic inspection to ASTM B 26 Grade C or B 108
Grade C criteria is required. The number of castings radiographed and the lot acceptance criteria shall be as follows:
B 26 Aluminum-Alloy Sand Castings
B 108 Aluminum-Alloy Permanent Mold Castings
Dimensional tolerances shall conform to Standards for
Aluminum Sand and Permanent Mold Castings.
The purchaser shall require the casting producer to report
tensile yield strengths. For sand castings, the purchaser shall
require that tensile ultimate and tensile yield strengths of
specimens cut from castings shall be at least 75% of the values specified in B 26.
Lot Size
Number of Castings
Required to be
Radiographed
Number of Castings
Required to Meet
Grade C to Pass Lot
2 through 50
2
2
51 through 500
8
7
over 500
13
11
8.2 Mechanical Properties
Minimum strengths shall be taken from Table 8.2-1 or
Table 8.2-1M.
Table 8.2-1
MINIMUM STRENGTHS OF CASTINGS
Alloy-Temper
Casting Type
356.0-T6
A356.0-T6
sand
sand
354.0-T61
permanent mold
C355.0-T61
permanent mold
356.0-T6
permanent mold
A356.0-T61
permanent mold
A357.0-T61
permanent mold
359.0-T61
permanent mold
359.0-T62
permanent mold
535.0-F
permanent mold
Minimum Tensile
Ultimate Strength
Ftu (ksi)
22.5
25.5
36
47
43
30
40
37
33
28.5
33
28
33.7
46
41
33.7
45
40
35.2
47
40
26.2
Minimum Tensile
Yield Strength
Fty (ksi)
15
18
27.7
36
33
22.5
30
30
22
19.5
26
26
27
36
31
25.5
34
30
28.5
38
30
13.5
Note
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
1) These strengths apply at any location in the casting if the purchaser does not specify test specimens be cut from castings.
2) These strengths apply in the locations specified by the purchaser if the purchaser specifies such locations. At other locations, the strengths
in (1) apply.
3) These strengths apply anywhere in the casting if the purchaser specifies that these strengths shall be met in specimens cut from the casting without designating a location.
January 2005
I-A-67
Table 8.2-1M
MINIMUM STRENGTHS OF CASTINGS
Alloy-Temper
Casting Type
356.0-T6
A356.0-T6
sand
sand
354.0-T61
permanent mold
C355.0-T61
permanent mold
356.0-T6
permanent mold
A356.0-T61
permanent mold
A357.0-T61
permanent mold
359.0-T61
permanent mold
359.0-T62
permanent mold
535.0-F
permanent mold
Minimum Tensile
Ultimate Strength
Ftu (MPa)
154
176
248
324
297
207
276
255
228
196
228
193
232
317
283
232
310
276
243
324
276
180
Minimum Tensile
Yield Strength
Fty (MPa)
105
124
191
248
228
155
207
207
152
134
179
179
186
248
214
175
234
207
196
262
207
93
Note
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
Notes
1) These strengths apply at any location in the casting if the purchaser does not specify test specimens be cut from castings.
2) These strengths apply in the locations specified by the purchaser if the purchaser specifies such locations. At other locations, the strengths
in (1) apply.
3) These strengths apply anywhere in the casting if the purchaser specifies that these strengths shall be met in specimens cut from the casting without designating a location.
The compressive yield strength Fcy of castings shall be
taken as the tensile yield strength Fty.
The modulus of elasticity E of castings shall be taken as
10,000 ksi (70,000 MPa).
The tension coefficient kt for the alloy-tempers in
Table 8.2-1 and Table 8.2-1M is 1.0.
8.3 Design
Design shall be in accordance with all the provisions of
this Specification.
8.4 Welding
Fillers shall be selected from Table 8.4-1. Minimum
welded strengths shall be those established in the AWS
D1.2 weld procedure qualification test.
I-A-68
February 2006
Table 8.4-1
WELD FILLERS FOR CAST ALLOYS
356.0
A356.0
A357.0
359.0
4043
(4047)
4145
4043
(4047)
4043
(4047)
4043
(4047)
DNW
DNW
DNW
4043
(4047)
4043
(4047, 4145, 4643)
4043
(4047)
4145
4145
(4043, 4047)
4145
(4043, 4047)
4145
(4043, 4047)
DNW
DNW
DNW
DNW
4145
4145
(note 1)
4043
(5356)
5356
4043
(note 1)
BASE METAL TO BASE METAL
535.0
1060, 1100, 3003, Alclad 3003
5356
2219
4043
3004, Alclad 3004
5356
5005, 5050
5356
5052
5356
5083, 5456
5086
5154
5356
5356
5356
5454
5356
6005, 6061, 6063,
6105, 6351, 6463
5356
7005
5356
354.0
C355.0
356.0, A356.0,
A357.0, 359.0
535.0
354.0
C355.0
4145
DNW
4145
(4043, 4047)
DNW
Notes
1) To weld C355.0 to itself, 4009 may be used; to weld A356.0 to itself, 4010 may be used; and to weld A357.0 to itself, 4011 may be used.
2) DNW = Do not weld
January 2005
I-A-69
Section 9. Testing
9.1 General
n
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Testing shall be considered to be an acceptable method
for substantiating the design of aluminum alloy load carrying members, assemblies or connections whose strengths
cannot otherwise be determined in accordance with Sections 1 through 8. Tests shall be conducted by an independent testing laboratory or by a manufacturer’s testing laboratory when certified by a qualified independent witness.
General provisions for testing are given in Sections
9.2 and 9.3. Specific provisions for building sheathing are
given in Section 9.4.
9.2 Test Loading and Behavior
In order to test a structure or load carrying member
adequately, the loading shall be applied in a fashion that
is representative of the loading during service. Further, the
structure or member shall be supported in a manner that is
equivalent to the supports available when the structure is
in service.
In tests that require measurement of deflection of a panel
or beam, a preload, that is a minimum of 20% of the design
load, shall be applied to set the specimen before testing, and
deflections shall be measured at the supports as well as at the
point of maximum critical deflection, so that the difference
will indicate the specimen deflection. The preload shall only
be taken as a zero load for deflection measurements when
proper account of this is taken in reporting deflections.
As an alternative, the structural performance of exterior
aluminum fenestration products such as windows, curtain
walls, and doors shall be determined in accordance with
ASTM E 330.
K
10.55
7.042
5.741
5.062
4.641
4.353
4.143
3.981
3.852
3.747
3.659
3.585
3.520
3.463
3.415
n
18
19
20
21
22
23
24
25
30
35
40
45
50
100
9.3.2 Tests for Determining Structural
Performance
Where practicable, in member and structural systems
tests the evaluation of test results shall be made on the basis
of not fewer than four identical specimens. If the deviation
from the average value exceeds ±10%, at least three more
tests of the same kind shall be made.
The allowable design value shall be taken as the average
of all test results divided by the safety factor, SF, determined as follows:
_____________
1.05α +1 eβ V + V + C V + V
SF = ___________
(Eq. 9.3.2-1)
√
MmFm( α + 1 )
2
9.3 Number of Tests and the Evaluation
of Test Results
9.3.1 Tests for Determining
Mechanical Properties
In determining yield strength and ultimate strength of
material or fasteners, sufficient tests shall be conducted
to statistically establish the strength at which 99% of the
material is expected to exceed with a confidence of 95%.
This strength shall be calculated as follows:
Xa = Xm – KSx
(Eq. 9.3.1-1)
where
Xa = strength at which 99% of the material is expected
to exceed with a confidence of 95%
Xm = mean of the test results
Sx = standard deviation of the test results
K = statistical coefficient based on the number of tests
(n). K is a one-sided factor for 99% of the population exceeding Xa with a confidence of 95%. Values of K for the following values of n are:
I-A-70
K
3.370
3.331
3.295
3.262
3.233
3.206
3.181
3.158
3.064
2.994
2.941
2.897
2.863
2.684
o
M
2
F
2
P
P
2
Q
where
n2 – 1
Cp = correction factor = ______
n2 – 3n
Dn = nominal dead load
e
= base for natural logarithms ≈ 2.72
Fm = mean value of the fabrication factor
Ln = nominal live load
Mm = mean value of the material factor
n
= number of tests
Xi = failure load of ith test
Xm = average value of failure loads in all tests
n
∑
Xi
i=1
= _______
n
VF = coefficient of variation of the fabrication factor
VM = coefficient of variation of the material factor
January 2005
Vp = coefficient of variation of the ratio of the observed
failure loads divided by the average value of all
the observed failure loads
___________________
=
√
(
n
)
2
∑X
X
_________
∑( ___
–
n
X )
n
i
2
i=1
Xi
___
m
m
i=1
__________________
n–1
VQ = coefficient
of variation of the loads
___________________
√( 0.105Dn )2 + ( 0.25Ln )2
= ____________________; in lieu of calculation
1.05Dn + Ln
by the above formula, VQ = 0.21
α = Dn /Ln ; in lieu of calculation by the above formula,
α = 0.2
βo = the target reliability index, 2.5 for columns, beams
and beam columns, 3.0 for tension members and
3.5 for connections.
The following values shall be used when documented
statistical data established from sufficient number of
results on material properties does not exist for the
member or connection:
Mm = 1.10 for behavior governed by the yield stress
= 1.00 for behavior governed by the ultimate stress
Fm = 1.00
VM = 0.06
VF = 0.05 for structural members and bolted connections
= 0.15 for welded connections
In evaluating test results, adjustment shall be made for
any differences between the yield strength of the material
from which the tested sections are formed and the minimum yield strength specified for the material which the
manufacturer intends to use. If the tensile yield strength of
the aluminum from which the tested sections are formed
is greater than the specified value, the test results shall be
adjusted down to the specified minimum yield strength of
the aluminum which the manufacturer intends to use. The
test results shall not be adjusted upward if the yield strength
of the test specimen is less than the minimum specified
yield strength. Similar adjustments shall be made on the
basis of tensile ultimate strength instead of yield strength
when tensile ultimate strength is the critical factor.
Adjustments shall also be made for differences between
nominal section properties and those of tested sections.
9.4 Testing Roofing and Siding
Where the configuration of roofing and siding installations are such that calculation of their strength cannot be
made in accordance with the provisions of this Specification, their bending strength shall be established from tests.
Tests are also required in the following cases:
a. When web angles θ are asymmetrical about the centerline of a valley, rib, flute, crimp, or other corrugation.
January 2005
b. When web angles θ are less than 45o.
c. When aluminum panels are alternated with panels
composed of any material having significantly different strengths or deflection characteristics.
d. When flats spanning from rib to rib or other corrugation in the transverse direction have a width to thickness ratio greater than either of the following:
447
1230
____
__ where
1) _____
3 __ where q is the design load in psf ( 3
√q
√q
q is the design load in kN/m2)
___
√
F
(37√___
q where F is in MPa and q is in kN/m ).
Fty
2) 435 ___
q where Fty is in ksi and q is in psf
___
ty
2
ty
e. When panel ribs, valleys, crimps, or other corrugations are of unequal depths.
f. When specifications prescribe less than one fastener
per rib to resist negative or uplift loading at each purlin, girt, or other transverse supporting member.
g. When panels are attached to supporting members by
profile interlocking straps or clips.
9.4.1 Test Method
Tests shall be conducted in accordance with ASTM E 1592.
9.4.2 Different Thicknesses
Only the thinnest and thickest specimens manufactured
are required to be tested when panels are of like configuration, differing only in material thickness. Where the failure
of the test specimens is from bending stress, the bending
strength for intermediate thicknesses shall be interpolated
as follows:
log ti – log tmin
log Mi = log M1 + ______________
( log M2 – log M1 )
log tmax – log tmin
(Eq. 9.4.2-1)
(
)
where
Mi = bending strength of member of intermediate thickness ti
M1 = bending strength of member of thinnest material
M2 = bending strength of member of thickest material
ti = thickness of intermediate thickness material
tmin = thickness of thinnest material tested
tmax = thickness of thickest material tested
9.4.3 Allowable Loads from Tests
Allowable loads shall be determined using the safety factors given in Section 9.3.2 for bending and Section 5 applied
to the minimum test strength achieved for fasteners.
9.4.4 Deflections
Live load deflections shall not exceed 1/60 of the span
length.
I-A-71
Aluminum Design Manual
PART I-B
Specification for
Aluminum Structures–
Building Load and
Resistance Factor Design
The Aluminum Association, Inc.
1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
Third Edition, January 2005
FOREWORD
The first edition of the Specification for Aluminum Structures Load and Resistance Factor Design was published in October,
1994, and a second edition in 2000. This third edition of the LRFD Specification, developed as a consensus document, includes
new or revised provisions concerning
• shear yield strengths
• welded strengths
• adding 6063-T52, 6351-T6, and 7005-T53
• materials for screws used to connect aluminum parts
• factors on welded tensile ultimate strength and compressive yield strength
• welded connections (groove, fillet, plug and slot, and stud welds)
• screw pull-over
• revision of Section 1.2, Materials
• revision of Section 5, Mechanical Connections
• revision of Section 6, Fabrication and Erection
• a new Section 8, Castings
• weighted average strengths
• design stresses for wind loads
• fatigue strength for welds with permanent backing
• net effective areas for channels, I beams, zees, angles, and tees
• single angles in flexure
• tapered thickness element strength
• web crippling of extrusions
• compressive strength of complex cross sections
• strength of elements in bending in their own plane
• unbraced length in bending
These improvements and additions are the result of studies sponsored by the Aluminum Association and others. The Aluminum
Association gratefully acknowledges the efforts of the Engineering and Design Task Force in drafting this Specification and the
Engineering Advisory Committee in reviewing them.
The Aluminum Association Engineering and Design Task Force
Steve Sunday, Alcoa Inc., chair
Frank Armao, Lincoln Electric Co.
Randy Killian, Conservatek Industries, Inc.
Randy Kissell, The TGB Partnership
Greg McKenna, Kawneer Company, Inc.
Craig C. Menzemer, University of Akron
George Olive, Larson Engineering of Missouri
Gerald Orrison, Temcor
Teoman Peköz, Cornell University
Frank Shoup, Alcoa Inc.
Mike Skillingberg, The Aluminum Association, Inc.
The Aluminum Association Engineering Advisory Committee
Includes the members of the Engineering and Design Task force and the following persons:
Robert E. Abendroth, Iowa State University
Francisco Castano, Geometrica, Inc.
Terence Cavanagh, Terrapin Testing, Inc.
Karen C. Chou, Minnesota State University, Mankato
Cynthia Ebert, Larson Engineering of Missouri
January 2005
I-B-3
Andrew J. Hinkle, S & K Technologies
Dimitris Kosteas, Technical University of Munich
LeRoy Lutz, Computerized Structural Design
Brian Malloy, Alcoa Engineered Products
Ray Minor, Hapco American Flag
Carl Wagus, American Architectural Manufacturers Association
Robert W. Walton, Texas Wall Systems
Guidelines for the Preparation of Technical Inquiries on the Specification for Aluminum Structures
Technical inquiries to obtain an interpretation or request a revision to the Specification for Aluminum Structures should be
directed to:
VP, Technology
The Aluminum Association
1525 Wilson Blvd. Suite 600
Arlington, VA 22209
Fax: 703-358-2961
email: mhskilli@aluminum.org
Comments on other parts of the Aluminum Design Manual are also welcome.
Inquiries should be typewritten and include the inquirer’s name, affiliation, and address. Each inquiry should address a single
section of the Specification unless the inquiry involves two or more interrelated sections. The section and edition of the Specification should be identified.
Requests for interpretations should be phrased, where possible, to permit a “yes” or “no” answer and include the necessary
background information, including sketches where appropriate.
Requests for revisions should include proposed wording for the revision and technical justification.
Inquiries are considered at the first meeting of the Engineering and Design Task Force following receipt of the inquiry.
I-B-4
November 2005
IB
Specification for Aluminum Structures – Load and Resistance Factor Design
TABLE OF CONTENTS
Section 1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Design Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Section 2. Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1 Section Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Section 3. General Design Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 Tables Relating to Mechanical Properties and Buckling Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 Design Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4.1
Tension, Axial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.2
Tension in Extreme Fibers of Beams – Flat Elements In Uniform Tension . . . . . . . . . . . . . . . . . . . . . . 26
3.4.3
Tension in Extreme Fibers of Beams – Round or Oval Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.4
Tension in Extreme Fibers of Beams – Flat Elements In Bending in Their Own Plane . . . . . . . . . . . . . 26
3.4.5
Bearing on Rivets and Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.6
Bearing on Flat Surfaces and Pins and on Bolts in Slotted Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.7
Compression in Columns, Axial, Gross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.7.1 Sections Not Subject to Torsional or Torsional-Flexural Buckling . . . . . . . . . . . . . . . . . . . . . 27
3.4.7.2 Doubly or Singly Symmetric Sections Subject to Torsional or
Torsional-Flexural Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4.7.3 Nonsymmetric Sections Subject to Torsional or Torsional-Flexural Buckling . . . . . . . . . . . . 27
3.4.8
Uniform Compression in Elements of Columns Whose Buckling Axis is an
Axis of Symmetry – Flat Elements Supported On One Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4.8.1 Uniform Compression in Elements of Columns Whose Buckling Axis is not an
Axis of Symmetry – Flat Elements Supported On One Edge . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4.9
Uniform Compression in Elements of Columns – Flat Elements Supported on Both Edges . . . . . . . . . 30
3.4.9.1 Uniform Compression in Elements of Columns – Flat Elements Supported on
One Edge and With Stiffener on Other Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4.9.2 Uniform Compression in Elements of Columns – Flat Elements Supported on
Both Edges and With an Intermediate Stiffener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.10 Uniform Compression in Elements of Columns – Curved Elements Supported on Both Edges . . . . . . . 35
3.4.11 Compression in Beams, Extreme Fiber, Gross Section – Single Web Shapes . . . . . . . . . . . . . . . . . . . . 35
3.4.12 Compression in Beams, Extreme Fiber, Gross Section – Round or Oval Tubes . . . . . . . . . . . . . . . . . . . 35
3.4.13 Compression in Beams, Extreme Fiber, Gross Section – Solid Rectangular and Round Sections . . . . . 36
3.4.14 Compression in Beams, Extreme Fiber, Gross Section – Tubular Shapes . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.15 Uniform Compression in Elements of Beams – Flat Elements Supported on One Edge . . . . . . . . . . . . 37
3.4.16 Uniform Compression in Elements of Beams – Flat Elements Supported on Both Edges . . . . . . . . . . . 37
3.4.16.1 Uniform Compression in Elements of Beams – Curved Elements
Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4.16.2 Uniform Compression in Elements of Beams – Flat Elements Supported on
One Edge and With Stiffener on Other Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4.16.3 Uniform Compression in Elements of Beams – Flat Elements Supported on
Both Edges and With an Intermediate Stiffener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4.17 Compression in Elements of Beams (Element in Bending in Own Plane) –
Flat Elements Supported on Tension Edge, Compression Edge Free . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
January 2005
I-B-5
3.4.18
Compression in Elements of Beams (Element in Bending in Own Plane) –
Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.19 Compression in Elements of Beams (Element in Bending in Own Plane) –
Flat Elements Supported on Both Edges and With a Longitudinal Stiffener . . . . . . . . . . . . . . . . . . . . . . 40
3.4.20 Shear in Elements – Unstiffened Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.21 Shear in Elements – Stiffened Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . 40
Section 4. Special Design Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
4.1 Combined Axial Load and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.1
Combined Compression and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.2
Combined Tension and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Torsion and Shear in Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Torsion and Bending in Open Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.4 Combined Shear, Compression, and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.5 Longitudinal Stiffeners for Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.6 Transverse Stiffeners for Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.6.1
Stiffeners for Web Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.6.2
Bearing Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.7 Effects of Local Buckling on Member Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.7.1
Local Buckling Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.7.2
Weighted Average Axial Compressive Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.7.3
Weighted Average Bending Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.7.4
Effect of Local Buckling on Column Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.7.5
Effect of Local Buckling on Beam Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.7.6
Effective Width for Calculation of Bending Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.7.7
Web Crippling of Flat Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.7.8
Combined Web Crippling and Bending for Flat Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.8 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.8.1
Constant Amplitude Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.8.2
Variable Amplitude Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.9 Compression in Single Web Beams Including Single Web Beams With Tubular Portions . . . . . . . . . . . . . . . . . . 52
4.9.1
Doubly Symmetric Sections and Sections Symmetric About the Bending Axis . . . . . . . . . . . . . . . . . . . 52
4.9.2
Singly Symmetric Sections Unsymmetric about the Bending Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.9.3
Singly Symmetric Sections Symmetric or Unsymmetric about the Bending Axis,
Doubly Symmetric Sections and Sections Without an Axis of Symmetry. . . . . . . . . . . . . . . . . . . . . . . . 52
4.9.4
Lateral Buckling Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.9.4.1 Doubly Symmetric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.9.4.2 Singly Symmetric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.9.4.3 Special Cases – Doubly or Singly Symmetric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.9.4.4 Cantilever Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.10 Compression in Elastically Supported Flanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.11 Single Angles in Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.11.1 Bending About Geometric Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.11.2 Bending About Principal Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.12 Tapered Thickness Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.13 Compressive Strength of Beam Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.13.1 Compressive Strength of Beam Elements – Flat Elements in Uniform Compression . . . . . . . . . . . . . . . 56
4.13.2 Compressive Strength of Beam Elements – Flat Elements in Bending In Their Own Plane . . . . . . . . . . 57
Section 5. Mechanical Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.1.1
Minimum Edge Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.1.2
Maximum Spacing of Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.1.3
Block Shear Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.1.4
Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.1.5
Effective Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.1.6
Long Grips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
I-B-6
January 2005
5.2
5.3
5.4
5.5
5.1.7
Strength and Arrangement of Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.1.8
Countersunk Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.1
Bolt Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.2
Holes and Slots for Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.3
Bolt Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.4
Bolt Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.5
Bolt Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.6
Minimum Spacing of Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.7
Lockbolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.8
Slip-Critical Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.8.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.8.2 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.8.3 Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.8.4 Design for Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.8.5 Design for Slip Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.8.6 Washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.8.7 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Riveted Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3.1
Rivet Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3.2
Holes for Cold-Driven Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3.3
Rivet Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3.4
Rivet Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3.5
Rivet Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3.6
Minimum Spacing of Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3.7
Blind Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3.8
Hollow-End (Semi-tubular) Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Tapping Screw Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4.1
Screw Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4.2
Screw Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4.2.1 Pull-Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4.2.2 Pull-Over . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4.3
Screw Shear and Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4.4
Minimum Spacing of Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Building Sheathing Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5.1
Endlaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5.2
Sidelaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5.3
Fasteners in Laps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5.4
Flashing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Section 6. Fabrication and Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
6.1 Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.1.1
Punch and Scribe Marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.1.2
Temperature Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2 Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2.1
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2.2
Edge Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2.3
Re-entrant Corners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2.4
Oxygen Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.3 Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.4 Holes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.4.1
Fabrication Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.4.2
Hole Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.5 Riveting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.5.1
Driven Head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.5.1.1 Flat Heads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.5.1.2 Cone-Point Heads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
January 2005
I-B-7
6.5.2
Hole Filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.5.3
Defective Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.6 Finishes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.6.1
Where Painting Is Required . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.6.2
Surface Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.7 Contact with Dissimilar Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.7.1
Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.7.2
Wood, Fiberboard, or Other Porous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.7.3
Concrete or Masonry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.7.4
Runoff From Heavy Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.8 Mechanical Finishes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.9 Fabrication Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.10 Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.11 Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.11.1 Erection Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.11.2 Bolt Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Section 7. Welded Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68
7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.2 Welded Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.2.1
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.2.2
Members with Part of the Cross Section Weld-Affected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.2.3
Columns or Beams with Transverse Welds Away from Supports and Cantilevers with
Transverse Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.3 Welded Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.3.1
Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.3.1.1 Complete Penetration and Partial Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.3.1.2 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.3.1.3 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.3.2
Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.3.2.1 Effective Throat and Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.3.2.2 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.3.3
Plug and Slot Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7.3.3.1 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7.3.3.2 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7.3.4
Stud Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7.4 Post-Weld Heat Treating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Section 8. Castings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73
8.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8.2 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8.3 Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
8.4 Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Section 9. Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
9.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
9.2 Test Loading and Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
9.3 Number of Tests and the Evaluation of Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
9.3.1
Tests for Determining Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
9.3.2
Tests for Determining Structural Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
9.4 Testing Roofing and Siding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
9.4.1
Test Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
9.4.2
Different Thicknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
9.4.3
Design Loads from Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
9.4.4
Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
I-B-8
January 2005
Section 1. General
1.1 Scope
1.3 Design Stresses
This Specification shall apply to the design of aluminum
alloy load-carrying members.
The design stresses ϕFL shall be larger than or equal to
the stresses computed for the factored nominal loads acting
on the structure. The method of analysis, nominal loads, load
factors, and load combinations are defined in Section 2. The
resistance factor (ϕ) accounts for the uncertainties inherent
in the prediction of limit stresses. Resistance factors shall be
determined in accordance with Sections 3, 4, 5, and 7.
1.2 Materials
This Specification applies to the aluminum alloys listed
in Tables 3.3-1, 5.2.3-1, and 5.3.4-1 and produced to the
following ASTM specifications:
B 209 Aluminum and Aluminum-Alloy Sheet and Plate
B 210 Aluminum and Aluminum-Alloy Drawn Seamless Tubes
B 211 Aluminum and Aluminum-Alloy Bar, Rod, and
Wire
B 221 Aluminum and Aluminum-Alloy Extruded Bars,
Rods, Wire, Profiles, and Tubes
B 241 Aluminum and Aluminum-Alloy Seamless Pipe
and Seamless Extruded Tube
B 247 Aluminum and Aluminum-Alloy Die Forgings,
Hand Forgings, and Rolled Ring Forgings
B 308 Aluminum-Alloy 6061-T6 Standard Structural
Profiles
B 316 Aluminum and Aluminum-Alloy Rivet and
Cold-Heading Wire and Rods
B 429 Aluminum Alloy Extruded Structural Pipe and
Tube
B 632 Aluminum Alloy Rolled Tread Plate
B 928 High Magnesium Aluminum-Alloy Sheet and
Plate for Marine Service
F 468 Nonferrous Bolts, Hex Cap Screws, and Studs
for General Use
This Specification also applies to castings that meet the
requirements of Section 8.1.
January 2005
I-B-9
Section 2. Design Procedure
2.1 Section Properties
Section properties such as cross-sectional area, moment
of inertia, section modulus, radius of gyration, and torsion
and warping constants shall be determined using nominal
dimensions. Cross section dimensions shall not vary by
more than the tolerances given in Aluminum Standards and
Data.
2.2 Procedure
Computations of forces, moments, stresses, and deflections shall be in accordance with accepted methods of elastic structural analysis and engineering design. Two types of
limit states are to be considered:
1) Ultimate limit states, the strength required to
resist loads, such as yielding, fracture, buckling,
crippling, and
2) Serviceability limit states, the ability to perform
the intended function under normal service
conditions, avoiding excessive deflection or the
appearance of buckling.
I-B-10
The forces, moments, and stresses for the ultimate limit
states shall be determined by structural analysis for the factored loads as defined in Section 2.3 and the deflections
for the serviceability limit states shall be calculated for the
unfactored (working) loads.
2.3 Loads
Building-type structures shall be designed for the nominal loads given in the applicable building code or performance specification. Nominal loads shall be factored and
combined in accordance with the applicable building code
or performance specification. In the absence of a code or
performance specification, ASCE 7-02, Minimum Design
Loads for Buildings and Other Structures, shall be used.
January 2005
Section 3. General Design Rules
3.1 Material Properties
Minimum mechanical properties used for non-welded
material shall be as listed in Table 3.3-1.
Minimum mechanical properties used for welded material
shall be as listed in Table 3.3-2.
The following properties shall be used unless more precise values are specified:
Coefficient of thermal 13 × 10-6/oF (23 × 10-6/oC)
expansion
Density
0.1 lb/in3
(2.7 × 103 kg/m3)
Poisson’s ratio
0.33
3.2 Nomenclature
A consistent set of units shall be used throughout this
Specification.
a = detail dimension parallel to the direction of
stress
ae = equivalent width of rectangular panel
al = shorter dimension of rectangular panel
a2 = longer dimension of rectangular panel
A = cross sectional area
Ac = area of compression element (compression
flange plus 1/3 of area of web between
compression flange and neutral axis)
Ah = gross area of cross section of longitudinal
stiffener
As = area of the stiffener
Asn = thread stripping area of internal thread per unit
length of engagement
Aw = the portion of area of cross section A lying
within 1.0 in. (25 mm) of a weld
b = width of section or element
be = effective width of flat element to be used in
deflection calculations
bo = width of element with an intermediate stiffener
as shown in Fig. 3.4.9.2-1
b/t = width to thickness ratio of a flat element of a
cross section
B = buckling formula intercept with the following
subscripts:
c – compression in columns
p – compression in flat elements
t – compression in curved elements
tb – bending in curved elements
br – bending in flat elements
s – shear in flat elements
c = distance from neutral axis to extreme fiber
C = buckling formula intersection (see B for
subscripts)
C = coefficient which depends on screw location
Cb = coefficient which depends on moment gradient
January 2005
Cf = constant to be determined from Table 4.8.1-1
and Figure 4.8.1-1
Cm = 0.6 - 0.4(M1/M2) for members whose ends are
prevented from sway
= 0.85 for members whose ends are not prevented
from swaying
CP = correction factor
Cw = torsional warping constant
____of the cross section
Cwa = t2 sin θ(0.46Fcy + 0.02√EFcy )
Cwb = Cw3 + Ri (1 – cosθ)
Cw1 = 5.4 in. (140 mm)
Cw2 = 1.3 in. (33 mm)
Cw3 = 0.4 in. or 10 mm consistent with other units used
C1 = coefficient defined in Section 4.9.4
C2 = coefficient defined in Section 4.9.4
d = depth of section or beam
df = distance between flange centroids
ds = flat width of lip stiffener shown in Fig. 3.4.9.1-1
d1 = clear distance from the neutral axis to the compression flange
D = buckling formula slope (see B for subscripts)
D = diameter
Dh = nominal hole diameter
Dn = nominal dead load
Ds = defined in Fig. 3.4.9.1-1
Dw = nominal washer diameter
Dws = larger of the nominal washer diameter and the
screw head
e = base for natural logarithms ≈2.72
E = compressive modulus of elasticity
(See Table 3.3-1)
f = calculated stress
fa = average stress on cross section produced by
axial load
fb = maximum bending stress produced by transverse
loads and/or bending moment
fs = shear stress caused by torsion or transverse
shear loads
Fa = design compressive stress for a member considered as an axially loaded column according to
Sections 3.4.7 through 3.4.10
Fao = design compressive stress of axially loaded
member considered as a short column according
to Section 4.7.2.
Fb = design bending stress for members subjected to
bending only
Fc = design compressive stress
Fcr = local buckling stress for element from
Section 4.7.1
Fcy = compressive yield strength
Fcyw = compressive yield strength across a groove weld
(0.2% offset in 2 in.
(50 mm) gage length)
I-B-11
Fe = elastic buckling stress multiplied by ϕcc
ϕccπ2E
= ______
(kL/r)2
Feb = elastic lateral buckling stress of beam calculated
using Eq. 3.4.11-3 or
Section 4.9 with ϕb = 1.0
Fec = elastic critical stress
Fec = design elastic lateral buckling stress of beam
calculated assuming that the elements are not
buckled
Fef = elastic torsional-flexural buckling stress
Fet = elastic torsional buckling stress
π2ECw
1 GJ + ______
Fet = ____
2
(Kt Lt)2
Ar o
(
)
πE
Fex = ______
kxLb 2
____
rx
FL = limit state stress
Fm = mean value of the fabrication factor
Fn = limit state stress for cross section 1.0 in.
(25 mm) or more from weld
Fpw = limit state stress on cross section, part of whose
area lies within 1.0 in. (25 mm) of a weld
Frb = limit state stress for beam with buckled elements
Frc = limit state stress for column with buckled
elements
Fs = design shear stress for members subjected only
to torsion or shear
FST = design stress according to Section 3.4.9.1 or
3.4.16.2
Fsu = shear ultimate strength
Fsuw = shear ultimate strength within 1.0 in. (25 mm) of
a weld
Ft = design tensile stress for the member loaded only
axially according to Section 3.4.1
Ftu = tensile ultimate strength
Ftuw = tensile ultimate strength across a groove weld
Ftu1 = tensile ultimate strength of member in contact
with the screw head
Ftu2 = tensile ultimate strength of member not in
contact with the screw head
Fty = tensile yield strength
Ftyw = tensile yield strength across a groove weld
(0.2% offset in 2 in. (50 mm) gage length)
FUT = design stress according to Section 3.4.9.1 or
3.4.16.2
Fw = limit state stress on cross section if entire area
were to lie within 1.0 in. (25 mm) of a weld
Fy = either Fty or Fcy, whichever is smaller
g = spacing of rivet or bolt holes perpendicular to
direction of load
go = distance from shear center to the point of
application of load
G = shear modulus
Gf = grip of rivet or bolt
2
( )
I-B-12
h = clear height of shear web
I = moment of inertia
Ib = required moment of inertia of bearing stiffener
Icy = moment of inertia of compression flange about
web
Ih = moment of inertia of longitudinal stiffener
Io = moment of inertia of the stiffener about the
centroidal axis of the stiffener parallel to the flat
element that is stiffened
Is = moment of inertia of transverse stiffener to resist
shear buckling
Ix = moment of inertia of a beam about axis
perpendicular to web
Iy = moment of inertia of a beam about axis parallel
to web
Iyc = moment of inertia of compression element about
axis parallel to vertical web
j = parameter defined by Eq. 4.9.3-5 or -6
J = torsion constant
k = the effective length factor. k shall be taken larger
than or equal to unity unless rational analysis
justifies a smaller value
kt = coefficient for tension members
kx = effective length coefficient for buckling about
the x-axis
ky = effective length coefficient for buckling about
the y-axis
k1 = coefficient for determining slenderness limit S2
for sections for which the limit state
compressive stress is based on ultimate strength
k2 = coefficient for determining design compressive
stress in sections with slenderness ratio above
S2 for which the limit state compressive stress is
based on ultimate strength
Ks = coefficient in Section 5.4.2.1
Kt = effective length coefficient for torsional
buckling. Kt shall be taken larger than or equal
to unity unless rational analysis justifies a
smaller value
L = unsupported length in the plane of bending
Lb = unbraced length for bending
Ln = nominal live load
Ls = length of tube between circumferential stiffeners
Lt = unbraced length for twisting
m = constant to be determined from Table 4.8.1-1
M = bending moment applied to the member
Ma = limit state bending moment for the member if
bending moment alone is applied to the member
MA = absolute value of moment at quarter-point of the
unbraced beam segment
MB = absolute value of moment at mid-point of the
unbraced beam segment
MC = absolute value of moment at three-quarter point
of the unbraced beam segment
January 2005
___
Me = elastic critical moment
Mi = bending strength of member with intermediate
thickness
Mm = mean value of the material factor
MMAX = absolute value of maximum moment in the
unbraced beam segment
M1 = bending strength of member of thinnest material
M2 = bending strength of member of thickest material
M1/M2 = ratio of end moments where M2 is the larger
of the two end moments and M1/M2 is positive
when the member is bent in reverse curvature,
negative when bent in single curvature
n = number of tests
n = number of threads per unit length for a screw
N = length of bearing at reaction or concentrated
load
N = number of cycles to failure
Ns = number of stress ranges in the spectrum
P = applied interior reaction or concentrated load
per web for flat webs
Pas = limit state shear force per screw
Pat = limit state tensile force per screw
Pbs = concentrated load on bearing stiffener
PL = limit state reaction or concentrated load
per web for flat webs calculated according to
Section 4.7.7
Pnot = nominal pull-out strength per screw
Pnov = nominal pull-over strength per screw
Pns = nominal shear strength per screw
Pnt = nominal tensile strength per screw
q = uniform design load
r = radius of gyration
_______________
ro = √r x2 + r y2 + x o2 + y o2
rs = radius of gyration of the stiffener
rx , ry = radii of gyration of the cross-section about the
centroidal principal axes (see Section 4.9.2 for
rye of singly symmetric sections unsymmetric
about the bending axis)
rye = effective radius of gyration
R = transition radius, the radius of an attachment of
the weld detail
Rb = mid-thickness radius of a round element or
maximum mid-thickness radius of an oval
element
Ri = bend radius at juncture of flange and web
measured to inside surface of bend
Rs = stress ratio, the ratio of minimum stress to
maximum stress
s = spacing of transverse stiffeners (clear distance
between stiffeners for stiffeners consisting of a
pair of members, one on each side of the web,
center-to-center distance between stiffeners
consisting of a member on one side of the web
only); spacing of rivet or bolt holes parallel to
direction of load
January 2005
√
E
S = 1.28 ___
Fcy
Sc = section modulus of a beam, compression side
Sra = the applied stress range
Srd = allowable stress range
Sre = equivalent stress range
Sri = the ith stress range in the spectrum
St = section modulus of a beam, tension side
Sw = size of a weld
Sx = standard deviation of the test results
S1, S2 = slenderness limits (with superscript for columns)
t = thickness of element
tavg = the average thickness of the element
tc = depth of full thread engagement of screw into t2
not including tapping or drilling point
ti = thickness of the intermediate thickness material
tested
tmax = thickness of thickest material tested
tmax = greater thickness of a tapered thickness element
tmin = thickness of thinnest material tested
tmin = lesser thickness of a tapered thickness element
t1 = thickness of member in contact with the screw
head
t2 = thickness of member not in contact with the
screw head
U = parameter defined by Eq. 4.9.3-8
V = shear force on web at stiffener location
VF = coefficient of variation of the fabrication factor
VM = coefficient of variation of the material factor
VP = coefficient of variation of the ratio of the
observed failure loads divided by the average
value of all the observed failure loads
VQ = coefficient of variation of the loads
xo = x - coordinate of the shear center
Xa = strength at which 99% of the material is
expected to conform at a confidence level
of 95%
Xi = failure load of ith test
Xm = mean of the test results
yo = y - coordinate of the shear center
α = Dn /Ln
αi = number of cycles in the spectrum of the ith
stress range divided by the total number
of cycles
αs = a factor equal to unity for a stiffener consisting
of equal members on both sides of the web and
equal to 3.5 for a stiffener consisting of a
member on one side only
β = 1 – (xo /ro)2
βo = the target reliability index
βs = spring constant (transverse force applied to the
compression flange of the member of unit length
divided by the deflection due to the force)
(tmax - tmin)
δ = _________
for tapered thickness elements
tmin
λ = slenderness parameter
I-B-13
λs = equivalent slenderness ratio for an intermediate
stiffener
ρst = ratio defined in Section 3.4.9.1 and 3.4.16.2
ϕ = resistance factor (depending on the
application this notation has different subscripts)
θ = angle between plane of web and plane of bearing surface (θ < 90º)
3.3 Tables Relating to Mechanical
Properties and Buckling Constants
This Section consists of the following tables concerning
formulas for determining allowable stresses and constants
and coefficients needed for these formulas:
3.3-1
Minimum Mechanical Properties for
Aluminum Alloys
3.3-1M
Minimum Mechanical Properties for
Aluminum Alloys
I-B-14
3.3-2
Minimum Mechanical Properties for Welded
Aluminum Alloys
3.3-2M
Minimum Mechanical Properties for Welded
Aluminum Alloys
3.3-3
Formulas for Buckling Constants for
Products Whose Temper Designation Begins
With -O, -H, -T1, -T2, -T3, or –T4
3.3-4
Formulas for Buckling Constants for
Products Whose Temper Designation Begins
With -T5, -T6, -T7, -T8, or –T9
January 2005
Table 3.3-1
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
1100-H12
-H14
2014-T6
-T651
-T6, T6510, T6511
-T6, T651
Alclad
2014-T6
-T6
-T651
3003-H12
-H14
-H16
-H18
-H12
-H14
-H16
-H18
Alclad
3003-H12
-H14
-H16
-H18
-H14
-H18
3004-H32
-H34
-H36
-H38
-H34
-H36
Alclad
3004-H32
-H34
-H36
-H38
-H131, H241, H341
-H151, H261, H361
3005-H25
-H28
3105-H25
5005-H12
-H14
-H16
-H32
-H34
-H36
5050-H32
-H34
-H32
-H34
THICKNESS
RANGE
in.
Ftu
ksi
Fty
ksi
Fcy
ksi
Fsu
ksi
All
All
0.040 to 0.249
0.250 to 2.000
All
All
14
16
66
67
60
65
11
14
58
59
53
55
10
13
59
58
52
53
9
10
40
40
35
38
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (ksi)
10,100
10,100
10,900
10,900
10,900
10,900
Sheet
Sheet
Plate
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Drawn Tube
Drawn Tube
0.025 to 0.039
0.040 to 0.249
0.250 to 0.499
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.006 to 0.128
All
All
All
All
63
64
64
17
20
24
27
17
20
24
27
55
57
57
12
17
21
24
12
17
21
24
56
58
56
10
14
18
20
11
16
19
21
38
39
39
11
12
14
15
11
12
14
15
10,800
10,800
10,800
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.006 to 0.128
0.025 to 0.259
0.010 to 0.500
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.006 to 0.128
0.018 to 0.450
0.018 to 0.450
16
19
23
26
19
26
28
32
35
38
32
35
11
16
20
23
16
23
21
25
28
31
25
28
9
13
17
19
15
20
18
22
25
29
24
27
10
12
14
15
12
15
17
19
20
21
19
20
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Sheet
Cold Fin. Rod & Bar
Drawn Tube
Cold Fin. Rod & Bar
Drawn Tube
0.017 to 0.249
0.009 to 0.249
0.006 to 0.162
0.006 to 0.128
0.024 to 0.050
0.024 to 0.050
0.013 to 0.050
0.006 to 0.080
0.013 to 0.080
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.017 to 2.000
0.009 to 0.249
All
27
31
34
37
31
34
26
31
23
18
21
24
17
20
23
22
25
22
20
24
27
30
26
30
22
27
19
14
17
20
12
15
18
16
20
16
17
21
24
28
22
28
20
25
17
13
15
18
11
14
16
14
18
15
16
18
19
21
18
19
15
17
14
11
12
14
11
12
13
14
15
13
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
All
25
20
19
15
10,100
PRODUCT
Plate, Drawn Tube,
)
(Sheet,
Rolled Rod & Bar
Sheet
Plate
Extrusions
Cold Finished Rod & Bar,
Drawn Tube
For all footnotes, see last page of this Table.
January 2005
I-B-15
Table 3.3-1
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
5052-O
-H32
-H34
-H36
5083-O
-H111
-H111
-O
-H116
-H32, H321
-H116
-H32, H321
5086-O
-H111
-H111
-O
-H112
-H112
-H112
-H112
-H116
-H32
-H34
5154-H38
5454-O
-H111
-H111
-H112
-O
-H32
-H34
5456-O
-H116
-H32, H321
-H116
-H32, H321
-H116
-H32, H321
6005-T5
6061-T6, T651
-T6, T6510, T6511
-T6, T651
-T6
-T6
6063-T5,
-T52
-T5
-T6
6066-T6, T6510, T6511
6070-T6, T62
6105-T5
6351 -T5
6351 -T6
6463-T6
7005-T53
PRODUCT
Sheet & Plate
Sheet & Plate
Cold Fin. Rod & Bar
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Extrusions
Extrusions
Extrusions
Sheet & Plate
Plate
Plate
Plate
Plate
Sheet & Plate
Sheet & Plate
Drawn Tube
Sheet & Plate
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Plate
Plate
Extrusions
Sheet & Plate
Extrusions
Cold Fin. Rod & Bar
Drawn Tube
Pipe
Extrusions
Extrusions
Extrusions
Extrusions & Pipe
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
(
)
THICKNESS
RANGE
in.
Ftu
ksi
Fty
ksi
Fcy
ksi
Fsu
ksi
0.006 to 3.000
All
All
25
31
34
9.5
23
26
9.5
21
24
16
19
20
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (ksi)
10,200
10,200
10,200
0.006 to 0.162
up thru 5.000
up thru 0.500
0.501 to 5.000
0.051 to 1.500
0.188 to 1.500
0.188 to 1.500
1.501 to 3.000
1.501 to 3.000
up thru 5.000
up thru 0.500
0.501 to 5.000
0.020 to 2.000
0.025 to 0.499
0.500 to 1.000
1.001 to 2.000
2.001 to 3.000
All
All
37
39
40
40
40
44
44
41
41
35
36
36
35
36
35
35
34
40
40
29
16
24
24
18
31
31
29
29
14
21
21
14
18
16
14
14
28
28
26
16
21
21
18
26
26
24
24
14
18
18
14
17
16
15
15
26
26
22
24
24
23
25
26
26
24
24
21
21
21
21
22
21
21
21
24
24
10,200
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
All
44
34
32
26
10,400
0.006 to 0.128
up thru 5.000
up thru 0.500
0.501 to 5.000
up thru 5.000
0.020 to 3.000
0.020 to 2.000
0.020 to 1.000
0.051 to 1.500
0.188 to 1.250
0.188 to 1.250
1.251 to 1.500
1.251 to 1.500
1.501 to 3.000
1.501 to 3.000
up thru 1.000
0.010 to 4.000
All
up thru 8.000
0.025 to 0.500
All
up thru 0.500
up thru 1.000
0.500 to 1.000
All
All
up thru 2.999
up thru 0.500
up thru 1.000
up thru 0.750
up thru 0.500
up thru 0.750
45
31
33
33
31
31
36
39
42
46
46
44
44
41
41
38
42
38
42
42
38
22
22
21
30
50
48
38
38
42
30
50
35
12
19
19
12
12
26
29
19
33
33
31
31
29
29
35
35
35
35
35
35
16
16
15
25
45
45
35
35
37
25
44
33
12
16
16
13
12
24
27
19
27
27
25
25
25
25
35
35
35
35
35
35
16
16
15
25
45
45
35
35
37
25
43
24
19
20
19
19
19
21
23
26
27
27
25
25
25
25
24
27
24
25
27
24
13
13
12
19
27
29
24
24
27
19
28
10,300
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,500
1. Ftu and Fty are minimum specified values (except Fty for 1100-H12, H14 Cold Finished Rod and Bar and Drawn Tube, Alclad 3003-H18 Sheet and
5050-H32, H34 Cold Finished Rod and Bar which are minimum expected values); other strength properties are corresponding minimum expected
values.
2. Typical values. For deflection calculations an average modulus of elasticity is used; this is 100 ksi lower than values in this column.
I-B-16
May 2005
Table 3.3-1M
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
1100-H12
-H14
2014-T6
-T651
-T6, T6510, T6511
-T6, T651
Alclad
2014-T6
-T6
-T651
3003-H12
-H14
-H16
-H18
-H12
-H14
-H16
-H18
Alclad
3003-H12
-H14
-H16
-H18
-H14
-H18
3004-H32
-H34
-H36
-H38
-H34
-H36
Alclad
3004-H32
-H34
-H36
-H38
-H131, H241, H341
-H151, H261, H361
3005-H25
-H28
3105-H25
5005-H12
-H14
-H16
-H32
-H34
-H36
5050-H32
-H34
-H32
-H34
THICKNESS
RANGE
mm
Ftu
MPa
Fty
MPa
Fcy
MPa
Fsu
MPa
All
All
1.00 to 6.30
6.30 to 50.00
All
All
95
110
455
460
415
450
75
95
400
405
365
380
70
90
405
400
360
365
62
70
275
275
240
260
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (MPa)
69,600
69,600
75,200
75,200
75,200
75,200
Sheet
Sheet
Plate
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Drawn Tube
Drawn Tube
0.63 to 1.00
1.00 to 6.30
6.30 to 12.50
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.15 to 3.20
All
All
All
All
435
440
440
120
140
165
185
120
140
165
185
380
395
395
85
115
145
165
85
115
145
165
385
400
385
70
95
125
140
75
110
130
145
260
270
270
75
85
95
105
75
85
95
105
74,500
74,500
74,500
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.15 to 3.20
0.63 to 6.30
0.25 to 12.50
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.15 to 3.20
0.45 to 11.50
0.45 to 11.50
115
135
160
180
135
180
190
220
240
260
220
240
80
110
140
160
110
160
145
170
190
215
170
190
62
90
115
130
105
140
125
150
170
200
165
185
70
85
95
105
85
105
115
130
140
145
130
140
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Sheet
Cold Fin. Rod & Bar
Drawn Tube
Cold Fin. Rod & Bar
Drawn Tube
0.40 to 6.30
0.20 to 6.30
0.15 to 4.00
0.15 to 3.20
0.60 to 1.20
0.60 to 1.20
0.32 to 1.20
0.15 to 2.00
0.32 to 2.00
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.40 to 6.30
0.20 to 6.30
All
185
215
235
255
215
235
180
215
160
125
145
165
120
140
160
150
170
150
140
165
185
205
180
205
150
185
130
95
115
135
85
105
125
110
140
110
115
145
165
195
150
195
140
170
115
90
105
125
75
95
110
95
125
105
110
125
130
145
125
130
105
115
95
75
85
95
75
85
90
95
105
90
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
All
170
140
130
105
69,600
PRODUCT
Plate, Drawn Tube,
)
( Sheet,
Rolled Rod & Bar
Sheet
Plate
Extrusions
Cold Finished Rod & Bar,
Drawn Tube
For all footnotes, see last page of this Table.
January 2005
I-B-17
Table 3.3-1M
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
5052-O
-H32
-H34
-H36
5083-O
-H111
-H111
-O
-H116
-H32, H321
-H116
-H32, H321
5086-O
-H111
-H111
-O
-H112
-H112
-H112
-H116
-H32
-H34
5154 -H38
5454-O
-H111
-H111
-H112
-O
-H32
-H34
5456-O
-H116
-H32, H321
-H116
-H32, H321
-H116
-H32, H321
6005-T5
6061-T6, T651
-T6, T6510, T6511
-T6, T651
-T6
-T6
6063-T5,
-T52
-T5
-T6
6066-T6, T6510, T6511
6070-T6, T62
6105 -T5
6351-T5
6351-T6
6463-T6
7005-T53
PRODUCT
(
Ftu
MPa
Fty
MPa
Fcy
MPa
Fsu
MPa
0.15 to 80.00
All
All
170
215
235
65
160
180
66
145
165
110
130
140
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (MPa)
70,300
70,300
70,300
0.15 to 4.00
up thru 13.00
up thru 12.70
12.70 to 130.00
1.20 to 6.30
4.00 to 40.00
4.00 to 40.00
40.00 to 80.00
40.00 to 80.00
up thru 130.00
up thru 12.70
12.70 to 130.00
0.50 to 50.00
4.00 to 12.50
12.50 to 40.00
40.00 to 80.00
1.60 to 50.00
All
255
270
275
275
275
305
305
285
285
240
250
250
240
250
240
235
275
275
200
110
165
165
125
215
215
200
200
95
145
145
95
125
105
95
195
195
180
110
145
145
125
180
180
165
165
95
125
125
95
115
110
105
180
180
150
165
165
160
170
180
180
165
165
145
145
145
145
150
145
145
165
165
70,300
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
All
300
235
220
180
71,700
0.15 to 3.20
up thru 130.00
up thru 12.70
12.70 to 130.00
up thru 130.00
0.50 to 80.00
0.50 to 50.00
0.50 to 25.00
1.20 to 6.30
4.00 to 12.50
4.00 to 12.50
12.50 to 40.00
12.50 to 40.00
40.00 to 80.00
40.00 to 80.00
up thru 25
0.25 to 100.00
All
up thru 200
0.63 to 12.50
All
up thru 12.50
up thru 25.00
12.50 to 25.00
All
All
up thru 80.00
up thru 12.50
up thru 25.00
up thru 20.00
up thru 12.50
up thru 20.00
310
215
230
230
215
215
250
270
290
315
315
305
305
285
285
260
290
260
290
290
260
150
150
145
205
345
330
260
260
290
205
345
240
85
130
130
85
85
180
200
130
230
230
215
215
200
200
240
240
240
240
240
240
110
110
105
170
310
310
240
240
255
170
305
230
85
110
110
90
85
165
185
130
185
185
170
170
170
170
240
240
240
240
240
240
110
110
105
170
310
310
240
240
255
170
295
165
130
140
130
130
130
145
160
180
185
185
170
170
170
170
165
185
165
170
185
165
90
90
85
130
185
200
165
165
185
130
195
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
72,400
THICKNESS
RANGE
mm
Sheet & Plate
Sheet & Plate
Cold Fin. Rod & Bar
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Plate
Plate
Sheet & Plate
Sheet & Plate
Drawn Tube
Sheet & Plate
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Plate
Plate
Extrusions
Sheet & Plate
Extrusions
Cold Fin. Rod & Bar
Drawn Tube
Pipe
Extrusions
Extrusions
Extrusions
Extrusions & Pipe
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
)
1. Ftu and Fty are minimum specified values (except Fty for 1100-H12, H14 Cold Finished Rod and Bar and Drawn Tube, Alclad 3003-H18 Sheet and
5050-H32, H34 Cold Finished Rod and Bar which are minimum expected values); other strength properties are corresponding minimum expected
values.
2. Typical values. For deflection calculations an average modulus of elasticity is used; this is 700 MPa lower than values in this column.
I-B-18
January 2005
Table 3.3-2
MINIMUM MECHANICAL PROPERTIES FOR WELDED ALUMINUM ALLOYS
All
All
TENSION
Ftuw1
Ftyw2
ksi
ksi
11
3.5
14
5
All
All
13
22
4.5
8.5
4.5
8.5
10
14
All
Sheet
All
All
All
Extrusions
Sheet & Plate
Plate
Extrusions
Plate
Sheet & Plate
Sheet
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Plate
Extrusions
All
All
All
Extrusions
Extrusions
Extrusions
Extrusions
21
17
15
18
25
39
40
39
35
35
35
30
31
31
31
42
41
24
24
24
17
24
24
17
40
8
6.5
5
6
9.5
16
18
17
14
14
14
11
12
12
12
19
18
13
15
11
8
15
11
8
24
8
6.5
5
6
9.5
15
18
17
13
14
14
11
11
12
12
18
17
13
15
11
8
15
11
8
24
13
12
9
12
16
23
24
24
21
21
21
19
19
19
19
25
25
15
15
15
11
15
15
11
22
ALLOY AND TEMPER
1100-H12, H14
3003-H12, H14, H16, H18
Alclad
3003-H12, H14, H16, H18
3004-H32, H34, H36, H38
Alclad
3004-H32, H34, H36, H38
3005-H25
5005-H12, H14, H32, H34
5050-H32, H34
5052-O, H32, H34
5083-O, H111
5083-O, H116, H32, H321
5083-O, H116, H32, H321
5086-O, H111
5086-H112
5086-O, H32, H34, H116
5154-H38
5454-O, H111
5454-H112
5454-O, H32, H34
5456-O, H116, H32, H321
5456-O, H116, H32, H321
6005-T5
6061-T6, T651, T6510, T65113
6061-T6, T651, T6510, T65114
6063-T5, T52, T6
6351-T5, T63
6351-T5, T64
6463-T6
7005-T53
PRODUCT
THICKNESS
RANGE
in.
0.188-1.500
1.501-3.000
0.250-2.000
0.188-1.500
1.501-3.000
up thru 0.250
over 0.375
over 0.375
0.125-0.500
up thru 0.750
COMPRESSION
Fcyw2
ksi
SHEAR
Fsuw
ksi
3.5
5
8
10
1. Filler wires are listed in Table 7.1-1. Values of Ftuw are AWS D1.2 weld qualification values.
2. 0.2% offset in 2 in. gage length across a groove weld.
3. Values when welded with 5183, 5356, or 5556 alloy filler wire, regardless of thickness. Values also apply to thicknesses less than or equal
to 0.375 in. when welded with 4043, 5554, or 5654 alloy filler wire.
4. Values when welded with 4043, 5554, or 5654 alloy filler wire.
January 2005
I-B-19
Table 3.3-2M
MINIMUM MECHANICAL PROPERTIES FOR WELDED ALUMINUM ALLOYS
ALLOY AND TEMPER
1100-H12, H14
3003-H12, H14, H16, H18
Alclad
3003-H12, H14, H16, H18
3004-H32, H34, H36, H38
Alclad
3004-H32, H34, H36, H38
3005-H25
5005-H12, H14, H32, H34
5050-H32, H34
5052-O, H32, H34
5083-O, H111
5083-O, H116, H32, H321
5083-O, H116, H32, H321
5086-O, H111
5086-H112
5086-O, H32, H34, H116
5154-H38
5454-O, H111
5454-H112
5454-O, H32, H34
5456-O, H116, H32, H321
5456-O, H116, H32, H321
6005-T5
6061-T6, T651, T6510, T65113
6061-T6, T651, T6510, T65114
6063-T5, T52, T6
6351-T5, T63
6351-T5, T64
6463-T6
7005-T53
PRODUCT
THICKNESS
RANGE
mm
TENSION
COMPRESSION
Fcyw2
MPa
SHEAR
Fsuw
MPa
25
35
55
70
All
All
Ftuw1
MPa
75
95
Ftyw2
MPa
25
35
All
All
90
150
30
60
30
60
70
95
All
Sheet
All
All
All
Extrusions
Sheet & Plate
Plate
Extrusions
Plate
Sheet & Plate
Sheet
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Plate
Extrusions
All
All
All
Extrusions
Extrusions
Extrusions
Extrusions
145
115
105
125
170
270
270
270
240
240
240
205
215
215
215
285
285
165
165
165
115
165
165
115
275
55
45
35
40
65
110
115
115
95
95
95
75
85
85
85
125
125
90
105
80
55
105
80
55
165
55
45
35
40
65
110
115
115
85
95
95
75
85
85
85
125
120
90
105
80
55
105
80
55
165
90
85
62
85
110
160
165
165
145
145
145
130
130
130
130
170
170
105
105
105
75
105
105
75
155
6.30-38.00
38.00-80.00
6.30-50.00
6.30-38.00
38.00-80.00
up thru 12.50
over 9.50
over 9.50
3.20-12.50
up thru 20.00
1. Filler wires are listed in Table 7.1-1. Values of Ftuw are AWS D1.2 weld qualification values.
2. 0.2% offset in 50 mm gage length across a groove weld.
3. Values when welded with 5183, 5356, or 5556 alloy filler wire, regardless of thickness. Values also apply to thicknesses less than or equal
to 9.5 mm when welded with 4043, 5554, or 5654 alloy filler wire.
4. Values when welded with 4043, 5554, or 5654 alloy filler wire.
I-B-20
January 2005
Table 3.3-3
FORMULAS FOR BUCKLING CONSTANTS FOR PRODUCTS WHOSE TEMPER
DESIGNATION BEGINS WITH –O, -H, -T1, -T2, -T3, OR -T4
Intercept
ksi
Type of Member and Stress
Intercept
MPa
[ ( )]
[ ( )]
[ ( )]
[ ( )]
[ ( )]
Slope
[ ( )]
[ ( ) ]
[ ( )]
[ ( )]
[ ( ) ]
Intersection
Compression in Columns
and Beam Flanges
Fcy 1/2
Bc = Fcy 1 + _____
1000
Fcy 1/2
Bc = Fcy 1 + _____
6900
B 6B 1/2
Dc = ___c ___c
20 E
( )
2B
Cc = ____c
3Dc
Axial Compression
in Flat Elements
Fcy 1/3
Bp = Fcy 1 + ______
7.6
Fcy 1/3
Bp = Fcy 1 + ______
14.5
Bp 6Bp 1/2
Dp = ___ ___
20 E
( )
2Bp
Cp = ____
3Dp
Axial Compression
in Curved Elements
Fcy 1/5
Bt = Fcy 1 + ______
5.8
Bending Compression
in Flat Elements
Bending Compression
in Curved Elements
( )
F
F
B 6B
B = 1.3F 1 +
B = 1.3F 1 +
D =
7
13.3
20 ( E )
F
F
B B
B = 1.5F 1 +
B = 1.5F 1 +
D =
2.7 ( E )
5.8
8.5
F
F
( F /√3 )
( F /√ 3 )
B 6B
B =
1+
B =
1+
D =
[
]
(E)
[
]
11.8
20
6.2
√3
√3
1/3
br
cy
cy
______
y
y
_____
Ultimate Strength of Flat
Elements in Compression
or Bending
s
ty
___
__
cy
k1 = 0.50,
cy
_____
br
1/5
tb
y
y
_____
__
1/3
ty
_________
B B 1/3
Dt = ___t __t
3.7 E
1/3
br
1/5
tb
__
Shear
in Flat Elements
Fcy 1/5
Bt = Fcy 1 + ______
8.5
s
ty
___
__
tb
1/3
ty
_________
s
br ____
br
___
tb ___
tb
___
___s ___s
1/2
Ct*
2Bbr
Cbr = ____
3Dbr
(
)
1/3
Btb - Bt 2
Ctb = _______
Dtb - Dt
1/2
2B
Cs = ____s
3Ds
k2 = 2.04
*Ct shall be determined using a plot of curves of limit state stress based on elastic and inelastic buckling or by trial and error solution.
January 2005
I-B-21
Table 3.3-4
FORMULAS FOR BUCKLING CONSTANTS FOR PRODUCTS WHOSE TEMPER
DESIGNATION BEGINS WITH -T5, -T6, -T7, -T8, OR -T9
Intercept
ksi
Type of Member and Stress
Intercept
MPa
[ ( )]
Slope
[ (
)]
B B 1/2
Dc = ___c __c
10 E
[
]
Bp Bp 1/2
Dp = ___ __
10 E
Compression in Columns
and Beam Flanges
Fcy 1/2
Bc = Fcy 1 + _____
2250
Axial Compression
in Flat Elements
( Fcy )1/3
Bp = Fcy 1 + ______
11.4
[
]
( Fcy )1/3
Bp = Fcy 1 + ______
21.7
Axial Compression
in Curved Elements
( Fcy )1/5
Bt = Fcy 1 + ______
8.7
[
]
( Fy )1/5
Bt = Fcy 1 +______
12.8
Bending Compression
in Flat Elements
( Fcy )1/3
Bbr = 1.3Fcy 1 + ______
7
Bending Compression
in Curved Elements
( Fy )1/5
Btb = 1.5Fy 1 + _____
8.7
Shear
in Flat Elements
Fty /√ 3 1/3
Fty
__ 1 + _________
Bs = ___
9.3
√3
Ultimate Strength of Flat
Elements in Compression
k1 = 0.35,
k2 = 2.27
Ultimate Strength of Flat
Elements in Bending
k1 = 0.50,
k2 = 2.04
[
[
[
[
(
__
Fcy 1/2
Bc = Fcy 1 + ______
15510
]
]
)
]
[
[
( Fy )1/5
Btb = 1.5Fy 1 + _____
12.8
]
[
(
__
( )
B
Cc = 0.41___c
Dc
( )
Bp
Cp = 0.41___
Dp
( )
Ct*
( )
2Bbr
Cbr = ____
3Dbr
( )
Btb - Bt 2
Ctb = ______
Dtb - Dt
( )
B
Cs = 0.41___s
Ds
B B 1/3
Dt = ___t __t
4.5 E
( Fcy )1/3
Bbr = 1.3Fcy 1 + _____
13.3
)
]
]
Fty /√3 1/3
Fty
__ 1 + _________
Bs = ___
17.7
√3
Bbr ____
6Bbr 1/2
Dbr = ___
20 E
Btb ___
Btb 1/3
Dtb = ___
2.7 E
]
Intersection
B B 1/2
Ds = ___s __s
10 E
(
)
*Ct shall be determined using a plot of curves of limit state stress based on elastic and inelastic buckling or by trial and error solution.
I-B-22
January 2005
3.4 Design Stresses
Design stresses ϕFL shall be determined in accordance
with the provisions of this Specification.
In the following subsections:
• The resistance factor ϕ shall be taken from Table 3.4-1.
• Values of coefficient kt shall be taken from Table 3.4-2.
• Values of k1 and k2 shall be taken from Tables 3.3-3
and 3.3-4.
The formulas of this Section are also listed in Table 3.4-3.
Table 3.4-1
COMMONLY USED RESISTANCE FACTORS
Resistance Factor
Value
Applicable Limit State
ϕy
0.95
general yield
ϕb
0.85
beams or elements of beams
ϕc
0.85
elements of columns
ϕu*
0.85
ultimate
ϕcc
1 – 0.21λ < 0.95 for λ < 1.2
0.14λ + 0.58 < 0.95 for λ > 1.2
columns
ϕcp
0.80
elastic buckling of tubes
ϕv
0.80
elastic shear buckling
ϕvp
0.90
inelastic shear buckling
ϕw
0.90
web crippling
*see Section 3.4.2 for an exception
Other resistance factors for connections are given throughout the Specification.
Table 3.4-2
COEFFICIENT kt
Alloy and Temper
Non-welded or Regions
Farther than 1.0 in.
(25 mm) from a Weld
Regions Within 1.0 in.
(25 mm) of a Weld
2014-T6, -T651, -T6510, -T6511
Alclad 2014-T6, -T651
1.25
–
6066-T6, -T6510, -T6511
1.1
–
6070-T6, -T62
1.1
–
All Others Listed in Table 3.3-1
1.0
1.0
kt is used in Sections 3.4.1, 3.4.2, 3.4.3, and 3.4.4.
January 2005
I-B-23
I-B-24
January 2005
4
5
Flat elements in bending in their
own plane (webs)
On rivets and bolts
10
Curved elements
supported on both
edges
bo
9.1
9.2
b
ϕyFcy
ϕyFcy
ϕyFcy
8.1
9
ϕyFcy
8
7
Sub- Design Stress
Sec.
S ≤ S1
Flat elements
supported on both
edges and with an
intermediate stiffener
Flat elements supported
COMPRESSION on both edges
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
bo
Type of Member or Element
6
1.17 ϕyFty or 1.24 ϕuFtu /kt
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted
holes
ϕyFty or ϕuFtu /kt
2
Flat elements in uniform tension (flanges)
(
)
ϕy Fcy 2
Bt – _____
ϕc
Rb
__
________
t =
Dt
)
)
)
(
√ )
Rb
ϕc Bt – Dt __
t
___
See Section 3.4.9.2
See Section 3.4.9.1
t
(
ϕy Fcy
Bp – _____
ϕc
b
__ = _________
t
1.6 Dp
ϕc
(
b
Bp – 1.6 Dp __
b
ϕc Bp – 5.1 Dp __
t
t
ϕy Fcy
Bp – _____
ϕc
b = _________
__
t
5.1 Dp
(
ϕc
b
Bp – 5.1 Dp__
See Section 3.4.7
Design Stress
S1 < S < S2
t
See 3.4.10
1.6 Dp
5.1
Cp
b = ___
__
5.1 Dp
k1 Bp
b = _____
__
t
t
k1 Bp
b = _____
__
Slenderness Limit
S2
( )(
Rb /t
√_____
Rb
16 __
t 1 + 35
2
)
2
ϕcp π E
________________
____
1.6 b/t
____
ϕc k2 √Bp E
_________
( 5.1 b/t )2
2
ϕc π E
________
5.1 b/t
____
ϕc k2√Bp E
_________
Design Stress
S ≥ S2
For tubes with circumferential welds, equations of Sections 3.4.10,
3.4.12, and 3.4.16.1 apply for Rb /t ≤ 20.
Table 3.4-3
GENERAL FORMULAS FOR
DETERMINING DESIGN STRESS
FROM SECTION 3.4
ϕy Fcy
Bp – _____
ϕc
b
__ = _________
t
5.1 Dp
Slenderness Limit
S1
2ϕuFtu /1.5
2ϕuFtu
for symmetric shapes:
1.3 ϕyFty or
1.42 ϕuFtu /kt
for unsymmetric shapes
see Section 3.4.4
ϕyFty
ϕuFtu /kt
Design Stress
1
SubSec.
Any tension member
gross section
net section
Type of Member or Element
COMPRESSION
IN COLUMNS,
All columns
axial, gross
section
Flat elements supported
on one edge—columns
buckling about a symmetry
axis
Flat elements supported
on one edge—columns
not buckling about a
symmetry axis
Type of Stress
BEARING
TENSION IN
BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
I-B-25
1.3ϕy Fcy
13
SHEAR IN
ELEMENTS,
gross section
21
Stiffened flat elements
supported on both edges
√3
ϕyFty
____
__
√3
ϕyFty
____
__
1.3ϕy Fcy
19
20
1.3ϕy Fcy
18
Unstiffened flat elements
supported on both edges
1.3ϕy Fcy
16.3
Flat elements
supported on both
edges and with an
intermediate stiffener
1.17ϕy Fcy
ϕy Fcy
ϕy Fcy
17
16.2
Flat elements supported on
one edge and with stiffener
on other edge
16
Flat elements supported on
both edges
16.1
15
Flat elements
supported on one edge
Curved elements supported
on both edges
14
Tubular shapes
Flat elements supported on
tension edge, compression
COMPRESSION
edge free
IN BEAM
ELEMENTS,
Flat elements supported on
(element in
both edges
bending in own
plane), gross
Flat elements supported on
section
both edges and with a
longitudinal stiffener
COMPRESSION
IN BEAM
ELEMENTS,
(element in
uniform
compression),
gross section
bo
1.17ϕy Fcy
12
Round or oval tubes
ϕy Fcy
ϕy Fcy
11
Sub- Design Stress
Sec.
S ≤ S1
Single web shapes
bo
Type of Member or Element
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and
gross section
round sections
Type of Stress
2
(
1.6 Dc
5.1 Dp
t
(
B – 1.17 ϕ F /ϕ
1.6 Dp
B – ϕ F /ϕ
( y cy b )
p
b _____________
__
=
t
√ )
)
√
[
[
p
p
t
√
)
]
]
t
Bbr – ( ϕy / ϕb )1.3Fcy
mDbr
t
__
1.25Ds
)
_
s – ϕyFty / ϕvp√ 3
h B____________
__
=
(
0.29 Dbr
h = ________________
__
t
1.25Ds
[
[
]
ae
1.375ϕvp Bs – 1.25Ds __
t
[
h
ϕvp Bs – 1.25Ds __
t
]
]
h
ϕb Bbr – 0.29Dbr _
t
[
h
ϕb Bbr – mDbr __
t
]
Bbr – ( ϕy / ϕb )1.3Fcy
3.5 Dbr
h = ________________
__
[
See Section 3.4.16.3
See Section 3.4.16.2
(
___
Rb
ϕb Bt – Dt __
t
b
ϕb Bp – 1.6Dp __
t
ϕb
b
B – 5.1D __
)
]
_______
Lb____
Sc
ϕb Bc – 1.6Dc _______
Cb√ Iy J/2
b
ϕb Bbr – 3.5 Dbr __
t
Bbr – ( ϕy / ϕb )1.3Fcy
)
2
√
)
___
Lb
d ___
ϕb Bbr – 2.3Dbr _
t Cb d
(
___
Rb
ϕb Btb – Dtb __
t
b = ________________
__
t
Dt
2
Bs – ϕyFty / ( 1.375ϕvp√ 3 )
ae _________________
__
=
t
)
( y cy b )
t
Rb
__
= ________________
t
(
Bp – ϕy Fcy /ϕb
b ___________
__
=
Cb√ IyJ/2
Bc – ( ϕy Fcy /ϕb )
Lb____
Sc
_______
= _____________
√
(
(
)
)
Dtb
Btb –1.17( Fcy ϕy /ϕb )
_____________
) (
(
(
Design Stress
S1 < S < S2
Dc Lb__
ϕb Bc – _______
1.2 ry√ Cb
___
Bbr – 1.3( ϕy Fcy / ϕb )
Lb
___
_____________
t Cb d =
2.3 Dbr
d
__
t
Rb
__
=
1.2 B – ϕ F /ϕ
( c y cy b )
L__
b
____
= _______________
Dc
ry√ Cb
Slenderness Limit
S1
t
t
0.29Dbr
See 3.4.21
See 3.4.20
t
k1Bbr
h _____
__
=
mDbr
3.5
k1Bbr
h _____
__
=
t
Cbr
b ___
__
=
t
1.6 Dp
Rb
__
=C
t
t
k B
5.1 Dp
1 p
b ______
__
=
t
k B
( 1.6 )
1 p
b ______
__
=
Cb √ Iy J/2
√
___
Lb
Cbr
___
= ___
Cb d 2.3
2
Dtb – ( ϕc/ϕb )Dt
Lb____
Sc
C
_______
= ___c
t
d
__
[
B – ϕ /ϕ B
( c b) t
tb
Rb _____________
__
=
L__
b
____
= 1.2 Cc
ry√ Cb
]
Slenderness Limit
S2
2
2
(
)
( )(
)
( 1.25ae /t )2
2
1.375ϕ
v π E
__________
( 1.25h/t )2
ϕ π2E
v
________
0.29h/t
ϕbk2√BbrE
________
____
mh/t
ϕbk2√ BbrE
_________
____
( 3.5 b/t )2
2
____ 2
√ Rb/t
1 + ______
35
ϕb π E
________
Rb
16 __
t
2
ϕcp π E
_________________
1.6 b/t
ϕb k2√ BpE
_________
____
5.1 b/t
ϕb k2√ Bp E
__________
____
Lb____
Sc
2.56 _______
Cb √ Iy J/2
2
ϕb π E
____________
(t) d
2
ϕb π ECb
________
Lb
d 2 __
5.29 _
Same as
Secion 3.4.10
1.2ry
Lb
____
( )
ϕb_______
π2 ECb
Design Stress
S ≥ S2
3.4.1 Tension, Axial
ϕFL = 1.3ϕy Fty
Axial tensile stress produced by the factored loads shall
not exceed
ϕFL = ϕy Fty
(Eq. 3.4.1-1)
on the gross area and
ϕFL = ϕuFtu /kt
(Eq. 3.4.1-2)
on the effective net area (see Section 5.1.5).
Values of kt are listed in Table 3.4-2.
3.4.2 Tension in Extreme Fibers of Beams—
Flat Elements In Uniform Tension
The design stress is the lesser of:
(Eq. 3.4.2-1)
and
(Eq. 3.4.2-2)
ϕu = 0.85
b. For elements unsymmetric about the bending axis, the
extreme fiber stress of the element shall not exceed the
limiting value from a. and the stress at midheight of
the element shall not exceed the stress given in Section
3.4.2.
ϕFL = 2ϕuFtu
(Eq. 3.4.5-1)
where ϕu = 0.85
This value shall be used for a ratio of edge distance to fastener diameter of 2 or greater. For smaller ratios this design
stress shall be multiplied by the ratio: (edge distance)/
(2 × fastener diameter). Edge distance is the distance from
the center of the fastener to the edge of the material in the
direction of the applied load and shall not be less than 1.5
times the fastener diameter to extruded, sheared, sawed,
rolled, or planed edges.
ϕFL = 2ϕu Ftu / 1.5
3.4.3 Tension in Extreme Fibers of Beams—
Round or Oval Tubes
The design stress is the lesser of:
(Eq. 3.4.3-1)
and
ϕFL = 1.24ϕuFtu /kt
(Eq. 3.4.4-2)
3.4.6 Bearing on Flat Surfaces and Pins and on
Bolts in Slotted Holes
where ϕy = 0.95
ϕFL = 1.17ϕy Fty
ϕFL = 1.42ϕuFtu /kt
3.4.5 Bearing on Rivets and Bolts
Block shear rupture strength provisions for the end connections of tension members are given in Section 5.1.3.
ϕFL = ϕuFtu /kt
and
where ϕy = 0.95, ϕu = 0.85
where ϕy = 0.95, ϕu = 0.85
ϕFL = ϕy Fty
(Eq. 3.4.4-1)
(Eq. 3.4.3-2)
where ϕy = 0.95
ϕu = 0.85
(Eq. 3.4.6-1)
where ϕu = 0.85
(See Section 5.2.2 for limits on slot lengths.)
3.4.7 Compression in Columns,
Axial, Gross Section
For members in axial compression, the design stress is the
lesser of that determined from this Section and Sections
3.4.8 through 3.4.10.
a. ϕFL = ϕccFcy
(Eq. 3.4.7-1)
for λ < S1
3.4.4 Tension in Extreme Fibers of Beams—
Flat Elements In Bending in Their
Own Plane
b. ϕFL = ϕcc( Bc – Dc*λ )
a. For elements symmetric about the bending axis, the
design stress is the lesser of:
ϕccFcy
c. ϕFL = ______
λ2
(Eq. 3.4.7-2)
for S1* < λ < S2*
(Eq. 3.4.7-3)
for λ > S2
I-B-26
January 2005
where
kl __
1 ______
λ = __
r π √ Fcy / E , slenderness parameter (Eq. 3.4.7-4)
( )( )
______
D *c = πDc√E / Fcy
(Eq. 3.4.7-5)
Bc –Fcy
S*1 = ______
D*c
_____
C
c
S*2 = __
π √ Fcy /E
In the above equations
x-axis is the centroidal symmetry axis
A
= cross-sectional area
Cw = torsional warping constant of the cross-section
E
= compressive modulus of elasticity (See
Table 3.3-1)
(Eq. 3.4.7-6)
Fex
(Eq. 3.4.7-7)
ϕcc = 1 – 0.21λ ≤ 0.95 for λ ≤ 1.2
(Eq. 3.4.7-8)
Fet
π2E
= ______
2
k____
xLb
rx
( )
(
π2ECw
1 GJ + ______
= ____
2
( KtLt )2
Ar
0
ϕcc = 0.14λ + 0.58 ≤ 0.95 for λ > 1.2
(Eq. 3.4.7-9)
k = the effective length factor by rational analysis. k shall
be taken larger than or equal to unity unless rational
analysis justifies a smaller value.
L = the unsupported length
r = radius of gyration of the column about the axis of
buckling
3.4.7.1 Sections Not Subject to Torsional or
Torsional-Flexural Buckling
For closed sections and other sections that are not subject to torsional or torsional-flexural buckling, kL/r shall
be the largest slenderness ratio for flexural buckling of the
column.
3.4.7.2 Doubly or Singly Symmetric Sections
Subject to Torsional or Torsional-Flexural
Buckling
For doubly or singly symmetric sections subject to torsional or torsional-flexural buckling kL/r shall be the larger
of the largest slenderness ratio for flexural buckling and
the equivalent slenderness ratio determined for torsionalflexural buckling as follows:
(r)
kL
___
e
___
√F
E
= π __
(Eq. 3.4.7.2-1)
e
where Fe is the elastic critical stress determined as follows:
G
J
kx
Kt
Lt
Lb
(Eq. 3.4.7.2-5)
)
(Eq. 3.4.7.2-6)
= shear modulus = 3E/8
(Eq. 3.4.7.2-7)
= torsion constant
= effective length coefficient for buckling about
the x-axis
= effective length coefficient for torsional
buckling. Kt shall be taken larger than or equal
to unity unless rational analysis justifies a
smaller value.
= unbraced length for twisting
= unbraced length for bending about the x-axis
___________
= √r x2 + r y2 + x o2
(Eq. 3.4.7.2-8)
polar radius of gyration of the cross-section
about the shear center.
rx, ry = radii of gyration of the cross-section about the
centroidal principal axes
xo = x - coordinate of the shear center
β
= 1 – (xo /ro)2
(Eq. 3.4.7.2-9)
ro
3.4.7.3 Nonsymmetric Sections Subject to
Torsional or Torsional-Flexural Buckling
For nonsymmetric sections subject to torsional or
torsional-flexural buckling kL/r shall be determined by
rational analysis.
3.4.8 Uniform Compression in Elements of
Columns Whose Buckling Axis is an
Axis of Symmetry – Flat Elements
Supported On One Edge
For torsional buckling:
Fe = Fet
(Eq. 3.4.7.2-2)
_________________
1 [ ( F + F ) – √( F + F )2 – 4βF F ]
Fe = Fef = ___
ex
et
ex
et
ex et
2β
(Eq. 3.4.7.2-3)
As an alternative, Fe for torsional-flexural buckling shall be
obtained as follows:
January 2005
(Eq. 3.4.8-1)
for b /t < S1
For torsional-flexural buckling:
FexFet
Fe = Fef = _______
Fex + Fet
a. ϕFL = ϕy Fcy
[
b
b. ϕFL = ϕc Bp – 5.1 Dp__
t
]
(Eq. 3.4.8-2)
for S1 < b /t < S2
____
ϕc k2√BpE
c. ϕFL = ________
5.1b/t
(Eq. 3.4.8-3)
for b /t > S2
(Eq. 3.4.7.2-4)
I-B-27
where
ϕy
Bp – __ Fcy
ϕc
S1 = _________
5.1Dp
k1Bp
S2 = _____
5.1Dp
(Eq. 3.4.8-4)
(Eq. 3.4.8-5)
b = distance from unsupported edge of element to toe of
the fillet or bend, except if the inside corner radius
exceeds 4 times the thickness; then the inside radius
shall be assumed equal to 4 times the thickness in
calculating b. Element width b is illustrated in Figure 3.4.8-1.
3.4.8.1 Uniform Compression in Elements of
Columns Whose Buckling Axis is not an
Axis of Symmetry – Flat Elements
Supported On One Edge
a. ϕFL = ϕy Fcy
(Eq. 3.4.8.1-1)
for b /t < S1
[
b
b. ϕFL = ϕc Bp – 5.1Dp__
t
]
(Eq. 3.4.8.1-2)
for S1 < b /t < S2
ϕy = 0.95
ϕcπ2E
c. ϕFL = _______
( 5.1b/t )2
ϕc = 0.85
for b /t > S2
(Eq. 3.4.8.1-3)
where
ϕy
Bp – __ Fcy
ϕc
S1 = _________
5.1Dp
Cp
S2 = ___
5.1
(Eq. 3.4.8.1-4)
(Eq. 3.4.8.1-5)
b = distance from unsupported edge of element to
toe of the fillet or bend, except if the inside corner radius exceeds 4 times the thickness; then the
inside radius shall be assumed equal to 4 times the
thickness in calculating b. Element width b is illustrated in Figure 3.4.8-1.
ϕy = 0.95
ϕc = 0.85
I-B-28
January 2005
Figure 3.4.8-1
FLAT ELEMENTS SUPPORTED ON ONE EDGE
if r > 4t, then use r = 4t to calculate b.
January 2005
I-B-29
3.4.9 Uniform Compression in Elements of
Columns—Flat Elements Supported on
Both Edges
a. ϕFL = ϕy Fcy
(Eq. 3.4.9-1)
for b /t ≤ S1
[
b
b. ϕFL = ϕc Bp – 1.6Dp __
t
]
(Eq. 3.4.9-2)
for S1 < b /t < S2
____
ϕc k2√BpE
c. ϕFL = ________
1.6b/t
(Eq. 3.4.9-3)
where
ϕy
Bp – __ Fcy
ϕc
S1 = _________
1.6Dp
k1Bp
S2 =_____
1.6Dp
(Eq. 3.4.9-4)
(Eq. 3.4.9-5)
b = distance from unsupported edge of element to
toe of the fillet or bend, except if the inside corner radius exceeds 4 times the thickness; then the
inside radius shall be assumed equal to 4 times the
thickness in calculating b. Element width b is illustrated in Figure 3.4.9-1.
ϕy = 0.95
for b /t ≥ S2
ϕc = 0.85
Figure 3.4.9-1
FLAT ELEMENTS SUPPORTED ON BOTH EDGES
if r > 4t, then use r = 4t to calculate b.
I-B-30
January 2005
3.4.9.1 Uniform Compression in Elements of
Columns—Flat Elements Supported
on One Edge and With Stiffener on
Other Edge
The provisions of this Section apply when Ds /b ≤ 0.8.
The design stress is the lesser of
ϕFL = ϕy Fcy
(Eq. 3.4.9.1-1)
and
ϕFL = FUT + ( FST – FUT )ρST ≤ FST
(Eq. 3.4.9.1-2)
For a simple straight lip edge stiffener of constant thickness, ϕFL shall not exceed the design stress for the stiffener
according to Section 3.4.8.
In the above equations
Ds = defined in Figure 3.4.9.1-1 and -2
FUT = design stress according to Section 3.4.8 neglecting the stiffener
FST = design stress according to Section 3.4.9
ρST = ratio to be determined as follows:
ρST = 1.0
for b/t ≤ S/3
rs
ρST = _________
≤ 1.0 for S/3 < b/t ≤ S
b/
1
9t ___t – __
S 3
(
)
rs = radius of gyration of the stiffener determined as
follows:
- For simple straight lip stiffeners of constant thickness similar to that shown in Fig. 3.4.9.1-1, rs shall
be calculated as:
ds sin
θ
__
rs = ______
√3
(Eq. 3.4.9.1-6)
- for other stiffeners, rs shall be calculated about the
mid-thickness of the element being stiffened
ds = flat width of lip stiffener shown in Figure 3.4.9.1-1
___
√
E
S =1.28 ___
Fcy
(Eq. 3.4.9.1-7)
b = distance from unsupported edge of element to toe
of fillet or bend, except if the inside corner radius
exceeds 4 times the thickness; then the inside radius
shall be assumed to equal 4 times the thickness
in calculating b. Element width b is illustrated in
Figures 3.4.9.1-1 and 3.4.9.1-2.
ϕy = 0.95
(Eq. 3.4.9.1-3)
(Eq. 3.4.9.1-4)
rs
ρST = ____________
≤ 1.0 for 2S > b/t > S
b/
1.5t ___t + 3
S
(Eq. 3.4.9.1-5)
(
January 2005
)
I-B-31
Figure 3.4.9.1-1
EDGE STIFFENED ELEMENTS
if r > 4t, then use r = 4t to calculate b.
Figure 3.4.9.1-2
EDGE STIFFENED ELEMENTS
if r > 4t, then use r = 4t to calculate b.
I-B-32
January 2005
3.4.9.2 Uniform Compression in Elements of
Columns—Flat Elements Supported on
Both Edges and With an Intermediate
Stiffener
a. ϕFL = ϕy Fcy
(Eq. 3.4.9.2-1)
for λs ≤ S1
b. ϕFL = ϕc( Bc – Dcλs )
(Eq. 3.4.9.2-2)
(Eq. 3.4.9.2-3)
for λs ≥ S2
The design stress ϕFL obtained above shall not be more
than the design stress according to Section 3.4.9 for the
sub-elements of the intermediately stiffened element.
The design stress ϕFL obtained above shall not be less
than that determined according to Section 3.4.9 ignoring
the intermediate stiffener.
January 2005
As = area of the stiffener
Io = moment of inertia of a section comprising the stiffener and one half of the width of the adjacent subelements and the transition corners between them
taken about the centroidal axis of the section parallel
to the element that is stiffened (Figure 3.4.9.2-1).
ϕyFcy
Bc – _____
ϕc
S1 = ________
(Eq. 3.4.9.2-4)
Dc
S2 = Cc
for S1 < λs < S2
ϕcπ2E
c. ϕFL = _____
λ 2s
In the above equations:
()
______________
√ √
1+
As / bt
b ______________
__________
λs = 4.62 __
t
10.67Io
1 + 1 + ______
bt3
(Eq. 3.4.9.2-5)
(Eq. 3.4.9.2-6)
ϕy = 0.95
ϕc = 0.85
I-B-33
Figure 3.4.9.2-1
FLAT ELEMENTS WITH AN INTERMEDIATE STIFFENER
Line o - o is the neutral axis of the stiffener and plate of width b/2 on each side of the stiffener. Io is the moment of inertia of the
portion shown in the partial section.
if r > 4t, then use r = 4t to calculate b.
I-B-34
January 2005
3.4.10 Uniform Compression in Elements of
Columns—Curved Elements Supported
on Both Edges
a. ϕFL = ϕy Fcy
(Eq. 3.4.10-1)
for Rb /t ≤ S1
___
√ ]
[
Rb
b. ϕFL = ϕc Bt – Dt __
t
(Eq. 3.4.10-2)
ϕcpπ2E
____
c. ϕFL = _________________
R /t 2
√
R
_____
b
16 __ 1 + b
t
35
for Rb /t ≥ S2
( )(
(
(Eq. 3.4.11-3)
( )
where
(
)
ϕyFcy
1.2 Bc – _____
ϕb
S1 = _____________
Dc
(Eq. 3.4.11-4)
S2 = 1.2Cc
for S1 < Rb /t < S2
where
ϕbCbπ2E
c. ϕFL = _______
Lb 2
____
1.2ry
L___
b
for _____
≥ S2
ry√Cb
)
)
ϕy
2
Bt – __ Fcy
ϕ
c
S1 = ________
Dt
(Eq. 3.4.10-3)
(Eq. 3.4.11-5)
ϕy = 0.95
ϕb = 0.85
(Eq. 3.4.10-4)
S2 = Rb /t at the intersection of Eqs. 3.4.10-2 and
3.4.10-3
ϕy = 0.95
ϕc = 0.85
ϕcp = 0.80
ry = radius of gyration of the shape (about an axis parallel to the web) (For shapes that are unsymmetrical
about the horizontal axis, ry shall be calculated as
though both flanges were the same as the compression flange).
Lb = length of the beam between bracing points or
between a brace point and the free end of a cantilever beam. Bracing points are the points at which
the compression flange is restrained against lateral
movement or the cross section is restrained against
twisting.
Cb = coefficient that depends on moment variation over
the unbraced length. Cb shall be as given in Section
4.9.4 or taken as 1.
For tubes with circumferential welds, the equations of
this Section apply for Rb /t < 20.
Alternatively, ϕFL may be calculated by replacing ry by
rye given in Section 4.9.
3.4.11 Compression in Beams, Extreme Fiber,
Gross Section—Single Web Shapes
3.4.12 Compression in Beams, Extreme Fiber,
Gross Section—Round or Oval Tubes
For single web shapes not subject to lateral buckling
(bent about the strong axis with continuous lateral support
or bent about the weak axis), determine the compressive
design stress ϕFL from Sections 3.4.15 through 3.4.19 as
applicable.
For single web shapes subject to lateral buckling (bent
about the strong axis without continuous lateral support),
the compressive design stress ϕFL is the lesser of that determined from Sections 3.4.15 through 3.4.19 as applicable
and the following:
a. ϕFL = ϕy Fcy
(Eq. 3.4.11-1)
L___
b
for _____
≤ S1
ry√Cb
[
Dc Lb___
b. ϕFL = ϕb Bc – ________
1.2ry√Cb
]
a. ϕFL = 1.17ϕy Fcy
for Rb /t < S1
(
(Eq. 3.4.12-1)
___
√ )
Rb
b. ϕFL = ϕb Btb – Dtb __
t
(Eq. 3.4.12-2)
for S1 < Rb /t < S2
c. For Rb /t > S2, the design bending stress shall be determined from the formulas for tubes in compression in Section 3.4.10 using the formula that is appropriate for the
particular value of Rb /t.
(Eq. 3.4.11-2)
L___
b
for S1 < _____
< S2
ry√ Cb
January 2005
I-B-35
In the above equations
Rb = mid-thickness radius of a round element or maximum mid-thickness radius of an oval element
(
)
Btb – 1.17Fcyϕy /ϕb 2
S1 = _______________
(Eq. 3.4.12-3)
Dtb
ϕ
2
Btb – __c Bt
ϕ
b
S2 = _________
(Eq. 3.4.12-4)
ϕc
__
Dtb – Dt
ϕb
For tubes with circumferential welds, the equations of
this Section apply for Rb /t ≤ 20.
( )
ϕy = 0.95
ϕc = 0.85
ϕb = 0.85
3.4.13 Compression in Beams, Extreme Fiber,
Gross Section—Solid Rectangular and
Round Sections
For rectangular sections bent about the weak axis, rod,
and square bar: ϕFL = 1.3ϕy Fcy.
For rectangular sections bent about the strong axis:
a. ϕFL = 1.3ϕy Fcy
(Eq. 3.4.13-1)
√
____
√
Lb
d ____
Bbr – 2.3Dbr __
t Cb d
)
(Eq. 3.4.13-2)
____
√
Lb
d ____
for S < __
<S
t Cb d
1
(Eq. 3.4.1-3)
___________
)
√
(Eq. 3.4.13-4)
(Eq. 3.4.13-5)
ϕy = 0.95
(Eq. 3.4.13-6)
ϕb = 0.85
(Eq. 3.4.13-7)
d = depth of section
Lb = length of the beam between bracing points or
between a brace point and the free end of a canti-
(Eq. 3.4.14-2)
L___
b Sc
for S1 < _________
< S2
Cb√Iy J / 2
ϕbπ2E
c. ϕFL = ________________
L___
bSc
2.56 __________
Cb( √Iy J / 2 )
L___
bSc
for _________
≥ S2
Cb√ Iy J / 2
(
)
)
ϕyFcy 2
Bc – _____
ϕb
S1 = _________
1.6Dc
where
I-B-36
(Eq. 3.4.14-1)
L___
b Sc
for __________
≤ S1
Cb( √Iy J / 2 )
where
√
ϕyFcy
Bbr – 1.3_____
ϕb
S1 = ___________
2.3Dbr
Cbr
S2 = ___
2.3
a. ϕFL = ϕy Fcy
(
2
ϕbπ2E Cb
c. ϕFL = _________
Lb
d 2__
5.29 __
t d
____
Lb
d
__
≥ S2
for t ____
Cb d
()
For the purposes of this Specification, tubular shapes are
defined as closed sections.
For tubular shapes not subject to lateral buckling (bent
about the strong axis with continuous lateral support or
bent about the weak axis) and round, square, hexagonal,
and octagonal tubes, determine the compressive design
stress ϕFL from Sections 3.4.12 and 3.4.15 through 3.4.19
as applicable.
For tubular shapes subject to lateral buckling (bent
about the strong axis without continuous lateral support),
the compressive allowable stress (ϕFL) is the lesser of that
determined from Sections 3.4.12 and 3.4.15 through 3.4.19
as applicable and the following:
L___
bSc
b. ϕFL = ϕb Bc – 1.6Dc ___________
Cb ( √Iy J / 2 )
t Cb d
(
3.4.14 Compression in Beams, Extreme Fiber,
Gross Section—Tubular Shapes
(
____
Lb
d ____
for __
≤ S1
b. ϕFL = ϕb
lever beam. Bracing points are the points at which
the compression flange is restrained against lateral
movement or the cross section is restrained against
twisting.
Cb = coefficient that depends on moment variation over
the unbraced length. Cb shall be as given in Section
4.9.4 or taken as 1.
( )
C 2
S2 = ___c
1.6
(Eq. 3.4.14-3)
(Eq. 3.4.14-4)
(Eq. 3.4.14-5)
ϕy = 0.95
ϕb = 0.85
Iy = moment of inertia of the beam about the minor axis
J = torsion constant
Lb = length of the beam between bracing points or between
a brace point and the free end of a cantilever beam.
Bracing points are the points at which the compression flange is restrained against lateral movement or
the cross section is restrained against twisting.
January 2005
Cb = coefficient that depends on moment variation over
the unbraced length. Cb shall be as given in Section
4.9.4 or taken as 1.
Alternatively, ϕFL may be calculated by using the equations in Section 3.4.11 and replacing ry by rye given in Section 4.9.
For narrow rectangular tubes bent about the strong axis
with a ___
depth-to-width ratio greater than or equal to 6, the
term √IyJ /2 may be replaced by Iy.
3.4.15 Uniform Compression in Elements of
Beams—Flat Elements Supported on
One Edge
a. ϕFL = ϕy Fcy
(Eq. 3.4.15-1)
for b /t < S1
[
b
b. ϕFL = ϕb Bp – 5.1Dp __
t
]
(Eq. 3.4.15-2)
(Eq. 3.4.16-3)
for b /t > S2
where
ϕy
Bp – __ Fcy
ϕb
S1 = _________
1.6Dp
(Eq. 3.4.16-4)
k1Bp
S2 = _____
1.6Dp
(Eq. 3.4.16-5)
b = distance from unsupported edge of element to
toe of the fillet or bend, except if the inside corner radius exceeds 4 times the thickness; then the
inside radius shall be assumed equal to 4 times the
thickness in calculating b. Element width b is illustrated in Figure 3.4.9-1.
ϕy = 0.95
ϕb = 0.85
for S1 < b /t < S2
____
ϕbk2√BpE
c. ϕF = ________
L
____
ϕb k2√BpE
c. ϕFL = ________
1.6b / t
(Eq. 3.4.15-3)
5.1b / t
for b /t > S2
where
3.4.16.1 Uniform Compression in Elements of
Beams—Curved Elements Supported
on Both Edges
a. ϕFL = 1.17ϕy Fcy
Bp – ϕyFcy / ϕb
S1 = ____________
5.1Dp
(Eq. 3.4.15-4)
k1Bp
S2 = _____
(Eq. 3.4.15-5)
5.1Dp
b = distance from unsupported edge of element to
toe of the fillet or bend, except if the inside corner radius exceeds 4 times the thickness; then the
inside radius shall be assumed equal to 4 times the
thickness in calculating b. Element width b is illustrated in Figure 3.4.8-1.
for Rb /t < S1
[
ϕb = 0.85
3.4.16 Uniform Compression in Elements of
Beams—Flat Elements Supported on
Both Edges
a. ϕFL = ϕy Fcy
(Eq. 3.4.16-1)
for b /t < S1
[
b
b. ϕFL = ϕb Bp – 1.6Dp __
t
]
(Eq. 3.4.16-2)
___
√ ]
Rb
b. ϕFL = ϕb Bt – Dt __
t
(Eq. 3.4.16.1-2)
for S1 < Rb /t < S2
ϕcpπ2E
_____
c. ϕFL = _________________
√Rb / t 2
Rb
__
______
16 t 1 +
35
for Rb /t > S2
( )(
)
(Eq. 3.4.16.1-3)
where
(
ϕy = 0.95
(Eq. 3.4.16.1-1)
)
Bt – 1.17Fcy ϕy /ϕb 2
S1 = ______________
Dt
(Eq. 3.4.16.1-4)
S2 = Ct
(Eq. 3.4.16.1-5)
ϕy = 0.95
ϕb = 0.85
ϕcp = 0.80
Ct shall be determined using a plot of the curves of
design stress for values of Rb /t less than and greater than S2
or by a trial and error solution.
for S1 < b /t < S2
January 2005
I-B-37
For tubes with circumferential welds, the equations of
this Section apply for Rb /t < 20.
3.4.16.2 Uniform Compression in Elements of
Beams—Flat Elements Supported on
One Edge and With Stiffener on
Other Edge
The provisions of this Section apply when Ds /b < 0.8.
The design stress is the lesser of
ϕFL = ϕy Fcy
(Eq. 3.4.16.2-1)
ϕFL = FUT + ( FST – FUT ) ρST ≤ FST
(Eq. 3.4.16.2-2)
For a straight stiffener of constant thickness, ϕFL shall
not exceed the design stress for the stiffener according to
Section 3.4.8.
In the above equations
Ds = defined in Figure 3.4.9.1-1 and -2
FUT = design stress according to Section 3.4.15 neglecting the stiffener
FST = design stress according to Section 3.4.16
ρST = ratio to be determined as follows:
ρST = 1.0
for b/t ≤ S/3
rs
ρST = ___________
for S/3 < b/t ≤ S
≤ 1.0
b
/
t – __
1
____
9t
S
3
rs
ρST = _____________
≤ 1.0 for 2S > b/t > S
b
/t+3
____
1.5t
S
(
)
(
ds
S
b
ϕy
a. ϕFL = ϕy Fcy
(Eq. 3.4.16.3-1)
for λs ≤ S1
b. ϕFL = ϕb ( Bc – Dcλs )
(Eq. 3.4.16.3-2)
for S1 < λs < S2
ϕbπ2E
c. ϕFL = _____
λ 2s
and
rs
3.4.16.3 Uniform Compression in Elements of
Beams—Flat Elements Supported on
Both Edges and With an Intermediate
Stiffener
)
= radius of gyration of the stiffener determined as
follows:
- For simple straight lip stiffeners of constant thickness similar to that shown in Figure 3.4.9.1-1, rs
shall be calculated as:
ds sin
θ
__
rs = ______
√3
- for other stiffeners, rs shall be calculated about the
mid-thickness of the element being stiffened
= flat width
___ of lip stiffener shown in Figure 3.4.9.1-1
E
= 1.28 ___
Fcy
= distance from unsupported edge of element to
toe of fillet or bend, unless the inside corner
radius exceeds 4t; then the inside radius shall be
assumed to be 4t to calculate b. Element width b
is illustrated in Figure 3.4.9.1-1.
= 0.95
√
(Eq. 3.4.16.3-3)
for λs ≥ S2
The design stress Fc obtained above shall not be more
than the design stress according to Section 3.4.16 for the
sub-elements of the intermediately stiffened element.
The design stress Fc obtained above shall not be less
than that determined according to Section 3.4.16 ignoring
the intermediate stiffener.
In the above equations:
As = area of the stiffener
Io = moment of inertia of a section comprising the stiffener and one half of the width of the adjacent subelements and the transition corners between them
taken about the centroidal axis of the section parallel
to the element that is stiffened (Figure 3.4.9.2-1).
ϕy
Bc – __Fcy
ϕ
b
S1 = _________
(Eq. 3.4.16.3-4)
Dc
S2 = Cc
______________
1+
A / bt
__________
( ) ______________
10.67I
______
b
λs = 4.62 __
t
√ √
s
(Eq. 3.4.16.3-5)
(Eq. 3.4.16.3-6)
o
1+ 1+
bt3
ϕy = 0.95
ϕb = 0.85
3.4.17 Compression in Elements of Beams
(Element in Bending in Own Plane)—
Flat Elements Supported on Tension Edge,
Compression Edge Free
a. ϕFL = 1.3ϕyFcy
(Eq. 3.4.17-1)
for b /t < S1
[
b
b. ϕFL = ϕb Bbr – 3.5Dbr __
t
]
(Eq. 3.4.17-2)
for S1 < b /t < S2
I-B-38
January 2005
ϕbπ2E
c. ϕFL = ________
( 3.5b / t )2
(Eq. 3.4.17-3)
for b /t > S2
where
Bbr – 1.3Fcy ϕy /ϕb
S1 = ______________
3.5Dbr
Cbr
___
S2 =
3.5
(Eq. 3.4.17-4)
(Eq. 3.4.17-5)
m = 1.15 + co /(2cc)
for –1 < co /cc < 1
m = 1.3/(1 – co /cc)
for co /cc < –1
cc = distance from neutral axis to extreme fiber of the
element with the greatest compressive stress
co = distance from neutral axis to other extreme fiber of
the element
Distances to compressive fibers are negative and distances to tensile fibers are positive.
h = clear height of web (illustrated in Figure 3.4.18-1)
ϕy = 0.95
ϕy = 0.95
ϕb = 0.85
3.4.18 Compression in Elements of Beams
(Element in Bending in Own Plane)—
Flat Elements Supported on Both Edges
a. ϕFL = 1.3ϕyFcy
ϕb = 0.85
(Eq. 3.4.18-1)
for h /t < S1
[
h
b. ϕFL = ϕb Bbr – mDbr __
t
]
(Eq. 3.4.18-2)
for S1 < h /t < S2
____
ϕbk2√BbrE
c. ϕFL = _________
( mh / t )
(Eq. 3.4.18-3)
for h /t > S2
where
Bbr – ( ϕy /ϕb )1.3Fcy
S1 = _______________
mDbr
(Eq. 3.4.18-4)
k1Bbr
S2 = _____
mDbr
(Eq. 3.4.18-5)
January 2005
Figure 3.4.18-1
DIMENSION NOTATION
I-B-39
3.4.19 Compression in Elements of Beams
(Element in Bending in Own Plane)—
Flat Elements Supported on Both Edges
and With a Longitudinal Stiffener
The provisions of this Section apply for stiffeners located
at 0.4d1 from the flange as shown in Figure 3.4.19-1.
a. ϕFL = 1.3ϕyFcy
(Eq. 3.4.19-1)
3.4.20 Shear in Elements—Unstiffened Flat
Elements Supported on Both Edges
ϕyFty
__
a. ϕFL = _____
√3
(Eq. 3.4.20-1)
for h /t ≤ S1
[
h
b. ϕFL = ϕvp Bs – 1.25Ds __
t
]
(Eq. 3.4.20-2)
for S1 < h /t < S2
for h /t ≤ S1
[
h
b. ϕFL = ϕb Bbr – 0.29Dbr __
t
]
(Eq. 3.4.19-2)
ϕvπ2E
c. ϕFL = _________2
( 1.25h / t )
(Eq. 3.4.20-3)
for h /t ≥ S2
for S1 < h /t < S2
____
ϕbk2√BbrE
c. ϕFL = _________
0.29h / t
(Eq. 3.4.19-3)
h = clear web height (see Fig. 3.4.18-1)
for h /t ≥ S2
__
Bs – Fty ϕy / ( ϕvp √3 )
S1 = _________________
1.25Ds
where
Bbr – 1.3ϕyFcy / ϕb
S1 = ______________
0.29Dbr
k
B
1 br
S2 = _______
0.29Dbr
where
(Eq. 3.4.19-4)
(Eq. 3.4.19-5)
h = clear web height (see Fig. 3.4.19-1)
d1 = clear distance from the neutral axis to the compression flange (see Fig. 3.4.19-1)
ϕy = 0.95
ϕb = 0.85
(Eq. 3.4.20-4)
S2 = h/t at the intersection of Eqs. 3.4.20-2 and 3.4.20-3
ϕy = 0.95
ϕv = 0.80
ϕvp = 0.90
3.4.21 Shear in Elements – Stiffened Flat
Elements Supported on Both Edges
ϕyFty
__
a. ϕFL = ____
√3
(Eq. 3.4.21-1)
for ae /t ≤ S1
[
ae
b. ϕFL = 1.375ϕvp Bs – 1.25Ds __
t
]
(Eq. 3.4.21-2)
for S1 < ae /t < S2
1.375ϕvπ2E
c. ϕFL = __________
( 1.25ae / t )2
(Eq. 3.4.21-3)
for ae /t ≥ S2
where
a1
___________
ae = ____________
a1 2
1 + 0.7 __
a2
a1 = shorter dimension of rectangular panel
a2 = longer dimension of rectangular panel
ϕyFty
__
Bs – __________
√
1.375
ϕ
3
vp
S1 = ______________
(Eq. 3.4.21-4)
1.25Ds
√
Figure 3.4.19-1
DIMENSIONS h AND d1
( )
S2 = ae /t at the intersection of Eqs. 3.4.21-2 and
3.4.21-3
ϕy = 0.95
ϕv = 0.80
ϕvp = 0.90
I-B-40
January 2005
Section 4. Special Design Rules
4.1 Combined Axial Load and Bending
4.1.1 Combined Compression and Bending
A member subjected to axial compression and bending
moment loads shall be proportioned in accordance with the
following two formulas (both equations must be checked):
Cmy fby
fa _____________
Cmxfbx
__
+
+ ____________ ≤ 1.0
Fa Fbx( 1 – fa / Fex )
Fby ( 1– fa / Fey )
(Eq. 4.1.1-1)
fby
fa ___
f
___
+ bx + ___ ≤ 1.0
Fao
Fbx
Fby
(Eq. 4.1.1-2)
When fa /Fa < 0.15, the following Equation 4.1.1-3 shall
be permitted to be used in lieu of Equations 4.1.1-1 and
4.1.1-2:
fby
fa ___
f
__
+ bx + ___ ≤ 1.0
Fa
Fbx
Fby
(Eq. 4.1.1-3)
In Equations 4.1.1-1, 4.1.1-2, and 4.1.1-3, the subscripts
x and y, combined with subscripts b, m, and e indicate the
axis of bending about which a particular stress or design
parameter applies and
= average compressive stress on cross section
produced by the factored compressive load
fb
= maximum compressive bending stress produced by the factored transverse loads and/or
end moments
Fa
= design compressive stress ϕFL for member
considered as axially loaded column according
either to Sections 3.4.7 through 3.4.10 or 4.7.2
Fb
= design compressive stress ϕFL for member
considered as a beam according to either Sections 3.4.11 through 3.4.19 or 4.7.2
Cm
= 0.6 – 0.4(M1/M2) for members whose ends are
prevented from sway
= 0.85 for members whose ends are not prevented
from swaying
M1/M2 = ratio of end moments where M2 is the larger
of the two end moments and M1/M2 is positive
when the member is bent in reverse curvature,
negative when bent in single curvature
Fao
= design compressive stress ϕFL of an axially loaded
member considered as a short column according
to Section 4.7.2 without consideration of Section
3.4.7
Fe
= design elastic buckling stress
fa
ϕccπ2E
= _______
( k L /r )2
January 2005
r
L
k
= radius of gyration about the bending axis
= unsupported length in the plane of bending
= effective length factor in the plane of bending
4.1.2 Combined Tension and Bending
A member subjected to axial tension and bending shall
be proportioned in accordance with the formula:
fby
fa ___
f
__
+ bx + ___ ≤ 1.0
Ft
Fbx
Fby
(Eq. 4.1.2-1)
In Equation 4.1.2-1, the subscripts x and y, combined
with the subscript b indicate the axis of bending about
which a particular stress or design parameter applies and
where
fa = average tensile stress on cross section produced by
the factored tensile load
fb = maximum tensile bending stress produced by the
factored transverse loads and/or end moments
Fb = design tensile stress for the member as a beam
according to Section 3.4.2 through 3.4.4 and 4.7.3
Ft = design tensile stress for the member loaded only
axially according to Section 3.4.1
4.2 Torsion and Shear in Tubes
Design shear stresses in round or oval tubes subjected
to torsion or shear loads shall be determined from Section
3.4.20 with the ratio h/t given by
( t ) ( __RL )
Rb
h = 2.9 __
__
t
5/8
s
b
1/4
(Eq. 4.2-1)
where
Rb = mid-thickness radius of a round tube or maximum
mid-thickness radius of an oval tube
t = thickness of tube
Ls = length of tube between circumferential stiffeners,
or overall length if no circumferential stiffeners are
present
4.3 Torsion and Bending in Open Shapes
The stresses in open sections caused by torsion due to
twisting moments applied directly or due to lateral loads
or supports not in the plane of the shear center of open
sections shall include shear, flexural and warping stresses.
The stresses thus computed plus those due to bending shall
not exceed the appropriate design stress for the type of
stress in the element considered.
I-B-41
4.4 Combined Shear, Compression,
and Bending
αs = 3.5, for stiffener consisting of member on only one
side of web
Design combinations of shear, compression, and bending
shall be determined from either of the following formulas:
a. For walls of curved surfaces or round tubular members:
(F )
fa
f
f 2
__
+ __b + __s ≤ 1.0
Fa
Fb
(Eq. 4.4-1)
s
b. For webs of rectilinear shapes, plates of built-up girders
or similar members:
(F) ( )
fa
f
__
+ __b
Fa
2
b
f 2
+ __s ≤ 1.0
Fs
(Eq. 4.4-2)
where
fa = average compressive stress produced by factored
axial compressive load
Fa = design compressive stress for members subjected
to compression only
fb = maximum bending stress (compression) produced
by applied factored bending moment
Fb = design bending stress (compression) for members
subjected to bending only
fs = shear stress caused by factored torsion or transverse shear loads
Fs = design shear stress for members subjected only to
torsion or shear
4.5 Longitudinal Stiffeners for Webs
If a longitudinal stiffener is used on a beam web, it shall
be located so that the distance from the toe of the compression flange to the centroid of the stiffener is 0.4 of the distance from the toe of the compression flange to the neutral
axis of the beam. The longitudinal stiffener shall have a
moment of inertia, about the web of the beam, not less than
that given by the expression:
0.02αs fth
I = _________
3
h
E
[(
)( h )
2
6A
1 + ___h __s + 0.4
ht
]
(Eq. 4.5-1)
where
Ah = gross cross sectional area of longitudinal stiffener
f = compressive stress at toe of flange
h = clear height of web between flanges
Ih = moment of inertia of the longitudinal stiffener. For
a stiffener consisting of equal members on both
sides of the web, the moment of inertia Ih shall be
the sum of the moments of inertia about the centerline of the web. For a stiffener consisting of a
member on one side only, the moment of inertia
shall be taken about the face of the web in contact
with the stiffener.
s = distance between transverse stiffeners
t = thickness of the web
αs = 1, for stiffener consisting of equal members on
both sides of web
I-B-42
4.6 Transverse Stiffeners for Webs
When a stiffener is composed of a pair of members, one
on each side of the web, the stiffener spacing s shall be
the clear distance between the pairs of stiffeners. When a
stiffener is composed of a member on one side only of the
web, the stiffener spacing s shall be the distance between
rivet lines or other connecting lines.
For a stiffener composed of members of equal size on
each side of the web, the moment of inertia of the stiffener
shall be computed about the centerline of the web. For a stiffener composed of a member on one side only of the web, the
moment of inertia of the stiffener shall be computed about
the face of the web in contact with the stiffener.
In the determination of the required moment of inertia
of stiffeners, the distance h shall be taken as the full clear
height of the web regardless of whether or not a longitudinal stiffener is present.
Unless the outer edge of a stiffener is continuously stiffened, its thickness shall not be less than 1/12th the clear
width of the outstanding leg.
4.6.1 Stiffeners for Web Shear
Stiffeners applied to beam webs to resist shear buckling
shall have a moment of inertia not less than the value given
by the following expression:
s ≤ 0.4,
__
0.55Vh2
Is = _______ __s
E
h
s > 0.4,
__
0.088Vh2 h
Is = ________ __
s
E
h
h
( )
(Eq. 4.6.1-1)
( )
(Eq. 4.6.1-2)
where
h = clear height of web
Is = moment of inertia of stiffener
s = stiffener spacing
V = unfactored shear force on web at stiffener location
Stiffeners shall extend from flange to flange but need
not be connected to either flange.
4.6.2 Bearing Stiffeners
Bearing stiffeners at points of support of concentrated
loads shall be connected to the web by enough rivets, or
other means, to transmit the load. Such stiffeners shall be
fitted to form a tight and uniform bearing against the loaded
flanges, unless welds, designed to transmit the full reaction
or load, are provided between flange and stiffener.
Only that part of a stiffener cross section which lies
outside the fillet of the flange angle shall be considered as
effective in bearing.
January 2005
The moment of inertia of the bearing stiffener shall not
be less than that given by the following expression:
1.95Pbsh2
Ib = Is + ________
π2E
(Eq. 4.6.2-1)
where
E = compressive modulus of elasticity
h = clear height of web between flanges
Ib = required moment of inertia of bearing stiffener
Is = moment of inertia required to resist shear buckling
Pbs = concentrated load on stiffener
4.7 Effects of Local Buckling on
Member Performance
4.7.1 Local Buckling Stresses
Where local buckling stress values are required to be calculated, the critical stresses, Fcr, given in Table 4.7.1-1 shall
be used. For cases not covered in Table 4.7.1-1, the value of
Fcr shall be determined using the expression for ϕFL in the
appropriate subsection of Section 3.4 for the case b/t > S2
with the resistance factors ϕ taken as 1.0.
Table 4.7.1-1
Section
Local Buckling Stress, Fcr
3.4.8 and 3.4.15
π2E
________
3.4.9 and 3.4.16
π2E
________
3.4.9.1 and 3.4.16.2
( ϕFL )
______
( 5.1b / t )2
π2E
_______
3.4.19
4.7.3 Weighted Average Bending Strength
As an alternative to using the least of the strengths of a
section’s elements for the bending strength of the section,
the strength shall be determined in accordance with this
Section.
The design stress in elements with stiffeners shall not
exceed the design stress in an intermediate stiffener or an
edge stiffener.
For shapes not subject to lateral buckling, the design
bending moment Ma is the lesser of the design compressive
bending moment and the design tensile bending moment.
The design compressive bending moment is
(Eq. 4.7.3-1)
where
ϕyFcy
( mh / t )2
πE
_________
for y
2
( 0.65h / t )2
As an alternative to using the least of the design compressive stresses of a section’s elements for the design
axial compressive stress of the section, the weighted average design axial compressive stress shall be determined in
accordance with this Section.
The weighted average design axial compressive stress
of a section is the average design stress of the section’s elements, where the design stress for each element is weighted
by the ratio of the area of the element to the total area of
the section.
The design stress in elements with stiffeners shall not
exceed the design stress in an intermediate stiffener or an
edge stiffener.
The design axial compressive stress of the section shall
not exceed that given by Section 3.4.7.
Mac = Fcf If / ccf + Fcw Iw / ccw
( 1.6b / t )2
2
3.4.18
4.7.2 Weighted Average Axial Compressive Stress
NA
π2E
_________
( 0.29h / t )2
= h/2
Fcf = the design compressive stress for the flat elements
in uniform compression
Fcw = the design compressive stress for the flat elements
in bending in their own plane
If = the moment of inertia of the flange group about
the neutral axis of the entire section. The flange
group consists of the flat elements in uniform
compression and the flat elements in uniform tension and their edge or intermediate stiffeners.
Iw = the moment of inertia of the web group about the
neutral axis of the entire section. The web group
consists of the flat elements in bending in their
own plane and their intermediate stiffeners.
ccf = the distance from the centerline of the compression
flange to the neutral axis of the entire cross-section
ccw = the distance from the web group’s extreme compression fiber to the neutral axis of the entire
cross-section
(See Figure 4.7.3-1).
January 2005
I-B-43
If there are stiffeners located farther than the compression flange from the neutral axis of the entire cross-section,
the design compressive bending moment shall not exceed
ϕyFcf If / ccs + Fcw Iw / ccw
(Eq. 4.7.3-2)
where
ccs = the distance from the neutral axis of the entire
cross-section to the extreme fiber of compression
flange stiffeners
The design tensile bending moment is
Mat = Ftf If / ctf + Ftw Iw / ctw
(Eq. 4.7.3-3)
If , Iw = the same as above
ctf = the distance from the extreme tension fiber to the
neutral axis of the entire cross-section
ctw = the distance from the web group’s extreme tension fiber to the neutral axis of the entire crosssection
For shapes subject to lateral buckling, the design bending moment Ma is the least of the design compressive bending moment Mac, the design tensile bending moment Mat,
and Fb S where
Fb = design compression bending stress given by Section
3.4.11 or 3.4.14
S = section modulus of the entire cross-section
where
Ftf
Ftw
= the design tensile stress for the flat elements in
uniform tension
= the design tensile stress for the flat elements in
bending in their own plane
Figure 4.7.3-1
I-B-44
January 2005
4.7.4 Effect of Local Buckling on
Column Strength
4.7.6 Effective Width for Calculation of
Bending Deflection
An additional limitation shall be placed on the design
stress for columns in which local buckling of the cross
section occurs at a stress that is less than the calculated
flexural buckling stress of the column, assuming that the
elements are not buckled. The design stress ϕFL shall not
exceed the value given by
The effective width concept shall be used to determine
an effective section for the moment of inertia used to calculate deflections.
For sections containing elements covered in Sections
3.4.15, 3.4.16, 3.4.18, or 3.4.19 with b/t or h/t values
exceeding 1.65S2 and elements covered in Sections 3.4.16.2
or 3.4.16.3 with Fcr < fa, the effective width be of a thin element subjected to direct compression stresses is:
ϕFrc = ϕuFec1/3Fcr2 /3
(Eq. 4.7.4-1)
For ϕuFcr < ϕFL
(Eq. 4.7.4-2)
If fa ≤ Fcr , be = b
(Eq. 4.7.6-1)
_____
where
If fa > Fcr , be = b√ Fcr /fa
ϕFL = design stress for column given in Section 3.4.7
Fcr = element local buckling stress given in Section 4.7.1
πE
Fec = ______
( kL /r )2
ϕFrc = design stress for column with buckled elements
ϕu = 0.85
2
The design stress also shall not exceed the design stress
given in Section 4.7.2.
4.7.5 Effect of Local Buckling on Beam Strength
The design compressive bending stress shall be reduced
for single web beams whose flanges consist of thin, flat
elements supported on one edge and in which local buckling of the cross section occurs at a stress that is less than
the lateral buckling stress of the beam, calculated assuming
that the elements are not buckled. The design stress shall
not exceed the value given by
ϕFrb = ϕy( Feb ) ( Fcr )
(Eq. 4.7.5-1)
For ϕyFcr < ϕFL
(Eq. 4.7.5-2)
1/3
2/3
(Eq. 4.7.6-2)
where
be = effective width of flat element to be used in deflection calculations
b = width of element as defined in Sections referred to
above
Fcr = local buckling stress for element from Section 4.7.1
fa = compressive stress for element due to applied
unfactored loads
The same expression is used to calculate the effective
width on the compression side of a web in bending, with
the maximum compressive bending stress due to the applied
loads, fb, replacing fa. In this case the effective web area is to
be placed next to the compression flange.
4.7.7 Web Crippling of Flat Webs
For interior reactions and concentrated loads:
ϕwCwa ( N + Cw1 )
ϕPL = _____________
Cwb
(Eq. 4.7.7-1)
For end reactions and concentrated loads:
where
Fcr = element local buckling stress given in Section 4.7.1
Feb = elastic lateral buckling stress of beam calculated
using Eq. 3.4.11-3 with ϕb = 1.0 or the equations
of Section 4.9
ϕFrb = design stress for beam with buckled elements
ϕFL = design stress for beam given in Section 3.4.11 or
Section 4.9
ϕy = 0.95
The design stress also shall not exceed the design stress
for the section given in Section 4.7.2.
January 2005
1.2ϕwCwa ( N + Cw2 )
ϕPL = ________________
Cwb
where
(Eq. 4.7.7-2)
____
Cwa = t 2 sin θ ( 0.46Fcy + 0.02√ EFcy )
(Eq. 4.7.7-3)
Cwb = Cw3 + Ri ( 1 – cos θ )
(Eq. 4.7.7-4)
Cw1 = 5.4 in. (140 mm)
Cw2 = 1.3 in. (33 mm)
Cw3 = 0.4 in. (10 mm)
E = compressive modulus of elasticity of the web
Fcy = compressive yield strength of the web
ϕ PL = design transverse force per web for flat webs
N = length of bearing at the reaction or concentrated
load
Ri : for shapes made by bending, Ri = bend radius at
juncture of the flange and web measured to the inside of
the bend; for extruded shapes, Ri = 0
I-B-45
t = web thickness
θ = angle between the plane of web and the plane of
the bearing surface (θ < 90 degrees)
ϕw = resistance factor = 0.90
4.7.8 Combined Web Crippling and Bending for
Flat Webs
Design combinations of interior reactions and concentrated loads and bending shall be determined from the following formula:
( ϕM ) ( ) ≤ 1.0
M
____
1.5
a
P
+ ___
ϕPL
1.5
(Eq. 4.7.8-1)
where
M = bending moment due to factored loads applied to
the member
ϕMa = design bending moment for the member if bending moment alone is applied to the member
P = applied interior reaction or concentrated load due
to factored loads per web for flat webs
ϕPL = design interior reaction or concentrated load per
web for flat webs calculated according to Section
4.7.7.
= the allowable stress range
Srd
= Cf N –1/m
(Eq. 4.8.1-2)
Cf , m = constants from Table 4.8.1-1 and shown in Figure 4.8.1-1
N
= the number of cycles to failure
If the applied stress range, Sra, is less than the constant
amplitude fatigue limit as given in Table 4.8.1-1, then no
further fatigue consideration shall be needed. The allowable stress range, Srd shall not be less than the value from
Equation 4.8.1-2 when N = 5 × 106 cycles and shall not be
greater than the value from Equation 4.8.1-2 when N = 105
cycles.
4.8.2 Variable Amplitude Loading
If the maximum stress range in the spectrum at unfactored loads is less than the fatigue limit, then no further
fatigue assessment shall be needed.
For variable amplitude loading:
Sre ≤ Srd
(Eq. 4.8.2-1)
where
4.8 Fatigue
Welded details, mechanically fastened joints and base
material of aluminum alloys subjected to repeated fluctuations of stress shall meet all the static requirements of this
Specification as well as the fatigue requirements of this Section. Fatigue design of castings and associated details shall
be made by testing in accordance with Section 9.
Categories of details for fatigue design parameters shall
be chosen from Figure 4.8-1 and Table 4.8-1.
The maximum and minimum stresses used to calculate
the stress range are nominal stresses caused by unfactored loads and determined by standard elastic methods.
Stresses perpendicular to the expected plane of cracking
shall be used.
4.8.1 Constant Amplitude Loading
Sre
= equivalent stress range
Sre
=
(∑ )
Ns
i=1
αi S rim
1/m
(Eq. 4.8.2-2)
Srd
= the allowable stress range at unfactored loads
Srd
= Cf N–1/m
(Eq. 4.8.2-3)
αi
= number of cycles in the spectrum of the ith stress
range divided by the total number of cycles
Sri = the ith stress range in the spectrum
Cf , m = constants from Table 4.8.1-1 and shown in
Figure 4.8.1-1
NS = the number of stress ranges in the spectrum
N
= the number of cycles to failure
The allowable stress range Srd shall not be greater than
the value from Equation 4.8.2-3 when N = 105 cycles.
For constant amplitude loading
Sra ≤ Srd
Srd
(Eq. 4.8.1-1)
where
Sra
I-B-46
= applied stress range at service loads, the algebraic
difference between the minimum and maximum
calculated stress in the member or detail
January 2005
Table 4.8-1
STRESS CATEGORY
General Condition
Detail
Detail
Category(1)
Fatigue Design
Details(2)
Plain Material
Base metal with rolled, extruded, drawn, or cold finished surfaces; cut
or sheared surfaces with ANSI/ASME B46.1 surface roughness of
1000μ in. (25μm) or less.
A
1, 2
Built up Members
Base metal and weld metal in members, without attachments, built-up
of plates or shapes connected by continuous full- or partial-penetration
groove welds or continuous fillet welds parallel to the direction of
applied stress.
B
3, 4, 5
Calculated flexural stress, fb, in base metal at toe of welds on girder
webs or flanges adjacent to welded transverse stiffeners.
C
6, 21
Base metal at end of partial-length welded cover plates having square
or tapered ends, with or without welds across the ends.
E
5
Rs ≤ 0
0 < Rs < 0.5
0.5 ≤ Rs
B
D
E
7
7
7
Base metal at the gross section of slip-critical connections and at the
net section of bearing connections, where the joint configuration results
in out-of-plane bending in connected material.
E
8
Base metal at intermittent fillet welds.
E
Base metal at junction of axially loaded members with fillet welded end
connections. Welds shall be disposed about the axis of the members so
as to balance weld stresses.
E
15, 17
Weld metal of continuous or intermittent longitudinal or transverse fillet
welds.
F
5, 15,18
Base metal and weld metal at full-penetration groove welded splices of
parts of similar cross section ground flush, with grinding in the direction
of applied stress and with weld soundness established by radiographic
or ultrasonic inspection.
B
9, 10
Base metal and weld metal at full-penetration groove welded splices at
transitions in width or thickness, with welds ground to slopes no steeper
than 1 to 2.5, with grinding in the direction of applied stress, and with
weld soundness established by radiographic or ultrasonic inspection.
B
11, 12
Base metal and weld metal at full-penetration groove welded splices,
with or without transitions having slopes no greater than 1 to 2.5, when
reinforcement is not removed and/or weld soundness is not established
by radiographic or ultrasonic inspection.
C
9, 10, 11, 12
Base metal and weld metal at full-penetration groove welds with permanent backing
E
22
Mechanically Fastened
Fillet Welds
Groove Welds
Base metal at the gross section of slip-critical connections and at the
net section of bearing connections, where the joint configuration does
not result in out-of-plane bending in the connected material and the
stress ratio (the ratio of minimum stress to maximum stress)3 Rs is
See last page of this table for footnotes.
January 2005
I-B-47
Table 4.8-1
STRESS CATEGORY
(Continued)
General Condition
Detail
Detail
Category(1)
Fatigue Design
Details(2)
Attachments
Base metal detail of any length attached by groove welds subject to
transverse and/or longitudinal loading, when the detail embodies a transition radius, R, not less than 2 in. (50 mm) and with the weld termination ground smooth:
R ≥ 24 in. (610 mm)
24 in. > R ≥ 6 in. (150 mm)
6 in. > R ≥ 2 in. (50 mm)
B
C
D
13
13
13
Base metal at a detail attached by groove welds or fillet welds, where
the detail dimension parallel to the direction of stress, a, is less than
2 in. (50 mm)
C
19
D
E
14
14, 19, 20
B
C
D
16
16
16
Base metal at detail attached by groove welds or fillet welds subject to
longitudinal loading, with transition radius, if any, less than 2 in.
(50 mm):
2 in. (50 mm ) ≤ a ≤ 12b or 4 in. (100 mm)
a > 12b or 4 in. (100 mm)
where
a = detail dimension parallel to the direction of stress
b = detail dimension normal to the direction of stress and the surface of
the base metal
Base metal at a detail of any length attached by fillet welds or partialpenetration groove welds in the direction parallel to the stress, when the
detail embodies a transition radius, R, not less than 2 in. (50 mm) and
weld termination ground smooth:
R ≥ 24 in. (610 mm)
24 in. (610 mm) > R ≥ 6 in. (150 mm)
6 in. (150 mm) > R ≥ 2 in. (50 mm)
1. See Table 4.8.1-1. All stresses are T and Rev., where “T” signifies range in tensile stress only; “Rev.” signifies a range involving reversal of
tensile or compressive stress; except Category F where stress range is in shear including shear stress reversal.
2. See Figure 4.8-1. These examples are provided as guidelines and are not intended to exclude other reasonably similar situations.
3. Tensile stresses are considered to be positive and compressive stresses are considered to be negative.
I-B-48
January 2005
Figure 4.8-1
FATIGUE DESIGN DETAILS
January 2005
I-B-49
Figure 4.8-1
FATIGUE DESIGN DETAILS
(continued)
I-B-50
January 2005
Table 4.8.1-1
CONSTANTS FOR S-N CURVES1
Cf
Detail Category3
ksi
MPa
A
96.5
665
130
B
C
D
E
F
m
Fatigue Limit2
ksi
MPa
6.85
10.2
70
900
4.84
5.4
37
278
1920
3.64
4.0
28
157
1080
3.73
2.5
17
160
1100
3.45
1.8
13
174
1200
3.42
1.9
13
1. Different constants are to be used for calculations in ksi and MPa
2. Fatigue limit is based on N = 5x106
3. See Table 4.8-1
Figure 4.8.1-1
SCHEMATIC FATIGUE CURVE
January 2005
I-B-51
4.9 Compression in Single Web Beams
Including Single Web Beams With
Tubular Portions
For compression in single web beams including single
web beams with tubular portions, analysis shall be conducted using either the provisions of Section 3.4.11 or by
replacing ry in Section 3.4.11 with rye determined in accordance with Sections 4.9.1 through 4.9.3. Sections with the
tension flange partially or fully braced and with the compression flange laterally unbraced shall be designed using
Section 4.9 without consideration of tensile flange restraint
or another rational method of analysis.
4.9.1 Doubly Symmetric Sections and Sections
Symmetric About the Bending Axis
For checking beam sections at brace or support points or
between brace or support points of beam spans subjected
to end moment only or to transverse loads applied at the
neutral axis of the beam:
____________________
________________
( )
√ √
Iyd
kyLb 2
J ____
1 ___
rye = ___
1 + 0.152 __
Iy d
1.7 Sc
(Eq. 4.9.1-1)
For checking beam spans between brace or support
points of beams subjected to transverse loads applied on
the top or bottom flange (where the load is free to move
laterally with the beam if the beam buckles):
_______________________________
__________________
√ [
√
( )]
Iy d
kyLb 2
J ____
1 ___
rye = ___
± 0.5 + 1.25 + 0.152 __
Iy d
1.7 Sc
(Eq. 4.9.1-2)
The minus sign in front of the term ‘0.5’ shall be used
when the load is on a flange acting towards the shear center; the plus sign shall be used when the load is on a flange
acting away from the shear center.
In the above equations
y-axis is the centroidal symmetry or principal axis
such that the tension flange has a positive y coordinate and bending is about the x-axis
rye = effective radius of gyration
Iy = moment of inertia of beam about axis parallel to web
Sc = section modulus of beam, compression side
J = torsion constant of beam. For non-tubular open sections an approximate value of J shall be calculated by
assuming the section to be composed of rectangles
and letting J equal the sum of the terms bt3/3 for each
rectangle where b is the larger dimension. The term
for each rectangle whose b/t ratio is less than 10 shall
be computed by the expression (1/3 – 0.2t/b) bt3.
For sections containing open parts and tubular portions, J shall be taken as the sum of J for the open
parts and the tubular parts.
I-B-52
ky = effective length coefficient for compression flange
about the y-axis. ky shall not be taken less than 1.
Lb = length of the beam between bracing points or between
a brace point and the free end of a cantilever beam.
Bracing points are the points at which the compression flange is restrained against lateral movement or
the cross section is restrained against twisting
d = depth of beam.
4.9.2 Singly Symmetric Sections Unsymmetric
about the Bending Axis
For a beam that is unsymmetric about the bending axis,
the rye in Section 4.9.1 is calculated by taking Iy, Sc, and J
as though both flanges were the same as the compression
flange with the overall depth remaining the same.
4.9.3 Singly Symmetric Sections Symmetric or
Unsymmetric about the Bending Axis,
Doubly Symmetric Sections and Sections
Without an Axis of Symmetry
For a loading that does not cause torsion or lateral bending a more accurate value of rye is determined according to
this Section. If the loading causes torsion and/or lateral bending, warping stress and/or lateral bending flexural stress, the
provisions of Section 4.3 shall apply.
√
____
Lb ___
Me
rye = ____
(Eq. 4.9.3-1)
1.2π ESc
where
Me = the elastic critical moment determined as follows:
___________
( )]
[ √
Fet
Me = AFey U + U2 + r o2 ___
Fey
(Eq. 4.9.3-2)
Me for cantilever beams shall be determined by rational
analysis unless the free end is braced or if the beam loading is covered in Section 4.9.4. References for rational
analysis are given in the Commentary.
In the above equations
y-axis is the centroidal symmetry or principal axis such
that the tension flange has a positive y coordinate and
bending is about the x-axis
A = cross-sectional area
C1 and C2 = coefficients to be taken from Section 4.9.4,
or, for cases not covered in Section 4.9.4,
determined by rational analysis
Cw = torsional warping constant of the cross section
E = compressive modulus of elasticity (see Table 3.3-1)
πE
Fey = ______
kyLb 2
____
ry
2
( )
π EC
F = 1 ( GJ +
KL) )
(
Ar
et
____
2
o
2
w
______
t
t
2
(Eq. 4.9.3-3)
(Eq. 4.9.3-4)
January 2005
G = shear modulus = 3E/8
g0 = distance from the shear center to the point of
application of the load; taken as + when the load
is applied directed away from the shear center and
– when the load is directed towards the shear center. When there is no transverse load (pure moment
cases) g0 = 0.
Iy = moment of inertia of the section about the y axis
J = torsion constant (See definition in Section 4.9.1)
j
1
= ___
2Ix
(
)
∫y dA + ∫ yx dA – y
2
3
A
A
o
4.9.4.1 Doubly Symmetric Sections
Cb:
(Eq. 4.9.4.1-1)
where
MMAX = absolute value of maximum moment in the
unbraced beam segment
MA = absolute value of moment at quarter point of
the unbraced beam segment
(Eq. 4.9.3-5)
MB = absolute value of moment at mid-point of the
unbraced beam segment
For doubly symmetric I sections, j = 0
For singly symmetric I sections, as an alternative to
equation 4.9.3-5,
)[ ( ) ]
(
2Icy
Iy 2
j = 0.45df ___ –1 1 – __
Iy
Ix
________________
ro
= √r + r + x + y
2
x
2
y
2
o
2
o
MC = absolute value of moment at three-quarter point
of the unbraced beam segment
Cb values for doubly symmetric section cantilever beams
unbraced at the free end are given in Section 4.9.4.4. Cb
values for cantilever beams braced at the free end can
be evaluated using Eq. 4.9.4.1-1.
(Eq. 4.9.3-6)
where Icy is the moment of inertia of the compression flange
taken about the web, Ix and Iy are the moments of inertia
of the entire section about the x- and y-axes and df is the
distance between the flange centroids or for T-sections df
is the distance between the flange centroid and the tip of
the stem.
For singly symmetric I sections where the smaller flange
is not less than 80 percent of the area of the larger flange j
shall be permitted to be taken as – yo.
ky
= effective length coefficient for compression flange
about the y-axis. ky shall not be taken less than 1.0.
Lt
= unbraced length for twisting.
C1:
When the moments vary linearly between the ends
of the unbraced segment C1 = 0. For some special
cases the values of C1 are given in Section 4.9.4.3.
For other variations, unless more accurate values are
available, C1 shall be taken as 0.5.
C2:
Since j = 0, a value of C2 is not needed.
4.9.4.2 Singly Symmetric Sections
Cb:
(Eq. 4.9.3-7)
= C1g0 - C2 j
xo
yo
= x - coordinate of the shear center
= y - coordinate of the shear center
(Eq. 4.9.3-8)
The origin of the coordinate system is the intersection
of the principal axes.
C1:
When the moments vary linearly between the ends of
the unbraced segment C1 = 0. For some special cases
the values of C1 are given in Section 4.9.4.3. For other
cases C1 shall be determined by rational analysis.
C2:
When the moments vary linearly between the ends
of the unbraced segment C2 = 1. For some special
cases the values of C2 are given in Section 4.9.4.3.
For other cases C2 shall be determined by rational
analysis.
4.9.4 Lateral Buckling Coefficients
For cases not covered in Sections 4.9.4.3 and 4.9.4.4,
coefficients Cb, C1 and C2 shall be determined as specified
in Section 4.9.4.1 or 4.9.4.2.
January 2005
For sections with Icy /Iy less than or equal to 0.1 or
greater than or equal to 0.9, Cb = 1.0
For sections with Icy /Iy greater than 0.1 and less than
0.9, the value of Cb shall be determined according to
Eq. 4.9.4.1-1.
When MMAX produces compression on the larger flange
and the smaller flange is also subjected to compression in the unbraced length, then the member shall
be checked at the location of MMAX as well as at the
location where the smaller flange is subjected to its
maximum compression. Cb at the location of MMAX
shall be calculated using Eq. 4.9.4.1-1. Cb for the
location where the smaller flange is subjected to its
maximum compression shall be taken as 1.67.
= Polar radius of gyration of the cross-section
about the shear center.
rx , ry = actual radii of gyration of the cross-section
about the centroidal principal axes
Sc
= section modulus for the extreme compression
fiber for bending about the x-axis
U
12.5MMAX
Cb = _________________________
2.5MMAX + 3MA + 4MB + 3MC
I-B-53
4.9.4.3 Special Cases—Doubly or Singly
Symmetric Sections
For simply supported beams with loadings listed below,
the following Cb, C1 and C2 values shall be used, except for
sections with Icy /Iy less than or equal to 0.1 or greater than
or equal to 0.9 where Cb shall be taken as 1.0:
a. Uniformly distributed load over the entire span
Cb = 1.13, C1 = 0.41Cb, C2 = 0.47Cb
b. One concentrated load placed at a distance aL from one
of the ends of span
Cb = 1.75 – 1.6a( 1 – a )
(Eq. 4.9.4.3-1)
Cb
C1 = _______
sin2πa
a( 1-a )π2
(Eq. 4.9.4.3-2)
Cb – C1
C2 = ______
2
(Eq. 4.9.4.3-3)
where
Ac = area of compression element (compression flange
plus 1/3 of the area of the web between the compression flange and the neutral axis
E = compressive modulus of elasticity
Iyc = moment of inertia of compression element about
an axis parallel to the vertical web
βs = spring constant (transverse force applied to the
compression flange of the member of unit length
divided by the deflection due to the force)
4.11 Single Angles in Flexure
The strength of a single angle in flexure (Mn) is given in
this Section. The design strength is ϕMn, where ϕ = 0.95
for yield limit states and ϕ = 0.85 for all other limit states.
a. For local buckling:
1) If a leg tip is a point of maximum compression (Figure 4.11-1):
c. Two concentrated loads placed symmetrically at a distance aL from each end of span
Cb = 1 + 2.8a3
(Eq. 4.9.4.3-4)
Figure 4.11-1
2C
C1 = ____2b sin2πa
aπ
(Eq. 4.9.4.3-5)
C
C2 = ( 1 – a )Cb – ___1
2
(Eq. 4.9.4.3-6)
Mn = 1.3FcyS
for b/t ≤ S1
Mn = [ Bbr – 4Dbr( b/t ) ]Sc
4.9.4.4 Cantilever Beams
For cantilever beams braced at the support and unbraced
at the free end Cb shall be taken as follows:
Concentrated load at free end
applied at the centroid
Cb = 1.28, ky = 1.0
Cb = 2.08, ky = 1.0
Uniform bending moment
Cb = 0.50, ky = 2.1
4.10 Compression in Elastically
Supported Flanges
for S1 < b/t < S2
Mn = π2ESc/( 4( b/t ) )2
( )
I-B-54
(Eq. 4.11-3)
for b/t ≥ S2
S1 = ( Bbr – 1.3Fcy )/ ( 4Dbr )
(Eq. 4.11-4)
S2 = Cbr /4
(Eq. 4.11-5)
2) If a leg is in uniform compression (Figure 4.11-2):
Design compressive stresses in elastically supported
flanges, such as the compression flange of a standing seam
roof or of a hat-shaped beam loaded with the two flanges
in compression, shall be determined from Section 3.4.11
with the following effective value of Lb /ry, substituted in
the formulas for design stress.
EA
Lb
Effective __
ry = 2.7 βsIyc
(Eq. 4.11-2)
where
Uniform transverse load applied
at the centroid
2 1/4
c
____
(Eq. 4.11-1)
(Eq. 4.10-1)
Figure 4.11-2
Mn = Fcy Sc
(Eq. 4.11-6)
for b/t ≤ S1
January 2005
Mn = [ Bp – 5.1Dp( b/t ) ]Sc
(Eq. 4.11-7)
for S1 < b/t < S2
Mn = π2ESc/( 5.1( b/t ) )2
(Eq. 4.11-8)
a. Angles with continuous lateral-torsional restraint:
Mn is the lesser of:
1) local buckling strength determined by Section
4.11a.
2) yield strength determined by Section 4.11b.
for b/t ≥ S2
where
S1 = ( Bp – Fcy )/ ( 5.1Dp )
(Eq. 4.11-9)
S2 = Cp /5.1
(Eq. 4.11-10)
b. For yielding (Figure 4.11-3):
b. Equal leg angles with lateral-torsional restraint only
at the point of maximum moment: Strengths shall be
calculated with Sc being the geometric section modulus. Mn is the least of:
1) local buckling strength determined by Section
4.11a.
2) yield strength determined by Section 4.11b.
3) If the leg tip is in compression, lateral-torsional
buckling strength determined by Section 4.11c
with
0.82Eb4tCb ______________
Me = _________
[ √1 + 0.78 ( Lbt / b2 )2 – 1 ] (Eq. 4.11.1-1)
L 2b
If the leg tip is in tension, lateral-torsional buckling
strength determined by Section 4.11c with
Figure 4.11-3
Mn = 1.3My
0.82Eb4tCb ______________
Me = _________
[ √1 + 0.78 ( Lbt / b2 )2 + 1 ] (Eq. 4.11.1-2)
L 2b
(Eq. 4.11-11)
where My = yield moment about the axis of bending.
c. Equal leg angles without lateral-torsional restraint:
Strengths shall be calculated with Sc being 0.80 of the
geometric section modulus.
If the leg tip is in compression, Mn is the lesser of:
c. For lateral-torsional buckling:
for Me ≤ My , Mn = ( 0.92 – 0.17Me /My )Me (Eq. 4.11-12)
______
for Me > My , Mn = ( 1.92 – 1.17√My /Me )My ≤ 1.3My
(Eq. 4.11-13)
where Me = elastic lateral-torsional buckling moment
from Section 4.11.1 or 4.11.2 as applicable.
Cb shall be determined in accordance with Section
4.9.4.1 but shall not exceed 1.5.
4.11.1 Bending About Geometric Axes
Bending about a geometric axis is shown in Figure
4.11.1-1.
1) local buckling strength determined by Section
4.11a(1)
2) lateral-torsional buckling determined by Section
4.11c with
0.66Eb4tCb ______________
Me = _________
[ √1 + 0.78 ( Lbt / b2 )2 – 1 ] (Eq. 4.11.1-3)
L 2b
If the leg tip is in tension, Mn is the lesser of:
1) yield strength determined by Section 4.11b
2) lateral-torsional buckling determined by Section
4.11c with
0.66Eb4tCb ______________
Me = _________
[ √1 + 0.78 ( Lbt / b2 )2 + 1 ] (Eq. 4.11.1-4)
L 2b
d. Unequal leg angles without lateral-torsional restraint:
moments about the geometric axes shall be resolved
into moments about the principal axes and the angle
shall be designed as an angle bent about a principal
axis (Section 4.11.2).
4.11.2 Bending About Principal Axes
Subsections a.
and b.
Subsection c.
Figure 4.11.1-1
January 2005
Bending about principal axes is shown in Figure 4.11.2-1.
a. Equal leg angles, major axis bending: Mn is the lesser
of:
1) local buckling strength determined by
Section 4.11a
I-B-55
b. For tapered thickness elements with the thin edge supported and the thick edge free, the slenderness ratio is
b
___
tavg
c. For tapered thickness elements supported on both
edges, the slenderness ratio is
( )
Minor Axis
Bending
Major Axis
Bending
( tb )
___
Figure 4.11.2-1
avg
2) lateral-torsional buckling strength determined by
Section 4.11c, with
0.46Cb Eb2t2
Me = __________
Lb
(Eq. 4.11.2-1)
b. Unequal leg angles, major axis bending: Mn is the
lesser of:
1) local buckling strength determined by Section
4.11a for the leg with its tip in compression
2) lateral-torsional strength determined by Section
4.11c, with
[
________________
I
Me = 4.9E __z2 Cb √βw2 + 0.052( Lbt / rz )2 + βw
Lb
where
b = width of the element
tmax + tmin
tavg = ________
2
= the average thickness of the element
tmin = lesser thickness
tmax = greater thickness
tmax – tmin
δ = ________
tmin
]
(Eq. 4.11.2-2)
Iz = minor principal axis moment of inertia
rz = minor principal axis radius of gyration
[∫
]
1 z( w2 + z2 )dA – 2z ,
βw = __
o
Iw
βw is a section property for unequal leg angles and is
positive when the short leg is in compression and negative
when the long leg is in compression. (See the Commentary
for values for common angle sizes and equations for determining βw.) If the long leg is in compression anywhere
along the unbraced length of the angle, βw is negative.
zo = coordinate along the z-axis of the shear center with
respect to the centroid
Iw = major principal axis moment of inertia
c. Equal and unequal leg angles, minor axis bending:
1) If the leg tips are in compression, Mn is the lesser
of the local buckling strength determined by Section
4.11a(1) and the yield strength determined by Section 4.11b.
2) If the leg tips are in tension, Mn is the yield strength
determined by Section 4.11b.
4.12 Tapered Thickness Elements
For uniform compression on elements with linearly
varying thickness where δ < 2.0:
a. For tapered thickness elements with the thick edge supported and the thin edge free, the slenderness ratio is
b
(1 – 0.12δ) ___
tavg
( )
I-B-56
Figure 4.12-1
(Eq. 4.11.2-3)
4.13 Compressive Strength of
Beam Elements
As an alternative to Section 3, the compressive strength
of elements of beams composed entirely of flat elements
addressed by Sections 3.4.15, 3.4.16, 3.4.16.2, 3.4.16.3, or
3.4.18 shall be determined as follows in Sections 4.13.1
and 4.13.2. The design stress for the shape shall then be
determined using Section 4.7.3, except that the strength of
any stiffened element need not be limited to the strength of
the stiffener.
4.13.1 Compressive Strength of Beam Elements–
Flat Elements in Uniform Compression
a. ϕFL = ϕyFcy
(Eq. 4.13.1-1)
for λeq ≤ S1
b. ϕFL = ϕb( Bp – Dpλeq )
(Eq. 4.13.1-2)
for S1 < λeq < S2
____
ϕbk2√ BpE
c. ϕF = ________
L
λeq
(Eq. 4.13.1-3)
for λeq ≥ S2
January 2005
where
Bp – ϕyFcy /ϕb
S1 = ___________
Dp
b. ϕFL = ϕb( Bbr – Dbrλeq )
(Eq. 4.13.1-4)
(Eq. 4.13.2-2)
for S1 < λeq < S2
____
k1Bp
S2 = ____
Dp
(Eq. 4.13.1-5)
___
√
E
λeq = π ___
Fcr
(Eq. 4.13.1-6)
Fcr = Mcr /Sc
where Mcr is the elastic buckling moment of the beam
under pure bending with continuous lateral support
determined by linear elastic analysis and Sc is the compressive section modulus of the entire cross section.
4.13.2 Compressive Strength of Beam Elements–
Flat Elements in Bending In Their
Own Plane
a. ϕFL = 1.3ϕyFcy
for λeq ≤ S1
January 2005
(Eq. 4.13.2-1)
ϕbk2√ BbrE
c. ϕFL = _________
λeq
(Eq. 4.13.2-3)
for λeq ≥ S2
where
Bbr – 1.3ϕyFcy /ϕb
S1 = ______________
Dbr
k____
B
S2 = 1 br
Dbr
(Eq. 4.13.2-4)
(Eq. 4.13.2-5)
___
√
E
λeq = π ___
Fcr
(Eq. 4.13.2-6)
Fcr = Mcr /Sc
where Mcr is the elastic buckling moment of the beam
under pure bending with continuous lateral support
determined by linear elastic analysis and Sc is the compressive section modulus of the entire cross section.
I-B-57
Section 5. Mechanical Connections
5.1 General
5.1.1 Minimum Edge Distance
If the distance from the center of a fastener to the edge
of the connected part in the direction of the force on the
fastener is less than 2D, the design bearing strength of the
connected part shall be factored by this distance divided by
2D, where D is the nominal diameter of the fastener. (See
Sections 3.4.5 and 3.4.6).
The distance from the center of a fastener to an edge of
a part shall not be less than 1.5D.
5.1.2 Maximum Spacing of Fasteners
The pitch and gage of fasteners joining components of
tension members shall not exceed (3 + 20t) in. [(75 + 20t)
mm] where t is the thickness of the outside component.
In outside components of compression members:
1) the pitch of fasteners in the direction of stress shall be
based on the design stress from Section 3.4.7 with an
effective length kL = s/2, where s is the pitch, and
2) the gage of fasteners perpendicular to the direction of
stress shall be based on the design stress from Section 3.4.9 with a width b = 0.8g where g is the gage.
If only one line of fasteners is used, the design stress
shall be based on Section 3.4.8.1 with a width b = the
edge distance of the fastener.
5.1.3 Block Shear Rupture
The block shear rupture design strength ϕRn of bolted
connections on a failure path with shear on some segments
and tension on the other segments is:
For Ftu Ant ≥ Fsu Anv
(
__
ϕRn = ϕ ( Fty /√ 3 )Agv + Ftu Ant
)
(Eq. 5.1.3-1)
Otherwise
ϕRn = ϕ( Fsu Anv + Fty Agt )
(Eq. 5.1.3-2)
The block shear rupture design strength ϕRn of welded
connections on a failure path with shear on some segments
and tension on the other segments is:
For Ftu Agt ≥ Fsu Agv
__
ϕRn = ϕ( ( Fty /√ 3 )Agv + Ftu Agt )
(Eq. 5.1.3-3)
Otherwise
ϕRn = ϕ( Fsu Agv + Fty Agt )
I-B-58
(Eq. 5.1.3-4)
where
ϕ = 0.85
Agv = gross area in shear
Agt = gross area in tension
Anv = net area in shear
Ant = net area in tension
5.1.4 Net Area
The net area An of a member is the sum of the products
of the thickness and the least net width of each element
computed as follows:
The width of holes shall be taken as the nominal hole
diameter for drilled or reamed holes and the nominal hole
diameter plus 1/32 in. (0.8 mm) for punched holes.
For a chain of holes extending across a part in any
diagonal or zigzag line, the net width of the part shall be
obtained by deducting from the gross width the sum of the
hole widths of all holes in the chain, and adding, for each
gage space in the chain, the quantity s2/4g where
s = longitudinal center-to-center spacing (pitch) of any
two consecutive holes
g = transverse center-to-center spacing (gage) between
fastener gage lines
For angles, the gage for holes in opposite legs shall be
the sum of the gages from the back of the angles less the
thickness.
Weld metal in plug or slot welds shall not be included
in the net area.
5.1.5 Effective Net Area
The effective net area for angles, channels, tees, zees,
and I-shaped sections shall be determined as follows:
1) If tension is transmitted directly to each of the crosssectional elements of the member by fasteners or
welds, the effective net area Ae is the net area.
2) If tension is transmitted by fasteners or welds through
some but not all of the cross-sectional elements of
the member, the effective net area Ae is:
_
_
y
x 1 – __
Ae = An 1 – __
L
L
(
)(
)
(Eq. 5.1.5-1)
where
An = net area of the member at the connection
L = length of the connection in the direction of load,
measured from the center of fasteners or the end
of welds
_
x = eccentricity of the connection in the x axis direction
_
y = eccentricity of the connection in the y axis direction
If the length of the connection L is zero, the net effective
area is the net area of the connected elements.
January 2005
5.1.6 Long Grips
If the grip (total thickness of parts being fastened) of an
aluminum fastener exceeds 4.5D, the fastener’s nominal shear
strength shall be reduced by dividing by [1/2+Gf /(9D)] where
Gf is the grip and D is the fastener’s nominal diameter.
5.1.7 Strength and Arrangement of Connections
If the center of resistance of a connection does not coincide with the resultant line of action of the load, members
and connections shall be proportioned to account for load
eccentricities at the connection.
5.1.8 Countersunk Holes
The bearing length for countersunk holes shall be the
part thickness less one-half the depth of the countersink.
5.2 Bolted Connections
5.2.1 Bolt Material
Bolt fastener material shall be one of the following:
a. Aluminum: Bolts shall meet ASTM F468 and be 2024-T4,
6061-T6, or 7075-T73. When 2024 bolts will be exposed
to contact with liquid water or humidity near the dew
point in the intended service, they shall have a minimum
0.0002 in. (0.005 mm) thick anodic coating. Nuts shall
meet ASTM F467. Nuts for ¼ in. (M6) bolts and smaller
shall be 2024-T4; larger nuts shall be 6061-T6 or 6262-T9.
Flat washers shall be Alclad 2024-T4. Spring lock washers shall be 7075-T6.
b. Carbon steel: Carbon steel bolts, nuts, and washers
shall be hot-dip galvanized to ASTM A153 or electrogalvanized to ASTM B633. Galvanizing thickness shall be
adequate to provide corrosion protection for the anticipated service. Hot-dipped galvanized A490 bolts shall
not be used. Galvanized steel fasteners shall be lubricated
to eliminate galling and assure adequate preload. When
other platings and/or coatings are used, evidence shall be
submitted to substantiate their corrosion resistance when
in contact in aluminum. Bolt hardness shall be less than
Rockwell C35.
c. Stainless steel: Stainless steel bolts, nuts and washers shall be 300 series stainless steel. Bolts shall meet
ASTM F593. Nuts shall meet ASTM F594.
5.2.2 Holes and Slots for Bolts
The nominal diameter of holes for bolts shall not be
more than 1/16 in. (2 mm) greater than the nominal diameter of the bolt unless slip-critical connections are used.
The nominal width of slots for bolts shall not be more
than 1/16 in. (2 mm) greater than the nominal diameter
of the bolt. If the nominal length of the slot exceeds 2.5D
or the edge distance is less than 2D, where D is the nominal
bolt diameter, the edge distance perpendicular to the slot
January 2005
length and slot length shall be sized to avoid overstressing the material along the slot. Unless slip-critical connections are used, the length shall be normal to the direction
of load.
5.2.3 Bolt Tension
The design tension load on an aluminum bolt is the root
area of the bolt (π/4[D − 1.191/n]2) times its design tensile
stress, which is 0.65Ftu, where n = number of threads/in.
(See Table 5.2.3-1 or Table 5.2.3-1M).
5.2.4 Bolt Shear
The design shear load on an aluminum bolt is its effective shear area times its design shear stress, which is
0.65Fsu. (See Table 5.2.3-1 or Table 5.2.3-1M). The effective shear area for bolts with no threads in the shear plane
shall be based on the nominal diameter. The effective shear
area for bolts with threads in the shear plane shall be based
on the root diameter (D − 1.191/n).
5.2.5 Bolt Bearing
The design bearing load applied by a bolt to an aluminum part is the part’s design bearing stress (see Sections 3.4.5 and 3.4.6) times the effective bearing area of
the bolt. The bolt’s effective bearing area is its nominal
diameter multiplied by the bearing length (see Section
5.1.8 for countersunk holes). This applies to threaded and
unthreaded surfaces.
5.2.6 Minimum Spacing of Bolts
The minimum distance between bolt centers shall be 2.5
times the nominal bolt diameter.
5.2.7 Lockbolts
Lockbolts shall meet the requirements in this Specification for conventional bolts and be installed in conformance
with the lockbolt manufacturer’s specifications. The bearing areas under the head and collar shall not be less than
those of a conventional bolt and nut.
5.2.8 Slip-Critical Bolted Connections
5.2.8.1 General
Slip-critical connections between aluminum members
or between aluminum and steel members shall comply
with the Research Council on Structural Connections
(RCSC) Specification for Structural Joints Using ASTM
A325 or A490 Bolts, Load and Resistance Factor Design,
except as modified here. The factored shear on a bolt in a
slip-critical connection shall not exceed the design shear
for the bolt (Section 5.2.8.4), the design bearing for the
connected members (Section 3.4.5), or the design slip load
(Section 5.2.8.5).
I-B-59
5.2.8.2 Material
Aluminum used in slip-critical connections shall have
a tensile yield strength of at least 15 ksi (105 MPa). Bolts
shall comply with ASTM A325, nuts shall comply with
ASTM A563 Grade DH or ASTM A194 Grade 2H, and
washers shall comply with ASTM F436. Bolts, nuts, and
washers shall be zinc coated by the hot-dip or mechanically
deposited processes as specified in ASTM A325.
5.2.8.3 Holes
Holes shall be standard holes, oversize holes, short slotted holes, or long slotted holes. The nominal dimensions
for each hole type shall not exceed those shown in the
RCSC Specification Table 1.
5.2.8.4 Design for Strength
The factored shear load on a bolt shall not exceed the
design shear strength of the bolt. The design shear strength
of a bolt is ϕRn
where
Rn = Fn Ab
(Eq. 5.2.8.4-1)
where
Rn = nominal bolt strength
Fn = 48 ksi for shear on bolts with threads in the shear
plane
Fn = 60 ksi for shear on bolts without threads in the
shear plane
Ab = nominal cross sectional area (unthreaded body
area) of a bolt
ϕ = resistance factor = 0.75
The factored shear load on a bolt divided by the nominal bolt diameter and the thickness of the connected part
shall not exceed the design bearing stress specified in
Section 3.4.5.
5.2.8.5 Design for Slip Resistance
In addition to the requirements of Section 5.2.8.4, bolts
shall be proportioned so that the design slip resistance is not
exceeded by the nominal loads. The design slip resistance is
ϕRs = ϕDµTm Ns
(Eq. 5.2.8.5-1)
where
ϕ = resistance factor
= 1.0 for standard holes
= 0.85 for oversized and short-slotted holes
= 0.70 for long-slotted holes transverse to the direction of load
= 0.60 for long-slotted holes parallel to the direction
of load
I-B-60
Rs = nominal slip resistance for a single bolt
D = 0.80, slip probability factor
µ = mean slip coefficient
= 0.50 for aluminum surfaces abrasion blasted with
coal slag to SSPC SP-5 to an average substrate
profile of 2.0 mils (0.05 mm) in contact with similar aluminum surfaces or zinc painted steel surfaces with a maximum dry film thickness of 4 mils
(0.1 mm) are Class B surfaces. For other surfaces,
slip coefficients shall be determined in accordance
with the RCSC Specification Appendix A.
Tm = minimum fastener tension specified in Section
5.2.8.7.
Ns = number of slip planes
The effect on slip resistance of temperature changes
from the installation temperature and the difference in
coefficients of thermal expansion of aluminum and steel
shall be addressed.
5.2.8.6 Washers
a. Washers shall be used under bolt heads and under nuts.
b. At a long slotted hole in an outer ply, a galvanized steel
plate washer or bar at least 5/16 in. (8 mm) thick with
standard holes, shall be used. The plate washer or bar
shall completely cover the slot but need not be hardened.
c. Where the outer face of the bolted parts has a slope
greater than 1:20 with respect to a plane normal to the
bolt axis, a beveled washer shall be used.
5.2.8.7 Installation
Bolts shall be tightened in accordance with the RCSC
Specification.
5.3 Riveted Connections
5.3.1 Rivet Material
Rivet material shall be one of the following:
a. Aluminum: Aluminum shall meet ASTM B 316.
b. Carbon steel: Carbon steel shall not be used unless the
aluminum is joined to carbon steel (see Section 6.7.1),
or corrosion resistance of the structure is not required,
or the structure is protected against corrosion.
c. Stainless steel: Stainless steel shall be 300 series.
5.3.2 Holes for Cold-Driven Rivets
The finished diameter of holes for cold-driven rivets
shall not be more than 4% greater than the nominal diameter of the rivet.
5.3.3 Rivet Tension
Rivets shall not be used to carry tensile loads.
January 2005
5.3.4 Rivet Shear
The design shear load on an aluminum rivet is its
effective shear area times its design shear stress, which is
0.65Fsu. (See Table 5.3.4-1 or Table 5.3.4-1M). The effective shear area of solid rivets shall be based on the nominal
hole diameter. (See Section 5.3.2 for hole size limits and
Section 5.3.8 for hollow-end rivets).
5.3.5 Rivet Bearing
The design bearing load applied by a rivet to an aluminum part is the part’s design bearing stress (see Section
3.4.5) times the effective bearing area of the rivet. The
rivet’s effective bearing area is the nominal hole diameter multiplied by the bearing length (see Section 5.1.8 for
countersunk holes).
5.3.6 Minimum Spacing of Rivets
The minimum distance between rivet centers shall be
3 times the nominal rivet diameter.
5.3.7 Blind Rivets
Grip lengths and hole sizes for blind rivets shall comply
with the rivet manufacturer’s specifications.
5.3.8 Hollow-End (Semi-tubular) Rivets
The shear strength of hollow-end rivets with solid cross
sections for a portion of the length shall be taken equal
to the strength of solid rivets of the same material if the
bottom of the cavity is at least 25% of the rivet diameter
from the plane of shear.
5.4 Tapping Screw Connections
This Section applies to tapping screws with a nominal
diameter from 0.164 in. (4.2 mm) through 0.25 in. (6.3 mm).
Screws shall be thread-forming or thread-cutting, with or without a self-drilling point. As an alternate to Sections 5.4.1 and
5.4.2, strengths shall be based on tests according to Section 9.
Screws shall be installed and tightened in accordance
with the manufacturer’s specifications.
The following nomenclature applies to this Section:
Asn = thread stripping area of internal thread per unit
length of engagement
C = coefficient that depends on screw location
D = nominal screw diameter
Dh = nominal hole diameter
Dw = nominal washer diameter
Dws = larger of the nominal washer diameter and the
screw head
Ftu1 = tensile ultimate strength of member in contact
with the screw head
Ftu2 = tensile ultimate strength of member not in contact with the screw head
January 2005
Fty1 = tensile yield strength of member in contact with
the screw head
Fty2 = tensile yield strength of member not in contact
with the screw head
Ks = coefficient that depends on member thickness
n = number of threads per unit length for a screw
ϕsc = resistance factor = 0.5
ϕu = resistance factor = 0.85
Pnt = nominal tensile strength of a screw
Pnot = nominal pull-out strength of a screw
Pnov = nominal pull-over strength of a screw
Pns = nominal shear strength of a screw
t1 = thickness of member in contact with the screw
head
t2 = thickness of member not in contact with the
screw head
tc = depth of full thread engagement of screw into t2
not including tapping or drilling point
5.4.1 Screw Material
Screws shall be:
a. aluminum,
b. austenitic stainless steel, or
c. if the screw will not be exposed to contact with liquid
water or humidity near the dew point in its intended
service:
1) non-austenitic stainless steel with a minimum nominal composition of 16% chromium and a Rockwell
hardness less than C35 in the load bearing portion of
the shank, or
2) coated or plated carbon steel with a Rockwell
hardness less than C35 in the load bearing portion of the shank. Screws shall be zinc coated per
ASTM A123, A641, or B633 or nickel/chromium
plated per ASTM B456, Type SC. When other
platings and/or coatings are to be used, evidence
shall be submitted to substantiate the corrosion
resistance of these products.
5.4.2 Screw Tension
For screws that carry tensile loads, the head of the screw
or washer, if a washer is provided, shall have a diameter
Dw not less than 5/16 in. (8 mm). Washers shall be at least
0.050 in. (1.3 mm) thick.
The design tension force on a screw is the least of:
1) ϕsc Pnot
(see Section 5.4.2.1)
2) ϕsc Pnov
(see Section 5.4.2.2)
3) ϕsc Pnt /1.25
5.4.2.1 Pull-Out
The nominal pull-out strength, Pnot, for pulling a screw
out of a threaded part, is:
1) For UNC threads (screw thread types C, D, F, G,
and T)
a. for 0.060 in. < tc < 0.125 in. (1.5 mm < tc < 3 mm)
I-B-61
Pnot = Ks D tc Fty2
(Eq. 5.4.2.1-1)
where Ks = 1.01 for 0.060 in. ≤ tc < 0.080 in.
(1.5 mm ≤ tc < 2 mm)
Ks = 1.20 for 0.080 in. ≤ tc ≤ 0.125 in.
(2 mm ≤ tc ≤ 3 mm)
b. for 0.125 in. < tc < 0.25 in. (3 mm < tc < 6.3 mm)
Pnot = 1.2DFty2(0.25 – tc) + 1.16AsnFtu2(tc – 0.125)
(Eq. 5.4.2.1-2)
c. for 0.25 in. ≤ tc ≤ 0.375 in. (6.3 mm ≤ tc ≤ 10 mm)
Pnot = 0.58 Asn tc Ftu2
(Eq. 5.4.2.1-3)
strength computed from equation 5.4.2.2-2 for countersunk
screws.
For countersunk screws with an 82o nominal angle head,
the nominal pull-over strength is:
Pnov = (0.27 + 1.45t1 /D) D t1Fty1
(Eq. 5.4.2.2-2)
for 0.06 in. ≤ t1 < 0.19 in. (1.5 mm ≤ t1 < 5 mm) and t1 /D ≤
1.1. If t1 /D > 1.1, use t1 /D = 1.1
5.4.3 Screw Shear and Bearing
The shear force on a screw shall not exceed the least of:
1) 2ϕu Ftu1 D t1. If the screw is countersunk, one-half the
depth of the countersink shall be deducted from t1.
2) 2ϕu Ftu2 D t2
3) 4.2 (t23D)1/2 ϕsc Ftu2 , for t2 < t1
4) ϕsc Pns /1.25
2) For spaced threads (screw thread types AB, B, BP,
BF, and BT)
5.4.4 Minimum Spacing of Screws
a. for 0.038 in. ≤ tc ≤ 2/n
The minimum distance between screw centers shall be
2.5 times the nominal screw diameter.
Pnot = Ks D tc Fty2
(1 mm < tc < 2/n)
(Eq. 5.4.2.1-4)
5.5 Building Sheathing Connections
5.5.1 Endlaps
where Ks = 1.01 for 0.038 in. ≤ tc < 0.080 in.
(1 mm ≤ tc < 2 mm)
Ks = 1.20 for 0.080 in. ≤ tc < 2/n (2 mm ≤ tc < 2/n)
b. for 2/n < tc < 4/n
Pnot = 1.2D Fty2 (4/n – tc) + 3.26D Ftu2 (tc – 2/n)
(Eq. 5.4.2.1-5)
c. for 4/n ≤ tc ≤ 0.375 in. (4/n ≤ tc ≤ 8 mm)
Pnot = 1.63D tc Ftu2
(Eq. 5.4.2.1-6)
The nominal pull-over strength, Pnov, for pulling connected material over the head of a screw or washer, if
present, is:
(Eq. 5.4.2.2-1)
where C is a coefficient that depends on screw location
(1.0 for valley fastening and 0.7 for crown fastening), and
Dws is the larger of the screw head diameter or the washer
diameter, but no greater than 5/8 in. (16 mm). (See Section
5.4.2 for the washer thickness requirement.) The nominal pull-over strength need not be less than the pull-over
I-B-62
5.5.2 Sidelaps
For a sinusoidal corrugated sheet, the minimum sidelap
for roofing shall have a width equal to the pitch of the corrugations, and the minimum sidelap for siding shall have a
width equal to half the pitch.
For a trapezoidal sheet of a depth greater than 1 in. (25 mm)
the minimum sidelap for both roofing and siding shall have
a developed width equal to the width of the narrowest flat
plus 2 in. (50 mm). A trapezoidal sheet with a depth of 1 in.
(25 mm) or less shall have an overlap of proven design including an anti-siphoning feature.
5.5.3 Fasteners in Laps
5.4.2.2 Pull-Over
Pnov = C t1 Ftu1 (Dws – Dh)
Minimum endlaps shall be those expressed in Table
5.5.1-1.
The minimum size of fasteners used in end laps and side
laps shall be #12 (5.5 mm) for screws and 3/16 in. (5 mm)
diameter for rivets. The maximum spacing for sidelap fasteners shall be 12 in. (300 mm). Endlap fasteners shall be
located no more than 2 in. (50 mm) from the end of the
overlapping sheet.
5.5.4 Flashing
Flashing shall be formed from aluminum sheet.
October 2005
Table 5.2.3-1
DESIGN STRESSES FOR BOLTS
Alloy and Temper
Minimum Shear
Ultimate Strength1
Fsu
(ksi)
Design Shear Stress
on Effective Area2
(ksi)
Minimum Tensile
Ultimate Strength1
Ftu
(ksi)
Design Tensile Stress
on Root Area 2
(ksi)
2024-T4
37
24
62
40
6061-T6
25
16
42
27
7075-T73
41
27
68
44
1. From ASTM B316/B316M and F468
2. ϕ = 0.65
Table 5.2.3-1M
DESIGN STRESSES FOR BOLTS
Alloy and Temper
Minimum Shear
Ultimate Strength1
Fsu
(MPa)
Design Shear Stress
on Effective Area 2
(MPa)
Minimum Tensile
Ultimate Strength1
Ftu
(MPa)
Design Tensile Stress
on Root Area 2
(MPa)
2024-T4
255
165
425
275
6061-T6
170
110
290
190
7075-T73
280
180
470
305
1. From ASTM B316/B316M
2. ϕ = 0.65
Table 5.3.4-1
DESIGN STRESSES FOR RIVETS
Designation
Before Driving
Minimum Shear
Ultimate Strength1
Fsu
(ksi)
Design Shear Stress on
Effective Area2
(ksi)
2017-T4
33
21
2024-T42
37
24
2117-T4
26
17
2219-T6
30
20
6053-T61
20
13
6061-T6
25
16
7050-T7
39
25
7075-T6
42
27
7075-T73
41
27
7178-T6
46
30
1. From ASTM B316/B316M for heat treated alloys.
2. ϕ = 0.65
January 2005
I-B-63
Table 5.3.4-1M
DESIGN STRESSES FOR RIVETS
Designation
Before Driving
Minimum Shear
Ultimate Strength1
Fsu
(MPa)
Design Shear Stress on
Effective Area2
(MPa)
2017-T4
225
145
2024-T42
255
165
2117-T4
180
115
2219-T6
205
135
6053-T61
135
90
6061-T6
170
110
7050-T7
270
175
7075-T6
290
190
7075-T73
280
180
7178-T6
315
205
1. From ASTM B316/B316M for heat treated alloys.
2. ϕ = 0.65
Table 5.5.1-1
MINIMUM END LAPS
Minimum End Laps
Depth of section
Roofing, slope
greater than 2 on 12,
less than 3 on 12
1 in. or less
(25 mm or less)
Roofing, slope 3 on 12 or
more
Siding
–
6 in.
(150 mm)
4 in.
(100 mm)
Greater than 1 in.,
less than 2 in.
(Greater than 25 mm, less
than 50 mm)
9 in.
(230 mm)
6 in.
(150 mm)
4 in.
(100 mm)
2 in. or more
(50 mm or more)
9 in.
(230 mm)
6 in.
(150 mm)
6 in.
(150 mm)
I-B-64
January 2005
Section 6. Fabrication and Erection
6.1 Layout
6.1.1 Punch and Scribe Marks
Punched or scribed layout marks shall not remain on
fabricated material designed for fatigue.
6.1.2 Temperature Correction
Table 6.3-1
TEMPERATURE EXPOSURE LIMITS
FOR ARTIFICIALLY AGED TEMPERS OF
6005, 6061, AND 6063
Temperature1
Time
o
F
o
A temperature correction shall be applied where necessary in the layout of dimensions. The coefficient of expansion used shall be 13 × 10-6 per oF (23 × 10-6 per oC).
450
230
5 min
425
220
15 min
6.2 Cutting
400
205
30 min
6.2.1 Methods
375
190
2 hr
350
175
10 hr
325
165
100 hr
6.2.2 Edge Quality
300
150
1,000 hr
Cut edges shall be true, smooth, and free from excessive
burrs or ragged breaks.
212
100
100,000 hr
Cutting shall be by shearing, sawing, nibbling, routing,
arc cutting, laser or abrasive water jet. Edges which have
been arc or laser cut shall be planed to remove edge cracks.
6.2.3 Re-entrant Corners
Re-entrant corners shall be filleted.
6.2.4 Oxygen Cutting
Oxygen cutting is prohibited.
6.3 Heating
Aluminum heated above 150oF (66oC) during fabrication
other than welding is subject to the following requirements:
a. Temperature controls and supervision shall be provided to ensure that time-temperature limits are met,
and time and temperature exposure shall be documented.
b. When heating reduces metal strengths, design stresses
shall be reduced consistent with the mechanical properties of the aluminum after the heating process.
Reduced design stresses need not be used for the
alloys and tempers in Table 6.3-1 if the cumulative
time at the elevated temperature does not exceed the
limits given.
January 2005
C
1) Interpolate time (t) for other temperatures (T) using
log( T2 / T )
logt = logt2 + __________ ( log t1/t2 )
log( T2 / T1 )
where
T1
T2
t1
t2
= next lower temperature in Table 6.3-1 than T
= next higher temperature in Table 6.3-1 than T
= time corresponding to T1
= time corresponding to T2
c. 5083, 5086, 5154, and 5456 shall not be held at temperatures from 150oF (66oC) to 450oF (230oC). To hot
form such alloys, they shall be
1) rapidly heated to a temperature not to exceed
550oF (290oC),
2) formed before the metal cools below 450oF
(230oC), and
3) rapidly cooled from 450oF (230oC) to 150oF (66oC).
6.4 Holes
6.4.1 Fabrication Methods
Holes shall be punched or drilled. Punching shall not be
used for castings or if the metal thickness is greater than
the diameter of the hole. The amount by which the diameter of a sub-punched hole is less than that of the finished
hole shall be at least ¼ the thickness of the piece but not
less than 1/32 in. (0.8 mm).
I-B-65
6.4.2 Hole Alignment
6.7 Contact with Dissimilar Materials
If holes must be enlarged to admit fasteners, they shall
be reamed. Poor matching holes shall be rejected. Holes
shall not be drifted in a manner that distorts the metal. All
chips and foreign matter between contacting surfaces shall
be removed before assembly.
Where aluminum is in contact with or fastened to the
materials specified in Sections 6.7.1 through 6.7.3, direct
contact between the aluminum and the other material shall
be prevented as specified in those sections or by placing a
compatible, nonporous isolator between the aluminum and
the other material.
6.5 Riveting
6.5.1 Driven Head
The driven head of aluminum rivets shall be flat or conepoint, with dimensions as follows:
6.5.1.1 Flat Heads
Flat heads shall have a diameter at least 1.4 times the
nominal diameter of the rivet and a height at least 0.4 times
the nominal diameter of the rivet.
6.5.1.2 Cone-Point Heads
Cone-point heads shall have a diameter at least 1.4 times
the nominal diameter of the rivet and a height to the apex
of the cone at least 0.65 times the nominal diameter of the
rivet. The nominal included angle at the apex of the cone
shall be 127o.
6.5.2 Hole Filling
Rivets shall fill holes completely. Rivet heads shall be
concentric with the rivet holes and shall be in continuous
contact with the surface of the part joined.
6.5.3 Defective Rivets
Defective rivets shall be removed by drilling. The drill
bit diameter shall not exceed the diameter of the replacement rivet.
6.6 Finishes
6.6.1 Where Painting Is Required
Aluminum shall be painted where:
a. 2014 is in the presence of moisture,
b. aluminum would otherwise be in contact with or fastened
to dissimilar materials as described in Section 6.7,
c. aluminum is exposed to corrosive conditions.
6.6.2 Surface Preparation
Surfaces to be painted shall be prepared immediately
before painting by:
a. a chemical cleaner (such as a solution of phosphoric
acid and organic solvents),
b. abrasion blasting,
c. unsealed anodizing,
d. chemical conversion coating, or
e. using the procedure specified by the coating supplier.
I-B-66
6.7.1 Steel
Steel surfaces to be placed in contact with uncoated
aluminum shall be painted with a coating suitable for the
service. Where very corrosive conditions are expected,
additional protection can be obtained by applying a sealant
that excludes moisture from the joint during service. Aluminized, hot-dip galvanized or electro-galvanized steel in
contact with aluminum need not be painted. Stainless steel
(300 series) in contact with aluminum need not be painted
except in high chloride environments.
6.7.2 Wood, Fiberboard, or Other
Porous Materials
Aluminum surfaces to be placed in contact with wood,
fiberboard, or other porous material that absorbs water shall
be factory painted or given a heavy coat of alkali resistant
bituminous paint or other coating providing the equivalent
protection before installation.
6.7.3 Concrete or Masonry
Aluminum shall not be embedded in concrete with corrosive additives such as chlorides if the aluminum will be
electrically connected to steel.
Unless the concrete or masonry will remain dry after
curing and no corrosive additives such as chlorides are
used, aluminum surfaces to be placed next to or embedded
in concrete or masonry shall be:
a. given one coat of suitable paint, such as zinc molybdate primer conforming to Federal Specification
TT-P-645B or equivalent, or
b. given a heavy coating of alkali resistant bituminous
paint, or
c. isolated with a suitable plastic tape or other isolation
material.
6.7.4 Runoff From Heavy Metals
Aluminum shall not be exposed to water that has come
in contact with a heavy metal such as copper. The heavy
metal shall be painted or coated or the drainage from the
metal diverted away from the aluminum or painted aluminum shall be used.
January 2005
6.8 Mechanical Finishes
6.11 Erection
Abrasion blasting shall not be used if it distorts, perforates, or significantly reduces the thickness of the material
blasted.
6.11.1 Erection Tolerances
6.9 Fabrication Tolerances
A fabricated member shall not vary from straight or
from its intended curvature by more than its length divided
by 960.
6.10 Bending
Tolerances on erected dimensions shall be suitable for
the intended service.
6.11.2 Bolt Installation
Unless the joint is a slip-critical connection, bolts shall
be installed snug tight, defined as the tightness that exists
when all plies in a joint are in firm but not necessarily continuous contact. Slip-critical connections shall be tightened
in accordance with Section 5.2.8.7.
Bend radii shall be large enough to avoid cracking.
January 2005
I-B-67
Section 7. Welded Construction
7.1 General
Welding shall comply with the American Welding Society’s D1.2 Structural Welding Code – Aluminum. Filler
alloys shall meet AWS A5.10 and be selected from Table
7.1-1.
7.2 Welded Members
7.2.1 General
The weld-affected zone shall be taken to extend 1 in.
(25 mm) to each side of the centerline of a weld. Mechanical properties for weld-affected metal shall be taken from
Table 3.3-2. The modulus of elasticity for weld-affected
metal is the same as for non-welded metal.
Design stresses calculated in accordance with Section
7.2.1 apply to:
1) Members in axial tension with transverse welds
affecting their entire cross section,
2) Bearing stresses at weld-affected metal,
3) Columns or beams supported at both ends with
transverse welds affecting their entire cross-section
and no farther than 0.05L from the ends,
4) Columns or beams of tubes or curved elements with
transverse welds affecting their entire cross section,
and
5) Flat elements of columns or beams with welds at the
supported edges only.
Design stresses for these welded members shall be calculated from the same formulas as for non-welded members with the following adjustments.
1) Design stresses for axial or flexural tension (Sections 3.4.1 through 3.4.4), bearing (Sections 3.4.5
and 3.4.6), and axial or flexural compression or shear
(Sections 3.4.7 through 3.4.21) with slenderness less
than S1 shall be calculated using welded mechanical
properties from Table 3.3-2.
2) Design stresses for tubes and curved elements in axial
or flexural compression or shear (Section 3.4.10,
3.4.12, and 3.4.16.1) with slenderness greater than
S1 shall be calculated using welded mechanical properties from Table 3.3-2 and buckling constants from
Table 3.3-3 regardless of temper before welding.
3) Design stresses for all other members and elements
in axial or flexural compression or shear (Sections
3.4.7 through 3.4.21) with slenderness greater than
S1 shall be calculated using non-welded mechanical
properties from Table 3.3-1 and buckling constants
from Table 3.3-3 or 3.3-4 as appropriate for the temper before welding.
I-B-68
7.2.2 Members with Part of the Cross Section
Weld-Affected
For members with part of the cross section weldaffected, the design stress is
A
ϕFpw = ϕFn – ___w ( ϕFn – ϕFw )
A
(Eq. 7.2.2-1)
where
ϕFpw = design stress on the cross section, part of which
is weld-affected.
ϕFn = design stress if no part of the cross section
were weld-affected. Use buckling constants for
unwelded metal from Table 3.3-3 or 3.3-4 and
mechanical properties from Table 3.3-1.
ϕFw = design stress if the entire cross sectional area
were weld-affected. Use buckling constants
for annealed material (Table 3.3-3) regardless
of the temper before welding, and mechanical
properties from Table 3.3-2.
A
= net cross sectional area of a tension member or
tension flange of a beam; gross cross sectional
area of a column or compression flange of a
beam. A beam flange shall consist of the portion
of the section farther than 2c/3 from the neutral
axis, where c is the distance from the neutral
axis to the extreme fiber.
Aw = weld-affected cross sectional area. If Aw < 0.15A,
Aw shall be taken as zero.
7.2.3 Columns or Beams with Transverse Welds
Away from Supports and Cantilevers with
Transverse Welds
For columns or beams supported at both ends with
transverse welds farther than 0.05L from the member ends
and cantilever beams with transverse welds, design stresses
shall be calculated in accordance with Section 7.2.2 as if
the entire cross sectional area were weld-affected.
7.3 Welded Connections
7.3.1 Groove Welds
7.3.1.1 Complete Penetration and Partial
Penetration Groove Welds
The following types of groove welds are complete penetration welds:
1) Welds welded from both sides with the root of the
first weld backgouged to sound metal before welding
the second side.
2) Welds welded from one side using permanent or
temporary backing.
January 2005
January 2005
I-B-69
4043
(4047)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
4043
(1100, 4047)
4043 (4047,
5183,5356,5556)
4145
4043
(1100, 4047)
6005, 6061,
6063, 6105,
6351, 6463
5454
5154
5086
5083, 5456
5052
5005, 5050
3004,
Alclad 3004
2219
1060, 1100,
3003,
Alclad 3003
2319
(4145)
DNW
DNW
DNW
DNW
DNW
DNW
DNW
4145
DNW
2219
5356
(5183, 5556)
5356
(4043, 4047,
5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183,5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(4043, 4047,
5183, 5556)
5356
(5183, 5556)
3004
Alclad 3004
5356
(4043, 4047,
5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5005
5050
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5356
(5183, 5556)
5052
5356
(5183, 5556)
5086
5556
(5183)
5356
5356
(5183, 5556) (5183, 5556)
5356
5356
(5183, 5556) (5183, 5556)
5356
5356
(5183, 5556) (5183, 5556)
5356
5356
(5183, 5556) (5183, 5556)
5556
(5183)
5083
5456
Notes:
1) This table is for structural applications subjected to normal atmospheric conditions using GTAW or GMAW.
2) DNW = Do Not Weld
5356
(5183, 5556)
1060
1100
3003
Alclad 3003
7005
Base Metal
Base Metal
Table 7.1-1
WELD FILLERS FOR WROUGHT ALLOYS
5654
(5183, 5356,
5556)
5654
(5183, 5356,
5556)
5356
(5183, 5556)
5356
(5183, 5556)
5154
5554
(5183, 5356,
5556)
5356
(5183, 5556)
5356
(5183, 5556)
5454
7005
5356
(4043, 4047,
5183, 5556)
5356
5556
(5183, 5556) (5183, 5356)
6005
6061
6063
6105
6351
6463
3) Welds welded from one side using AC-GTAW root
pass without backing
4) Welds welded from one side using PAW-VP in the
keyhole mode.
All other groove welds are partial penetration welds.
7.3.1.2 Effective Area
1) Size: The weld size of a complete joint penetration groove weld is the thickness of the thinner part
joined. The weld size of a partial joint penetration
groove weld is the depth of preparation Sw (see Figure 7.3-1) for all V and bevel groove welds with an
included angle greater than 45o, and the depth of
preparation for all J and U groove welds.
2) Length: The effective weld length for tension and
compression is the length of the weld perpendicular
to the direction of tensile or compressive stress. The
effective weld length for shear is the length of the
weld parallel to the direction of shear stress.
3) Area: The effective area of a groove weld is the
effective weld length times the weld size.
7.3.1.3 Design Strength
The design tensile or compressive strength of a groove
weld (Pgw) is
Pgw = ϕuFtuw Awe
(Eq. 7.3.1.3-1)
where
Ftuw = least of the welded tensile ultimate strengths
of the base metals and the filler. Welded tensile
ultimate strengths of base metals shall be taken
from Table 3.3-2 and tensile ultimate strengths
of fillers from Table 7.3-1.
Awe = weld effective area
ϕu = 0.85
The design shear strength of a groove weld (Vgw) is
Vgw = ϕFsuw Awe
(Eq. 7.3.1.3-2)
where
Fsuw = least of the welded shear ultimate strengths of
the base metals and the filler. Welded shear ultimate strengths of base metals shall be taken from
Table 3.3-2 and shear ultimate strengths of fillers
from Table 7.3-1.
Awe = weld effective area
ϕu = 0.85
7.3.2 Fillet Welds
7.3.2.1 Effective Throat and Effective Length
The effective throat is the shortest distance from the
joint root to the face of the diagrammatic weld.
The weld effective length Lwe is the overall length of the
weld, including boxing. If the effective length of a fillet weld
is less than 4 times its nominal size Sw (see Figure 7.3-2), the
effective weld size shall be considered to be 25% of its effective length. The minimum length of segments of an intermittent fillet weld shall be 1½ in. (40 mm). The maximum
effective length of a longitudinal fillet weld is 100 times its
nominal size.
7.3.2.2 Design Strength
Stress on a fillet weld shall be considered to be shear for
any direction of applied load. The design shear strength of
a fillet weld (Vw) is
Vw = ϕuFsw Lwe
(Eq. 7.3.2.2-1)
where
Fsw = least of:
1) the product of the filler’s shear ultimate strength and
the effective throat.
Figure 7.3-1
PARTIAL JOINT PENETRATION GROOVE WELD
DEPTH OF PREPARATION Sw
I-B-70
January 2005
where
Fsw = lesser of the welded shear ultimate strengths of the
filler and the base metal under the weld. Welded
shear ultimate strengths of base metals shall be
taken from Table 3.3-2 and shear ultimate strengths
of fillers from Table 7.3-1
Awe = weld effective area
ϕu = 0.85
7.3.4 Stud Welds
The design tensile strength of a stud weld (Tw) is
Tw = ϕuTuw
Figure 7.3-2
EFFECTIVE THROAT OF A FILLET WELD
2) for base metal in shear at the weld-base metal joint,
the product of the base metal’s welded shear ultimate
strength and the fillet size Sw at the joint;
3) for base metal in tension at the weld-base metal
joint, the product of the base metal’s welded tensile
ultimate strength and the fillet size Sw at the joint.
Welded shear and tensile ultimate strengths of base
metals shall be taken from Table 3.3-2 and shear ultimate
strengths of fillers from Table 7.3-1.
Lwe = weld effective length
ϕu = 0.80
(Eq. 7.3.4-1)
where
Tuw = minimum tensile strength of the stud in Table 7.3-2
ϕu = 0.85
Table 7.3-1
FILLER STRENGTHS
Filler
Minimum Tensile
Ultimate Strength
(ksi)
Minimum Shear
Ultimate Strength
(ksi)
1100
11
7.5
2319
35
16
4043
24
11.5
4047
–
13
4643
–
13.5
7.3.3 Plug and Slot Welds
5183
40
21
7.3.3.1 Effective Area
5356
35
17
5554
31
17
5556
42
20
5654
30
12
The effective area of plug or slot welds is the nominal
area of the hole or slot in the plane of the faying surface.
Slot lengths shall not exceed 10 times the slotted material’s
thickness.
Table 7.3-1M
FILLER STRENGTHS
7.3.3.2 Design Strength
The design shear strength of a plug or slot weld (Vw) is
Vw = ϕuFsw Awe
(Eq. 7.3.3.2-1)
Figure 7.3-3
SLOT WELD PLAN VIEW
January 2005
Filler
Minimum Tensile
Ultimate Strength
(MPa)
Minimum Shear
Ultimate Strength
(MPa)
1100
75
50
2319
240
110
4043
165
80
4047
–
90
4643
–
95
5183
275
145
5356
240
115
5554
215
115
5556
290
140
5654
205
85
I-B-71
Table 7.3-2
MINIMUM TENSILE STRENGTHS FOR
5183, 5356, AND 5556 STUDS
Stud Size
Arc
(lb)
Capacitor Discharge
(lb)
6-32
–
375
8-32
–
635
10-24
770
770
1/4-20
1360
1360
5/16-18
2300
2300
3/8-16
3250
–
7/16-14
4400
–
1/2-13
5950
–
7.4 Post-Weld Heat Treating
For alloy 6005 lighting pole assemblies, up through
0.250 in. (6 mm) thick which are welded in the –T1 temper
with filler alloy 4043 and precipitation heat treated (artificially aged) to the –T5 temper by an approved method
after welding, the design stresses within 1.0 in. (25 mm) of
the weld shall be 85% of the values for non-welded alloy
6005-T5.
For alloy 6063 lighting pole assemblies, up through
0.375 in. (10 mm) thick which are welded in the –T4 temper with filler alloy 4043 and precipitation heat treated
(artificially aged) to the –T6 temper by an approved method
after welding, the design stresses within 1.0 in. (25 mm) of
the weld shall be 85% of the values for non-welded alloy
6063-T6.
Table 7.3-2M
MINIMUM TENSILE STRENGTHS FOR
5183, 5356, AND 5556 STUDS
Stud Size
Arc
(N)
Capacitor Discharge
(N)
6-32
–
1670
8-32
–
2820
10-24
3420
3420
1/4-20
6050
6050
5/16-18
10,200
10,200
3/8-16
14,500
–
7/16-14
19,600
–
1/2-13
26,500
–
I-B-72
January 2005
Section 8. Castings
8.1 Materials
Section 8 of this Specification applies to castings listed
in Table 8.2-1 and produced to the following ASTM Specifications:
B 26
B 108
radiographed and the lot acceptance criteria shall be as
follows:
Aluminum-Alloy Sand Castings
Aluminum-Alloy Permanent Mold Castings
Dimensional tolerances shall conform to Standards for
Aluminum Sand and Permanent Mold Castings.
The purchaser shall require the casting producer to
report tensile yield strengths. For sand castings, the purchaser shall require that tensile ultimate and tensile yield
strengths of specimens cut from castings shall be at least
75% of the values specified in B 26.
Radiographic inspection to ASTM B 26 Grade C or B
108 Grade C criteria is required. The number of castings
Lot Size
2 through 50
51 through 500
over 500
Number of
Castings
Required to be
Radiographed
2
8
13
Number of
Castings
Required to Meet
Grade C to Pass
Lot
2
7
11
8.2 Mechanical Properties
Minimum strengths shall be taken from Table 8.2-1 or
Table 8.2-1M.
Table 8.2-1
MINIMUM STRENGTHS OF CASTINGS
Alloy-Temper
Casting Type
Minimum Tensile
Ultimate Strength
Ftu (ksi)
356.0-T6
sand
22.5
A356.0-T6
sand
25.5
18
36
27.7
(1)
47
36
(2)
43
33
(3)
30
22.5
(1)
40
30
(2)
37
30
(3)
33
22
(1)
28.5
19.5
(1)
33
26
(2)
28
26
(3)
33.7
27
(1)
46
36
(2)
354.0-T61
permanent mold
C355.0-T61
permanent mold
356.0-T6
permanent mold
A356.0-T61
permanent mold
A357.0-T61
359.0-T61
359.0-T62
535.0-F
permanent mold
permanent mold
permanent mold
permanent mold
Minimum Tensile
Yield Strength
Fty (ksi)
15
Note
41
31
(3)
33.7
25.5
(1)
45
34
(2)
40
30
(3)
35.2
28.5
(1)
47
38
(2)
40
30
(3)
26.2
13.5
(1)
1) These strengths apply at any location in the casting if the purchaser does not specify test specimens be cut from castings.
2) These strengths apply in the locations specified by the purchaser if the purchaser specifies such locations. At other locations, the strengths
in (1) apply.
3) These strengths apply anywhere in the casting if the purchaser specifies that these strengths shall be met in specimens cut from the casting without designating a location.
January 2005
I-B-73
Table 8.2-1M
MINIMUM STRENGTHS OF CASTINGS
Alloy-Temper
Casting Type
Minimum Tensile
Ultimate Strength
Ftu (MPa)
356.0-T6
sand
154
105
A356.0-T6
sand
176
124
248
191
(1)
324
248
(2)
297
228
(3)
207
155
(1)
276
207
(2)
354.0-T61
permanent mold
Minimum Tensile
Yield Strength
Fty (MPa)
Note
C355.0-T61
permanent mold
255
207
(3)
356.0-T6
permanent mold
228
152
(1)
196
134
(1)
A356.0-T61
permanent mold
228
179
(2)
193
179
(3)
232
186
(1)
317
248
(2)
283
214
(3)
232
175
(1)
A357.0-T61
359.0-T61
359.0-T62
535.0-F
permanent mold
permanent mold
permanent mold
permanent mold
310
234
(2)
276
207
(3)
243
196
(1)
324
262
(2)
276
207
(3)
180
93
(1)
Notes
1) These strengths apply at any location in the casting if the purchaser does not specify test specimens be cut from castings.
2) These strengths apply in the locations specified by the purchaser if the purchaser specifies such locations. At other locations, the strengths
in (1) apply.
3) These strengths apply anywhere in the casting if the purchaser specifies that these strengths shall be met in specimens cut from the casting without designating a location.
The compressive yield strength Fcy of castings shall be
taken as the tensile yield strength Fty.
The modulus of elasticity E of castings shall be taken as
10,000 ksi (70,000 MPa).
The tension coefficient kt for the alloy-tempers in
Table 8.2-1 and Table 8.2-1M is 1.0.
8.3 Design
Design shall be in accordance with all the provisions of
this Specification.
8.4 Welding
Fillers shall be selected from Table 8.4-1. Minimum
welded strengths shall be those established in the AWS
D1.2 weld procedure qualification test.
I-B-74
February 2006
Table 8.4-1
WELD FILLERS FOR CAST ALLOYS
BASE METAL
TO
BASE METAL
535.0
356.0
A356.0
A357.0
359.0
354.0
C355.0
1060, 1100, 3003,
Alclad 3003
5356
4043
(4047)
4145
2219
4043
4145
4145
3004,
Alclad 3004
5356
4043
(4047)
4145
(4043, 4047)
5005, 5050
5356
4043
(4047)
4145
(4043, 4047)
5052
5356
4043
(4047)
4145
(4043, 4047)
5083, 5456
5356
DNW
DNW
5086
5356
DNW
DNW
5154
5356
DNW
DNW
5454
5356
4043
(4047)
DNW
6005, 6061, 6063,
6105, 6351, 6463
5356
4043
(4047, 4145, 4643)
4145
(4043, 4047)
7005
5356
4043
(4047)
DNW
354.0
C355.0
DNW
4145
4145
(note 1)
356.0, A356.0,
A357.0, 359.0
4043
(5356)
4043
(note 1)
535.0
5356
Notes
1) To weld C355.0 to itself, 4009 may be used; to weld A356.0 to itself, 4010 may be used; and to weld A357.0 to itself, 4011 may be used.
2) DNW = Do not weld
January 2005
I-B-75
Section 9. Testing
9.1 General
(n). K is a one-sided factor for 99% of the population exceeding Xa with a confidence of 95%. Values
of K for the following values of n are:
Testing shall be considered to be an acceptable method
for substantiating the design of aluminum alloy load carrying members, assemblies or connections whose strengths
cannot otherwise be determined in accordance with Sections 1 through 8. Tests shall be conducted by an independent testing laboratory or by a manufacturer’s testing laboratory when certified by a qualified independent witness.
General provisions for testing are given in Sections
9.2 and 9.3. Specific provisions for building sheathing are
given in Section 9.4.
n
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
9.2 Test Loading and Behavior
In order to test a structure or load carrying member
adequately, the loading shall be applied in a fashion that
is representative of the loading during service. Further, the
structure or member shall be supported in a manner that is
equivalent to the supports available when the structure is
in service.
In tests that require measurement of deflection of a
panel or beam, a preload, that is a minimum of 20% of the
design load, shall be applied to set the specimen before
testing, and deflections shall be measured at the supports
as well as at the point of maximum critical deflection, so
that the difference will indicate the specimen deflection.
The preload shall only be taken as a zero load for deflection measurements when proper account of this is taken in
reporting deflections.
As an alternative, the structural performance of exterior
aluminum fenestration products such as windows, curtain
walls, and doors shall be determined in accordance with
ASTM E 330.
9.3 Number of Tests and the Evaluation of
Test Results
K
3.370
3.331
3.295
3.262
3.233
3.206
3.181
3.158
3.064
2.994
2.941
2.897
2.863
2.684
9.3.2 Tests for Determining Structural
Performance
Where practicable, in member and structural systems
tests the evaluation of test results shall be made on the basis
of not fewer than four identical specimens. If the deviation
from the average value exceeds ±10%, at least three more
tests of the same kind shall be made.
The design value shall be taken as the average of all test
results multiplied by the resistance factor, ϕ, determined
as follows:
ϕ= 1.5MmFm e–βo√ V + V + C V + V
2
M
In determining yield strength and ultimate strength of
material or fasteners, sufficient tests shall be conducted
to statistically establish the strength at which 99% of the
material is expected to exceed with a confidence of 95%.
This strength shall be calculated as follows:
(Eq. 9.3.1-1)
where
Xa = strength at which 99% of the material is expected
to exceed with a confidence of 95%
Xm = mean of the test results
Sx = standard deviation of the test results
K = statistical coefficient based on the number of tests
I-B-76
n
18
19
20
21
22
23
24
25
30
35
40
45
50
100
______________
9.3.1 Tests for Determining
Mechanical Properties
Xa = Xm – KSx
K
10.55
7.042
5.741
5.062
4.641
4.353
4.143
3.981
3.852
3.747
3.659
3.585
3.520
3.463
3.415
2
F
2
P
P
2
Q
(Eq. 9.3.2-1)
where
n –1
Cp = correction factor = ______
n2 – 3n
Dn = nominal dead load
e = base for natural logarithms ≈ 2.72
Fm = mean value of the fabrication factor
Ln = nominal live load
Mm = mean value of the material factor
n = number of tests
Xi = failure load of ith test
Xm = average value of failure loads in all tests
2
n
=
∑X
i
i=1
________
n
January 2005
VF = coefficient of variation of the fabrication factor
VM = coefficient of variation of the material factor
Vp = coefficient of variation of the ratio of the observed
failure loads divided by the average value of all
the
observed failure loads
___________________
√
(
n
n
X
∑ ___
X
i
)
2
X
∑( ___
– _________
n
X )
i
2
i=1
m
m
i=1
= __________________
n–1
VQ = coefficient of variation of the loads
___________________
√( 0.105Dn ) + ( 0.25Ln )
= ____________________ ; in lieu of calculation
1.05Dn + Ln
by the above formula, VQ = 0.21
α = Dn / Ln ; in lieu of calculation by the above formula, α = 0.2
βo = the target reliability index, 2.5 for columns, beams
and beam columns, 3.0 for tension members and
3.5 for connections.
2
2
The following values shall be used when documented
statistical data established from sufficient number of results
on material properties does not exist for the member or
connection:
Mm = 1.10 for behavior governed by the yield stress
= 1.00 for behavior governed by the ultimate stress
Fm = 1.00
VM = 0.06
VF = 0.05 for structural members and bolted connections
= 0.15 for welded connections
In evaluating test results, adjustment shall be made for
any differences between the yield strength of the material
from which the tested sections are formed and the minimum yield strength specified for the material which the
manufacturer intends to use. If the tensile yield strength of
the aluminum from which the tested sections are formed
is greater than the specified value, the test results shall be
adjusted down to the specified minimum yield strength of
the aluminum which the manufacturer intends to use. The
test results shall not be adjusted upward if the yield strength
of the test specimen is less than the minimum specified
yield strength. Similar adjustments shall be made on the
basis of tensile ultimate strength instead of yield strength
when tensile ultimate strength is the critical factor.
Adjustments shall also be made for differences between
nominal section properties and those of tested sections.
9.4 Testing Roofing and Siding
Where the configuration of roofing and siding installations are such that calculation of their strength cannot be
made in accordance with the provisions of this Specification, their bending strength shall be established from tests.
Tests are also required in the following cases:
a. When web angles θ are asymmetrical about the centerline of a valley, rib, flute, crimp, or other corrugation.
January 2005
b. When web angles θ are less than 45o.
c. When aluminum panels are alternated with panels
composed of any material having significantly different strengths or deflection characteristics.
d. When flats spanning from rib to rib or other corrugation in the transverse direction have a width to thickness ratio greater than either of the following:
447
1230
__ where q is the design load in psf (____
__
1) _____
3
3
√q
√q
where q is the design load in kN/m2)
___
___
√
√
Fty
Fty
___
2) 435 ___
q where Fty is in ksi and q is in psf (37 q
where Fty is in MPa and q is in kN/m ).
e. When panel ribs, valleys, crimps, or other corrugations are of unequal depths.
f. When specifications prescribe less than one fastener
per rib to resist negative or uplift loading at each purlin, girt, or other transverse supporting member.
g. When panels are attached to supporting members by
profile interlocking straps or clips.
2
9.4.1 Test Method
Tests shall be conducted in accordance with ASTM E
1592.
9.4.2 Different Thicknesses
Only the thinnest and thickest specimens manufactured
are required to be tested when panels are of like configuration, differing only in material thickness. Where the failure
of the test specimens is from bending stress, the bending
strength for intermediate thicknesses shall be interpolated
as follows:
(
)
log ti – log tmin
log Mi = log M1 + ______________
( log M2 – log M1 )
log tmax – log tmin
(Eq. 9.4.2-1)
where
Mi = bending strength of member of intermediate
thickness ti
M1 = bending strength of member of thinnest material
M2 = bending strength of member of thickest material
ti = thickness of intermediate thickness material
tmin = thickness of thinnest material tested
tmax = thickness of thickest material tested
9.4.3 Design Loads from Tests
Design loads shall be determined using the resistance factors given in Section 9.3.2 for bending and Section 5 applied
to the minimum test strength achieved for fasteners.
9.4.4 Deflections
Live load deflections shall not exceed 1/60 of the span
length.
I-B-77
Aluminum Design Manual
PART II-A
Commentary on
Specification for
Aluminum Structures–
Allowable Stress Design
The Aluminum Association, Inc.
1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
Eighth Edition, January 2005
IIA
Commentary on Specification for Aluminum Structures—Allowable Stress Design
TABLE OF CONTENTS
Section 1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Safety Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Section 2. Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
2.1 Section Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Section 3. General Design Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
3.4 Allowable Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.4.1
Tension, Axial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.4.2
Tension in Extreme Fibers of Beams—Flat Elements In Uniform Tension . . . . . . . . . . . . . . . . . . . . . . . 8
3.4.3
Tension in Extreme Fibers of Beams—Round or Oval Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4.4
Tension in Extreme Fibers of Beams—Flat Elements In Bending in Their Own Plane . . . . . . . . . . . . . . 8
3.4.5
Bearing on Rivets and Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4.6
Bearing on Flat Surfaces and Pins and on Bolts in Slotted Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4.7
Compression in Columns, Axial, Gross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4.7.2 Doubly or Singly Symmetric Sections Subject to Torsional or TorsionalFlexural Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.4.7.3 Nonsymmetric Sections Subject to Torsional or Torsional-Flexural Buckling . . . . . . . . . . . . . 9
3.4.8
Uniform Compression in Elements of Columns Whose Buckling Axis is an Axis of
Symmetry—Flat Elements Supported On One Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.4.8.1 Uniform Compression in Elements of Columns Whose Buckling Axis is
not an Axis of Symmetry—Flat Elements Supported On One Edge . . . . . . . . . . . . . . . . . . . . 9
3.4.9
Uniform Compression in Elements of Columns—Flat Elements Supported on
Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.4.9.1 Uniform Compression in Elements of Columns—Flat Elements Supported
on One Edge and With Stiffener on Other Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.4.9.2 Uniform Compression in Elements of Columns—Flat Elements Supported
on Both Edges and With an Intermediate Stiffener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.4.10 Uniform Compression in Elements of Columns—Curved Elements Supported on
Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.4.11 Compression in Beams, Extreme Fiber, Gross Section—Single Web Shapes . . . . . . . . . . . . . . . . . . . . 10
3.4.12 Compression in Beams, Extreme Fiber, Gross Section—Round or Oval Tubes . . . . . . . . . . . . . . . . . . . 10
3.4.13 Compression in Beams, Extreme Fiber, Gross Section—Solid Rectangular and Round Sections . . . . . 11
3.4.14 Compression in Beams, Extreme Fiber, Gross Section—Tubular Shapes . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4.15 Uniform Compression in Elements of Beams—Flat Elements Supported on
One Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4.16 Uniform Compression in Elements of Beams—Flat Elements Supported on
Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4.16.1 Uniform Compression in Elements of Beams—Curved Elements
Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4.16.2 Uniform Compression in Elements of Beams—Flat Elements Supported
on One Edge and With Stiffener on Other Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4.16.3 Uniform Compression in Elements of Beams—Flat Elements Supported
on Both Edges and With an Intermediate Stiffener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4.17 Compression in Elements of Beams (Element in Bending in Own Plane)—
Flat Elements Supported on Tension Edge, Compression Edge Free . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
January 2005
II-A-3
3.4.18
Compression in Elements of Beams (Element in Bending in Own Plane)—
Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4.19 Compression in Elements of Beams (Element in Bending in Own Plane)—
Flat Elements Supported on Both Edges and With a Longitudinal Stiffener . . . . . . . . . . . . . . . . . . . . . . 13
3.4.20 Shear in Elements—Unstiffened Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . 13
3.4.21 Shear in Elements—Stiffened Flat Elements Supported on Both Edges . . . . . . . . . . . . . . . . . . . . . . . . . 13
Section 4. Special Design Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1 Combined Axial Load and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1.1
Combined Compression and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1.2
Combined Tension and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Torsion and Shear in Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.4 Combined Shear, Compression, and Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.5 Longitudinal Stiffeners for Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.6 Transverse Stiffeners for Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.7 Effects of Local Buckling on Member Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.7.1
Local Buckling Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.7.2
Weighted Average Axial Compressive Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.7.3
Weighted Average Bending Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.7.4
Effect of Local Buckling on Column Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.7.5
Effect of Local Buckling on Beam Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.7.6
Effective Width for Calculation of Bending Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.7.7
Web Crippling of Flat Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.7.8
Combined Web Crippling and Bending for Flat Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.8 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.8.1
Constant Amplitude Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.8.2
Variable Amplitude Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.9 Compression in Single Web Beams Including Single Web Beams With Tubular Portions . . . . . . . . . . . . . . . . . . 16
4.9.1
Doubly Symmetric Sections and Sections Symmetric About the Bending Axis . . . . . . . . . . . . . . . . . . . 16
4.9.2
Singly Symmetric Sections Unsymmetric about the Bending Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.9.3
Singly Symmetric Sections Symmetric or Unsymmetric about the Bending Axis,
Doubly Symmetric Sections and Sections Without an Axis of Symmetry. . . . . . . . . . . . . . . . . . . . . . . . 16
4.9.4
Lateral Buckling Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.10 Compression in Elastically Supported Flanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.11 Single Angles in Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.11.1 Bending About Geometric Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.11.2 Bending About Principal Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.12 Tapered Thickness Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.13 Compressive Strength of Beam Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Section 5. Mechanical Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.1.1
Minimum Edge Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.1.2
Maximum Spacing of Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.1.3
Block Shear Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.1.4
Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.1.5
Effective Net Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.1.8
Countersunk Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.2 Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.2.1
Bolt Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.2.3
Bolt Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.2.4
Bolt Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.2.5
Bolt Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.2.7
Lockbolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
II-A-4
January 2005
5.2.8
5.3
5.4
5.5
Slip-Critical Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2.8.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2.8.2 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2.8.3 Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2.8.4 Design for Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2.8.5 Design for Slip Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2.8.6 Washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.2.8.7 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Riveted Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.3.1 Rivet Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.3.4 Rivet Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.3.7 Blind Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Tapping Screw Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.4.1 Screw Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.4.2 Screw Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.4.2.1 Pull-Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.4.2.2 Pull-Over . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.4.3 Screw Shear and Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Building Sheathing Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.5.2 Sidelaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.5.3 Fasteners in Laps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Section 6. Fabrication and Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
6.1 Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.1.1 Punch and Scribe Marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.2 Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.2.3 Re-Entrant Corners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.3 Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.6 Finishes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.7 Contact with Dissimilar Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.7.3 Concrete or Masonry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.7.4 Runoff from Heavy Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.9 Fabrication Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.10 Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.11 Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.11.2 Bolt Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Section 7. Welded Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
7.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
7.2 Welded Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
7.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
7.2.2 Members with Part of the Cross Section Weld-Affected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.2.3 Columns or Beams with Transverse Welds Away from Supports and Cantilevers
with Transverse Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.3 Welded Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.3.1 Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.3.1.1 Complete Penetration and Partial Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.3.2 Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.3.2.1 Effective Throat and Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.3.2.2 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.3.3 Plug and Slot Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.3.4 Stud Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.4 Post-Weld Heat Treating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
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Section 8. Castings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
8.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
8.2 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
8.3 Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
8.4 Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Section 9. Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
9.3 Number of Tests and the Evaluation of Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
9.3.1
Tests for Determining Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
9.4 Testing Roofing and Siding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
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January 2005
Section 1. General
1.1 Scope
This Specification applies to normal ambient temperature uses of aluminum alloys. For higher temperatures,
strengths and other properties (such as corrosion resistance) of different alloys are affected to varying degrees.
Part V of the Aluminum Design Manual, Table 9, Typical
Tensile Properties at Various Temperatures, provides typical, but not minimum, properties and is not to be used for
design. For information regarding properties at elevated
temperatures, the supplier should be consulted.
1.2 Materials
The alloys addressed by the Specification are those used
for general structural purposes and registered with the
Aluminum Association. The Specification may be applied
to alloys and tempers not listed in Table 3.3-1 if the engineer has the properties needed for proper design, including
notch sensitivity. Additional information on alloys, temper
designations, and products available is published in Aluminum Standards and Data (1).
1.3 Safety Factors
The Specification is not limited as to type of structure.
The general formulas in Table 3.4-3 can be applied to any
structure, with appropriate values substituted for the factors
of safety ny and nu. The values of factors of safety are given
for in Table 3.4-1 for “Building Type Structures” and for
“Bridge Structures”. “Building Type Structures” include
highway signs, luminaires and traffic signals. The “bridge
structures” cover bridges that are not designed according to
References (2) or (3).
Section 2. Design Procedure
2.1 Section Properties
Section properties for many shapes are given in this
Manual in Part VI. Formulas for calculating section properties are also given in Part VI.
Nominal (rather than minimum) dimensions are used
to calculate section properties. This is because safety or
resistance factors account for the fact that an actual dimension might be less than the nominal dimension, as long as
tolerances do not exceed standard mill tolerances (given in
Aluminum Standards and Data).
2.2 Procedure
Calculated stresses in the members resulting from external loading are compared with the appropriate allowable
stresses. Alternatively, the provisions of Section 9, Testing, can be used. Procedures for using the Specification are
January 2005
demonstrated in illustrative examples in Part VIII of this
Manual.
2.3 Loads
The Specification for Aluminum Structures no longer
includes a 1/3 allowable stress increase for wind or seismic loads. ASCE 7-98 and later ASCE 7 editions already
include the factors that would fulfill the purpose of the previously permitted stress increase.
Section 3. General Design Rules
The allowable stresses specified in subsections of
this Section are listed in tables throughout the Specification. Part V Material Properties provides the basis for
the mechanical properties for various alloys, tempers and
product forms used in this Specification. The values of the
allowable stresses are also given for various alloys in Part
VII Design Aids.
3.4.1 Tension, Axial
The axial tensile strength is the lower of 1) the yield
strength of the gross section, and 2) the ultimate (fracture)
strength of the net section. This is because the net section
usually exists over only a short portion of the overall length
of the member, and the elongation of the member resulting
from yielding across the net section is small. Thus, yielding
on the net section is not a limit state.
In general, the allowable tensile stress for building structures is the lower of two values that results from applying
a factor of safety of 1.65 to the yield strength or 1.95 to the
tensile strength. The corresponding factors of safety used
to determine allowable tensile stresses for bridge structures
are 1.85 and 2.2. These factors of safety are the same as
those that were used in the ASCE papers published in 1962
(4, 5) and have been used in the Aluminum Association
specifications since that time.
In the general formula for determining allowable tensile stress on the basis of the ultimate tensile strength, the
factor of safety nu is multiplied by a factor kt. For regions
farther than 1 in. (25 mm) from a weld, this factor is l.0 for
most alloys that appear in the Specification. The exceptions
are 2014-T6, 6066-T6, and 6070-T6. The value of kt for
2014-T6 is 1.25 and 1.1 for 6066-T6 and 6070-T6. This
factor is introduced to take account of the fact that these
high-strength alloys are somewhat more notch sensitive
than the other alloys listed in the Specification. The resulting allowable tensile stress for bridge structures of 2014T6 is the same as that used in specifications for structures
of this alloy published by the American Society of Civil
Engineers (6).
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3.4.2 Tension in Extreme Fibers of Beams—Flat
Elements In Uniform Tension
Sections 3.4.2 and 3.4.4 apply to tension elements of
beams and can be used in two ways:
a. The least tensile strength of all the elements of the
shape may be conservatively used for the entire
shape. For example, for an I beam the strength would
be the least of the strengths of the flange elements
computed by Section 3.4.2 and the web element
computed by Section 3.4.4.
b. The tensile strength of the elements may be determined using Sections 3.4.2 and 3.4.4 and then Section 4.7.3 may be used to determine a weighted average strength for the entire shape.
3.4.3 Tension in Extreme Fibers of Beams—
Round or Oval Tubes
The allowable tensile stresses for round or oval tubes
subjected to bending are somewhat higher than for structural shapes. Analysis and tests (7) have demonstrated that
yielding or failure of tubular beams does not occur until the
bending moment considerably exceeds the yield moment
predicted by the ordinary flexure formula. This results from
the non-linear distribution of stress in the inelastic range.
Yielding does not become apparent as soon as the calculated stress in the extreme fiber reaches the yield strength
because the less highly stressed fibers near the center of the
beam are still in the elastic range. The constants 1.17 and
1.24 can be considered as shape factors for yielding and
ultimate strength, respectively.
These constants were picked from curves of yield
strengths at 0.2 percent offset for tubes of representative
proportions. The shape factors on ultimate strength were
deduced from apparent and actual stress-strain curves at a
stress corresponding to tensile strength of the material.
3.4.4 Tension in Extreme Fibers of Beams—Flat
Elements In Bending in Their Own Plane
As in the case of round tubes and solid rounds, theory
and tests have shown that aluminum alloy members of
these shapes can undergo bending moments that are considerably greater than those predicted on the basis of the
ordinary flexure formula (8). In this case, the shape factors used for yielding and ultimate strength, respectively,
are 1.30 and 1.42. For elements unsymmetric about the
bending axis, it is conservative to use the allowable stress
obtained from 3.4.2.
3.4.5 Bearing on Rivets and Bolts
Bearing failure is reached when elongation of the fastener hole becomes excessive. Bolted or riveted joints may
also fail by shear of the fasteners, by shear rupture of the
material between the holes and the end of the connected
part, or by fracture on the net section. The factor of safety
is higher for fastener shear (2.34) than the other failure
modes (1.95) because the structural integrity of fasteners is
less reliable than base metal. This is because fasteners are
subjected to additional hazards that base metal is not—they
may be improperly installed (for example, by being over- or
under-tightened, missing nuts or washers, or with threads
in the shear plane when this was not accounted for in the
design). Prior to the 7th edition of the Specification the factor of safety on bearing failure was the same as for fastener
shear. The shear rupture provisions (Section 5.1.3), however, added in the 7th edition of the Specification, produce
calculated strengths for some connections that are less than
those calculated under the provisions of earlier editions
which did not contain this check.
Bearing tests show (9) that for ratios of edge distance
to fastener diameter as small as 1.5, it is conservative to
reduce the allowable bearing stress by the ratio of the edge
distance to twice the fastener diameter. The Specification
does not allow ratios of edge distance to fastener diameter
smaller than 1.5.
Tests (10) have demonstrated that a relatively even distribution of load among the fasteners is achieved before
ultimate failure of mechanically fastened joints in structural aluminum alloys.
3.4.6 Bearing on Flat Surfaces and Pins and on
Bolts in Slotted Holes
The bearing strength for flat surfaces, elements with pins
in holes and elements with pins or bolts in elongated holes
is 2/3 the bearing strength of elements joined by properly
fitting rivets and bolts. This requirement originally was
adopted from steel specifications. A lower bearing strength
appears to be reasonable in these cases because the applied
pressure can be much more concentrated than that in riveted or bolted joints, because the diameter of the loading
element (pin) can be small compared to the diameter of the
opening in the element that is being loaded. Good practice in bolted and riveted joints requires a reasonable fit
between fastener and hole diameter.
3.4.7 Compression in Columns, Axial,
Gross Section
The formulas in this Section for values of kL/r exceeding S1 approximate the column strength given by the tangent modulus column formula. The tangent modulus formula is
π2E
(kL /r)
t
Fcr = _____
2
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(Eq. C3.4.7-1)
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where
Fcr = column strength
Et = tangent modulus (slope of stress strain curve)
corresponding to Fcr
kL = effective length of column
r = least radius of gyration of column
In the elastic range, this formula is simply the Euler
column formula, which is used as a basis for allowable
stresses for values of kL/r exceeding S2. For values of kL/r
between S1 and S2 the tangent modulus formula is approximated closely by the straight line (8), which is used as a
basis for the allowable stress formula.
Numerous tests have shown that these formulas closely
predict the strength of essentially straight columns (8, 11).
To ensure adequate safety in the presence of accidental
eccentricity and initial crookedness, which may reduce the
strength of practical columns (12, 13), the factor of safety
nu rather than ny is applied to column strength.
The effective length of columns is normally defined as a
factor k times the length of the column between lateral support. Background for this can be found in Reference (14).
For values of kL/r less than Sl, the compressive strength
of columns is the compressive yield strength. Such columns are sometimes referred to as stub columns, for which
the failure mode is yielding rather than buckling.
A great deal of background information relating to columns and other buckling problems can be found in Reference (15).
3.4.8 Uniform Compression in Elements of
Columns Whose Buckling Axis is an Axis of
Symmetry—Flat Elements Supported On
One Edge
Reference (18) addresses Sections 3.4.8(a) and 3.4.8(b).
Section 3.4.8(c) is based on the post-buckling strength
rather than the buckling strength of unstiffened plate elements (19). Tests performed on stub-columns with cruciform cross sections show post-buckling strength. These
provisions apply to wide flange shapes buckling about
either axis and channels buckling in the strong direction.
3.4.8.1 Uniform Compression in Elements of
Columns Whose Buckling Axis is not an
Axis of Symmetry—Flat Elements
Supported On One Edge
In columns buckling about a principal axis that is not
an axis of symmetry the centroid of the stresses may not
be the same as that for the full section. This is due to the
non-linear stress distribution in the post-buckling range of
the flat plate elements of the section. In such cases though
some postbuckling strength may exist, it may not be as
large as that if the buckling axis were an axis of symmetry. For this reason the provisions of this Section limits the
strength to local buckling strength. Column sections such
as channels buckling about the weak axis are covered by
these provisions.
3.4.7.2 Doubly or Singly Symmetric Sections
Subject to Torsional or Torsional-Flexural
Buckling
3.4.9 Uniform Compression in Elements of
Columns—Flat Elements Supported on
Both Edges
Based on data in Reference (16), Reference (17) shows
that the column design equations of Section 3.4.7 can be
used for torsional-flexural buckling if an equivalent slenderness ratio is defined. The redefinition is based on (kL/r)e
the elastic torsional-flexural buckling stress. The inelastic
torsional-flexural buckling stress is then calculated using
the column design equations used for flexural buckling.
For point symmetric sections such as cruciforms, torsional
buckling is the most likely mode of failure and Fe becomes
equal to Fet.
The ultimate strength of a plate supported on both edges
may be appreciably higher than the local buckling strength.
Thus the allowable stress is obtained by applying the factor
of safety nu to a formula that gives a conservative approximation to the ultimate strength of the plate (20).
In the inelastic stress range, the ultimate strength is the
same as local buckling strength, so the allowable stress is
based on the local buckling formula with an equivalent
slenderness ratio of 1.6 b/t and a factor of safety nu.
The coefficient 1.6 is approximately the value that applies
to a plate simply supported on two longitudinal edges.
3.4.7.3 Nonsymmetric Sections Subject to
Torsional or Torsional-Flexural Buckling
Nonsymmetric sections that are subject to torsional or
torsional-flexural buckling may be designed as follows:
- determine the elastic torsional-flexural buckling stress
according to the torsional-flexural theory.
- determine the equivalent slenderness ratio using Equation 3.4.7.2-1.
- determine the limiting or allowable stress with the equations of Section 3.4.7.
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3.4.9.1 Uniform Compression in Elements of
Columns—Flat Elements Supported on
One Edge and With Stiffener on
Other Edge
Equation 3.4.9.1-2 provides a transition between the
allowable stress in an unstiffened plate element and the
allowable stress in an edge stiffened plate element with a
fully adequate stiffener. The predicted capacities using the
provisions in this Section correlate well with the experimental capacities obtained from test on stub columns with
edge stiffeners (19).
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Equations 3.4.9.1-3 through 3.4.9.1-5 are the r s /R a
ratios for different ranges of the (b/t) ratios where rs is the
radius of gyration of an edge stiffener about the plate midthickness surface and Ra is the radius of gyration of a stiffener adequate to make the flange being stiffened function
as a plate element supported on both longitudinal edges.
Equations for Ra are given by the denominators of Equations 3.4.9.1-4 and 3.4.9.1-5. The equations for determining Ra are adapted from the AISI Specification (21) and
compared with the equation proposed in Reference (23).
The elastic buckling analysis in Reference (23) shows that
an edge stiffener is adequate if rs = 6t. Elastic buckling
begins at a (b/t) ratio equal to S where S is the limiting (b/t)
ratio at which a stiffened element is fully effective. At this
value of (b/t) ratio, the value of Ra obtained from Equation
3.4.9.1-4 is identical to the value of rs derived in Reference
(23). A linear relationship is assumed between Ra and (b/t)
ratio if the (b/t) ratio is between S/3 and S.
The value of rs necessary to be considered as an adequate
edge stiffener is larger than 6t in the post-buckling range of
the element being stiffened. Post-buckling strength exists in
an edge stiffened plate element with a (b/t) ratio exceeding
S. Equation 3.4.9.1-5 is valid for values of the (b/t) ratios
between S and 2S. Sufficient test data does not exist to
develop an equation for Ra when the (b/t) ratio exceeds 2S.
The limitation on the Ds /b ratio prevents any adverse
interaction between the local buckling of the lip stiffener
and the flange.
It should be noted that Fc determined according to Equations 3.4.9.1-1 and -2, should not exceed the value of Fc determined for the stiffening lip according to Section 3.4.8.
In this Section as well as in some of the subsequent sections, it is stated that if the inside corner radius exceeds
4 times the thickness then the inside radius shall be assumed
equal to 4 times the thickness in calculating b. This rule was
reached on the basis that a radius that is too large would be
detrimental to the post buckling strength of the element and
that the flat element width would be too unconservative to
take in calculating the strength.
3.4.9.2 Uniform Compression in Elements of
Columns—Flat Elements Supported on
Both Edges and With an
Intermediate Stiffener
The provisions in this Section are based on Reference
(23) which is discussed further in Section 3.4.16.3.
3.4.10 Uniform Compression in Elements of
Columns—Curved Elements Supported
on Both Edges
In theory, the elastic buckling strength of an ideal cylindrical shell loaded in compression can be determined by
substituting an equivalent slenderness ratio of 4.0Rb /t into
the column formula. The buckling strength of actual shells,
however, is strongly affected by imperfections in the geomII-A-10
etry and end conditions of the shells. Tests indicate that this
effect tends to increase with increasing Rb /t. This effect of
imperfections is taken into account by the formulas in this
Section, which are conservative when compared with the
results of numerous tests on tubes and cylinders (7, 24). The
formulas of this Section are based on local buckling strength,
since severe deformations occur at this load.
The strength of circumferentially welded tubes has been
shown to be given accurately by the same equations as those
for unwelded tubes for cases in which Rb /t < 20 (approximately). For circumferentially welded cylinders with much
higher Rb /t, recent studies show that the provisions may be
very unconservative (17), thus the restriction of Rb /t < 20
for tubes with circumferential welds.
3.4.11 Compression in Beams, Extreme Fiber,
Gross Section—Single Web Shapes
The allowable compressive stresses in single-web structural shapes and built-up sections bent about the strong axis
are based on the lateral, torsional buckling strength of beams
with a factor of safety ny. In the inelastic stress range the formulas employ the straight line approximation to the tangent
modulus buckling curve that is also used for columns. Tests
have shown this curve to be conservative for beams (8). The
basis for the lateral torsional buckling of single web beams
about their strong axis is in Reference (25).
A simple span beam restrained against movement laterally and vertically at the supports, but free to rotate about the
vertical and horizontal axes at the ends is assumed. A symmetrical section and uniform moment are also assumed. The
expressions derived for lateral buckling (25) were rather complicated. To simplify calculations an approximate method
for estimating lateral buckling strength was developed.
An effective slenderness ratio L/1.2ry was found to provide conservative answers for standard aluminum shapes.
Because of the conservatism of the approximate method,
Section 4.9 allows the designer to calculate a more precise
value for ry based on the “exact” solution.
The factor of safety applied to beam buckling is ny rather
than the value used for columns, nu. The assumptions on
restraint at ends and at loads are conservative. In addition,
continuous beams can redistribute moment and beams attached
at their ends can carry some load in membrane actions. All the
assumptions err on the conservative side, and thus the lower
factor of safety was used.
3.4.12 Compression in Beams, Extreme Fiber,
Gross Section—Round or Oval Tubes
For values of Rb /t below the slenderness limit S1, the
allowable stress is increased over the basic allowable compressive design stress for single web beams, since tests have
demonstrated that a shape factor of 1.17 can be applied to
the yielding of round tubes. For values of Rb /t between S1
and S2, the allowable stress is based on a formula that gives
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a close approximation to experimental values of buckling
strength for round tubes in bending (7).
The value of S2 in this Section is the value of Rb /t at
which the curve for bending strength intersects the curve
for buckling stress under axial compression. For greater
values of Rb /t, the conservative assumption is made that the
allowable stress in bending is the same as that in direct
compression. The limitation that the equations apply for
Rb /t < 20 for tubes with circumferential welds is the same
as that applied in Section 3.4.10.
3.4.13 Compression in Beams, Extreme Fiber,
Gross Section—Solid Rectangular and
Round Sections
If a solid rectangular beam is laterally unsupported and
is sufficiently narrow in cross section, it can fail by lateral
torsional buckling. This type of____
failure is taken into account
in this Section, using 2.3(d/t)√Lb /d as the equivalent slenderness ratio. If the beam is sufficiently wide, it will not
buckle, and the allowable
stress is controlled by the yield
____
strength. When 2.3(d/t)√Lb /d < S1 a shape factor of 1.3 for
yielding is assumed as for Section 3.4.4. In the intermediate
slenderness ratio range, the buckling strength is considerably affected by a redistribution of stress that accompanies
plastic yielding, so that the apparent stresses at buckling
are appreciably higher than values for single web beams.
The formula used to represent buckling strength has been
shown to agree well with the results of buckling tests on
rectangular beams (8).
The formulas are based on the conditions of a uniform
moment on a single span beam, simply supported, with the
ends prevented from lateral deflection, but free to rotate
about the vertical axis.
The factor of safety applied to beam buckling is ny, as
in Section 3.4.11. Experience indicates this factor of safety
is adequate.
small in comparison to the term that represents St. Venant
torsion. The two terms are equal when Cw = 0.038J(ky Lb)2.
If Cw is not small compared to 0.038J(ky Lb)2 the use of
Section 3.4.11 with the rye value calculated according to
Section 4.9.3 gives more accurate ___
results.
√IyJ
___
This Section allows replacing 2 in the denominator of
the slenderness term with Iy for narrow rectangular tubes. Iy
is___an approximation, and since it is typically greater than
√IyJ
___
, using Iy gives less conservative results. This unconser2
vatism is limited to about 10% by limiting the use of Iy to
tubes with a depth to width ratio of 6 or more.
The torsional constant J for a closed section is
4A2
J = ____m
(Eq. C3.4.14-1)
ds
∫__
t
where Am is the mean of the areas between the inner and
outer boundaries and ds is the incremental length along the
perimeter of thickness t. For uniform thickness t, this equation becomes:
4A2mt
J = ____
s
(Eq. C3.4.14-2)
where s is the length of the boundary at mid-thickness. The
expression for a hollow rectangular tube is
2t2t1(a – t2)2 (b – t1)2
J = ______________
at + bt – t 2 – t 2
2
1
2
1
(Eq. C3.4.14-3)
The dimensional notation is illustrated in Figure C3.4.14-1.
3.4.14 Compression in Beams, Extreme Fiber,
Gross Section—Tubular Shapes
This section applies to closed shapes. The wall thickness need not be uniform.
The allowable stresses in this Section are based on the
lateral torsional buckling strength of tubular shapes. The
safety factor is ny, for the same reasons as discussed in Section 3.4.11.
Since the Specification may be used for a wide variety
of extruded or formed shapes, the conservative assumption
was made that the shape factor for yielding is 1.0.
The expression used____
for equivalent slenderness ratio of
2L___
S
____
a tubular shape is 1.6 b c . This expression is more accu______
√IyJ
rate than the slenderness ratio of 1.6√LbSc/Ic which was
based on References (4) and (5). It was derived using the
more general theoretical equation for lateral buckling strength
and ignoring the term that represents the warping resistance
of the beam, since, for closed sections, this term is usually
√
January 2005
Figure C3.4.14-1
CROSS-SECTIONAL NOTATION
II-A-11
3.4.15 Uniform Compression in Elements of
Beams—Flat Elements Supported on
One Edge
Allowable stresses for values of b/t exceeding S1 were
obtained by applying the factor of safety ny to the ultimate strength of an outstanding flange simply supported
on one edge (20). If this Section were to be applied only
to standard structural shapes, it would have been possible
to assume some restraint against rotation at the supported
edge of the flange, which would have resulted in somewhat
higher allowable stresses. However, this Section also covers other extruded shapes and formed sheet members, in
which the web may offer little restraint against flange rotation. Therefore, the conservative assumption of simple support was made.
This Section permits the designer to take advantage of the
fact that the ultimate strength may exceed the local buckling
strength for very thin sections.
Formulas (b) and (c) are based on the ultimate strength
of an outstanding flange simply supported on one edge.
3.4.16 Uniform Compression in Elements of
Beams—Flat Elements Supported on
Both Edges
This is similar to Section 3.4.9 for components of columns, except that the factor of safety used is ny rather than
nu because the strength prediction of beams and beam elements are thought to be more conservative than those of
compression members.
Equations 3.4.16-2 and 3.4.16-3 are based on the ultimate strength of a plate simply supported on both edges.
3.4.16.1 Uniform Compression in Elements of
Beams—Curved Elements Supported on
Both Edges
These expressions for curved sections are taken from
Reference (26). They apply to curved components of beams
other than round or oval tubes, which are covered in Section 3.4.12. For values of Rb /t between S1 and S2 the stresses
allowed by Section 3.4.16.1 are somewhat lower than those
allowed by Section 3.4.12 because tests have shown that
not all beams with curved sections of these proportions can
sustain the high apparent stresses developed by round or
oval tubes.
3.4.16.2 Uniform Compression in Elements of
Beams—Flat Elements Supported on
One Edge and With Stiffener on
Other Edge
The predicted capacities using the provisions in this
Section, in conjunction with the weighted allowable stress
approach, correlate well with the experimental capacities
obtained from beam tests (19).
3.4.16.3 Uniform Compression in Elements of
Beams—Flat Elements Supported on
Both Edges and With an
Intermediate Stiffener
The provisions in this Section are based on work performed by Sharp (23). Equation 3.4.16.3-6 is the equivalent slenderness ratio to be used with the column buckling
equations given by Equations 3.4.16.3-2 and 3.4.16.3-3.
The predicted capacities using the provisions in this Section, in conjunction with the weighted allowable stress
approach, correlate well with the experimental capacities
obtained from beam tests as shown in (19).
3.4.17 Compression in Elements of Beams
(Element in Bending in Own Plane)—
Flat Elements Supported on Tension
Edge, Compression Edge Free
The coefficients in the formula for inelastic buckling
strength were assumed to be the same as for rectangular
beams (Section 3.4.13) because calculations and tests have
shown that the apparent stress (Mc/I) at which the yield
strength is reached in the outer fiber of sections such as
tees, angles and channels is even higher than for rectangular beams. The equivalent slenderness ratio was assumed to
be 3.5b/t, which implies partial restraint against rotation at
the supported edge.
This is based on elastic buckling strength. This type of
component is assumed to have negligible post-buckling
strength.
3.4.18 Compression in Elements of Beams
(Element in Bending in Own Plane)—
Flat Elements Supported on Both Edges
The comments under Section 3.4.17 concerning shape
factor and buckling formula constants apply here also. When
the neutral axis is at the midheight of the element, the equivalent slenderness ratio is 0.65h/t, which applies to a plate in
bending with both edges simply supported. Simple support
was assumed because the boundary conditions at the compression edge are more important than those at the tension
edge and it is possible that compression elements supporting the compression flange may buckle at the same time
as the web.
The provisions in this Section are similar to that in Section 3.4.9.1. The commentary for Section 3.4.9.1 is equally
applicable for this Section as well.
II-A-12
January 2005
3.4.19 Compression in Elements of Beams
(Element in Bending in Own Plane)—
Flat Elements Supported on Both Edges
and With a Longitudinal Stiffener
Comments made with regard to Sections 3.4.17 and
3.4.18 apply here also. The equivalent slenderness ratio
is 0.29h/t based on simple support at the edges and at the
stiffener (27).
3.4.20 Shear in Elements—Unstiffened Flat
Elements Supported on Both Edges
Allowable shear stresses in unstiffened flat webs are determined by applying the factor of safety ny to the calculated
buckling strength for a web with partial restraint against rotation at the attachment to the flanges. The corresponding value
of the equivalent slenderness ratio is 1.25h/t (27, 28). The
formulas for the buckling coefficients in the inelastic range
were developed originally for shear buckling of tubes (7) but
they apply also to flat plates in shear.
3.4.21 Shear in Elements—Stiffened Flat
Elements Supported on Both Edges
A stiffened flat web that has buckled in shear can continue to carry load by diagonal tension action in the web
(29, 30, 31). Thus it is not necessary to use the same factor of safety against shear buckling of the stiffened web
as is used for an unstiffened web in which local buckling
could bring about collapse. However, it was assumed that
it would not be desirable to have local buckling of webs at
design loads, both from the standpoint of appearance and
because of the possibility of fatigue failure. Thus, the factor of safety na was applied to the local buckling strength
of stiffened flat webs in shear. This factor of safety is used
to ensure that stresses at design loads are less than the local
buckling stress. The edges were assumed to be partially
restrained against rotation, giving an equivalent slenderness ratio of
1.25a1
____________
__________
a 2
t 1 + 0.7 __1
√
(a )
4.2 Torsion and Shear in Tubes
The equation for equivalent h/t is based on the theoretical elastic buckling strength of cylinders in torsion. Tubes
loaded in torsion are not as sensitive to the effect of initial imperfections in the geometry as are tubes loaded in
axial compression. The theoretical buckling strength has
been found to give good agreement with the results of tests
on thin cylinders that fail in the elastic range (32) and the
use of this expression with the inelastic buckling equations
employed in the Specification also gives good agreement
with experimental results in the inelastic stress range (7).
4.4 Combined Shear, Compression and
Bending
The formula for interaction of combined stresses in
walls of curved surfaces or round tubular members is
based on investigations reported in (15, 28, 33). Likewise,
the interaction equation for combined stresses in webs of
rectilinear shapes and plates of built-up girders or similar
members is based on the buckling strength of these members (15, 27).
4.5 Longitudinal Stiffeners for Webs
This Section requires that if a longitudinal stiffener is
used on a beam web, it shall be located so that the distance
from the toe of the compression flange to the centroid of the
stiffener is 0.4 of the distance from the toe of the compression flange to the neutral axis of the girder. This is the optimum location for increasing the buckling strength of the
web under the influence of compressive bending stresses in
the web. The resulting increase in allowable compressive
stress in the web is reflected in Section 3.4.19 (27). The
formula for stiffener moment of inertia which is the same
as that used in earlier specifications published by ASCE
(4, 5), agrees closely with the size recommended on the
basis of theoretical considerations (27) and is also in good
agreement with the results of tests (22). The factor α takes
account of the effect of eccentricity for a stiffener on one
side of the web only (34).
2
Section 4. Special Design Rules
4.1 Combined Axial Load and Bending
4.1.1 Combined Compression and Bending
Provisions on combined compression and bending in
this Section agree with the allowable stress design versions
of other metal structural specifications (21).
4.1.2 Combined Tension and Bending
The provisions in the Section are the same as those used
in other metal structural specifications (21).
January 2005
4.6 Transverse Stiffeners for Webs
The stiffener size recommended is sufficient to limit
local buckling of shear webs to the panels between stiffeners and to provide considerable post-buckling strength
in the web. These formulas were also used in the specifications published by ASCE (4, 5). They agree well with
the results of tests (35) and are conservative in comparison
with stiffener sizes derived from theoretical considerations
(36). Background for these provisions is discussed further
in (37) and (38).
The Section requires that the moment of inertia of a
stiffener at a point of bearing should be equal to the sum of
the moment of inertia required to resist the tendency of the
II-A-13
web to buckle and the moment of inertia required for the
stiffener to carry the bearing load as a column with the
length equal to the height of the web.
4.7 Effects of Local Buckling on Member
Performance
This Section applies to either thin or heavy gage construction. In some cases, consideration shall be given to the
design of members that incorporate elements having relatively large ratios of width to thickness. In the following
paragraphs such elements are referred to as “thin”, meaning that they are thin relative to their width, even though
the thickness itself may be any value.
4.7.1 Local Buckling Stresses
In Sections 3.4.8, 3.4.9, 3.4.9.1, 3.4.15, 3.4.16, 3.4.16.2,
3.4.18 and 3.4.19 for thin plate elements, namely, elements
having b/t ratios in excess of S2, the ultimate load carrying capacity is based on the post buckling strength which
can be quite significantly higher than the local buckling
strength.
For these cases where the post buckling strength is the
basis for design, the local buckling stresses are needed
in certain situations. All the equations for local buckling
stresses except in Sections 3.4.9.1 and 3.4.16.2 are based
on plate or stiffener buckling theories. In Sections 3.4.9.1
and 3.4.16.2, the local buckling stress is based on the derivation given below. Limiting the stresses to the local buckling stress divided by a factor of safety of 1.2 would limit
the appearance of buckling at allowable loads.
One can visualize the post buckling strength in terms of
the effective width approach as is done for deflection calculations. Using the effective width approach, the ultimate
axial load capacity of a plate element supported by webs on
both longitudinal edges is determined as follows:
Pult = tbeFcy
(Eq. C4.7.1-1)
where Fc y is the yield stress, be is the effective width and t
is the thickness of the plate.
Using the average stress approach as is done in Section
4.7.2, the load capacity of the plate can be determined as
follows:
Pult = tbnyFc
(Eq. C4.7.1-2)
where b is the plate width, ny is the factor of safety, Fc is
the allowable stress.
Setting Equations C4.7.1-1 and -2 equal, the following expression for the effective width at ultimate load is
obtained:
ny Fc
be = b ____
Fcy
II-A-14
(Eq. C4.7.1-3)
The effective width according to the effective width equations in Section 4.7.6 can be written as
___
√
Fcr
be = b ___
Fcy
(Eq. C4.7.1-4)
where Fcr is the plate buckling stress.
Setting Equations C4.7.1-3 and -4 equal, the following
expression for Fcr is obtained:
(nyFc)2
Fcr = ______
Fcy
(Eq. C4.7.1-5)
Equation C4.7.1-5 is the equation used for the case of Section 3.4.16.2.
For cases where post buckling strength is used, the
allowable compressive stresses given may result in visible
local buckling, even though an adequate margin of safety is
provided against ultimate failure.
In applications where any appearance of buckling must
be avoided, the stresses for thin sections should not exceed
the value of Fcr given divided by 1.2. The factor 1.2 is based
on experience.
4.7.2 Weighted Average Axial Compressive Stress
The ultimate strength of a member consisting of a number of slender elements can be estimated by simply adding
up the ultimate or buckling strengths of the individual elements (39).
4.7.3 Weighted Average Bending Strength
Tests of formed sheet beams (20) were the basis for
the weighted average allowable compression and tensile
bending stresses in Specification editions prior to 2005.
More recent research (83) documents modifications to the
weighted average method, improving its accuracy for a
variety of members. The distance c for a tensile flange is
the distance to its extreme fiber because tension fracture
initiates there. The distance c for a compression flange is
the distance to its centerline because buckling is based on
the flange’s average stress.
4.7.4 Effect of Local Buckling on
Column Strength
Sections 3.4.8 and 3.4.9 take advantage of the postbuckling strength of plate elements, because in general such elements may buckle without causing failure of the member.
However if the local buckling stress of the section is lower
than the flexural buckling strength of the column, the reduced
stiffness that accompanies local buckling may reduce the
allowable column stress as given by Section 3.4.7. The formula in Section 4.7.4 for allowable stress is based on an
equation (40) that has been found to give good agreement
with the results of compression tests on H-section and box
section columns incorporating thin elements (41).
The local buckling values used in the calculations referenced in Section 4.7.1 are accurate for shapes such as
January 2005
square boxes and conservative for all other shapes. These
values can be quite conservative for sections in which the
edge restraint of the elements is much higher than the simply supported cases used.
4.7.5 Effect of Local Buckling on Beam Strength
The provisions of this paragraph take into account the
effect that the reduced stiffness due to local buckling may
have on the lateral buckling strength of single web beams.
The basic relationship that applies to columns has been
found to be useful also for beams (40). The local buckling
values used in the calculations, referenced in Section 4.7.1,
are based on flanges with a simply supported attached
edge, and thus can be quite conservative for sections
in which the edge restraint is much higher than the simply
supported case.
4.7.6 Effective Width for Calculation of
Bending Deflection
One way to take into account the effect of local buckling on the post-buckling behavior of structural members is
to consider that at stresses above the local buckling stress,
only part of the cross-section of the buckled element is
effective in carrying load. The formula given here has been
found to be generally conservative for aluminum elements
(19, 20).
As noted in Section 4.7.1 the allowable compressive
stresses may in certain instances result in some local buckling at design loads for very thin sections, even though an
adequate margin of safety is provided against ultimate failure. This local buckling may result in increased deflections
for sections with plate elements covered by Sections 3.4.8,
3.4.9, 3.4.15, 3.4.16, 3.4.18 and 3.4.19 with b/t values
exceeding 1.65S2 where the value of S2 is obtained for the
element in question.
The formulation of Sections 3.4.9.1 and 3.4.16.2 is
somewhat different and a different criterion is used for
deciding when the effective section is to be used.
4.7.7 Web Crippling of Flat Webs
The formulas given in this Section are based on Reference
(42) which is also described in Reference (17). If the edge load
is concentrated over a portion of the element length, web crippling needs to be considered. This failure mode is confined to
the area of the web under the load. The equation for maximum
strength for interior loads is given by Equation 4.7.7-1, and
that for end loads is given by Equation 4.7.7-2. The strengths
are effectively post-buckled values. Thus thin webs will have
lateral displacements at the calculated strengths.
4.7.8 Combined Web Crippling and Bending for
Flat Webs
The formulas given in this Section are based on Reference (42) which is also described in Reference (17).
January 2005
4.8 Fatigue
The provisions of this Section are modifications of the
original fatigue specifications (43). The modifications include
changes to the fatigue strength curves and the addition of a
method to determine life of parts under spectrum loading.
The changes are based on recent tests of full scale welded
beams in the United States (44) and Europe (45).
The analyses consider that the major factors affecting
fatigue behavior are the number of stress cycles, the magnitude of the stress range and the type and location of the
member or detail. The fatigue crack will generally grow
perpendicular to the plane of maximum stress. This Section
of the Specification uses a nominal stress range determined
by elastic analysis. The effect of stress concentrations are
accounted for through the proper selection of fatigue details.
Many other factors, including environment, detrimental weld
quality, and post-weld mechanical treatment can have an
effect, but are not considered within the scope of this document. Special analysis or tests are required for details and
conditions not specifically covered by the Specification.
Loads and number of load applications are not covered.
If the information exists for structures of other materials,
the same values may be used for aluminum structures of the
same type. Wind induced vibrations of undamped structures
or components can cause large numbers of cycles and high
stresses and thus need to be avoided. Alternatively, vibration
dampers may be used to limit wind induced vibrations.
The fatigue strength of mechanically fastened connections with a stress ratio less than or equal to zero is based
on Reference (74). This reference includes data from about
750 tests of bearing and friction joints with a wide variety of conditions. The data used to determine the fatigue
strength of joints with a stress ratio of zero conservatively
include numerous tests with a stress ratio of 0.1.
4.8.1 Constant Amplitude Loading
The equations for allowable stress are based on the 95%
confidence for 97.7% probability of survival. The results of
the recent beam tests account for the revision of the previous values. The fatigue limit was assumed to occur at 5 ×
106 cycles for each detail. Static strength provisions in the
other sections of the Specification limit the design fatigue
strength for low numbers of cycles.
4.8.2 Variable Amplitude Loading
Real load histories are frequently more complicated than
the constant amplitude loading discussed in the previous Section. This Section provides a method by which the engineer
may design for more random variable amplitude loadings
experienced by many structures. The equivalent stress method
is based on nominal stress ranges, linear damage accumulation, and no sequencing effects. The engineer should also use
a standard cycle counting algorithm, such as rainflow counting (71, 72) to determine the equivalent stress range.
II-A-15
The equation for the equivalent stress range is derived
directly from Miner’s Rule when the S-N curve is a straight
line in log-log space. Miner’s rule is given by
∑
ni
____
≤ 1.0
Ni
(Eq. C4.8.2-1)
where
ni = number of cycles of the ith stress range
Ni = number of cycles constituting failure at the ith stress
range
The equation states that when this fraction approaches
unity, some of the details within the group have begun to
fail. The engineer may wish to use the Miner’s rule formulation over the equivalent stress range when assessing the
remaining life of an existing structure or when fatigue data
is not linear in the log(stress)-log(life) space.
The analysis is made as specified in Section 4.8.1 except
that the fatigue limit is not used. In this case, the equations for allowable stress are also used for number of cycles
greater than 5 × 106 because available data for spectrum
loads show continuing decrease at long lives.
4.9 Compression in Single Web Beams
Including Single Web Beams with
Tubular Portions
The formulas of Section 3.4.11 for single-web beams
are based on an approximation in which the term Lb /ry
replaces a more complicated expression involving several
properties of the cross section. Because of this approximation, the formulas give very conservative results for certain
conditions, namely for values of Lb /ry exceeding about 50
and for beams with transverse loads applied to a flange and
in a direction away from the beam’s shear center. To compute more precise allowable compressive stresses for these
cases, the value of ry in Section 3.4.11 may be replaced by
an “effective ry” denoted rye given by one of the formulas
of Section 4.9.
For doubly symmetric sections either Section 4.9.1 or
4.9.3 may be used. The latter Section is more accurate and in
general, yields higher design stresses. For singly-symmetric
sections unsymmetric about the bending axis Section 4.9.2
or 4.9.3 may be used. The latter Section is the more accurate
of the two.
This Section also recognizes the possibility of taking
advantage of the effect of bracing the tension flange using a
method of rational analysis. An example of a rational analysis is given in Reference (46). In this reference an expression
for the elastic critical moment Me for a singly symmetric Isection with the tension flange prevented from lateral displacement but free to rotate is derived. For pure bending:
EIc dπ2 ___
Me = ______
+ GJ
d
L2b
(Eq. C4.9-1)
rye can be evaluated for this case using this Me in Equation
4.9.3-1. Equation C4.9-1 which was derived for uniform
II-A-16
moment is conservative for the case of uniform loading.
In the above equation Ic is the moment of inertia of the
compression flange about the web, d, Lb, and J are as defined
in Section 4.9.1.
4.9.1 Doubly Symmetric Sections and Sections
Symmetric about the Bending Axis
Allowable stresses are determined at the ends or at the
brace points of beams as well as between brace points. At
brace or support points of a doubly symmetric beam Equation 4.9.1-1 is to be used to calculate the allowable stress.
The same equation is to be used between brace points if
the beam is subjected to lateral loads that are applied only
at the shear center of the section. Equation 4.9.1-2 is used
to calculate the allowable stress between brace or support
points when a transverse load is applied to the top or bottom flange of the beam and the load is free to move laterally
with the beam if it should buckle.
The selection of the proper equation for rye can be illustrated using Figure C4.9-1. At point B for both beams,
Equation 4.9.1-1 is to be used. The same equation is also
to be used for point A if the distributed load is applied at
the level of the neutral axis. If the distributed load is not
applied at the level of the neutral axis then Equation 4.9.1-2
is to be used. The approach for checking the moment at
point C will be discussed in connection with the selection
of Cb in Section 4.9.3.
4.9.2 Singly Symmetric Sections Unsymmetric
about the Bending Axis
For beams that are unsymmetrical about the x-axis, rye
in Section 4.9.1 can be calculated approximately by taking ry, Iy, Sc and J as though both flanges were the same as
the compression flange with the overall depth remaining
the same. This approximation is always quite conservative
when the smaller flange is in compression. The approximation may be somewhat unconservative when the larger
flange is in compression. Any unconservatism inherent in
assuming a larger than actual section in the case of larger
flange in compression, may or may not be compensated by
the conservative nature of the equations of Section 4.9.1.
4.9.3 Singly Symmetric Sections Symmetric or
Unsymmetric about the Bending Axis,
Doubly Symmetric Sections and Sections
without an Axis of Symmetry
This Section is applicable to any beam bent about the
strong axis by moments or by lateral loads applied through
the shear center of the section. Equation 4.9.3-2 is derived in
Reference (25) based on the elastic torsional-flexural buckling theory. This expression considers non-symmetry of the
section about the bending axis as well as the location of the
laterally applied load with respect to the shear center.
January 2005
Beam
A
A
Moment diagram
B
Beam
B
C
Moment diagram
Figure C4.9-1
BEAM AND MOMENT DIAGRAM EXAMPLES
In calculating the section properties as well as the
parameter g, it is essential to use the axis orientation specified. The orientation of the axes and the cross-sectional
notation are illustrated in Figure C4.9-2.
The magnitudes of yo, torsion constant J and the warping constant Cw can be determined from the expressions
given in references such as Reference (47).
The approximate formula for j given in Equation 4.9.3-6
as well as the approach for reverse curvature bending is based
on information given by Reference (48). For cases when the
areas of the compression and tension flanges are approximately equal, j can also be approximated by -yo.
4.9.4 Lateral Buckling Coefficients
The increase in lateral buckling capacity due to moment
variation over the unbraced length Lb is accounted for by
using the factor Cb in Sections 3.4.11, 3.4.13, and 3.4.14.
A somewhat different form of the equation for Cb (Equation 4.9.4.1-1) was originally proposed by Prof. M. Horne.
It was later modified by Prof. D. Nethercot. The equation
in the form given here is the same as in the second Edition
of the AISC-LRFD Specification (49).
January 2005
The expressions for Cb, C1 and C2 for the special cases
are based on the work reported in Reference (50). The Cb
expressions are somewhat simplified versions of the ones
given in the reference.
Application of the Cb factor to singly symmetric sections in the same manner as for doubly symmetric sections
has been shown to be unconservative in certain situations
by Reference (48). The unconservative cases arise if the Cb
factor is applied to the critical moment determined for the
case of larger flange in compression, ML, when it is possible
that somewhere in the unbraced segment the smaller flange
may be subject to compression. In such cases the proper Cb
factor should also be applied to the critical moment determined for the case of smaller flange in compression, MS.
The application of the coefficients Cb, C1 and C2 can be
discussed with the help of examples given in Figures C4.9-1
and C4.9-3. In the single span beam of Figure C4.9-1, if the
top flange is the smaller flange and MMAX occurs at a section (point B) with the smaller flange in compression, the
application of the Cb factor to MS would be used in determining the critical moment.
II-A-17
Figure C4.9-2
ORIENTATION OF THE AXES AND CROSS-SECTIONAL NOTATION
If the top flange is the larger flange of the single span
beam in Figure C4.9-1, and MMAX occurs at a section with
the large flange in compression (at point B), then determining the critical moment as Cb ML may be unconservative
because the presence of a segment with a smaller flange in
compression could lead to a lower actual critical moment.
A lower bound to the lateral buckling moment at the end
with the smaller flange in compression (point C) can be
found assuming the moment gradient in the beam to be
as shown in Case 2 of Figure C4.9-3 and using the corresponding value of Cb.
The application of the coefficients Cb, C1 and C2 to end
moment cases can be demonstrated for the four beams shown
in Figure C4.9-3. If the top flange is the smaller flange, the
Cb factor can be applied to MS conservatively in each case.
II-A-18
The resulting lateral buckling moments are required to be
larger than the actual applied maximum moments.
If the top flange is the larger flange, the Cb factor cannot
be applied to ML conservatively in Case 3 without checking
to see if a lower lateral buckling moment is possible, due to
the fact that over a portion of the beam the smaller flange is in
compression. A lower bound to the buckling moment for the
case with the smaller flange in compression over a portion of
the span can be found by assuming that the smaller flange is
subjected to a moment distribution as shown for Case 2 with
the small flange in compression, namely Cb = 1.67.
For Case 4 where the end moments are equal and opposite, only the smaller flange at the right end needs to be
checked. For this check Cb = 2.27 according to Equation
4.9.4.1-1.
January 2005
Figure C4.9-3
BEAM AND MOMENT DIAGRAM EXAMPLES
In summary, Cb can be determined as usual for all cases
except when MMAX produces compression on the larger
flange and the smaller flange is also subjected to compression in the unbraced length. In this case, the member need
also be checked at the location where the smaller flange is
subjected to its maximum compression.
If one of the two flanges is small such that Icy /Iy is less
than or equal to 0.1 or greater than or equal to 0.9 then
Cb shall be taken as 1.0 based on the information given
in Reference (48). Cb is also to be taken as 1.0 when the
rotational restraint is considered (ky < 1) since Equation
4.9.4.1-1 overestimates Cb when ky less than 1 is used.
January 2005
For continuous beams there are no directly derived values of C1 and C2. For this reason rational analysis must be
used in estimating the values of these coefficients for such
applications. It can be shown that for loading as shown in
Figure C4.9-2, reasonably conservative results are obtained
by taking:
- C1 = 0.41Cb and C2 = 0.47Cb when the smaller (top)
flange is in compression (shown in the top two cases of
Figure C4.9-2) and
- C1 = 0 and C2 = 0 when the larger (top) flange is in
compression (shown in the bottom two cases of Figure
C4.9-2).
II-A-19
Alternatively, for continuous beams finite element programs that are shown to be correct for those cases covered
in this Section may be used.
Extensive provisions for cantilevers are not given in
the Specification due to the complexity of the subject particularly for singly symmetric sections. Guidance for the
design of such members can be found in References (51,
52, 53, and 54).
4.10 Compression in Elastically
Supported Flanges
Additional information on the use of Section 4.10 is presented in Part VIII Illustrative Examples. The formula may
be used for determining the allowable stress at the centroid
of the compression flange of a beam that has lateral stays
only at the tension flange where the stays are intermittent,
such as stringers, girts, or purlins. This type of analysis is
described in Reference (55). If the rotational stiffness of
the joint between the stringer and the tension flange is not
known, it should be measured experimentally and introduced in the equation for βs (56).
4.11 Single Angles in Flexure
The strength of single angles in flexure in this Section is
the similar to the AISC Load and Resistance Factor Design
Specification for Single-Angle Members, 2000.
One difference from the AISC Specification for Single-Angle
Members is that the yield strength is limited to 1.3My rather than
1.5My. This is done to be consistent with Aluminum Specification Sections 3.4.4, 3.4.13, and 3.4.17 through 3.4.19.
The local buckling strength of an angle leg depends on
the degree of end fixity that the other leg provides and the
variation in stress across the width of the angle leg. The lower
bound on end fixity is a pinned support and the upper bound
is a fixed support. Buckling strengths (from Sharp’s Behavior and Design of Aluminum Structures (17) Table 7.1) are
summarized in Table C4.11-1 for an angle leg of width b and
thickness t:
Table C4.11-1
LOCAL BUCKLING STRENGTHS FOR ANGLE LEGS
Case
Stress distribution on
leg of angle
Equivalent
slenderness
ratio/(b/t)
(pinned support)
Equivalent
slenderness
ratio/(b/t)
(fixed support)
5.13
2.89
4.45
2.62
3.64
2.27
2.56
1.36
Angle orientation
free edge
1
supported edge
free edge
2
supported edge
free edge
3
supported edge
free edge
4
supported edge
II-A-20
January 2005
Case 1, uniform compression in an angle leg, is addressed
in Section 4.11a(2). Cases 2, 3, and 4 are addressed in Section
4.11a(1) by conservatively using the worst case (Case 2) and
assuming that the support is restrained slightly more than the
pinned condition so that a factor of 4 (vs. 4.45) can be used.
4.11.1 Bending About Geometric Axes
Bending about geometric axes occurs when the moment
is applied about an axis parallel to a leg of the angle as
shown in Figure 4.11.1-1. In such cases, when an angle
is laterally restrained at the point under consideration, the
neutral axis is the geometric axis as shown on the left side
of Figure 4.11.1-1 and addressed in subsections a and b.
When the angle is laterally unrestrained, the section will
deflect laterally as well as normal to the bending axis, causing the neutral axis to incline as shown on the right side of
Figure 4.11.1-1 and addressed in subsection c.
4.11.2 Bending About Principal Axes
Bending about principal axes is shown below:
βw is positive or negative depending on the direction of
bending.
4.12 Tapered Thickness Elements
This section has been developed to provide a method for
determining a more accurate slenderness ratio for members
which have linearly tapered thickness elements with δ < 2.0
(i.e., tmax < 3tmin). The tapered flanges of American Standard
channels and American Standard I beams meet this criterion.
Three types of edge supports for elements with tapered
thickness are addressed in the Specification: (83)
a. Tapered thickness elements with the thick edge supported and the thin edge free (Figure C.4.12-1(a)):
For such elements, it is conservative to use b/tavg for
the slenderness ratio. Using b/tavg gives a slenderness ratio that is conservative by as much as 28%
compared to finite element analysis for δ = 2. Section
4.12a. provides an approximate expression for the
slenderness ratio that is less conservative and more
accurate than using b/tavg.
b. Tapered thickness elements with the thin edge supported and the thick edge free (Figure C.4.12-1(b)):
For such elements, the slenderness ratio can be
b
approximated by (1.02) ___
t . Using b/tavg understates
( )
avg
the slenderness ratio by only 3% compared to finite
element analysis, so the Specification allows the use
of b/tavg.
c. Tapered thickness elements supported on both edges
(Figure C.4.12-1(c)): The slenderness ratio can be
b
approximated by (1.02 + 0.02δ) ___
t . Using b/tavg
( )
Figure C4.11.2-1
avg
Angle Size (in.)
βw (in.)
understates the slenderness ratio by only 5% at most
compared to finite element analysis, so the Specification allows the use of b/tavg.
Once the slenderness ratio has been determined, use the
Specification section for a constant thickness element with
the same edge conditions to determine the allowable uniform compressive stress of the element.
(tmax – tmin)
Section 4.12 is limited to elements with δ = _________
≤ 2.0.
t
8×6
3.31
For other elements, use a rational method of analysis.
8×4
5.48
7×4
4.37
Formulas for determining βw are given in Part VI. Since
these formulas are cumbersome, βw values for some common angle sizes are given in Table C4.11.2-1. βw varies
only slightly with angle thickness.
TABLE C4.11.2-1
6×4
3.14
6 × 3.5
3.69
5 × 3.5
2.40
5×3
2.99
4 × 3.5
0.87
4×3
1.65
3.5 × 3
0.87
3.5 × 2.5
1.62
3 × 2.5
0.86
3×2
1.56
2.5 × 2
0.85
equal legs
0.00
January 2005
min
4.13 Compressive Strength of
Beam Elements
Specification Sections 3.4.15 through 3.4.19 for determining compressive strengths of beam elements assume
that the supported edges of elements are fixed against translation and free to rotate. Section 4.13 provides an alternate
method by which a more accurate assessment of element
support conditions can be used to determine the compressive strength. Section 4.13 is also reasonably accurate for
any shape composed entirely of flat elements, including
those with single or multiple intermediate stiffeners. For
examples, see Reference (83).
When Section 4.13 is used in combination with the
weighted average strength method given in Section 4.7.3,
II-A-21
Figure C4.12-1
the strength of a stiffened element need not be limited to the
strength of the stiffener since the elastic buckling strength
determined is the strength of the entire section, accounting
for all elements.
To apply Section 4.13:
a. First determine Fcr , the elastic buckling strength of the
beam with continuous lateral support, using a linear
elastic analysis. An example is a numerical method
called the finite strip method, by which a member is
divided into strips which run the length of the member (CUFSM (2003) v2.5, author Ben Schafer, www.
ce.jhu.edu/bschafer/cufsm (visited on 9/25/03)).
b. Next, determine the
___equivalent slenderness ratio for
E.
the shape λeq = π ___
Fcr
c. Determine the design stress for the flat elements in
uniform compression using Section 4.13.1 and the
design stress for the flat elements in bending in their
own plane using Section 4.13.2.
d. Determine the strength for the entire shape using the
weighted average method given in Section 4.7.3.
√
Section 5. Mechanical Connections
5.1 General
5.1.1 Minimum Edge Distance
Edge distance requirements (2D for full bearing strength
and a minimum of 1.5D with reduced bearing strength)
have been selected so that for a single fastener, the block
shear strength equals or exceeds the bearing strength. So
for a single fastener, meeting the bearing requirements
negates the need to check block shear.
5.1.2 Maximum Spacing of Fasteners
The maximum spacing of fasteners in built-up compression members is based on preventing buckling of the components between points of attachment.
The limits on fastener spacing for components of tension members are based on experience rather than tests or
theory. Limiting the spacing of fasteners joining components of tension members helps avoid buckling if unanticipated compression acts on the member.
5.1.3 Block Shear Rupture
The block shear rupture strength in this Specification is
the same as in the AISC LRFD Specification for Structural
Steel Buildings 1993 edition, section J4.3 (76).
5.1.4 Net Area
Figures C5.1.4-1 and 5.1.4-2 illustrate the notation of
this Section. The net section area for the strap shown in
Figure C5.1.4-1 is
(
)
s2 t
Anet = b – 2d + ___
4g
(Eq. C5.1.4-1)
where t is the thickness of the strap and d is the diameter of
the hole. In Figure C5.1.4-2, the angle section is flattened
out into a strap for the purpose of calculating the net section. The flattened width is a + b – t.
Figure C5.1.4-1
STRAP IN TENSION
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January 2005
Figure C5.1.4-2
ANGLE IN TENSION
5.1.5 Effective Net Area
A study of angles, tees, and channels connected by some
but not all of their elements showed that the effective area
in tension is less than the net area due to the non-uniform
stress distribution across the section at the connection. This
is accounted for by using the net effective area given by
Equation 5.1.5-1 to calculate the tensile stress in the section.
Designers should not combine bending stress due to the connection eccentricity with axial stress on the net effective area
since the effect of the eccentricity is accounted for in the net
effective area determination.
To determine the eccentricities:
a. For tees connected only by their flanges (Figure C5.1.51(a)), the eccentricity in the y direction is the distance
from the outside face of the flange to the neutral axis
of the tee parallel to the flange. The eccentricity in the
x direction is zero. For I beams connected only by their
flanges (Figure C5.1.5-1(b)), split the section at the neutral axis parallel to the flanges to create two tees.
b. For channels connected only by their webs the eccentricities are as shown in Figure C5.1.5-2.
c. For angles connected only by one leg, the eccentricity in one direction is the distance from the face of
the connected leg to the neutral axis of the angle parallel to the connected leg (Figure C5.1.5-3(a)). The
eccentricity in the other direction is determined from
a section obtained by subtracting the portion of the
connected leg outside the centerline of the fastener
closest to the unconnected leg. The eccentricity is the
distance perpendicular to the unconnected leg from
the centerline of the fastener closest to the unconnected leg to the neutral axis of the remaining section
(Figure C5.1.5-3(b)).
d. For I beams connected only by the web, eccentricities are determined as shown in Figure C5.1.5-4.
If there is only one row of bolts in the direction of load
or the only weld has an axis perpendicular to the direction
of load, the length of the connection L is zero and the net
effective area is the net area of the connected elements.
Figure C5.1.5-1
January 2005
II-A-23
Figure C5.1.5-2
Figure C5.1.5-3
II-A-24
January 2005
Figure C5.1.5-4
5.1.8 Countersunk Holes
5.2.3 Bolt Tension
Caution should be exercised when the depth of the
countersink approaches the thickness of the part, creating a
knife-edge on the hole which may be easily damaged.
The use of the root area for determining the tensile
strength of aluminum fasteners rather than the slightly larger
tensile stress area used for steel fasteners is based on Reference (79). The root area is based on the nominal minor
diameter of external threads (D – 1.191/n) given in ASME
B1.1-1989, Unified Inch Screw Threads (the most current
version of this document, reaffirmed in 2001) section 10.1.
Part VII, Table 5-5 gives tensile strengths for 2024-T4
and 7075-T73 bolts and cap screws.
5.2 Bolted Connections
5.2.1 Bolt Material
a. (1) ASTM F468, Nonferrous Bolts, Hex Cap Screws,
and Studs for General Use, includes 2024-T4, 6061T6, and 7075-T73 aluminum bolts and provides the
minimum strengths that are used in Table 5.2.3-1.
Bolt dimensions are given in Part VII, Table 5-15.
(2) ASTM F467, Nonferrous Nuts for General Use,
includes 2024-T4, 6061-T6, and 6262-T9 aluminum
nuts. Nut dimensions are given in Part VII, Tables
5-16 and 5-17. (3) Spring lock washer dimensions
are given in Part VII, Table 5-18. Plain flat washer
dimensions are given in Part VII, Table 5-19.
b. The AISC Specification for Structural Steel Buildings
includes design rules for ASTM A307, A325, and A449
steel bolts. The Rockwell C35 hardness limit is intended
to avoid hydrogen-assisted stress corrosion cracking of
the bolt (see 5.4.1 commentary).
c. ASCE 8-02, Specification for the Design of ColdFormed Stainless Steel Structural Members, provides
design rules for fasteners meeting ASTM F593,
Stainless Steel Bolts, Hex Cap Screws, and Studs.
AAMA TIR-A9, Metal Curtain Wall Fasteners, (75) provides design rules for carbon and stainless steel fasteners.
January 2005
5.2.4 Bolt Shear
Rather than using approximate relationships between
the threaded and unthreaded areas of bolts and a different
allowable stress when threads are in the shear plane, the
same allowable stress is used in both cases and the effective
shear area is adjusted appropriately.
Part VII, Table 5-5 gives shear strengths for 2024-T4
and 7075-T73 bolts and cap screws with threads in and out
of the shear plane.
5.2.5 Bolt Bearing
The bearing strength (2Ftu) is the load at which hole
deformation is approximately D/4, where D is the nominal
diameter of the bolt (84).
See also Section 5.1.1 Commentary.
5.2.7 Lockbolts
A lockbolt assembly includes a pin, which is similar
to a bolt, and a collar, which performs the function of a
nut. The collar is swaged onto locking grooves on the pin.
II-A-25
Lockbolts are available in carbon steel, stainless steel, and
aluminum.
5.2.8 Slip-Critical Connections
5.2.8.1 General
This Section is based on specifications and research from
Europe and testing conducted in the US (73). Aluminum slipcritical connections are included in Canadian, British, ISO, and
proposed Eurocode specifications. In the US, use of high strength
steel bolts is governed by the Research Council on Structural
Connections (RCSC) Specification for Structural Joints Using
ASTM A325 or A490 Bolts. The RCSC Specification addresses
the use of these high strength steel bolts to connect steel parts,
and so is modified here for connections using aluminum parts.
All parts of the RCSC Specification not modified by the provisions of Section 5.2.8 (for example, provisions on inspection)
apply to aluminum slip-critical connections.
Slip-critical connections resist shear by friction between
the faying surfaces of the connected parts, which are tightly
clamped together by high strength steel bolts. Slip-critical
connections are used when it is desirable to prevent movement of connected parts relative to one another. Such connections are useful for joints subjected to dynamic or fatigue
loads, as well as joints in which both bolts and welds share
the load, joints with oversize holes, and joints with slotted
holes with loads not applied normal to the axis of the slot.
In addition to the requirements for bearing connections, slip-critical connections are subject to the additional
requirement that the slip resistance of the joint be greater
than the applied shear loads. The design strength of slipcritical connections cannot be greater than the design
strength of the same connection designed as a bearing connection. The design strength of a slip-critical connection
is limited to the lesser of the design strength of the bolt in
shear and bearing and the slip resistance of the joint.
ASTM A325 allows both hot-dip galvanizing and mechanical galvanizing of fasteners. A325 further requires that all
components of a fastener assembly (bolt, nut, and washer) be
coated by the same process, since mixing bolts and nuts galvanized by different processes may result in an unworkable
assembly.
5.2.8.3 Holes
For convenience, nominal hole dimensions from the
RCSC Specification are given in the following table:
Hole Dimensions (in.)
Bolt
Diameter Standard Oversized Short Slotted Long Slotted
(Width ×
(Width ×
(in.)
(Diameter) (Diameter)
Length)
Length)
1/2
9/16
5/8
9/16 × 11/16
9/16 × 1 1/4
5/8
11/16
13/16
11/16 × 7/8
11/16 × 1 9/16
3/4
13/16
15/16
13/16 × 1
13/16 × 1 7/8
7/8
15/16
1 1/16
15/16 × 1 1/8 15/16 × 2 3/16
1
1 1/16
1 1/4
1 1/16×1 5/16 1 1/16 × 2 1/2
>1 1/8
d + 1/16
d + 5/16
(d + 1/16) ×
(d + 3/8)
(d + 1/16) ×
(2.5 d )
5.2.8.4 Design for Strength
Slip-critical connections must be designed assuming slip
could occur, placing shear on the bolt and bearing on the sides
of the hole. Bolt shear strengths are the same as in the RCSC
Specification. Bolt design shear strengths should be reduced
appropriately in long connections since bolts at the end of
such connections bear a higher shear force than bolts near the
middle of the length of these connections. (The RCSC Specification requires shear strengths be reduced by 20% in connections whose length between extreme fasteners measured
parallel to the line of force exceeds 50 in. (1300 mm)).
5.2.8.2 Material
5.2.8.5 Design for Slip Resistance
Since hot-dip galvanizing may cause embrittlement of
A490 bolts and galvanizing is required to discourage galvanic corrosion between the steel fastener and the aluminum parts, A490 bolts are not allowed in aluminum slipcritical connections.
The RCSC Specification limits the bearing stress under
the bolt head in steel to 64 ksi for steel with a yield strength
less than 40 ksi, by requiring such steel with A490 bolts to
have washers. The Specification for Aluminum Structures
requires the use of washers under bolt heads and nuts, and
bearing stresses under the washer can reach approximately
24 ksi (165 MPa) with A325 bolts. Therefore, aluminum
slip-critical connections are limited to those alloys with a
tensile yield strength of 15 ksi (105 MPa) or greater.
Thin parts such as aluminum sheet and drawn tube are
effectively prohibited from slip-critical connections by
bearing stress limitations on the sides of the hole.
Slip coefficients are given for two contact surfaces:
roughened aluminum on roughened aluminum, and roughened aluminum on zinc-rich painted steel. These surfaces
were tested in accordance with the test method given in the
RCSC Specification for both slip and creep (73). Slip coefficients for other surfaces may be determined by testing in
accordance with the RCSC Specification.
Because aluminum has a higher coefficient of thermal
expansion than steel, the tension in the steel bolt may change
if an aluminum slip resistant connection is subjected to a
change in temperature from the installation temperature.
When the temperature drops below the installation temperature, the bolt tension may decrease since the aluminum in
the grip would contract more than the steel fastener if the
aluminum were unrestrained. For temperature drops the
design shear strength may be reduced using a rational analysis that takes into account the proportions of the joint and
the properties of the materials. The effect of temperature
II-A-26
January 2005
drops may also be accounted for by conducting the RCSC
tests for creep at a lower temperature than installation and
determining the slip coefficient accordingly. The steel bolts
are installed at a tension slightly above their yield strength,
so a temperature increase above the installation temperature will generally not cause significant additional tension
since the bolt strain hardens. The temperature increase
may, however, result in permanent elongation of the bolt
and consequent partial loss of pretension on subsequent
temperature drops. For this reason the effect of temperature
changes depends on the temperature extremes the bolted
assembly will experience.
References (77) and (78) offer more information on the
effect of temperature on slip-critical bolted aluminum joints.
Galvanizing increases the friction between the bolt and
nut threads and makes torque-induced tension more variable, but lubrication both reduces the torque and makes it
more consistent. Therefore, ASTM A325 requires that a
galvanized bolt and lubricated galvanized nut be assembled in a steel joint with a galvanized washer and tested in
accordance with ASTM A563 by the manufacturer prior to
shipping to assure that the fastener can be rotated beyond
the required rotation from the snug-tight condition without
breaking. Since some lubricants are water soluble, galvanized bolts and nuts should be shipped in plastic bags in
wood or metal containers.
In joints where bolts and welds share the load, bolts
should be installed and tightened first.
5.2.8.6 Washers
5.3 Riveted Connections
Washers are required under all bolt heads and nuts. This
requirement is intended to minimize galling of the outer
ply of aluminum and creep relaxation of bolt tension.
5.3.1 Rivet Material
5.2.8.7 Installation
For convenience, minimum bolt tensions from the RCSC
Specification are given in the following table:
Bolt Diameter (in.)
A325 Bolt Tension (kips)
½
12
5
⁄8
19
¾
28
7
⁄8
39
1
51
1
1 ⁄8
56
1¼
71
13⁄8
85
1½
103
Turn-of-nut tightening is performed by bringing the
assembly to a snug tight condition and then applying a prescribed number of turns of the nut. (A snug tight condition
is achieved when all plies in a joint are in firm but not necessarily continuous contact. This may be attained by a few
impacts of an impact wrench or the full effort of a man using
an ordinary spud wrench). Aluminum’s lower modulus of
elasticity versus steel means more turns would be needed
for aluminum assemblies than for steel assemblies if the bolt
tension at the start of turn-of-nut tightening were the same
for both steel and aluminum assemblies. However, the flexibility of aluminum parts enables them to be brought closer to
full contact by snug tightening than steel, resulting in higher
bolt tension in aluminum assemblies at the beginning of
turn-of-nut tightening. The net effect, confirmed by testing,
is that aluminum assemblies require approximately the same
number of turns as steel assemblies after the snug tight condition is attained to reach the bolt tension prescribed above.
January 2005
ASTM B316, Aluminum and Aluminum-Alloy Rivet
and Cold-Heading Wire and Rods, provides the minimum
strengths that are used in Table 5.3.4-1. Rivet head styles
are shown in Part VII, Table 5-6.
5.3.4 Rivet Shear
The shear strength of aluminum rivets is based on the
rivet filling the hole so the effective shear area of the rivet
is the nominal hole diameter. Recommended hole sizes are
given in Part VII, Table 5-8 for cold-driven rivets. Part VII,
Table 5-1 gives rivet shear strengths.
5.3.7 Blind Rivets
Blind rivets can be installed with access to only one side
of a connection.
5.4 Tapping Screw Connections
Results of over 3500 tests on light-gage steel and aluminum connections worldwide were analyzed to formulate
screw connection provisions (57). European Recommendations (58) and British Standards (59) were considered and
modified as appropriate. These provisions are intended to be
used when a sufficient number of test results is not available
for the particular application. A higher degree of accuracy
can be obtained by testing any particular application.
Proper installation of screws is important to achieve satisfactory performance. Power tools with adjustable torque
controls and driving depth limitations are usually used.
Screw connection tests used to formulate the provisions
included single fastener specimens as well as multiple fastener specimens. However, it is recommended that at least
two screws should be used to connect individual elements.
This provides redundancy against under torquing, over
torquing, etc., and limits lap shear connection distortion of
flat unformed members such as straps.
II-A-27
5.4.1 Screw Material
The material for screws used to connect aluminum parts
is selected to meet strength and corrosion resistance considerations. Steel screws with a Rockwell hardness of C35 or
greater may suffer hydrogen-assisted stress corrosion cracking (HASCC) where exposed to certain dissimilar metals,
moisture, and tension stress due to installation or loading.
For this reason, steel screws with a Rockwell hardness of
C35 or greater are no longer permitted in the Specification. Aluminum and austenitic stainless steel screws do not
experience HASCC. When fasteners will not be exposed to
contact with liquid water or humidity near the dew point,
certain other steels, with appropriate hardness, and appropriately coated and/or plated are also acceptable. An example
is 430 stainless steel, which has a nominal composition of
16% chromium.
5.4.2 Screw Tension
5.4.2.1 Pull-Out
The equations for pull-out are derived from research conducted by AAMA, including over 400 pull-out tests (75).
These equations are based on three regions of behavior: yield
(circumferential stretching and bending of the aluminum
around the screw), shearing of the internal threads in the hole,
and a transition region between yield and shearing. For most
cases they are less conservative than the pull-out equation in
the 6th edition (Pnot = 0.85tc DFtu2), especially for UNC threads
in aluminum parts thicker than 0.084 in. (2.1 mm). Pull-out
strengths are a function of the type of thread: coarse (UNC)
or spaced. A UNC thread is often referred to as a “machine”
thread and a spaced thread screw is termed a “sheet metal”
screw. Internal thread stripping areas (Asn in equations 5.3.2.12 and 5.3.2.1-3) are given in Part VII Table 5-20 for Class 2B
UNC threads.
5.4.2.2 Pull-Over
The pull-over strength equation for non-countersunk
screws is based on Reference (17). Screws may be placed
through the valley or the crown of corrugated roofing and
siding. (See Figure C5.4.2-1). A coefficient of 0.7 is used
when the connected parts are not in contact, such as for
fastening through the crown of roofing when a spacer block
is not used between the roofing and the structural member
supporting the roofing. The test strengths of such screwed
connections are more variable than those with the connected parts in direct contact at the connection such as the
fastener through the valley in Figure C5.4.2-1.
The equation for the pull-over strength of countersunk
screws is based on over 200 tests using 5 different flathead
screw sizes, 6 sheet thicknesses, and 2 alloy-tempers (85).
Testing was limited to commonly used screws with 82
degree nominal angle heads, so the equation is not known
to apply to other head angles.
Variation in actual diameters of hand-drilled countersunk
holes can have a significant effect on pull-over strength.
Caution should be used to avoid excessive oversizing of
countersunk holes. Oversizing should be limited so that the
top of the screw head is no more than the lesser of t1/4 and
1/32 in. (0.8 mm) below the top of the sheet.
5.4.3 Screw Shear and Bearing
Screw connections loaded in shear can fail in one mode
or in combination of several modes. These modes are screw
shear, edge tearing, tilting and subsequent pull-out of the
screw and bearing of the joined materials.
Tilting of the screw followed by threads tearing out of the
lower sheet reduces the connection shear capacity from that of
the typical connection bearing strength. Equation 5.4.3-4 covers the cases when the screw tilting can lower the strength.
Diameter and rigidity of the fastener head assembly as
well as sheet thickness and tensile strength have a significant effect on the shear failure load of a connection. There
are a variety of washers and head styles in use. Washers
must be at least 0.050 in. (1.3 mm) thick to withstand bending forces with little or no deformation.
Based on limited testing, it appears that the bearing
force on a screw should be limited to that which produces
Figure C5.4.2-1 FASTENERS IN ROOFING
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March 2005
a hole elongation of D/8 to avoid threads disengaging from
the sides of the hole. Testing is recommended to establish
the bearing strength of screwed connections. This recommendation is only for those screw connections which are
subjected to both bearing and tensile loads.
5.5 Building Sheathing Connections
5.5.2 Sidelaps
Sidelaps should, where possible, be oriented to give
maximum protection against the prevailing winds; i.e., during installation the horizontal progress in placing sheets on
the building should be in the direction opposite to that of
the prevailing winds.
5.5.3 Fasteners in Laps
Minimum size of #12 screws or 3/16 in. (5 mm) diameter rivets is specified in end laps and side laps to give neat,
weather-resistant closures. In many cases, the primary,
sheet-to-support fasteners will give satisfactory closures at
the endlaps, but in sidelaps additional fasteners should be
used if the joint does not interlock.
Section 6. Fabrication and Erection
6.1 Layout
6.1.1 Punch and Scribe Marks
Hole centers are commonly located by punching and cutoff lines are often scribed. Center punching and scribing
should be avoided where such marks would remain on
fabricated material if appearances are a concern.
6.2 Cutting
6.2.1 Methods
Special attention should be paid to edge cracking in heat
treatable alloys cut by laser or arc.
6.2.3 Re-Entrant Corners
Fillets are needed to reduce corner stress. The appropriate corner radius varies depending on the item and its use.
AWS D1.1:2000, the steel structural welding code, Section
5.16, uses a minimum fillet radius of 1 in.. AWS D1.2:2003,
the aluminum welding code, Section 4.11.6, requires ½
in. for statically loaded members and ¾ in. for cyclically
loaded members. In Specification Table 4.8-1, the smallest
radius for attachments for which fatigue categories are provided is 2 in.. Since the Specification also applies to small
parts, it is impractical to specify a minimum radius.
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6.3 Heating
The strength of tempered metal can be reduced after
exposure to elevated temperature processes (such as factory paint curing, firing of porcelain enamel coatings, and
hot forming). The amount of the reduction in strength varies with alloy, temper, and temperature exposure. Suppliers may be consulted for strengths of material subjected to
such processes. Because the reduction in strength will not
exceed 5% for the alloys, tempers, and exposures given in
Table 6.3-1, no reduction in design stresses is necessary for
these temperature limits. The logarithmic formula is needed
for accurate interpolation between Table 6.3-1 values.
5XXX series alloys with magnesium contents greater
than 3% held within the temperature range of 150oF (66oC)
to 450oF (230oC) may subsequently suffer exfoliation and
stress corrosion cracking. The length of time at temperature
is a critical factor in determining the degree of sensitization
to exfoliation and stress corrosion cracking.
6.6 Finishes
The American Architectural Manufacturers Association
offers these Voluntary Specification, Performance Requirements and Test Procedures for coating aluminum:
AAMA 2603 Pigmented Organic Coatings on Aluminum
Extrusions and Panels
AAMA 2604 High Performance Organic Coatings on Aluminum Extrusions and Panels
AAMA 2605 Superior Performing Organic Coatings on
Aluminum Extrusions and Panels
Abrasion blasting can be used to clean material or finish
the surface. Abrasive media includes steel grit, silica sand,
aluminum oxide, crushed walnut shells, or coal slag. Peening
can be used to improve fatigue strength by introducing compressive stress near the surface and is achieved with steel or
stainless steel shot. Residual stresses from blasting or peening
can curl thin material.
Where water is allowed to stand between aluminum
parts in contact, oxidation called water staining may result.
While this oxidation has no effect on material strength and
will not progress after the water is removed, it is unsightly
and difficult to remove. It can be prevented by keeping aluminum dry or out of contact with other aluminum parts
when moisture can be present.
6.7 Contact with Dissimilar Materials
Isolators such as Teflon, neoprene, and 300 series stainless steel may be placed between aluminum and other materials to prevent contact. The isolator should be nonporous
to avoid trapping water or other substances in the joint, and
compatible with both the aluminum and the dissimilar material in the intended service.
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6.7.3 Concrete or Masonry
To avoid staining and surface corrosion, mill finished aluminum and anodized aluminum should be protected from
uncured concrete, mortar, and similar alkaline substances
and muriatic acid used in cleaning concrete and masonry.
Masonry products designed to remain at a relatively low
pH during and after curing (such as magnesium phosphate
grout, which does not exceed a pH of 8.5) do not corrode
aluminum.
cal properties in the vicinity of a weld is illustrated by the
typical distribution in Figure C7-1. When designing welded
members this decrease in strength shall be considered in
addition to the design rules outlined in Section 3.
6.7.4 Runoff from Heavy Metals
Heavy metals can cause deposition corrosion of aluminum. Copper is the most common of these of metals used
in construction, but terne-coated steel (which has a lead/tin
coating) may also have this effect.
6.9 Fabrication Tolerances
The L/960 straightness tolerance was chosen so that the
reduction in buckling strength versus a perfectly straight
member is no less than about 20%. The standard tolerance
for some mill products does not meet the L/960 straightness
tolerance for fabricated members required here. (An example is T6511 extrusions with wall thicknesses less than 0.095
in.). Such members may require additional straightening or
tighter tolerance specifications to meet the requirements of
this section.
Figure C7-1
DISTRIBUTION OF MECHANICAL
PROPERTIES NEAR A WELD
Minimum bend radii for 90o cold forming of sheet and
plate are given in Part VII Table 6-1 for a number of alloys
and tempers. These radii are approximate and are a function of the direction of the bend line with respect to the rolling or extruding direction. Cracking of heat treated alloys
is more readily avoided with the bend line perpendicular to
the rolling or extrusion direction, while the opposite is true
for non-heat treatable alloys.
The effect of welding heat on aluminum mechanical
properties has been discussed extensively (60, 61, 62, 63).
For the non-heat-treatable alloys, the strength in the heataffected zone after welding is essentially that of annealed
material. The strength of welds in heat-treated alloys, such
as 6061-T6, lies between the annealed strength and that of
the original heat-treated material.
The minimum ultimate tensile strength of welded alloys
given in Table 3.3-2 are the AWS D1.2 weld qualification
strengths, which are the same as the annealed strengths for
non-heat treatable alloys and slightly less than the solution
heat treated strengths for heat treatable alloys (64).
6.11 Erection
7.2 Welded Members
6.11.2 Bolt Installation
7.2.1 General
Snug tightness can usually be attained by a few impacts
of an impact wrench or the full effort of person using an
ordinary spud wrench. A specific clamping force is not necessary in non-slip-critical connections because the design
accounts for parts slipping relative to each other.
Welds have little effect on buckling strength except in the
range of slenderness ratios where the strength is controlled
by the welded yield strength (68), so unwelded parent metal
minimum mechanical properties (from Table 3.3-1) are used
in the formulas for buckling constants (Table 3.3-3 or 3.3-4
as appropriate) for most welded members. Welded tubes (sections 3.4.10, 3.4.12, and 3.4.16.1) are an exception. For these,
welded compressive yield strengths (from Table 3.3-2) are
used in the formulas for buckling constants, which are taken
from Table 3.3-3 regardless of the temper of the parent metal
before welding. Buckling tests on welded tubes have shown
this approach to be conservative (7).Other exceptions are columns with welds at locations other than the ends and cantilevers with a weld at the supported end.
6.10 Bending
Section 7. Welded Construction
7.1 General
Most of the structural aluminum alloys attain their strength
by heat treatment or strain hardening. Welding causes local
annealing which produces a zone of lower strength along
both sides of the weld. The resulting variation in mechani-
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January 2005
Compressive tests on welded aluminum plates (62, 69)
have demonstrated that the welds have little effect on postbuckling strength.
7.2.2 Members with Part of the Cross Section
Weld-Affected
The equation in this Section is based on the fact that the
strength of a cross section with only part of its area heat
affected can be estimated by adding up the strength of the
softened material in the heat-affected zone and the unaffected material outside this zone (62, 67).
The yield strength of heat-affected material is based on a
2 in. (50 mm) gage length yield strength provided in Table
3.3-2. For calculating the column buckling strength of the
heat-affected material the buckling formula constants given
in Table 3.3-3 are used for all alloys and tempers because
they best represent the heat affected material (17).
7.2.3 Columns or Beams with Transverse Welds
Away From Supports and Cantilevers with
Transverse Welds
Welds at the center of a column supported on both ends
or at the fixed end of a cantilever column may have an
appreciable effect on the buckling strength. For these cases
the strength is calculated as though the entire column were
of welded material. This procedure is conservative (17).
7.3 Welded Connections
Aluminum welded connection types include groove welds,
fillet welds, plug and slot welds, and stud welds. Numerous
tests have been conducted on these welds (63, 66).
7.3.1 Groove Welds
7.3.1.1 Complete Penetration and Partial
Penetration Groove Welds
Groove welds are classified as either complete penetration or partial penetration for the purpose of determining
the weld size. The method of classifying a groove weld is
the same as that in AWS D1.2. Groove welds made with
permanent backing have less fatigue strength than groove
welds without permanent backing.
7.3.2 Fillet Welds
7.3.2.1 Effective Throat and Effective Length
The effective throat of an equal leg fillet weld of size Sw
is 0.707Sw.
7.3.2.2 Design Strength
The shear strengths of 4047, 4643, and 5183 are taken
from Reference (80); shear strengths of the other fillers are
taken from Reference (65). Both references use the same
January 2005
method and tests to determine the shear strength of other
fillers should also follow this method.
7.3.3 Plug and Slot Welds
Plug and slot welds are primarily used to transmit
shear in the plane of the weld. An example is a cover plate
attached to a flange with plug welds.
7.3.4 Stud Welds
The strengths of stud welds are taken from AWS D1.2.
7.4 Post-Weld Heat Treating
The allowable stresses for 6005 and 6063 lighting pole
assemblies heat treated (artificially aged) after welding are
based on numerous tests.
Section 8. Castings
8.1 Materials
ASTM B 26 and B 108 do not specify minimum tensile yield strengths for some of the cast alloy-tempers they
include (for example, sand cast 356.0-T7, which appeared in
the Specification for Aluminum Structures 7th edition in Table
3.4-4). These alloy-tempers are not included in Table 8.2-1
(and therefore are excluded from the scope of the Specification) since design usually requires the yield strength. There
are also other alloy-tempers in B 26 or B 108 that are not
included in Table 8.2-1 and therefore not included in the
Specification.
Since ASTM B 26 and B 108 do not require conformance with dimensional standards (tolerances) as do
ASTM specifications for wrought products (for example,
B 209), standards for castings must be established in the
Specification. Dimensional standards required in this Specification are those in the Aluminum Association Standards
for Aluminum Sand and Permanent Mold Castings.
The minimum strengths specified in ASTM B 26 Table 2
for sand castings are for separately cast test bars and not for
the castings themselves. As stated in section 11.3 of ASTM
B 26 “When specified, the tensile strength, yield strength,
and elongation values of specimens cut from castings shall
not be less than 75% of the tensile and yield strength values
and not less than 25% of the elongation values specified in
Table 2.” Therefore, the minimum strengths as given in Table
8.2-1 are based on 75% of the ASTM B 26 Table 2 minimum strengths to represent what a purchaser would expect
to receive if he specifies testing of the actual castings.
Castings are more prone to discontinuities than wrought
products. Therefore, the Specification includes discontinuity standards for castings in order for them to be designed
to the same Specification provisions as wrought products.
The quality standards are based on the following:
ASTM B 26 and B 108 (section 20) both include options
for liquid penetrant and radiographic inspection that may
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be specified by the purchaser. Liquid penetrant inspection
detects only surface flaws and so it is insufficient. ASTM
B 26 and B 108 only require radiographic inspection be
performed if the purchaser specifies such inspection.
If such inspection is specified, the purchaser must also
specify which of 4 quality grades: A, B, C, or D, must be
met. Grade A allows no discontinuities at all; this is more
stringent than wrought product quality levels and so it is
unwarranted. When Grade D is specified, no tensile tests of
coupons cut from castings can be required. Therefore, only
grade B or C are suitable for the type of structural components addressed by the Specification. Grade C is used, since
Grade C allows gas holes no larger than approximately
⅛ in. and this is the same as the ultrasonic inspection Grade
B flaw size limit for wrought plate in Aluminum Standards
and Data (Table 6.3). (Only a few 2xxx and 7xxx wrought
alloys have any specified discontinuity limits in Aluminum
Standards and Data).
Once the acceptance criteria for an individual casting is
determined, the number of castings from a given lot to be
radiographed and the acceptance criteria for the lot must
be set. Standards for Aluminum Sand and Permanent Mold
Castings establishes 4 frequency levels for inspection, 1
being the most frequent inspection. Inspection level 2 is used
here since level 1 requires radiographing every casting, level
3 leaves the inspection frequency up to the foundry and so it
is unspecified, and level 4 requires no radiographs.
8.2 Mechanical Properties
Strengths given in Table 8.2-1 and Table 8.2-1M are
taken from ASTM B 26 for sand castings and B108 for permanent mold castings. B 26 allows the purchaser to require
that the minimum strength of coupons cut from production
castings be 75% of the specified strength, so the values in
Table 8.2-1 are the B 26 values factored by 0.75. B 108 has
the same requirement, but for certain alloy-tempers allows
the purchaser to specify either 1) locations in the casting
that shall have certain B 108-specified tensile strengths;
or 2) that any location in the casting shall have certain B
108-specified tensile strengths. The strengths for case 2)
are usually lower than those for case 1). For both cases
1) and 2), the minimum strengths in Table 8.2-1 are the B
108-specified strengths without any factors.
Kaufman’s Fracture Resistance of Aluminum Alloys
Figure 5.4 provides notch-strength-to-yield-strength ratios
for various sand and permanent mold alloy-tempers. The
alloy-tempers in Section 8 have notch-yield ratios > 1.0,
so no reduction in tensile fracture strength is required for
notch sensitivity for these alloy-tempers and the tension
coefficient kt is 1.0.
8.3 Design
The design of castings is the same as the design of wrought
products, except that Section 4.8, Fatigue, applies different
rules for castings than for wrought products. Castings must be
tested to establish their fatigue strength.
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8.4 Welding
356.0 is the only cast alloy-temper included in Section
8 with a welded strength given in AWS D1.2:2003 Table
3.2, which gives a value of 23 ksi. This is apparently for a separately cast coupon rather than a coupon cut from a casting,
since the minimum unwelded strength of coupons cut from
356.0-T6 sand castings is 22.5 ksi (see Table 8.2-1). Because
of this and since D1.2:2003 provides no welded strengths
for the other alloy-tempers in this Specification, welded
strengths are not given in Section 8. Instead, they must be
established from the weld procedure qualification required
by D1.2:2003.
Section 9. Testing
9.3 Number of Tests and the Evaluation
of Test Results
9.3.1 Tests for Determining Mechanical
Properties
Equation 9.3.1-1 is from the ASTM volume 02.02, Aluminum and Magnesium Alloys, article “Statistical Aspects
of Mechanical Property Assurance” by W.P. Goepfert (70).
Values for K are taken from Juran’s Quality Control Handbook, edited by Juran, J.M., 4th ed., published by McGrawHill, and are one-sided factors affording 95% confidence
that at least 99% of the population would fall above the predicted minimum value. (See Part V, Section 1.0 for further
discussion of the statistical basis for minimum mechanical
properties of aluminum alloys).
9.4 Testing Roofing and Siding
The ASTM standard test method referenced in this Section
is E1592, Structural Performance of Sheet Metal Roof and
Siding Systems by Uniform Static Air Pressure Difference.
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and Ductility of Welds in Aluminum Alloy Plate,” The
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65. Nelson, F. G. Jr., and Rolf, R. L., “Shear Strength of
Aluminum Alloy Fillet Welds,” The Welding Journal,
February, 1966.
66. Sharp, M. L., Rolf. R. L., Nordmark, G. E., and Clark,
J. W., “Tests of Fillet Welds in Aluminum,” The Welding Journal, April, 1982.
67. Hill, H. N., Clark, J. W., and Brungraber, R. J., “Design
of Welded Aluminum Structures,” Transactions ASCE,
Vol. 127, Part II, p. 102, 1962.
68. Brungraber, R. J., and Clark, J. W., “Strength of Welded
Aluminum Columns,” Transactions ASCE, Vol. 127,
Part II, p. 202, 1962.
69. Conley, W. F., Becker, L. A., and Allnutt, R. B., “Buckling and Ultimate Strength of Plating Loaded in Edge
Compression. Progress Report 2: Unstiffened Panels,”
Report 1682, David Taylor Model Basin, U. S. Department of the Navy, Washington, DC, May, 1963.
70. Goepfert, W.P., “Statistical Aspects of Mechanical Property Assurance”, Aluminum and Magnesium Alloys,
ASTM Volume 02.02, 1994.
January 2005
71. Fuchs, H. O. and Stephens, R. I., Metal Fatigue in
Engineering, John Wiley & Sons, New York, 1980.
72. Smith, I. F. C, Castiglioni, C. A. and Keating. P. B.,
“An Analysis of Fatigue Recommendations Considering New Data”, Proceedings IABSE Meeting, December 1988.
73. Kissell, J.R. and Ferry, R.L., “Aluminum Friction
Connections”, Proceedings of Structures Congress XV,
April, 1997.
74. Atzori, B., Lazzarin, P., and Quaresimin, M., “A ReAnalysis on Fatigue Data of Aluminum Alloy Bolted
Joints,” International Journal on Fatigue, Vol. 19, No.
7, 1997.
75. American Architectural Manufacturers Association,
AAMA TIR-A9-91 Metal Curtain Wall Fasteners, with
2000 Addendum, Schaumberg, IL, 2001.
76. Menzemer, Craig, “Failure of Bolted Connections in an
Aluminum Alloy,” Journal of Materials Engineering
and Performance, ASM, Vol. 8, No. 2, April, 1999.
77. Luttrell, C. R., “Thermal Cycling of Slip-Critical Aluminum Joints”, Proceeding of Structures Congress XVII,
American Society of Civil Engineers, Reston, VA, April,
1999.
March 2005
78. Fortlin, Beaulieu, and Bastien, Experimental Investigation of Aluminum Friction-Type Connections, INALCO
2001, Munich, 2001.
79. Dewalt, W.J. and Mack, R.E., Design Considerations
for Aluminum Fasteners, SAE Technical Paper 800455,
1980.
80. Menzemer, C. and Iasconne, R., “Reestablishing the
Shear Strength of Aluminum Alloy Fillet Welds”, Welding Journal, April, 2002.
81. Kaufman, J. G., Fracture Resistance of Aluminum
Alloys, ASM International, Materials Park, OH, 2001.
82. ASTM International, B 26-99 Standard Specification for
Aluminum-Alloy Sand Castings, West Conshohocken,
PA, 1999.
83. Kim, Yongwook, Behavior and Design of Aluminum
Members in Bending, Cornell University, Ithaca, NY,
2003.
84. Menzemer, C.C, Ortiz-Morgado, R., Iascone, R., and
Srivatsan, T., INALCO 2001, Bearing Capacity of Aluminum Alloys in Bolted Connections, Munich, 2001.
85. LaBelle, James C. and Dolby, Tanya, INALCO 2004,
Flat Head Fastener Pullover in Thin Aluminum with
Countersunk Holes, Cleveland, 2004.
II-A-35
Aluminum Design Manual
PART II-B
Commentary on
Specification for Aluminum Structures
Load and Resistance Factor Design
The Aluminum Association, Inc.
1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
Third Edition, January 2005
General Introduction
This Commentary is not intended to provide a general primer to probability-based Load
and Resistance Factor Design (LRFD) criteria. This is provided in Reference (2) and the
further references cited therein. The purpose of this commentary is to give an explanation
for the reasons for the recommended resistance factors in Part IB, Load and Resistance
Factor Design of Buildings and Similar Type Structures.
Section 2.3 Loads
Factored load combinations for building type structures
given in ASCE 7-02 are:
1) 1.4(D + F)
2) 1.2(D + F + T) + 1.6(L + H) + 0.5(Lr or S or R)
3) 1.2D + 1.6 (Lr or S or R) + (L or 0.8W)
4) 1.2D + 1.6W + L + 0.5(Lr or S or R)
5) 1.2D + 1.0E + L + 0.2S
6) 0.9D + 1.6W + 1.6H
7) 0.9D + 1.0E + 1.6H
Exceptions:
1. The load factor on L in combinations (3), (4), and (5)
is permitted to equal 0.5 for all occupancies in which
L is less than or equal to 100 psf, with the exception of
garages or areas of public assembly.
2. The load factor on H shall be set equal to zero in combinations (6) and (7) if the structural action due to H
counteracts that due to W or E. Where lateral earth pressure provides resistance to structural actions from other
forces, it shall not be included in H but shall be included
in the design resistance.
where
D = dead load
E = earthquake load
F = loads due to fluids with well-defined pressures and
maximum heights
H = load due to lateral earth pressure, ground water pressure, or pressure of bulk materials
L = live load
Lr = roof live load
R = rain load
S = snow load
T = self-straining force
W = wind load
Section 3. General Design Rules
The general procedure of applying the Load and Resistance Factor Design (LRFD) method for aluminum building structures consists of the following steps:
1) Determine the stress due to the factored loads, f, by conventional elastic structural analysis. The factored loads
are the code-specified dead, live, wind, rain, snow or
earthquake loads multiplied by the load factors given
in Section 2.3.
2) Compute the factored limit state stress ϕFL from Section 3.4 and verify that ϕFL ≥ f
Section 3.4 gives the resistance factor ϕ and the limit
state stress FL for a variety of commonly encountered aluminum structural members and elements. The limit state
stress FL is dependent on the material properties and the
member geometry. It reflects the ultimate load carrying
capacity of the member or element, be that yield, fracture,
plastification, buckling or crippling. The limit state stresses
January 2005
in these LRFD criteria are identical to those which are
given in the ASD Specification for Aluminum Structures.
They can be determined simply by setting the factors of
safety equal to unity in the various formulas given in Section 3.4 of Part IA.
The resistance factor ϕ accounts for the uncertainties
of determining the limit state stress. It is computed by the
method of first-order second-moment probabilistic analysis presented in Reference (2) for a target reliability index
of βT = 2.5 for the yield limit state and βT = 3.0 for the fracture limit state. Following is a detailed account presenting
the background for each of the resistance factors used in
Section 3.4 of the LRFD criteria.
Prior to this detailed account it will be instructive to discuss in a simple manner the basic concepts of probabilistic
design. Failure is defined when the resistance, as characterized by a limit state, is less than or equal to the load effect
on the structural element. The load effect in these LRFD
criteria for aluminum structures is characterized by the
II-B-3
stress computed by elastic analysis from the forces acting
on the structure. Both the resistance R and the load effect Q
are random quantities (Fig.C1).
Limit states are either ultimate or serviceability limit states.
These LRFD criteria pertain to the ultimate limit states of
yield, fracture, plastification, buckling and crippling, although
the serviceability limit states of deflection and the appearance
of buckling are also featured (in Section 4).
Failure is then not necessarily the total collapse of the
member, but the reaching of a practically defined ultimate limit state. It occurs when R < Q. Alternately, failure
also is defined as in ln(R/Q) ≤ 0, as shown in Fig.C2. The
probability of exceeding a limit state is the shaded area.
According to present practice, it is not necessary to define
a desired probability of failure, but a “reliability index”
β is determined such that the “target reliability index” βT
for a new code is approximately equal to the value of β
inherent in the traditional specification for standard design
situations (2). This process of selecting a target reliability
index is called “code calibration.” It will be illustrated for
the simple case of tension members.
According to first-order statistical derivations, the value
of β from Fig.C2 is expressed by the following formula.
__ __
ln(
R/Q)
_______
β = ________
(1)
√VR2 + VQ2
__
__
In this equation R and Q and are the mean values of the
resistance R and the load effects Q, respectively, and VR and
VQ are the corresponding coefficients of variation.
The resistance of a tension member for the limit state
of yielding is
R = A Fty
(2)
____
R = AFty
and
________
VR = √ VA2 + V 2Fty
(4)
The available data on dimensions and yield stress of aluminum structures were evaluated in Reference (3), and the
following conservative estimates of the statistical properties were suggested:
__
__
Fty = 1.10Ftyn, VFty = 0.06, A = An, VA = 0.05
where Ftyn is the minimum specified yield stress and An
is the handbook area. These are the “nominal” values the
designer uses. With these values
___________
__
R = 1.10Rn and VR = √0.055 + 0.062 = 0.08
and thus
__
Figure C-2
DEFINITION OF THE RELIABILITY
INDEX ß
Rn is the “nominal” resistance, Rn = An Ftyn.
(3)
The load effect Q is the tensile force in the member due
to the applied loads. For purposes of illustration only dead
and live load will be used, i.e.,
Q=D+L
__
__
(5)
__
Q =D+L
(6)
_____________
__
__
√(DVD__) +__(LVL)
VQ = ______________
2
2
D+L
(7)
The following statistical data about load are taken from
Reference (2):
Figure C-1
SCHEMATIC REPRESENTATION OF
PROBABILITIES OF THE LOAD EFFECT
AND THE RESISTANCE
II-B-4
__
__
D = 1.05Dn, L = Ln, VD = 0.1 , VL = 0.25
where Dn and Ln are the “nominal”, code specified, loads.
January 2005
Rearrangement of Eqs. 6 and 7 leads to the following
equations:
The calculations show the following results:
__
ϕ
D/L
ß
0.95
0.2
2.5
0.95
0.1
2.5
0.85
0.2
3.1
0.85
0.1
2.9
Q = Ln (1.05 D/L + 1)
(8)
__________________
√(1.05 × D/L) + 0.25
VQ = ___________________
1.05 D/L + 1
2
2
(9)
where D/L is the nominal dead-to-live load ratio.
The process of calibrating to the ASD Specification is
performed as follows:
An Ftyn/F.S. = Dn + Ln
(10)
or
Rn = F.S. (Dn + Ln) = F.S. (Ln)(D/L + 1)
(11)
F.S. is the specified factor of safety, which is equal to 1.65
in the ASD Specification for the limit state of yield.
Substitution of F.S.
__ __= 1.65 into Eq. 11, and use of Eq. 11
in the relationship R/Q gives
__
× 1.65 (D/L + 1)
R = 1.0
__
_________________
__
Q
(12)
1.05 D/L + 1
__ __
R/Q and VQ (Eq. 9), and thus also β (Eq. 1), depend on
the dead-to-live load ratio. Aluminum structures usually
have a low dead-to-live load ratio. Following are values of
β determined from Eq. 1 for the limit state of yield (F.S. =
1.65) and the
__ limit state of fracture (F.S. = 1.95). For this
latter case R = 1.10 Rn and VR = 0.08, as for the limit state
of yield (Reference 3).
D/L
ß Yield
ß Fracture
0.2
2.6
3.4
0.1
2.5
3.2
ϕ An Ftyn = γD Dn + γL Ln
Again, using Rn = An Ftyn, and γD = 1.2 and γL = 1.6 as
recommended in Reference (2),
L
Rn = __n (1.2 D/L + 1.6)
ϕ
(14)
[
1.10 1.2
D/L + 1.6
___________
R/Q = ____
1.05 D/L +1
ϕ
January 2005
(16)
(Rn)LRFD = Ln (1.2 D/L + 1.6)(1/ϕ)
(17)
when (Rn)ASD is the nominal design requirement according
to Part I-A, and (Rn)LRFD is the requirement of the LRFD
criteria. The ratio LRFD/ASD is then
(18)
The curves in Fig. C-3 show the variation of this ratio
for various values of ϕ and for F.S. = 1.65 and 1.95 for
the range D/L = 0.2 to 0.5. It can be seen that the ratio
decreases with an increase of the dead-to-live load ratio.
The following portions of this commentary will give the
basic data used to arrive at the recommended ϕ-factors in
Section 3.4.
3.4.1 Tension, Axial
The selection of ϕy = 0.95 and ϕu = 0.85 was discussed
in the previous part of this Commentary.
from which
__ __
limit state fracture
(Rn)ASD = Ln (D/L + 1)(F.S.)
ϕ (F.S.) (D/L + 1)
(13)
limit state yield
The values of ϕ were rounded off to the nearest 0.05,
and comparison of the β’s indicates that for typical deadto-live load ratios of aluminum structures (i.e., D/L of 0.2
to 0.1) the values of β are near the target of 2.5 for the limit
state of yield, and the target of βT = 3.0 for the fracture limit
state. This difference reflects the fact of the greater reliability demanded for the more serious type of limit state,
as already recognized in the ASD Specification with its
two kinds of safety factors, i.e., 1.65 and 1.95. These target
reliability indices are similar to those used by the AISI for
cold-formed steel.
Based on the results presented above ϕ = 0.95 is recommended for the limit state of yield, and ϕ = 0.85 for
the limit state of fracture. Methods are available to easily
check the consequences of changing ϕ as regards reliability. The economic consequences can also be ascertained
by comparing designs required by the ASD and the LRFD
method, as follows:
1.2 D/L + 1.6
_______________
A similar exercise can also be performed for the proposed LRFD method. According to this approach
}
}
]
(15)
II-B-5
3.4.2 through 3.4.4
Tension in Extreme Fibers of Beams
Two limit states apply to the tension flange: limit state
of yield when the strain is that corresponding to the yield
stress Fty, and limit state of fracture. The resistance is the
bending moment M, and its mean value and coefficient of
variation is, for the yield limit state,
__
__ _ ___
R = Sxt g Fty
(19)
and
____________
VR = √ V 2S + V 2g +V 2F
(20)
ty
xt
where Sxt is the elastic section modulus on the tension side,
g is the “shape factor”, and Fty is the tensile yield stress.
The same expressions hold for the limit state of fracture,
with the exception that Fty is replaced by Ftu. The shape factor accounts for partial plastification due to the non-linear
nature of the stress-strain curves. The nominal resistance is
RN = Sxtn gn Ftyn
(21)
and so
__
_
__
( ) ( )( )
_
Fty
g ___
Sxt __
R = Rn = ___
Sxtn gn Ftyn
(22)
Reference (3), as noted before for the tension member,
gives the values
_
__
Sxt = Sxt, VSxt = 0.05, Fty = 1.10Ftyn, VFty = 0.06
It will be assumed that gn equals the shape factors in Part
I-A, and equals the values given in Reference (4), which
were also corroborated for some sections and alloys in Reference
(5). It will be assumed that Vg = 0.0. From these data
__
R and VR can be determined as
__
_
___________
R = Rn (1.1g/gn) and VR = √0.055 + 0.062 = 0.08
Figure C-3
THE EFFECTS OF CHANGING
THE RESISTANCE FACTOR Ф
ON THE REQUIRED AREA
FOR TENSION MEMBERS
II-B-6
The results of the analysis for the recommended ϕ-factors
are given in Table C-3.4.1. The values of β are near the target
values.
3.4.5 and 3.4.6 Bearing
In the absence any statistically significant data on bearing capacities, it was decided to use ϕu = 0.85, giving essentially the same requirements as the ASD Specification.
January 2005
3.4.7 Compression in Columns, Axial,
Gross Section
The mean resistance of an ideally pinned-end but initially crooked column was shown to be equal to (3, 5):
The nominal column strength equations of the ASD
Specification were retained, i.e.,
__
FL = Bc – Dc kL/r ≤ Fcy
__ __
__ __
R = A σTM BT Bu
(26)
The coefficient of variation is then
(23)
__________________
VR = √ V 2A + V 2σ + V 2B + V 2Bu
for kL/r ≤ S2 = Cc, and
TM
π E
FL = ______
(kL/r)2
2
(24)
(27)
T
The terms in Eq. 26 are defined as follows:
__
A : mean cross-sectional area of column
for kL/r ≥ Cc
__
It was found convenient in the background research to
introduce a non-dimensional slenderness ratio
kL __
1 _____
λ = ___
r π √Fcy /E
( )
(25)
and the equations actually given in Section 3.4.7 are in
terms of λ rather than the effective slenderness ratio. The
definitions of Bc, Dc, S2 and Cc remain the same as in Part
I-A. The relationship between the nominal limit state stress
FL and the factored limit state stress ϕ FL, and the slenderness parameter λ, is shown in Fig. C-4 for one particular
alloy.
The resistance factor ϕcc varies with the slenderness
parameter. The particular equation for ϕcc given in Section
3.4.7 is similar to, but not identical to, the resistance factors
recommended in References (3) and (5), where considerable work was done in the development of LRFD provisions for columns, and therefore, a detailed accounting is
presented on the way ϕcc was selected.
In accordance with previous usage, A = An and VA =
0.05, where An is the nominal area.
σTM : mean buckling stress of an ideally straight column as
determined by the tangent modulus theory, i.e.,
π2 Et
σTM = ______
(kL/r)2
(28)
In the derivation of References (3) and (5) a RambergOsgood type stress-strain curve was assumed, and thus the
tangent modulus Et is equal to
E
Et = ____________________
σ n-1
E ___
1 + 0.002n ___
σ0.2 σ0.2
(29)
( )( )
In this equation E is the elastic modulus, σ is the average stress under this buckling load, σ0.2 is the compressive
stress when the strain is equal to 0.2 percent, and n is the
strain-hardening parameter. The coefficient of variation of
σTM, VσTM , was shown to be 0.06 in Reference (5).
Table C-3.4-1
DATA FOR TENSION IN EXTREME FIBERS OF BEAMS
Cross Section and Flexure Plane
Article
in LRFD
Criteria
I and C shapes major axis flexure
3.4.2
I shapes minor axis flexure
3.4.4
Box shapes
3.4.2
Circular tubes
3.4.3
Solid rectangular bars
3.4.4
January 2005
_
__
Limit
State
gn
g
(Ref. 5)
R/Rn
ϕ
ß
(D/L = 0.2)
Yield
Fracture
Yield
Fracture
Yield
Fracture
Yield
Fracture
Yield
Fracture
1.0
1.0
1.30
1.42
1.0
1.0
1.17
1.24
1.30
1.42
1.07
1.16
1.30
1.50
1.10
1.22
1.17
1.35
1.30
1.50
1.18
1.28
1.10
1.16
1.21
1.34
1.10
1.20
1.10
1.16
0.95
0.85
0.95
0.85
0.95
0.90
0.95
0.85
0.95
0.85
2.9
3.7
2.5
3.3
3.0
3.7
2.5
3.4
2.5
3.3
II-B-7
__
BT : mean value of the ratio of test results of straight
columns to the tangent modulus load. Analysis of the available test results in Reference (3) resulted in the following
statistics:
gated (Table C-3.4.2). A number of types of relationship
for ϕ were tried, and the following expressions were finally
selected as being reasonably accurate and yet still fairly
simple:
__
BT = 1.0 and VBT = 0.05
ϕc = 1 - 0.21λ ≤ 0.95 for λ ≤ 1.2
This means that the tangent modulus theory is indeed a
very good predictor for straight columns.
ϕc = 0.58 + 0.14λ ≤ 0.95 for λ > 1.2
__
Bu : mean value of the ratio of the ultimate strength of
an initially crooked pinned end column to the strength predicted by the tangent modulus theory for straight columns. It
was assumed that the initial crookedness of the column is a
sine-wave with a maximum amplitude of one-thousandths of
the length. This is in accordance with the procedure recommended by the Structural Stability Research Council (Ch. 3,
Reference (6)).
The following formulas were derived in Reference (5)
for the ratio Bu:
__
Bu = 1.0 for λ ≤ 0.263
__
Bu = 1.05 - 0.19 λ for 0.263 ≤ λ ≤ 1.20
__
Bu = 0.63 + 0.16 for 1.20 ≤ λ ≤ 2.0
__
Bu = 0.95 for λ ≤ 2.0
VBu = 0.10
}
(30)
A calibration study similar to that presented previously
for tension members was performed, using Eq. 1 to determine β, and employing Eqs. 23 and 24 as the nominal column strength: Four different kinds of alloys were investi-
}
(31)
The resistance factor thus varies linearly as the slenderness
parameter λ. The β values resulting from the use of ϕcc
(Eq. 31) is the LRFD design criteria are shown as the solid
curve in Fig. C-5. The target value of βT = 2.5 is fairly
closely approximated.
In Reference (5) considerable work was done on one additional aspect of column design. Real pinned-end columns
rarely exist in practice. Even nominally pinned columns have
some end restraint, and most columns are actually restrained
by the connection to the base or to members framing into their
ends. Furthermore, intentionally axially loaded members are
also rare, most compression members being actually beamcolumns subjected to both compression and bending. It was
shown that each of these effects have a conservative influence
and thus they tend to increase β. A number of additional cases
were studied, showing the same general trend of a somewhat
increased value of β due to restraint.
3.4.8 through 3.4.21
The statistical basis for selecting the ϕ values in these
Sections is presented in Reference (3). The same values of
ϕy were recommended as for tension of the corresponding
member types of Sections 3.4.2 through 3.4.4, thus equat-
Figure C-4
COLUMN CURVE FOR 6061-T6 ALLOY
II-B-8
January 2005
ing the reliability of short compressed members and elements to that underlying tension elements. The relevant
data for choosing the ϕ values, which apply to buckling or
crippling type limit states, are summarized in Tables C-3.4-3,
C3.4-4, C3.4-5, and C3.4-6. For certain alloys and Specification Sections, a negative S1 slenderness limit may result
from the equations given in Table 3.4-3. In such cases S1
should be taken as 0.
Figure C-5
Table C-3.4-2
DATA USED IN COLUMN CALIBRATION STUDIES
Ref.
Material
Heat
Treatment
n
σ0.2
ksi
E
ksi
Fcy
ksi
VR
***
7
European
No
8
22.78
10,180
20.7*
0.14
8
–
Yes
18.55
40.15
10,100
36.5*
0.14
7
European
Yes
28.60
43.99
10,790
40.0*
0.14
9
6061-T6
Yes
15.5
40.8
10,100
35**
0.14
* Fcy = σ0.2/1.1, assuming σ0.2 to be the mean yield stress
** Specified value
_______________________
___________________
__________________
*** VR = √0.052 + 0.062 + 0.052 + 0.102 = √ V 2A + V 2σTM + V 2B + V 2B
T
January 2005
u
II-B-9
Table C-3.4-3
SUMMARY OF STATISTICAL DATA
Sec. in
Ref. 1
Limit
State
F.S.
Pm
Mm
Fm
Rm
___
VP
VM
VF
VR
Category
3.4.1, 2,
3, 4
3.4.8, 9
Y
U
Y
B
Y
IB
EB
Y
B
Y
IB
EB
Y
B
Y
IB
EB
ny
kt nu
ny
nu
ny
nu
nu
ny
ny
ny
ny
ny
ny
ny
ny
ny
ny
1.0
1.0
1.0
1.0
1.0
1.0
1.24
1.0
1.03
1.0
1.01
1.24
1.0
1.0
1.0
1.07
0.93
1.10
1.10
1.10
1.0
1.10
1.0
1.0
1.10
1.0
1.10
1.0
1.0
1.10
1.0
1.10
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.10
1.10
1.10
1.0
1.10
1.0
1.24
1.10
1.03
1.10
1.01
1.24
1.10
1.0
1.10
1.07
0.93
0
0
0
0.05
0
0.05
0.27
0
0.11
0
0.05
0.27
0
0.05
0
0.09
0.09
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.08
0.08
0.08
0.09
0.08
0.09
0.28
0.08
0.13
0.08
0.09
0.28
0.08
0.09
0.08
0.12
0.12
A
B
C
D
C
D
E
A
F
A
G
H
A
I
A
J
K
3.4.10
3.4.11,
13, 14
3.4.12,
16.1
3.4.15,
16, 17
3.4.20
Table C-3.4-4
LIMIT STATE CATEGORIES
Category FS
__
R/Rn
VR
Description
Table C-3.4-5
RELIABILITY INDICES FOR ASD
SPECIFICATION
Category
β
for D/L = 0.1
β
for D/L = 0.2
1.65 1.10 0.08 yield in compression
A
2.46
2.64
1.95 1.00 0.09 buckling of column
components
inelastic column buckling
B
3.16
3.40
C
2.87
3.09
D
2.72
2.92
E
2.44
2.51
F
2.01
2.13
G
2.08
2.22
H
1.98
2.03
I
2.04
2.18
J
2.20
2.34
K
1.65
1.75
A
1.65 1.10 0.08 yield in tension
B
1.95 1.10 0.08 fracture in tension
C
D
E
1.95 1.24 0.28 elastic column buckling
F
1.65 1.03 0.13 beam buckling, overall
G
1.65 1.01 0.09 inelastic local buckling
H
1.65 1.24 0.28 elastic local buckling
I
1.65 1.00 0.09 local buckling of beams
J
1.65 1.07 0.12 inelastic shear buckling
K
1.65 0.93 0.12 elastic shear buckling
II-B-10
Rn
January 2005
Table C-3.4-6
RESISTANCE FACTORS FOR LRFD SPECIFICATION
Category
Target β
ϕ
for D/L = 0.1
ϕ
for D/L = 0.2
ϕ
Rounded off
A
2.5
0.94
0.96
0.95
B
3.0
0.83
0.86
0.85
C
2.5
0.94
0.96
0.95
D
2.5
0.85
0.86
0.85
E
2.5
0.78
0.79
0.80
F
2.5
0.83
0.85
0.85
G
2.5
0.85
0.87
0.85
H
2.5
0.78
0.79
0.80
I
2.5
0.85
0.86
0.85
J
2.5
0.88
0.89
0.90
K
2.5
0.76
0.78
0.80
recommended for use in LRFD Spec.
January 2005
II-B-11
Section 5. Mechanical Connections
The value of ϕ = 0.65 for shear stress on rivets and
bolts was determined by the following derivation. It was
assumed that the “typical” shear strength values for rivets
given in Reference (10) represent mean values. The ratio
of the mean to the “minimum expected” values was found
to be 1.15. A coefficient of variation of 0.1 was assumed. It
was also assumed that the nominal rivet area is equal to the
mean, with a coefficient of variation of 0.1. The mean shear
capacity of a rivet is thus
__
__ __
R = A Fsu = 1.0 × 1.15 An Fsun
(32)
and
________
_________
VR = √ V 2A + V 2F = √0.12 + 0.12 = 0.14
(33)
su
With these statistics a calibration was performed using
Eq. 1, and for a D/L = 0.2 it was found that ASD design gave
β = 3.9. The LRFD design with ϕ = 0.65 gave β = 4.0.
Section 7. Welded Construction
The design shear stress for fillet welds is based on ϕ = 0.80.
This value was determined so that an ASD-sized weld would
be approximately the same size as an LRFD-sized weld:
The mean shear strength of a fillet weld is equal to
__
_ __
R = τu A
(34)
__
_
where τu is the mean shear strength and A is the weld throat
area. From Reference (11):
Table C-7.1
FILLET WELD STRENGTHS
Filler Alloy
1100
1100
4043
__
Vsu /Fw
1.62
1.78
1.45
Vsu
0.18
0.23
0.17
Assuming the coefficient of variation Vsu = 0.2 (compared to 0.18,
__ 0.23, and 0.17 in Table C-7.1) and the mean
resistance R = 1.5 Rn (compared to 1.62, 1.78, 1.45 in Table
C-7.1), and the mean weld area equals the nominal area
with VA = 0.1, the safety index β ranged from 3.9 to 4.4
for D/L ranging from 0.1 to 0.5 for a safety factor of 2.34.
With the change in safety factor from 2.34 to 1.95 on fillet
welds, the safety index β ranges from 3.3 to 3.7. Because
weld quality is considered to have improved since 1966,
the safety index now is probably higher, but data has not
been collected recently.
Orientation of Weld
longitudinal
transverse
longitudinal
Table C-7.2
RATIO OF FILLET WELD AREAS REQUIRED BY LRFD TO THAT
REQUIRED BY THE ALLOWABLE STRESS SPECIFICATION
LRFD/ASD for ϕ = 0.80 and SF = 1.95 for
D/L = 0.1
D/L = 0.25
D/L = 0.5
1.00
0.97
0.94
Section 9. Testing
The test criteria are very similar to those in the ASD
Specification, except they provide guidance in determining
II-B-12
a resistance factor (as opposed to a safety factor) on the
basis of tests (Section 9.3.2).
January 2005
References
1.
Aluminum Association, Specifications for Aluminum
Structures, Fifth Ed., December, 1986.
2.
B. Ellingwood, T.V. Galambos, J.G. MacGregor, C.A.
Cornell “Development of a Probability Based Load Criterion for American National Standard A58-Building Code
Requirements for Minimum Design Loads in Buildings
and Other Structures” National Bureau of Standards, Special Publication 577, June 1980.
3.
T.V. Galambos, “Load and Resistance Factor Design
for Aluminum Structures” Research Report No. 54,
Civil Engineering Department, Washington University,
St. Louis, Mo.
4.
J.W. Clark, “Design of Aluminum Structural Members”, Ch. 10 in Structural Engineering Handbook, ed.
E.H. Gaylord and C.N. Gaylord, McGraw-Hill Book
Co., New York, 1979.
5.
J.C. Chapuis and T.V. Galambos, “Design Criteria for
Aluminum Columns and Beam-Columns” Research
Report No. 58, Civil Engineering Department, Washington University, St. Louis, Mo.
January 2005
6.
B.G. Johnston, Editor, Guide to Stability Design Criteria for Metal Structures, Third Ed., John Wiley and
Sons, Inc., New York, 1976.
7.
A. Bernard, F. Frey, J. Janss, C. Massonnet, “Research
on the Behavior and Buckling of Aluminum Bars” (in
French), LABSE Publications, Vol. 33-I, 1973.
8.
R.H. Batterman, G.G. Johnston, “Behavior and Maximum Strength of Metal Columns” Journal of the Structural Division, ASCE, Vol. 93, ST2, April 1967.
9.
J.W. Clark, “Statistical Aspects of Strength of Aluminum”, ALCOA Report No. 76-74-10, June 20, 1974.
10. ASCE Task Committee on Lightweight Alloys, “Suggested Specifications for Structures of Aluminum
Alloys 6061-T6 and 6062-T6” Journal of the Structural
Division, ASCE, Vol. 88, ST6, Dec. 1962.
11. F.G. Nelson, R.L. Rolf, “Shear Strengths of Aluminum
Alloy Fillet Welds” Welding Journal Research Supplement, Feb. 1966.
II-B-13
Aluminum Design Manual
PART III
Design Guide
The Aluminum Association, Inc.
1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
Third Edition, January 2005
III
Design Guide
TABLE OF CONTENTS
1.0
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
2.0
Design of Aluminum Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
2.1
Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2
Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.3
Alloys and Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.4
Aerospace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.5
Automotive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.6
Bridges and Highway Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.7
Railroad Cars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.8
Ships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.9
Storage Tanks, Pressure Vessels, and Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.10 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.11 Other Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.0
Member and Component Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1
Tension Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2
Tension Flange of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3
Bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4
Compression in Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.5
Compression in Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.6
Compression in Flat Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.6.1
Elements with Constant Thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.6.2
Elements with Non-Uniform Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.7
Compression in Tubes and Curved Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.8
Shear in Flat Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.8.1
Buckling of Stiffened and Unstiffened Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.8.2
Tension Field Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.8.3
Corrugated Webs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.9
Shear in Tubes and Curved Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.10 Combined Stresses/Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.11 Stiffeners for Flat Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.12 Pipe Bursting Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.13 Biaxial and Triaxial Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.0
Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
5.0
Joints and Joining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
5.1
Mechanical Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2
Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.2.1
Welding Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.2.2
Design of Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.3 Adhesive Bonded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.3.1
Advantages and Disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.3.2
Adhesive Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.3.3
Types of Adhesives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.3.4
Aluminum Surface Pretreatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.3.5
Joint Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.3.6
Current Adhesive Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
January 2005
III-3
6.0
Sandwich Panels and Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
7.0
Extrusion Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.1
Replacement of Fabrications with Extrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
7.2
Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.3
Design Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
7.4
Design for Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
8.0
Prevention of Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
9.0
Fire Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44
10.0
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
III-4
January 2005
1.0 Introduction
This part of the design handbook provides general, nonmandatory information that may be of interest to a designer
of aluminum products of any type. Included are references
to the strength formulas given in Part IA, Allowable Stress
Design Specification (Part IB, LRFD Specification, has similar equations). These formulas are applicable to the design
of all types of products; such as building, bridges, ships,
railroad cars, automobiles, trucks, highway structures and
machinery. For example, the formulas for a column given
in the Specification apply equally well to a column for a
patio roof, a member in a latticed roof, a strut in a rail car
or automobile, a member in a bridge truss, and a stanchion/
pillar in a ship. When formulas exist in the Specification
and are discussed in this part, they are referenced by number (italicized) and thus are not duplicated.
January 2005
The designer can determine the strength of the part from
the formulas given in the Specification by setting the factors of safety on appearance, yielding and ultimate strength
equal to 1.0. The designer can also incorporate other factors of safety into the formulas for the product commensurate with the uncertainties of the load and member strength
and with the importance of the structure, and the safety of
the user of the structure. Of course the margins of safety
for buildings and bridges are specified in the requirements
of Part IA and IB.
Also covered in this part are topics that are not currently
in the Specification but are believed to be of interest to the
designer. Commentary of the Specification, past handbooks
from the aluminum producers and published and unpublished reports are the major resources of this material.
III-5
2.0 Design of Aluminum Structures
The various parts of this handbook provide most of the
information that designers need to properly design aluminum structures. Part IV Materials, provides general information about aluminum and alloys, the alloy and temper
designation system, and comparative characteristics and
applications. Part V Material Properties, gives mechanical
and physical properties of alloys. Part VI Section Properties, has tables of section properties of many shapes and
general equations for the calculation of various section
properties, including torsional and warping values. Part
VII Design Aids, has charts and tables containing allowable stresses for various alloys and beam formulas. Part
VIII Illustrative Examples of Design, provides detailed
calculations for the design of many specific components
and the location of necessary information provided in the
parts of this manual. Some additional general guidance for
design is provided in this section along with references to
other technical literature that provide additional resource
material.
2.1 Considerations
Part IV discusses attributes of aluminum that allow it
to be used as a cost effective material in structures. Most
of the applications make use of a favorable life cycle cost;
the combined costs of the material and its fabrication into
the finished product, erection or installation of the product,
operation and maintenance, and disposal or reuse of the
material after its useful life in the product. For example,
aluminum is the principal material in aerospace structures,
primarily because of its high strength to weight ratio. The
density of aluminum is about ⅓ that of steel and aluminum alloys have strengths similar to those of constructional
steels. The aerospace structures are cost effective because
smaller engines and less fuel are needed during service
compared to those that would be required for heavier structures. The excellent corrosion resistance of aluminum (see
Section 8.0) also is a factor in minimizing maintenance
costs. Weights of aluminum structures generally are ⅓ to
½ those of steel (see Section 3.0). Light weight and corrosion resistance are also the major factors for the selection of aluminum for trucks, automobiles and railroad cars.
Low maintenance and fuel savings are the important issues.
Aluminum’s corrosion resistance in the environment and its
appearance, bare or finished, are the major factors in its
use in commercial and residential buildings. Many aluminum structures, such as light poles, overhead sign trusses,
latticed roofs, bridges and bridge decks are not painted because
of the good corrosion resistance of aluminum. Appearance
and light weight are also important in truck and automobile wheels.
Sheet, plate, extrusions, forgings and castings are made
of aluminum. Alloys and tempers that possess both good
III-6
strength and corrosion resistance are available for use in
most structures. Aerospace alloys are generally not used
for other types of structures because their cost is higher
and their corrosion resistance is lower than those of the
moderate strength alloys. Examples of the common alloys
and tempers used for each product form are given in the
following table. A more complete list of commonly used
alloys and their properties and applications are given in
Parts IA, IV and V.
Product form
Sheet and Plate
Extrusions
Forgings
Castings
Application
Building
Heavy Duty
Structures
Building
General Purpose
Wheels
General Purpose
High Elongation
Alloys
3105-H25, 5052-H34,
3004-H16
5083-H116, 5086-H116,
5456-H116, 6061-T6
6063-T6
6061-T6
6061-T6
356.0-T6
A444.0-T4
The extrusion process is unique to aluminum (compared
to steel), and allows the designer to place the material
where it is most effective. Section 7.0 provides details on
extrusion design. The extrusion process consists of pushing
hot aluminum through a die, likened to pushing tooth paste
out of the tube. Cross sections generally must stay constant
along the length but they can have detailed cross sections.
Often fabrication costs can be lowered by consolidation of
parts or the incorporation of aids for assembly by the use of
extrusions. Extrusions up to about 30 in. are possible, but
the more common ones fit within a circle size of 15 in.
All the common joining methods may be used for
attachment of assemblies of aluminum structures; welding,
mechanical fastening, adhesive bonding, and a combination of adhesive bonding and one of the other joining methods (see Section 5.0). Welding is done in the shop or in an
enclosure because the shielding gas must cover the arc and
wind can remove the shield.
Although aluminum has excellent corrosion resistance
(see Section 8.0) protection is needed when it is attached
to steel, or it is joined by steel bolts, to prevent galvanic
action. Painting the parts and galvanizing the bolts is a
minimum treatment. Sometimes it is desired to protect an
aluminum part from pitting or further oxidation. Clear and
decorative finishes can be applied to these cases.
2.2 References
The following references are additional sources of information on aluminum structural design. References marked
* are available from the Aluminum Association (www.
aluminum.org)
January 2005
2.2.1 General
1. Sharp, Maurice L., Behavior and Design of Aluminum Structures, McGraw-Hill, Inc., New York, NY,
1993.
*2. Kissell, J. Randolph, and Ferry, Robert L., Aluminum Structures, 2nd ed., John Wiley & Sons, New
York, NY, 2002.
3. Sharp, M.L., Nordmark, G.E., and Menzemer, C.C.,
Fatigue Design of Aluminum Components and Structures, McGraw-Hill, Inc., New York, NY, 1996.
*3. AT6 Aluminum Automotive Extrusion Manual,
Aluminum Association, Washington, DC, 1998.
*4. A Guide to Practices for the Repair of Automotive
Sheet Aluminum, Aluminum Association, Washington, DC, 1998.
2.2.6 Bridge and Highway Structures
1.
2.
2.2.2 Fabrication
*1. Forming and Machining Aluminum, Aluminum
Association, Washington, DC, 1988.
*2. AWS D1.2/D1.2M:2003 Structural Welding CodeAluminum, American Welding Society, Miami, FL,
2003.
*3. Welding Aluminum: Theory and Practice, 4th ed.,
Aluminum Association, Washington, DC, 2002.
*4. Minford, J. Dean, Handbook of Aluminum Bonding
Technology and Data, Marcel Dekker, Inc., New
York, NY, 1993.
2.2.3 Alloys and Products
*1. Aluminum Standards and Data, 2003, Aluminum
Association, Washington, DC, 2003.
*2. Aluminum Standards and Data Metric SI 2003,
Aluminum Association, Washington, DC, 2003.
*3. Standards for Aluminum Sand and Permanent Mold
Castings, Aluminum Association, Washington, DC,
14th ed., 2000.
*4. AWS A5.10/A5.10M: 1999 Specification for Bare
Aluminum and Aluminum-Alloy Welding Electrodes
and Rods, American Welding Society, Miami, FL,
2000.
2.2.4 Aerospace
1. DOT/FAA/AR-MMPDS-01, Metallic Materials Properties Development and Standardization
(MMPDS), (formerly MIL Handbook 5) Chapter 3,
January, 2003, U.S. Department of Transportation,
Federal Aviation Administration, Washington, DC.
Copies available through the National Technical
Information Service (NTIS), 5285 Port Royal Road,
Springfield, VA 22161-0001; www.ntis.gov or downloadable from http://www.tc.faa.gov/its/worldpac/
techrpt/armmpds-01.pdf
2.2.5 Automotive
*1. AT3 Aluminum for Automotive Body Sheet Panels,
Aluminum Association, Washington, DC, 1996.
*2. AT5 Automotive Aluminum Crash Energy Management Manual, Aluminum Association, Washington,
DC, 1998.
January 2005
3.
AASHTO LRFD Bridge Design Specifications,
2nd ed., American Association of State Highway and
Transportation Officials, Washington, DC, 1998.
Guide Specifications for Aluminum Highway Bridges,
American Association of State Highway and Transportation Officials, Washington, DC, 1991.
Standard Specifications for Structural Supports for
Highway Signs, Luminaires and Traffic Signals,
4th ed., American Association of State Highway and
Transportation Officials, Washington, DC, 2001.
2.2.7 Railroad Cars
1.
2.
Manual of Standards and Recommended Practices
Section C, Part II, Design, Fabrication, and Construction of Freight Cars, Association of American Railroads, Transportation Technology Center,
Pueblo, CO.
AWS D15.1:2001 Railroad Welding Specification–
Cars and Locomotives, American Welding Society,
Miami, FL, 2001.
2.2.8 Ships
*1. ANSI/AWS D3.7:2004 Guide for Aluminum Hull
Welding, American Welding Society, Inc., Miami,
FL, 2004.
2. Rules for Building and Classing Aluminum Vessels,
American Bureau of Shipping, Houston, TX, 1996.
2.2.9 Storage Tanks, Pressure Vessels, and Pipe
1.
ASME B31.3:2002 Edition, Process Piping, American Society of Mechanical Engineers, New York,
NY, 2002.
2. ASME Boiler and Pressure Vessel Code, Section II,
Materials, American Society of Mechanical Engineers, New York, NY, 2004.
3. ASME B96.1-1999, Welded Aluminum-Alloy Storage Tanks, American Society of Mechanical Engineers, New York, NY, 2000.
4. API Standard 620, Design and Construction of Large,
Welded, Low-Pressure Storage Tanks, 10th ed., American Petroleum Institute, Washington, DC, 2002.
5. API Standard 650, Welded Steel Tanks for Oil Storage, 10th ed., American Petroleum Institute, Washington, DC, 1998.
*6. Aluminum Alloys for Cryogenic Applications,
Aluminum Association, Washington, DC, 1999.
III-7
2.2.10 Material Properties
*1. Kaufman, J. Gilbert, Fracture Resistance of Aluminum Alloys: Notch Toughness, Tear Resistance, and
Fracture Toughness, ASM International, Materials
Park, OH, 2001.
*2. Kaufman, J. Gilbert, Properties of Aluminum Alloys:
Tensile, Creep, and Fatigue Data at High and Low
Temperatures, ASM International, Materials Park,
OH, 1999.
III-8
2.2.11 Other Codes
1.
Structural Use of Aluminium. Code of Practice for
Design, British Standard BS 8118-1, 1991.
2. ENV 1999 Eurocode 9 Design of Aluminium Structures, European Committee for Standardization
(CEN), Brussels, 1998.
3. CSA S157 Strength Design in Aluminum, Canadian
Standards Association, Rexdale, Ontario, Canada,
1983.
January 2005
3.0 Member and Component Behavior
structures are designed for aluminum, not converted from
an existing steel design.
The availability of economical aluminum extrusions
allows the designer to consolidate parts normally made
by fabrication, thereby saving on joining costs. Also the
designer can place the material in the section to optimize
the section property governing the design. Various quick
attachment schemes can be employed. Section 7.0 gives
more details on extrusion design.
The inherent corrosion resistance of aluminum offers
positive potential for long life structures that require a
minimum of maintenance. Many aluminum structures,
e.g., light poles, have performed satisfactorily for decades
without painting. Life cycle considerations should be used
when comparing the merits of aluminum structures with
those of other materials, particularly when the other structures need periodic painting and other maintenance. Life
cycle should include the costs of the as-fabricated structure,
erection/installation, operation/maintenance and disposal/
recycling. Information on corrosion resistance is given in
Section 8.0.
The following subsections provide more detailed design
information for the components and members covered in
the Specification. As noted previously other information
has been included when available.
The structural design of aluminum components and
structures is very similar to that for steel and other metal
structures. The primary difference is that properties of the
various alloys, some of which are different from those of
steel, are incorporated into the equations defining structural behavior. Because many engineers are trained in steel
technology to a larger extent than aluminum technology,
similarities and differences between aluminum and steel
are summarized in Table 3.0-1(1).
Because of the difference in properties (modulus for
example) an aluminum design should be different than
that for steel in order to use the material effectively. An
example is illustrated in Figure 3.0-1; the relative weights
of box beams of aluminum and steel with the same bending strength and deflection. The yield strength of the two
materials is the same. The weight of the aluminum part
is about 50% that of the steel part when its size is about
1.4 times that of steel. Other configurations generally will
provide weight savings but less than the optimum. Weights
of aluminum structures of 50% that of steel structures have
been achieved for bridge girders, automotive frames and
other transportation vehicles, in which deflection and
fatigue are controlling. For structures controlled by static
strength, such as automobile hoods and decklids, and some
building panels, weights of aluminum structures of about
⅓ that of steel have been achieved. In all these cases the
Table 3.0-1
DIFFERENCES—ALUMINUM AND STEEL (1)
Property
Steel
Aluminum
Importance for
Design
Modulus of elasticity
29 × 103 ksi
Weight per volume
0.284 lb/in3
Thermal expansion
7 × 10 in/in/ F
13 × 10 /in/in/ F
Thermal expansion
Thermal stress
Stress-strain curves
Varies
Varies
Depends on alloys
Steel often has higher
strength and elongation at room
temperature
Aluminum has better
performance at low
temperatures
Fatigue
Varies
Varies
For joints, aluminum has about 1/3 to
½ fatigue strength as steel for same
detail
Corrosion resistance
Needs protection
Often used unpainted
Aluminum usually is
maintenance free
Aluminum is nonstaining
Strain rate effects—
mechanical properties
High strain rates increase
properties—varies with type
of steel
Much less change in
properties compared to steel
Need to use dynamic
properties for high-strain rate
loadings
January 2005
-6
10.1 × 103 ksi
Deflection of members
Vibration
Buckling
0.10 lb/in3
o
-6
Weight of Product, Vibration
o
III-9
Figure 3.0-1
MINIMUM WEIGHT OF SQUARE TUBULAR SECTIONS
3.1 Tension Members
The accepted measure of ductility of aluminum alloys
is fracture toughness and many of the high strength alloys
used for aerospace applications have been evaluated (2).
The alloys considered in the Specification (non-aerospace
applications) are too ductile to be evaluated by fracture
mechanics methods. Thus, “ductility” generally is not a
design issue for wrought products. The best proof of adequate ductility of alloys is the satisfactory service in buildings, bridges, automobiles, trucks, railroad cars etc. Laboratory fracture tests show that the normalized resistance
curves (same fatigue strength) of parts made from one of
the alloys, 5456-H116 were higher than those of A36 steel,
at temperatures from –200 to +75 oF(3). Additional information on ductility/toughness of aluminum alloys has been
published (1).
Some practical members, such as angles attached by
one leg, have not only the stress concentration at the bolt,
but also the non-uniform stresses across the cross section
from the eccentricity of the load. This effect is accounted
for by the use of the net effective area of the cross section,
where the area on which the tensile stress is calculated is
reduced below the net area.
The ultimate or yield strength of tensile members with
elements of different strength may be estimated by the use
of the weighted average method. In this case the weighted
average strength is the sum of the quantities, each element
area times the element strength, divided by the total area.
Some increase in strength of welded parts can be
achieved by either welding in the –T4 temper and aging,
III-10
or by resolution heat treating and aging after welding.
The light pole manufacturers, for example, have justified
improved as-welded strength as a result of post weld treatment. Usually ductility of transversely welded structures is
reduced by post weld thermal treatment because the width
of the zone of lower strength material is decreased (plastic deformation may be confined to a narrow zone). Post
weld processes usually are not employed without careful
evaluation of strength, ductility and corrosion resistance
implications.
3.2 Tension Flange of Beams
The strengths of beams of round or oval tubes (Part IA,
Equations 3.4.3-1,2) and of shapes bent about the weak axis,
rectangular bars, solid round bars and plates (Part IA, Equations 3.4.4-1,2) are higher than those calculated assuming
failure when yield or tensile strengths are calculated at the
extreme fiber. Figure 3.2.-1 shows the stress-strain behavior
of axially loaded and bending members of the same alloy.
The beams exhibit higher strength compared with that for
the axially loaded members. The ratio of the beam yield or
ultimate to that for the tensile properties is referred to as
the shape factor, and is dependent upon the cross sectional
shape, the alloy, temper and the failure condition; yield or
ultimate. Values used in the Specification are summarized
in Table 3.2-1. The values for shape factors for aluminum
are less than the rigid plastic cases commonly used for mild
steel, because of the rounded stress-strain curves for aluminum alloys. The effect of alloy on shape factor is not very
large, so only one set of values is given for each shape. The
January 2005
yield or tensile strength of the alloy is multiplied by the
shape factor to define the higher strength values for beam
behavior. Shape factors for other shapes, and methods to
estimate these factors from rigid plastic cases are available
(1, p. 96).
The use of shape factors greater than 1.0 may be unconservative at locations of transverse welds in some beams
because of the limited deformation capacity across the
weld (1, p. 97). Tests may be required to establish beam
strength in this case. A shape factor of 1.0 is always conservative and may be used.
The ultimate or yield strength of the beam flange can
be estimated by the use of the weighted average method as
described in Section 3.1. The strength of flanges with welds
also are calculated using the same equations as defined for
tension members. The flange area includes a portion of the
web as defined previously.
3.3 Bearing
Figure 3.2-1
STRESS-STRAIN CURVES FOR
AXIAL AND BEAM MEMBERS
Table 3.2-1
SHAPE FACTORS FOR
ALUMINUM BEAMS
USED IN THE AA SPECIFICATION
Shape
Factor on
Yield
Factor on
Ultimate
1.0
1.0
1.17
1.24
1.30
1.42
The bearing strength for the part when using rivets or
bolts is given by Equation 3.4.5-1 of Part IA. The strengths
are for the sheet or plate being joined and apply for edge
distances (center of hole to edge of part in the direction of
the applied load) equal to 2.0 times the fastener diameter
or more. For edge distances less than 2.0 times the fastener
diameter, the bearing strength is reduced by the ratio of
edge distance divided by twice the fastener diameter. These
bearing strengths apply when pressure is toward the edge
of the part. Figure 3.3-1 shows that the bearing strength
when pressure is parallel to the edge of part is higher than
that when the load is toward the edge (1). In this figure the
bearing strength has been divided by the tensile strength
of the material. The joints covered are those in which
Figure 3.3-1
BEARING STRENGTHS
January 2005
III-11
there is a proper fit between fastener and hole; the rivet
fills the hole and the hole for the bolt is no more than ⅟₁ ₆ in.
oversized.
3.4 Compression in Columns
The strength of columns under flexural buckling is
given by Equations 3.4.7-1,2,3 of Part IA. The strength of
columns under flexural-torsional buckling is determined
using these same formulas and the equivalent slenderness
ratio given by Equation 3.4.7.2-1. The effective length factor suggested in the Specification is 1.0 for members supported at both ends and 2.0 for cantilevers. However, the
designer can input other values appropriate for the structure. Conservative values of the slenderness ratio should be
chosen, because they compensate somewhat for the reduction of strength due to crookedness that is not included in
the column formulas. Some values of effective length are
provided in Figure 3.4-1(1), with some guidance for “practical columns”.
In the case of torsional buckling, “design” values are
not shown in Figure 3.4-1 because of lack of information. However, based on laboratory test results shown in
Figure 3.4-2, it is likely that the theoretical values of k for
pinned ends (k = 1.0) should be used for flexural-torsional
buckling.
More information on effective length of columns is
available in the literature (4). Columns are usually parts
of a structure. Thus in determining an effective length, the
entire structure needs to be considered. The characteristics
of the joints and the resistance of the structure to rotation
and translation of the ends of the column have a large effect
on column strength.
The equation for flexural-torsional buckling of unsymmetrical shapes is not covered in the Specification but
is available elsewhere (1, p. 84). The equivalent slenderness ratio may be solved by trial, and is always larger than
those for torsional buckling and flexural buckling about the
x and y axes.
Welding decreases column strength for most alloys and
tempers. For columns with only longitudinal welds, the
strength is reasonably given by the same equation provided
for tension members (7.3-1). The column strengths calculated assuming all parent and all reduced strength material are used in this equation. The column strengths for
the reduced strength material are best estimated using
Figure 3.4-1
EFFECTIVE LENGTH FACTORS FOR CENTRALLY LOADED COLUMNS (1)
III-12
January 2005
Figure 3.4-2
FLEXURAL TORSIONAL BUCKLING (1)
buckling constants from Table 3.3-3. This procedure
apparently is sufficient to cover effects of both the reduced
strength material and the residual stresses due to welding.
The strength of columns with transverse welds depends
on the location and number of welds. If the welds are at the
ends only, the column is designed as a pinned-end column
with a limiting stress equal to the compressive yield strength
of welded construction provided in Table 3.3-2. Transverse
welds away from the ends of the column reduce the strength
below that for welds at the ends only. In this case the column should be designed as though the entire column has a
compressive strength as given in Table 3.3-2. Figure 3.4-3
shows the strength (factor of safety = 1.0) of 6061-T6 and
5083-H116 transversely welded and unwelded columns. If
the column has both longitudinal and transverse welds, the
provisions for transverse welds generally govern.
3.5 Compression in Beams
Strength equations for lateral buckling are available for
three general types of cross sectional shapes as summarized
in Table 3.5-1. The designer has the option of using more
accurate but more complicated equations than the basic
equations. The basic equations are very conservative. In
order to get efficient designs the “more accurate equations”
(column b) or “most accurate equations” (column c) should
be used. Figure 3.5-1 compares the calculated equivalent
slenderness ratios of 17 American Standard I-beams, to the
basic (column a) and the more accurate equations (column
b). The basic equations are overly conservative for moderate and high slenderness ratios and for all of the sections, in
many cases by a factor of two or more. Comparisons of test
data and calculations using the equations given in column
b show that this method is conservative (1).
January 2005
Figure 3.4-3
EFFECT OF TRANSVERSE WELD
In the inelastic region of the buckling curves, single web
and rectangular tube beams are assumed to have a shape factor of 1.0. The inelastic buckling curve is the same as that
used for columns. The inelastic curve for lateral buckling
of solid rectangular shapes, however, is much higher (see
Table 3.5-1
COMPRESSIVE STRENGTH OF
BEAMS IN BENDING
III-13
Figure 3.5-2
LATERAL BUCKLING OF BEAMS
Figure 3.5-1
EQUIVALENT SLENDERNESS RATIOS
FOR LATERAL BUCKLING
3. For members with transverse welds interior to the points
of lateral support, calculate the strength as though the
entire member had the strength corresponding to that
across a butt weld.
Figure 3.5-2) reflecting the shape factor of 1.3 on yield
strength used for these sections. Most sections have a shape
factor greater than 1.0 and the strength would lie somewhere
between the solid lines in Figure 3.5.2; there currently have
been no engineering methods proposed to calculate the
inelastic buckling curves for these intermediate values.
For welded beams, the compressive strength may be
calculated using the same principles employed for column
design. The flange is defined similarly to that for tension
members; that portion of the member further than 2c/3
from the neutral axis, where c is the distance from the neutral axis of the beam to the extreme fiber in compression.
The principles are the following.
If there are loads on the beams that do not pass through the
shear center torsional moments are generated. The stresses
and deformation due to the torsion must be considered. Calculation procedures are given in Reference 5.
1. For members with longitudinal welds, the strength is
calculated by the addition of the strength for the parts of
the section with parent material and those with reduced
strength material.
2. For members with transverse welds at the points of
lateral support, assume that the member is simply supported about the axis normal to the axis of bending, and
limit the bending stress to the strength of the material
across a butt weld.
III-14
3.6 Compression in Flat Elements
3.6.1 Elements with Constant Thickness
Five types of elements and loading have been defined
for aluminum structures as shown in Table 3.6-1. Also
shown are the equivalent slenderness ratios for each case
and the strength equations. The basic strength equations
(factor of safety = 1.0) for Cases 1 and 2 are the same for
columns and beams, but the applied factors of safety in the
Specification are different. Cases 3, 4 and 5 apply to webs
of beams only. The equivalent slenderness values are the
parameters introduced in the general strength equation,
both for buckling and ultimate strength of the element.
Figure 3.6-1 shows an example (6061-T6) of the various
inelastic, straight-line equations used for aluminum elements and members. Columns, single web beams and rectangular tubes are represented by the lower curve, which is
an approximation to the tangent modulus curve. Plates in
January 2005
uniform compression best fit a straight line that is intermediate to a tangent modulus and a secant modulus curve, but
higher than that for columns. Plates under bending employ
the same curve as that utilized for lateral buckling of solid
rectangular beams, and the straight line is much higher
than the other two cases, primarily because of the effect of
shape factor.
Post buckling strength is allowed for all cases except
Case 3 (Table 3.6-1), where the strength is limited to the
buckling value. Figure 3.6-2 shows an example of buckling and post buckling strength (ultimate strength). If the
design of a beam is based on stresses above the buckling
value, the use of full section properties in beam formulas
will underestimate deflections. The calculation of section
properties for the buckled shape using an effective width
of elements as given by Equations 4.7.6-1,2, and beam
equations, will provide a good estimate of deflections.
The strength of a section is obtained by the weighted
average concept; the addition of the strength contribution
of all elements (strength of element times the ratio of area
of element to the area of the entire cross section).
In the Specification the same strength equations for
compression on unwelded plates are applied to plates with
welds. The strength of the welded plate, however, is limited
to the strength of the material across a butt weld. There is
some information on welded plates (1), that indicates that
this design procedure can be somewhat unconservative for
ultimate strength for alloys with a large difference between
welded and base metal strengths, particularly for thin sheet.
To design welded plates assuming that the plate has all heat
affected material, however, would be ultraconservative. Thus
if more accurate estimates are desired, advanced analytical
methods or tests are needed to verify performance.
Another area that needs additional research is the definition of plate width for calculating post-buckling strength,
particularly when the ends have radii. The equations for
post buckling strength of elements is based on the redistribution of stresses and end conditions that support the edges
of the plate sufficiently to develop the yield strength of the
material at these edges. The requirement that the radius at
the edges be limited to 4t for determination of width of the
element (for calculating post buckling strength) is to provide for the necessary strength and support at the corners.
3.6.2 Elements with Non-Uniform Thickness
Strength equations are provided for elements of constant
thickness. Some limited studies show that the buckling load
for an element much thicker at the edges than at the center
can be over 40% higher than that for an element of constant thickness, but having the same area (1, p. 283). Post
buckling strength may also be higher, but there are no
Table 3.6-1
STRENGTH EQUATIONS FOR ELEMENTS UNDER COMPRESSION
Case
(1)
Strength Equations
Equivalent Slenderness Ratio
Columns
Beams
5.1 b/t
3.4.8-1,2,3
3.4.15-1,2,3
1.6b/t
3.4.9-1,2,3
3.4.16-1,2,3
3.5h/t
—
3.4.17-1,2,3
0.67h/t
—
3.4.18-1,2,3
0.29h/t
—
3.4.19-1,2,3
Plate supported on one edge under uniform
compression
(2)
Plate supported on two edges under uniform
compression
(3)
Plate suppoted on one edge under bending
with free edge in compression
(4)
Plate supported on two edges under bending
(5)
Plate supported on two edges under bending
with stiffener in compressive region
January 2005
III-15
studies available. Advanced analyses and/or tests are needed
to verify the improved performance in plates of nonuniform
thickness. The extrusion process should be able to produce
the geometries of the more efficient sections.
3.7 Compression in Tubes
and Curved Panels
Figure 3.6-1
PLATE BUCKLING EQUATIONS
The strength of unwelded cylinders, tubes and curved
panels supported on the edges is given by Equations 3.4.101,2,3. The bending strength of cylinders, and round and
oval tubes is provided by Equations 3.4.12-1,2 and Equations 3.4.10-2,3. For curved panels in bending members the
strength is given by Equations 3.4.16.1-1,2,3. These equations are provided by 6061-T6 members in Figure 3.7-1. All
of these provisions are based on the local buckling strength
of accurately fabricated tubes and curved panels: thus for
large R/t ratios the strength is the same for all parts.
The lower set of curves, two straight lines and a curved
line, applies to both tubes and curved panels under uniform compression. The upper set of curves, three straight
lines and one curved line, applies to the bending of tubes.
The higher strengths at low R/t ratios reflect the additional
strength due to the shape factor on bending for a tube (1.17
used). For larger R/t ratios the strength equations for axial
compression also apply to bending members. For curved
elements in bending members, the experience with building sheathing products shows that their strength is lower
than that for complete cylinders for low R/t ratios, and thus
the dashed line on Figure 3.7-1 is used for this case.
Figure 3.6-2
BUCKLING/POST BUCKLING BEHAVIOR
OF FLAT PLATE ELEMENTS
Figure 3.7-1
TUBES/CURVED PANELS UNDER
COMPRESSION AND BENDING
III-16
January 2005
For circumferentially welded cylinders with low R/t
ratios the same strength formulas apply. In this case the yield
strength across a butt weld is used and the buckling constants
are obtained from Table 3.3-3. Test data for cylinders with
circumferential welds and with R/t ratios less than about 20,
show that this procedure is accurate. There is some limited
data, however, that suggest that the compressive strength of
circumferentially welded cylinders with much higher R/t
ratios, can be much lower than that given by the specified
strength equations (1, p. 185). Apparently the circumferential welds can cause more severe geometric imperfections
in the thin-walled cylinder than those that were present in
the cylinders used in the original derivations of the strength
formulas. The strength of cylinders with longitudinal welds
only, seems to be consistent with that given by the specified
strength equations (1). More research is needed in this area
to establish accurate design rules. However, the designers of
tanks with large R/t ratios should consider the design implications of the limited data provided above.
3.8 Shear in Flat Webs
3.8.1 Buckling of Stiffened and Unstiffened Webs
There are two sets of strength equations available for
shear in webs, one for unstiffened webs given by Equations
3.4.20-1,2,3; the other for stiffened webs given by Equations
3.4.21-1,2,3. These provisions are based on the buckling
strength of shear panels with supported edges partially fixed
against rotation. The same equations are utilized for welded
construction. The maximum strength is limited to shear yield
or ultimate strength of the welded material.
3.8.2 Tension Field Webs
The static strength of thin, stiffened webs is much higher
than the buckling strength provided by the above equations
because of the “tension field action” that develops in the
web at loads above the buckling value. There is some information available on the behavior of tension field girders
(1). A much more efficient structure can result from a static
strength design using tension field behavior. Figure 3.8-1
shows the strength available above the buckling value for
one case. There are a number of considerations that need
to be addressed when designing girders for ultimate rather
than shear buckling as summarized below (1, p. 151).
1. The ultimate strength of the web is a function of the
material properties and the strength and stiffness of the
beam flanges and intermediate stiffeners.
2. Additional forces are imposed on flanges and intermediate stiffeners by the tension field stresses that must be
taken into account in the design of these members.
3. Intermediate stiffeners must be sufficiently thick so they
are not distorted in torsion by the buckles in the web,
and fail because of this imposed distortion.
4. If appearance is important, the amount of stress allowed
above the shear buckling stress must be limited.
January 2005
Figure 3.8-1
STRENGTH OF SHEAR PANELS (1)
5. The buckles in the web will cause local bending stresses
at the boundaries of the panel that will be detrimental
for fatigue. The current fatigue design guidelines do not
include a case in which buckling is allowed. Fatigue
tests will be needed to verify performance.
3.8.3 Corrugated Webs
Corrugated webs and shear diaphragms are efficient in
carrying shear loads. Corrugated panels can be the web of
a girder or the side and roof of a building. The strength and
stiffness of a corrugated panel under shear are dependent
on the alloy, configuration of the corrugation, size of the
panel, and the type and configuration of the fastening to
the framing members. Some of the design considerations
based on information presented elsewhere (1, p. 165) are
listed below.
1. Overall shear buckling of the panel may control strength.
An equivalent slenderness ratio is defined for this mode
of failure that is used with the buckling equations for
shear.
2. Local buckling of the shear elements of the corrugations
is given by the same equations as those for unstiffened
webs covered previously in this section.
3. Failure of the corrugations and of the fastening at the
supports need to be calculated. Local failure of the corrugations at their attachment to supporting members,
can occur particularly if only part of the shape is connected.
4. The shear deflection of the panel is much larger than a
flat panel of the same size. The major factors are size
III-17
of panel, shape and thickness or corrugation, and the
type and arrangement of the attachments. Equations of
behavior are provided for several standard shapes.
Additional information on building diaphragms and their
interaction with the building frames is given in Reference 6.
3.9 Shear in Tubes and Curved Panels
Shear buckling of tubes is calculated by the use of an
equivalent slenderness ratio (Equation 4.2-1), which is
based on buckling of the walls between circumferential
stiffeners from torsional loads. This equation can be very
conservative for long tubes with both longitudinal and
circumferential stiffeners. Figure 3.9-1 shows the change
in the coefficient in Equation 4.2-1 with length of tube.
A coefficient of 2.9 is specified for all cases (solid line in
Figure 3.9-1). A more accurate and less conservative value
for long tubes is less than 2.9 as illustrated by the dashed
line in Figure 3.9-1. The ordinate in this figure is a rearrangement of Equation 4.2-1. The addition of longitudinal stiffeners as well as circumferential stiffeners usually
increases the shear strength of a tube compared to a tube
with circumferential stiffeners only. The behavior of all of
the above cases has been published (1, p. 191).
3.10 Combined Stresses/Loading
There are five cases of combined loading that are available to the designer. All make use of an interaction equation. Information on each is provided below.
Combined Axial Compression and Compression due
to Bending—Beam-column interaction equations are given
by Equations 4.1.1-1,2. The equations provide for the estimated strength of a member that is loaded both axially as a
column and in bending as a beam. They apply to all of the
failure modes for beams and columns.
Combined Axial Tension and Tension due to Bending—
This interaction formula is given by Equation 4.1.2-1, and
limits the combined tensile stresses in members.
Combined Shear, Compression and Compression
due to Bending—For walls of curved surfaces or round
tubular shapes the interaction equation is Equation 4.4-1,
and for rectangular shapes and plates of built-up girders
the equation is Equation 4.4-2. Both of these equations are
based on local buckling of the elements.
Combined Local and Overall Buckling—If local
buckling of the elements occurs at an elastic stress below
that for overall buckling of a column or beam, the strength
of the member is less than that calculated for the member
assuming no local buckling. The strength of the member
with buckled elements is given by Equation 4.7.4-1 (columns) and Equation 4.7.5-1 for beams. The strength is limited by the weighted average crippling strength (maximum
strength) of the section. If buckling of the elements occurs
in the inelastic range, the strength of the column or beam
is limited to the local buckling stress. Figure 3.10-1 illustrates the use of these interaction curves. The solid curves
are the strengths assuming no buckled elements, the dashed
lines are for members with buckled elements.
Combined Web Crippling and Bending of Members—
Equation 4.7.8-1 gives interaction between the concentrated load causing web crippling and the moment causing
failure of the compression flange (weighted average). The
empirical relationship is based on available test data.
3.11 Stiffeners for Flat Plates
Figure 3.9-1
SHEAR BUCKLING OF TUBES WITH
CIRCUMFERENTIAL STIFFENERS
III-18
Longitudinal stiffeners for elements under compression
and stiffeners for girder webs are discussed here. Normally
stiffeners improve the efficiency of the design resulting in
a lower weight. The fabrication cost of adding stiffeners
can be low (or essentially zero). Formed in stiffeners are
effective on sheet products (7) and stiffeners can be added
to extruded shapes easily.
Plates with One Edge Supported and the Other Edge
with Stiffener—The strength of the stiffened plate is given
by Equations 3.4.9.1-1,2 for components of columns and
by Equations 3.4.16.2-1,2 for compressive components
of beams in the Specification. Two sets of equations are
used because of differences in factors of safety applied to
columns and beams; the strengths (factor of safety of 1.0)
are the same. The provisions cover all sizes of stiffener,
from those too small to effect the strength of the plate to
those sufficient to fully support the edge of the plate. The
stiffener itself also must be checked, to ensure that it has
sufficient buckling strength.
These provisions apply to a stiffener of the same thickness as the flange and are conservative for other types of
stiffeners. Stiffening bulbs and other complex shapes may
January 2005
the spring constant needed in Equation 4.10-1. More discussion on the behavior of this type of member is available
(1, p. 146).
Longitudinal Stiffeners for Beam Webs—The required
moment of inertia for a longitudinal stiffener on a beam
web, to support the web at that location against compressive buckling is given by Equation 4.5-1. The distance of
the stiffener from the toe of the compression flange is 0.4
times the distance from the toe of the compression flange
to the neutral axis. With a sufficient stiffener the compressive buckling strength of the web is given by Equations
3.4.19-1,2,3.
Transverse Stiffeners for Shear Webs—The moment
of inertia needed for intermediate stiffeners on girder webs
is given by Equations 4.6-1,2. The requirement is based on
the minimum requirements of a stiffener to subdivide the
web into panels, and to develop the shear buckling strength
of the panel. This moment of inertia is multiplied by the
ratio of the applied shear load to the shear load causing
buckling to allow for some adjustment of size of stiffener
depending on the actual load applied. Equation 4.6-3 provides for additional moment of inertia for cases in which an
additional concentrated load is carried by the stiffener.
3.12 Pipe Bursting Pressure
Figure 3.10-1
COMBINED LOCAL AND OVERALL
BUCKLING - 6061-T6
provide higher strengths than those provided for in the
Specification. A method for estimating buckling strength
for these other shapes is given elsewhere (1, p. 135).
Plates with Both Edges Supported and With an
Intermediate Stiffener—The equivalent slenderness ratio
to be used in column buckling equations is given by Equation 3.4.9.2-6 for column elements and Equation 3.4.16.3-6
for compressive elements of beams. The two equations are
the same.
These provisions apply to a plate with one intermediate
stiffener, which probably is the most efficient arrangement.
Provisions elsewhere (1, p. 138) give the general formula
for buckling of panels with one or more stiffeners.
Unsupported Compression Flanges—Equation 4.10-1
is a slenderness ratio to be used in column buckling equations. These provisions apply to sections whose compression flanges are not supported against lateral movement,
but the tension flange is supported laterally and provides
some resistance to lateral movement of the compression
flange. A hat section with the two flanges in compression is
an example of the type of member covered. The resistance
to rotation at the tension flange may be continuous or intermittent. Calculations or tests may be required to evaluate
January 2005
The bursting pressure of aluminum pipe may be estimated
from the equation (1, p. 178):
2tF K
tu
P = _____
D – 0.8t
Where:
P = bursting pressure
t = pipe wall thickness
Ftu = tensile ultimate strength
K = 0.73 + 0.33Fty /Ftu
D = pipe outside diameter
Fty = tensile yield strength
Specific applications of aluminum pipe may be governed by standards for that use. For example, aluminum
pipe used in chemical plants and petroleum refineries is
often designed in accordance with ASME B31.3, which
provides a slightly different equation and factors of safety
appropriate to such applications.
3.13 Biaxial and Triaxial Stresses
The Aluminum Specification predates finite element
analysis (FEA) and doesn’t directly address issues that
arise from such analyses. For example, the Specification
provides design stresses for prismatic members primarily under uniaxial stress, such as columns. FEA, on the
other hand, can provide triaxial stresses by reporting, in
addition to longitudinal stresses, through-thickness and
transverse stresses. Many FEA programs calculate a von
Mises stress (explained below) from the triaxial stresses
at a given element.
III-19
Yielding occurs in ductile materials like aluminum when
( f1 - f2)2 + (f2 - f3)2 + (f3 - f1)2 > 2 Fty2
where
f1, f2, f3 = principal stresses (the normal stress on
each of three orthogonal surfaces such that the
shear stresses on the surfaces are zero)
Fty = tensile yield stress
This equation is called the von Mises criterion or distortion energy criterion. It predicts that yielding will occur
when the distortion energy equals the distortion energy in
an axially loaded member at yield. The above equation is for
the general triaxial stress state. If stresses are biaxial, f3 = 0,
and the equation above predicts yielding when
(f1 - f2)2 + f 22 + f 12 > 2 F 2ty
For convenience, the von Mises stress is defined from
the von Mises criterion as
____________________
√
(f1 - f2)2 + (f2 - f3)2 + (f3 - f1)2
___________________
2
so that it may be compared directly to the yield stress to
determine if yielding will occur. In the biaxial stress state,
the von Mises stress becomes
__________
√f 12 - f1 f2 + f 22
shear yield strength. In the case of pure shear, the shear
stresses in a biaxial stress element are τ and – τ. Mohr’s
circle can be used to show that the principal stresses f1 and f2
are, then, also τ and – τ, so the von Mises stress is
___________
__
√τ2 - τ(-τ) + τ2 = τ√3
When the von Mises stress equals Fty, yielding occurs, so
shear yield τy is
Fty
__
τy = ___
√3
Local yielding in a member may not limit its usefulness
if the amount of material that yields is small or positioned
so as to have only a negligible effect on the shape and loadcarrying capacity of the member. Where yielding does represent a limit state, the von Mises stress should be limited
to the yield strength of the material divided by the safety
factor on yield. This limit is:
________________________
F
( f - f ) + ( f - f ) + ( f - f ) ___
≤ n
√________________________
2
1
2
2
2
3
2
3
1
2
ty
y
where
f1, f2, f3 = principal stresses (the normal stress on
each of three orthogonal surfaces such that the
shear stresses on the surfaces are zero)
Fty = tensile yield strength
ny = safety factor on yield
The von Mises criterion is used in the Aluminum Specification to determine the shear yield strength of aluminum
alloys, since there is no established test method to measure
III-20
January 2005
4.0 Fatigue
Design of components for fatigue is covered by Equations 4.8.1-1 and 4.8.1-2 for constant amplitude loadings
and by Equations 4.8.2-1 and 4.8.2-3 for spectrum loadings. Various standard details are provided and stress/
number of cycle (S-N) curves are given for all the details.
The S-N curves are based on the curve providing 97.7%
probability of survival with 95% confidence level. The procedure for design is to use the fatigue strength of the standard detail that most closely approximates the new detail
being designed.
When designing for fatigue there are defined or assumed
cyclic loads and a number of cycles. Joints or geometrical
discontinuities, such as holes, are usually areas in which
fatigue cracks originate. The designer must establish
the geometry and joining method such that the resulting
stresses are within those given by Equations 4.8.1-1 and
4.8.2-1.
The aluminum component generally must be different
from the steel component for the same load spectrum. Figure 4.0-1 shows fatigue strengths for aluminum and steel
for groove welds (a Category C detail). For long lives the
fatigue strength of aluminum groove welds is about 40%
that for steel. There is a smaller difference at short lives.
The design of the aluminum component must be consistent
with the fatigue strength curves for aluminum.
There are a number of factors that should be considered
when designing for fatigue.
1. The light weight of the aluminum structure may result
in reduced design loads. Examples are automotive
frames and some ship structures in which the loading
is proportional to the mass of the structure. In cases in
which the imposed loads are large compared to the mass
of the structure, the design loads are about the same for
all materials.
Figure 4.0-1
FATIGUE DESIGN CURVES
FOR ALUMINUM AND STEEL
January 2005
2. There are some general guidelines (as compared to steel
design) that will provide for more efficient aluminum
structures. Aluminum members in bending should be
deeper than those of steel. The spacing of stiffeners on
plates should be smaller for aluminum components compared to that for steel components. These geometrical
differences will help meet any deflection requirements
for the aluminum component and will lower the stresses
in the parts, helping with any fatigue requirements.
3. Joints may be eliminated by the use of extrusions and
castings, thus removing sites for fatigue crack initiation.
In some cases the designer can locate joints or discontinuities in areas of low stress, thus improving fatigue
resistance.
4. The type of joint affects fatigue strength significantly,
whether welded, mechanically fastened or adhesively
bonded. The designer should select the joint that best
meets the need.
5. There are enhancements to joints that can improve fatigue
strength. These include shaping the weld toes and peening the edges of the welds. Adhesives can be employed
in mechanically fastened (and spot welded) joints. All
of these enhancements increase fatigue strength. Tests
will be needed to establish fatigue strength.
Much more information is available on designing for
fatigue (1,3,8). In many cases the cause of fatigue behavior has to be minimized or eliminated. Wind induced vibration of members can be prevented by proper design or by
the addition of damping. Vibration of structures caused by
unbalanced forces from machinery, can be minimized by the
use of properly designed vibration mounts and proper design
of the structure (natural frequency less than ½ or more than
2 times the exciting frequency). Design for fatigue would not
be possible without the control of the forces in these cases.
Fatigue resistant joints should always be employed.
Gradual changes in geometry of components and joints and
avoiding areas of concentrated load and stress are two of
many good design practices. Because most fatigue failures
initiate at areas of localized high stress, particularly joints,
these details need to be designed carefully. Environment,
temperature, air quality and corrosive substances can influence fatigue strength in some cases.
The use of S-N curves is the most common but only
one of perhaps four methods of designing for fatigue. The
others are hot spot (30), strain-life, fracture mechanics and
good practice design methods. All of the techniques have
merit and can be applied to most types of structures (8).
Components under constant amplitude loading generally have a fatigue endurance limit, a stress below which
failure should not occur. Components of variable amplitude loading may not exhibit an endurance limit, because
a crack can be initiated by the higher stress cycles of the
spectrum and propagate at stresses below the constant
III-21
amplitude endurance limit. Miner’s rule is generally used
for spectrum loading with the straight-line portion of the
fatigue curves (assuming no endurance limit) (8). There
also may not be an endurance limit in mechanical connections that fail by fretting. Tests may be required to evaluate
the possibility of fretting failures.
III-22
The stress amplitudes in a spectrum usually are difficult
to determine unless a cycle-counting procedure is employed.
Of the several procedures that are available (8), the rainflow
counting method is commonly used.
January 2005
5.0 Joints and Joining
Mechanical, welded and adhesive joints are discussed
in this section. Joining affects most of the design considerations for structures.
5.1 Mechanical Joints
Bolts, rivets, screws, staples and clinches are employed
in aluminum structures. Aluminum, stainless steel (300
series), and galvanized steel fasteners are the acceptable
materials. For aluminum fasteners the tensile and shear
strengths can be determined by multiplying the tensile and
shear strengths by the net area of the fastener. The strengths
of fasteners of other materials should be obtained from
their manufacturer.
Figure 5.1-1 shows a riveted or bolted joint. The joint
is normally designed as a bearing joint. Several modes of
failure need to be considered.
1. Shear failure of the fasteners. The fasteners will be
equally loaded at failure.
2. Bearing failure. Edge distance is a factor with loads
directed toward the edge or directed parallel to the edge
(see Section 3.3).
3. Tension failure of the net section. The horizontal line is
the width to use in calculating net area.
4. Tearout of bolt group (9). The cross hatched area in Figure 5.1-1 can tear out. The strength can be estimated
by adding the shear portion (shear area on each side of
the cross hatched area times the shear strength of the
material) plus the tension portion (tension area at the
top of the cross hatched area times the tensile strength
of the material).
Aluminum parts connected with high strength steel bolts
have been tested for their resistance to slip under shear
forces. Tests of mill finish aluminum surfaces degreased
and dried have generally achieved relatively low coefficients of friction. The Research Council on Structural Connections (RCSC) Specification for Structural Joints Using
ASTM A325 or A490 Bolts provides a test method to determine the coefficient of friction for various surfaces. Tests
conducted by this method of aluminum surfaces abrasion
blasted with coal slag to SSPC SP-5 to an average substrate
profile of 2.0 mils in contact with similar aluminum surfaces or zinc painted steel surfaces gave results for Class B
surfaces, which have a design slip coefficient of 0.50. The
British Standards (10) allow a coefficient of friction of 0.33,
if the total thickness of parts exceeds the bolt diameter and
the faying surfaces are blasted with aluminum oxide grit
to achieve the necessary roughness. Temperature changes
cause a reduction or increase in the friction capacity due to
the different coefficients of thermal expansion of steel and
aluminum and should be considered in design. Bolts must
be tightened in accordance with the RCSC Specification to
achieve the required preload.
January 2005
Bolts may also be designed to resist shear by bearing on
the sides of the holes rather than by friction between the
faying surfaces. No definite rules for determining the magnitude of the tightening torque for such connections have
been established because test results vary widely depending on the friction developed in the threads and other bearing surfaces. One recommendation that is sometimes made
for establishing a tightening torque for aluminum bolts is
as follows: Tighten several bolts of any given size and type
to the breaking point under the same conditions of lubrication as will be encountered on the job and then use 70% or
80% of the lowest torque obtained from the tests. The 70%
value should be used for “temporary” bolts, or those that
may need to be removed occasionally, while the 80% value
applies to “permanent” bolts. The use of a lubricant on the
threads and bearing surfaces is useful.
These recommendations for tightening may be modified
for bolts or other threaded parts that carry fluctuating axial
tensile loads that can cause fatigue failures. Under these
conditions, the tightness (initial axial tensile load) should
be slightly more (about 5%) than the maximum tensile load
on the bolts during service.
Figure 5.1-1
FAILURE MODES OF
BOLTED/RIVETED JOINT
III-23
Aluminum bolts, particularly those with lubricated threads
and bearing surfaces, may loosen under cyclic loading or
vibration. There are many devices available to prevent loosening, and guidance available for their use in practical structures (11). Devices commonly used are various types of lock
washers, less commonly used are locking inserts built into
the nut threads.
5.2 Welded Joints
5.2.1 Welding Fabrication
The general recommendations and regulations for welding are provided in the American Welding Society D1.2
Structural Welding Code Aluminum. Acceptable weld profiles, standard welding symbols, inspection, and joint procedure qualification requirements are also provided in this
code. Inspection methods are described in this code but are
not required unless specified in contract documents.
5.2.2 Design of Welded Joints (12,13,14)
5.2.2.1 General
Continuous structural integrity between components in
a fabricated structure is the key to good design for welding. Strength loss and any interference with the continuous
distribution of stresses across a joint should be minimized.
When welding, accessible joints between components
of identical alloys are preferred. Mixed alloy joints can
be made between compatible alloys. In these joints, the
mechanical properties of the lower strength material must
be utilized for design.
5.2.2.2 Groove Welds
Groove welds (Figure 5.2-1) are utilized for butt joints.
The butt joint is easily designed. The strength of a sound
groove weld meets or exceeds the weld qualification strength
of the alloy, for a given temper and filler alloy. There is
rarely a problem of joint inaccessibility for welding. Groove
welds are shaped for ease of root penetration, to allow for
less dilution of the filler by the base metal (where hot cracking is a problem), or to permit a desirable sequence of weld
bead strength depositions when welding in other than flat
positions. Fatigue strength can be significantly increased by
removing the weld bead reinforcement.
5.2.2.3 Fillet Welds
Fillet welds (Figure 5.2-2) are used to join surfaces to
each other in lap, T, or corner joints; the welds determine
the strength of these joints. A sounder and more economical structure results from using continuous welds as opposed
to intermittent ones. While an intermittent weld may reduce
time, filler wire, heat input or distortion, it may exhibit unfavorable local stress concentrations at its ends. The possibility
for poor metal quality and end craters in the weld increases
with the repeated stopping and restarting of the welding
III-24
Figure 5.2-1
equipment. Since the cost of fillet welds is mainly a function
of the square of their size, large intermittent welds are not
as efficient in carrying loads as small continuous fillets. In
addition, some design standards specify that the ends of each
weld are to be considered non load carrying, which means
that intermittent welds must be longer than theoretically necessary. Intermittent welds also make a structure more susceptible to moisture infiltration which may ultimately lead
to corrosion.
Fillet welds exhibit different strengths depending on the
geometry of the part and the type of loading on the weld.
The fillet weld strengths as provided in Tables 7.2-2,3 are
based on tests of longitudinal fillet welds (see Figure 5.22a). Transverse welds (Figure 5.2-2b is one type) can have
higher strengths in some cases. Table 5.2-1 presents some
strengths relative to that for longitudinal welds (1). The
stress condition in the fillet weld affects the strength, with
the lowest strengths for the one sided fillet welds. Tests may
be required to determine fillet weld strength in components
that are different from those previously evaluated.
5.2.2.4 Unequal Thickness Transition
A butt joint between different thicknesses of metal
should have the thicker one beveled to match the thinner
one (Figure 5.2-3). This tends to balance the heat sink for
uniform melting and good fusion, and reduces the stress
raiser caused by change in thickness.
January 2005
a. Longitudinal Fillet
b. Transverse Fillet
c. Corner Weld
Figure 5.2-2
Table 5.2-1
FILLET WELD STRENGTHS
Case
(1)
Filler Metal
Ratio:
4043
5356
5556
1.3
1.5
1.5
5356
5556
0.8
0.7–1.0
Strenth of Fillet Weld
Str. of Longit. Fillet Weld
Symmetrical fillets on plate
(2)
One sided fillets on tube
5.2.2.5 Welded Joint at Point of Flexure
When a thin gauge of metal is welded to a thicker piece
(Figure 5.2-4), the weld seam should be away from the
point of flexure for improved stress resistance.
5.2.2.6 Welds in Low Stress Areas
Welds may have lower strength than the base metal (e.g.,
welds in 6061-T6 alloy). One way to reduce the inherent
loss of load carrying capacity is by locating the welds in
areas of low stress. Beams loaded in bending can be fabricated by welding together longitudinal extrusions with
Figure 5.2-3
January 2005
joints located in webs near the neutral axis (Figure 5.2-5).
Since the web’s metal thickness is often much thinner than
the flanges, quantity and cost of welding is reduced.
5.2.2.7 Doubler Plates
The commonly used rectangular doubler plate welded
on four sides offers transverse welds which reduce the
main member strength. If only the sides of this doubler
are welded, the longitudinal welds may become so highly
stressed that they progressively fail. When a doubler plate
is necessary, it should be diamond shaped (Figure 5.2-6),
avoiding sudden cross-sectional change.
No welding should be done across the ends. The doublers should be as wide as possible, consistent with leaving
Figure 5.2-4
III-25
Figure 5.2-7
5.2.2.10 Combined Lap and Butt Joints
Figure 5.2-5
room for a fillet weld on each side. The doubler length (l)
should be much greater than its width (w) (ratio of at least
3 to 1), which orients the fillet welds nearly parallel to the
stress direction.
5.2.2.8 Stiffeners
When stiffening a panel or member, care must be taken
to avoid sudden cross-sectional changes. If a member must
be reinforced, the reinforcing plate must provide for a
gradual change in cross-section (Figure 5.2-7), otherwise
fatigue cracks at the ends of the plate may result.
5.2.2.9 Corner Constructions
A common design problem is joining members at corners to give an economical, structurally sound connection
that has good appearance. Figure 5.2-8 illustrates various
corner designs with comments on their relative suitability.
Double fillets, or bends to allow a butt or a lap joint should
be used.
Figure 5.2-6
III-26
When sheet metal panels are to be welded to extruded
members, an attempt is sometimes made to use a joint
opening between panels and set the welding procedure to
make a groove weld and also provide adequate attachment
to the extrusion (Figure 5.2-9). In effect, what is desired
resembles a slot weld which seldom proves practical. The
joint fit and the welding procedure are both critical if the
sheet edges are hot enough to melt back from the joint
when the welding current is high enough to penetrate the
extrusion. Therefore, conventional lap joints are typically
specified for this application.
5.3 Adhesive Bonded Joints
An adhesive can be defined as a substance capable of
holding materials, similar and dissimilar, together by surface attachment. The critical substrate surfaces can be held
together by chemical and/or mechanical adhesion at the
interfacial layer of contact between surfaces (15).
5.3.1 Advantages and Disadvantages
Some of the advantages of adhesive bonding are (16,17)
• Ability to bond a variety of materials which may exhibit
differing coefficients of thermal expansion, moduli, thickness, etc., with proper joint design and material selection.
• Improved cosmetics of the finished product by the elimination of protruding mechanical fasteners, such as rivets
or bolts.
• Excellent strength to weight ratio in comparison to other
joining methods.
• Good joint stiffness and fatigue performance, with appropriate choice of adhesive.
• Elimination of stress concentrations inherent to mechanical fastening methods, and a more uniform stress distribution over the bonded surface area.
• Adaptable to many production processes because of
the variety of forms (pastes, films, emulsions, etc.) and
methods of application of adhesives.
January 2005
Figure 5.2-8
The advantages of adhesive bonding are most evident
when joining relatively thin materials and components.
The cost advantages and joint efficiencies decrease as the
members become thick.
Some of the disadvantages of adhesive bonding are
(16,17)
Figure 5.2-9
January 2005
• Expert joint design is critical in order to minimize peel
and/or cleavage stresses.
• Temperature limitations may restrict the use of many
adhesives from high temperature applications.
• Adhesives will require surface pretreatment of the aluminum
unless the adhesive manufacturer recommends no pretreatment necessary. Even with this recommendation, the durability required for the application should be verified.
• Difficulties in inspecting for initial bond integrity and
an insufficient understanding of the effects of in-service
damage on subsequent bond performance limit confidence in adhesive bonding as a primary structural joining method.
III-27
5.3.2 Adhesive Selection
Of the several classes of adhesives, there are literally
thousands of commercial adhesives available from each
class, in order to select the proper adhesive for a particular application the adhesive end-user needs a systematic
approach to adhesive selection. Listed below is an outline
of major areas to address prior to undertaking an adhesive
bonding application:
• Substrates
• Pretreatment
• Application
• Production
• Service Environments
• Design
5.3.3 Types of Adhesives (18)
Adhesives are categorized into two generic groups:
thermoplastics and thermosets. Thermoplastics are materials
which can be repeatedly softened by heat and hardened by
cooling to ambient temperature. Thermosets are materials
that undergo chemical reactions initiated by heat, catalyst,
UV light, etc., which lead to relatively infusible state or
phase. Thermosets are generally more durable than thermoplastics.
From the two groups of adhesives extend several classes
of adhesives which include anaerobic, contact, cyanoacrylate, film, hot melt, one-part and two-part. Anaerobic adhesives are generally esters or acrylics in which, upon the
restriction/lack of air/oxygen, curing of the adhesive initiates. Anaerobic adhesives can also be cured by UV exposure. Contact adhesives are coated to both substrate surfaces and a solvent is allowed to evaporate before assembly of the substrates. Cyanocrylates are known as instant
cure adhesives. They are derivatives of unsaturated acrylates which cure at room temperature without the aid of
a catalyst. Films are uniform layers of adhesives which
are generally rolled onto coils. Films can be supported
(with reinforcing fibers), unsupported, heat-activated, or
pressure-sensitive. Hot melts are generally solvent-free
thermoplastics which are solids at room temperature but
soften and flow at heat activation temperature. Upon cooling the hot melt regains its structural strength. One-part
adhesives are usually 99–100% solid systems. This class
of adhesives includes epoxies, moisture activated silicones,
and polyimides which can be waterborne or organic solvent
based. Two-part epoxies and acrylics are generally cured at
room temperature or accelerated with heat.
chemically incompatible with the proposed pretreatment.
Over the years many aluminum surface pretreatments have
been examined to determine which are the better adhesive
substrates for bonding. It is commonly accepted that chemically pretreating the surface yields a more durable bond
strength than that of mechanically abrading the aluminum
surface. Some of the most popular chemical pretreatment
systems to improve the adhesion of “as-received” aluminum are degreasing, acid etching, and phosphoric acid
anodizing.
5.3.5 Joint Design
The decision to use adhesive bonding to a joining method
must consider joint geometry, the nature and magnitude of
loading, the properties of the adhesive and the members to be
joined, failure modes, and ease and reliability of manufacturing. Adapting a joint design intended for other joining methods often results in ineffective designs. The design must also
consider the assembly scheme including needs for surface
pretreatment, part tolerances, and fixturing.
The stresses present in adhesive-bonded joints are classified based on loading conditions: normal, shear, peel,
and cleavage (Figure 5.3-1). Cleavage and peel conditions
describe a combination of normal and shear stresses specific to these two loading conditions. Cleavage stresses
are concentrated on one side of the joint, while peel loads
can occur with flexible members (18). Though technically
different, tensile stresses normal to the bond line are also
referred to as peel stresses in the literature. Because adhesives perform best when subjected to compressive and
shear loads, joint design should distribute the loads in the
adhesive layer as a combination of compressive and shear
stresses to avoid tensile, cleavage and peel loadings.
There are four basic types of joints: angle, tee, butt, and
surface or lap joints (Figure 5.3-2). In service, these joints
may be subjected to the types of stresses mentioned in the
previous paragraph. Most practical adhesive joint designs
5.3.4 Aluminum Surface Pretreatments
In adhesive bonding of aluminum substrates, a surface
pretreatment prior to bonding is usually necessary in order
to achieve long-term bond strength, although in some cases
an adhesive manufacturer may state that their adhesive
requires no surface pretreatment or that their adhesive is
III-28
Figure 5.3-1
TYPES OF STRESSES: A) SHEAR,
B) TENSION, C) PEEL, D) CLEAVAGE
January 2005
Figure 5.3-2
TYPES OF JOINTS: A) ANGLE,
B) TEE, C) BUTT, D) SURFACE
can be classified as variations of lap joints. Lap joint configurations are usually preferred because they require little
or no machining. For low loads, using overly complex configurations when simpler geometries are adequate results
in unnecessarily expensive designs. On the other hand,
simple configurations are unacceptable if smooth uninterrupted surfaces are required, if high stresses are present in
the bond or if high load levels must be sustained in the
structure.
In single lap joints which are not supported or restrained
against joint rotation, bending within the joint and at the
ends of the overlap causes locally high transverse tensile
stresses in the bond. In joints which are designed to prevent
or minimize joint rotation, the bond strength can exceed
the full nominal strength of the members.
Although adhesive bonding has benefits in joining dissimilar materials, the application imposes additional design
considerations. Using materials with different moduli may
result in reduced joint efficiencies. If the materials do not
have similar thermal expansion coefficients, temperature
changes during elevated temperature cures and due to
inservice thermal cycles can increase stresses in adhesive
bonds and lower joint strengths (19). If member materials
are not identical, the design should equalize the in-plane
and bending stiffnesses and the materials should have similar thermal expansion coefficients.
The identification of possible failure modes is crucial
to effective joint design and satisfactory performance. For
joints consisting of ductile isotropic materials such as aluminum alloys, four common failure modes are: (1) tensile
or buckling failure of the member outside the joint area,
January 2005
(2) shear failure of the adhesive, (3) tensile cracking in the
adhesive layer due to tensile or cleavage forces in the joint,
and (4) adhesion failure at the adhesive/member interface.
Failures outside of the joint area are the most desirable,
with 100% joint efficiency developed.
Adhesion failures are least desirable because such interfacial failures typically result in low, inconsistent joint
strengths. If the adhesive fails to adhere to the aluminum,
this indicates incompatibility of the surface oxide of the
aluminum with that particular adhesive. If the aluminum
is pretreated, and failure occurs at that interface between
the pretreatment and the adhesive, this indicates adhesive/
pretreatment incompatibility.
The adhesive properties for joint designs may be obtained
from mechanical tests. Tensile properties can be obtained
using cast adhesive specimens as described in ASTM D638
(20). Adhesive shear properties can be generated using thick
adherend tests (21) or a torsion test described in ASTM
E229 (22). Properties should be obtained for temperatures
throughout the range expected in service. Temperature can
affect adhesive properties, ductility and toughness, which
will affect joint design and performance, including stiffness
and failure loads and modes. The adequacy of the design
should be checked for the range of service temperatures.
Recent summaries of technology and data are provided in
Reference 23.
For critical applications in complex structures, a complete analysis of the stress components is recommended
along with the identification of the potential failure modes.
Nonlinear behavior of the adhesive and members should be
accounted for in the most effective method of conducting
such analysis. Mechanical tests to simulate typical service
conditions of adhesive-bonded joints should be performed
to verify the predicted failure location and modes.
5.3.6 Current Adhesive Applications
Adhesives are gaining popularity as a viable structural
means of joining aluminum. Today, aluminum adhesive bonding is being used in the transportation, construction products,
automotive, marine, aerospace and electronic industries.
Examples in each category are:
• Transportation: buses, trains and trailers
• Construction products: bridges and architectural panels
• Automotive: seats, hoods and air bags
• Marine: boats, ships and desalination plants
• Aerospace: space vehicles, aircraft and helicopter
• Electronics: antennas, computer boards and cable wires
III-29
6.0 Sandwich Panels and Beams
A typical aluminum sandwich panel consists of thin aluminum facings, a plastic core and an adhesive layer that
attaches the facings to the core (see Figure 6.0-1). Many
other options are available, such as additional aluminum
layers through the thickness, and other core materials;
honeycomb, fiber reinforced composites and high density
plastics. The product can have advantages in that the different materials act together, resulting in superior properties
such as bending stiffness, bending strength, insulation, fire
resistance, fatigue, etc. as compared to the properties of the
monolithic construction. There are no well defined design
procedures, nor design specifications in the United States
for this product. Thus, commercial products have generally been developed by the manufacturer for specific types
of panel and for specific applications. Some of the design
considerations are as follows.
1. Adhesive bonding is used to attach the skins to the core.
Adhesive selection surface preparation and fabrication
practice are important to achieve the proper attachment of
skin to core and performance of the panel. There is no good
way to nondestructively test the integrity of the bond.
2. Panels often have a requirement that they will not support combustion, are fire resistant and do not have undesirable fumes.
3. Facings may need to have resistance to denting.
4. The panels will need to be designed for general column
and beam strength. In addition the compressive wrinkling strength of the face may be important.
5. The thermal gradient across the thickness of the panel
may cause bowing of the panel or creep buckling of the
panel.
6. The strength and stiffness of the core is important for
deflection of the panel and for the strength of the panel
and facing.
The most recent work in the area has been done in Europe.
Both good practice and design are considered (24,25).
In a similar product, an aluminum-elastomer sandwich
beam, the components comprising the structural elements
also act together creating a combined strength and other
characteristics which are greater than the sum of the parts.
The composite beam may have to resist stresses due to a
temperature gradient through the section as well as stresses
from wind and dead loads. The amount of composite action
can be determined by analysis (26) or tests.
Figure 6.0-1
SANDWICH PANEL
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January 2005
7.0 Extrusion Design
Extrusions may be customized to achieve unique shapes
up a circle size of about 30 in. Their cost is competitive
with other product forms, and varies with type of extrusion,
alloy and size of part. The information in this section is
extracted from an existing publication (27).
7.1 Replacement of Fabrications with Extrusions
As shown at right, several rolled and riveted
structural shapes (left) can be combined into a
single aluminum extrusion, thus eliminating all
joining costs.
Machined and stamped sections can be
replaced by aluminum sections extruded to
exact size and shape.
As another example, the machining cost and
weight of a framing member is reduced by
redesigning the member as an extruded
section.
Aluminum extrusions may also replace wood
sections. They can be made lighter, stiffer, and
stronger, thus eliminating steel reinforcement.
January 2005
III-31
Welded assemblies are frequently redesigned into extruded sections. Not only is
cost reduced, but accuracy and strength are
increased.
Because extrusions permit infinite changes in
cross sectional design, they can be produced
more readily to meet specific design requirements than rolled sheet sections.
Crimped tubular sections frequently permit
redesign in extruded shapes, with gains in both
stiffness and strength. Cost of manufacture is
also reduced.
Small castings, forgings, and parts machined
from bar stock may also permit redesign as an
extrusion, as long as the cross section is symmetrical in at least one plane.
III-32
January 2005
7.2 Design Parameters
Five major factors should be considered in the detailed
development of an aluminum extrusion design:
• Shape configuration.
• Tolerances.
• Surface finish.
• Alloy.
• Circumscribing circle size.
A Class 2 hollow shape is defined by three other
requirements:
a) It is not a Class 1 hollow (its internal void may not be
round or, if round, may not be large enough to qualify
for Class 1).
b) It has a single void no smaller than 0.375 in. in diameter, or 0.110 in2 in area.
c) The entire shape fits within a circle no larger than 5 in.
in diameter (a 5 in. “circumscribing circle”).
These parameters are interrelated in their effect on the
extrusion design and its application.
Shape Configuration
The designer’s first priority is to satisfy a specific need,
and aluminum extrusion allows you to design the shape
that best meets your structural and esthetics requirements.
Since extrusion dies cost little, designers can afford to use
several different shapes, if that’s the best way to achieve
their objectives.
Users of computer-aided design programs will find aluminum extrusions a uniquely satisfying product because
the cross-section can be profiled to meet optimum structural requirements.
Extrusions can be designed to aid in assembly, improve
product appearance, reduce or eliminate forming and welding operations, and achieve many other purposes.
Extruded shapes are described in three general
categories—solid, semihollow, and hollow. Dies to produce solid shapes are the least complex. But the difference
between a solid shape and a semihollow shape may not be
obvious at first glance. It’s easier to describe and understand all three categories by working in reverse, starting
with hollow shapes.
A hollow shape…
…is simply an extruded shape which, anywhere in its
cross section, completely encloses a void. The void itself
may have any sort of shape, and the complete profile may
include a variety of other forms; but if any part of it encloses
a void, it’s classified as a “hollow.”
Extruders further divide hollow shapes into three classes:
A Class 1 hollow shape is defined by three requirements:
a) Its internal void is round.
b) This round void is one inch or more in diameter.
c) The weight of the shape is balanced, that is, equally distributed on opposite sides of two or more equally spaced axes.
An example of a Class 1 Hollow Extruded Shape
January 2005
An example of a Class 2 Hollow Extruded Shape
A Class 3 hollow shape is any hollow extruded shape
that is not a Class 1 or Class 2; it may, for example, have
more than one enclosed void.
An example of a Class 3 Hollow Extruded Shape
Tube and Pipe are specific forms of hollow shapes.
“Tube” is a hollow section that is long in comparison
to its cross-sectional size. It is symmetrical and has uniform wall thickness except as affected by corners. It may
be round or elliptical, or square, rectangular, hexagonal, or
octagonal. “Extruded tube,” as the name indicates, is tube
produced by hot extrusion; “drawn tube” is produced by
drawing through a die.
“Pipe” is a tube with certain standardized combinations
of outside diameter and wall thickness. These are commonly
designated by “Nominal Pipe Sizes” and by “ANSI (American National Standards Institute) Schedule Numbers.”
A semihollow shape…
…is one that partially encloses a void—for example, a
circle or rectangle with a gap in one side; but a solid shape
can also partially enclose a void, and the difference may
not be obvious. It is defined mathematically, by comparing the area of the partially enclosed void to the size of the
gap (actually, to the mathematical square of the gap size).
If that ratio is larger than a certain number, the shape is
classified as semihollow; if the ratio is smaller, the shape is
considered a solid.
These typical semihollow shapes illustrate the selection
of void areas and gap widths to be used in calculating the
III-33
ratio. In each example, use either the innermost void and
gap, or the complete void and gap—whichever combination yields the largest calculated ratio.
The ratios that distinguish semihollow from solid shapes
are listed in a standard table. But before you can use it, you
must make one more determination about the shape: is it a
“Class 1” or a “Class 2” shape?
Void Area (sq. in.) / [Gap (in.)]2 = Ratio
Class 1 and Class 2 semihollow shapes are differentiated by whether or not they are symmetrical.
A Class 1 semihollow is symmetrical about the centerline of the gap (or gaps, if there is more than one partially
enclosed void): the shape on one side of each gap centerline is an exact mirror-image of the other side.
A Class 2 semihollow is not symmetrical about the centerline of the gap or gaps. The shape on one side is different
from the other side, either in form or wall thickness.
For example, these two shapes are both
Class 1 semihollows
These two shapes are examples of
Class 2 semihollows
Now, here’s the Classification Table that determines
whether a shape that partially encloses a void is a semihollow or a solid shape:
An example: Suppose that one of the examples shown
above has a square void measuring 1.5 in. on each side, and
a gap 0.80 in. wide. Also, suppose it is a Class 2 shape (not
symmetrical), and is to be extruded from one of the alloys
in Group A
The void area is: 1.5 × 1.5 = 2.25
The gap squared is: .80 × .80 = 0.64
The ratio, then, is: 2.25 / .64 = 3.51
Typical semihollow extruded shapes. Use void area D and
gap width B or void areas C & D and gap width A, whichever results in a larger ratio.
III-34
The Classification Table shows that a Class 2 shape with
Group A alloys and a gap-width between 0.500 and 0.999
in. must have a ratio greater than 3.5 to be classified as a
semihollow.
In this example, the ratio is 3.51. This is larger than 3.5,
so the shape is a semihollow.
Of significance here is that the dies required to make
semihollow shapes are moderately more expensive than
solid shape dies, and the output of those dies tends to
approach tolerance limits, rather than tolerance nominals. Tooling life and productivity are both improved with
decreasing ratios, thus reducing cost.
January 2005
CLASSIFICATION—SEMIHOLLOW EXTRUDED SHAPES
Class 1
Gap Width
Inches
Class 2
Group A
Alloys1
Group B
Alloys2
Group A
Alloys1
Group B
Alloys2
0.040–0.062
2.0
1.5
2.0
1.0
0.063–0.124
0.125–0.249
3.0
2.0
2.5
1.5
3.5
2.5
3.0
2.0
0.250–0.499
4.0
3.0
3.5
2.5
0.500–0.999
4.0
3.5
3.5
2.5
1.000–1.999
3.5
3.0
3.0
2.0
2.000 and over
3.0
2.5
3.0
2.0
Ratio
Group A alloys are 1060, 1100, 1350, 3003, 5454, 6061, 6063
Group B alloys are 2011, 2014, 2024, 5083, 5086, 5456, 7050, 7075
1
2
A solid extruded shape…
…is any shape that is not a hollow or a semihollow.
This covers a wide range including, for example, compact cross-sections with or without projections; angular or
curved shapes; and those wrap-around shapes whose void
area/gap2 ratios are too low for the semihollow-class.
cost savings in secondary operations; such savings may
range from modest to very large, depending on circumstances. The designer should consider his requirements
carefully and order special tolerances only where they are
really needed.
If extruded parts are to interlock in any manner, the
designer should work with the supplier to make sure that
tolerances will provide a proper fit.
Surface Finish
Example of a solid shape
Extruded rod is a solid shape with a round cross-section
at least 0.375 in. in diameter.
Extruded bar is a solid shape whose cross-section is
square, rectangular, hexagonal or octagonal, and whose
width between parallel faces is a least 0.375 in.
If the dimension across any of these rod- or bar-type
shapes is less than 0.375 in., it is classified as wire.
Tolerances
In many applications in which the extrusion will be part
of an assembly of components, tolerances are critical. A
designer should be aware of the standard dimensional tolerances to which extrusions are commercially produced. These
tolerances generally cover such characteristics as straightness, flatness, and twist, and such cross-sectional dimensions
as thickness, angles, contours and corner or fillet radii.
Aluminum extrusions are often designed to minimize or
eliminate the need for machining. If desired, extrusions can
be produced to closer-than-standard tolerances, generating
January 2005
One advantage of aluminum extrusions is the variety of
ways the surface can be finished, and this offers another
range of choices to the designer.
As-extruded, or “mill,” finish can range from “structural,” on which minor surface imperfections are acceptable, to “architectural,” presenting uniformly good appearance. It should be understood that under normal circumstances aluminum will be marred because it is a soft metal
and that special care is required if a blemish free surface is
desired, i.e., this would not be a normal surface to expect.
Other finishes include scratch finishing, satin finishing
and buffing. Aluminum can also be finished by clear or
colored anodization, or by painting, enamelling or other
coatings.
If a product will have surfaces that are exposed in use,
where normal processing marks may be objectionable, the
extruders should be told which surfaces are critical. They
can design a die that orients the shape to protect those surfaces during the extrusion process; they can also select
packaging that will protect the product during shipment.
Alloy Selection
Aluminum extrusions are made in a wide variety of alloys
and tempers to meet a broad spectrum of needs. Selection
is made to meet the specific requirements in strength, weldability, forming characteristics, finish, corrosion resistance,
machinability, and sometimes other properties.
III-35
The complete list of registered aluminum alloys is quite
long, but in practice a few alloys are chosen repeatedly for
extrusion because of their versatility and highly suitable
characteristics. Extruders generally stock the three or four
most frequently used alloys. When their specialized markets justify it, individual companies include in their inventories additional alloys which will vary with the needs of
their major customers. Thus, a substantial variety of extrusion alloys is regularly available.
The 6000-series of aluminum alloys (those whose four
digit registration numbers begin with a 6) is selected for
nearly 75 percent of extrusion applications. Of those, alloys
6063 and 6061 are used most frequently.
Alloy 6063 is used for a broad range of solid and hollow
products. It is easily welded, and it has a pleasing natural
finish and excellent corrosion resistance. 6063 is used in
architecture and in many moderate-stress applications.
III-36
Alloy 6061 is a good all-purpose extrusion alloy, combining high mechanical properties with good corrosion resistance, weldability and machining characteristics. Alloy 6061
is used in many structural applications.
Many other alloys are used for extrusions, to meet particular requirements. For example, to mention only a few:
Characteristics
High strength
High corrosion
resistance
High electrical
conductivity
Alloys
7050, 7075, 2014
1100, 3003
6101
For further details, the designer should consult current
alloys and temper tables and discuss specific needs with the
extrusion supplier.
January 2005
Circumscribing Circle Size
One measurement of the size of an extrusion is the
diameter of the smallest circle that will entirely enclose
its cross-section—its “circumscribing circle.” This dimension is one factor in the economics of an extrusion. In gen-
January 2005
eral, extrusions are most economical when they fit within
a medium-sized circumscribing circle that is, one with a
diameter between one and ten inches.
The example shown here would be classified as a 3-to-4 in.
circle size shape.
III-37
7.3 Design Guidelines
Good Extrusion Design Practices
At this stage in the development of an extruded product,
the designer has determined its functional shape and size,
and considered appropriate tolerances, surface finishes and
alloys.
Before proceeding, it makes sense to review the extruder’s available standard shapes. It may be possible to adapt
a standard shape to the needs of the product, with little or
no modification.
If a standard shape is not readily adaptable, the design
can be completed as a custom shape perfectly suited to the
requirements of the product.
Here are a few tips on good practices in custom-designing
aluminum extrusions:
of the tongue can ease metal flow and so help to keep the
extruded dimensions more uniform. Even corners rounded
to only ⅙₄ in. radius can make extrusion easier.
Visualize the shape of the die that must produce your
design, and try to minimize shapes that would weaken the
die or impede metal flow.
Use “Metal Dimensions” for Best Tolerance
Dimensions measured across solid metal are easier to produce to closer tolerances than those measured across a gap
or angle. So rely on “metal dimension” as much as possible
when designing close-fitted mating parts or other shapes
requiring closer tolerances. Standard industry dimensional
tolerances are entirely adequate for many applications, but
special tolerances can be specified if necessary.
Specify the Most Appropriate Metal Thicknesses
Specify metal thicknesses that are just heavy enough
to meet your structural requirements. Even in low stress
areas, however, keep sufficient thickness to avoid risking
distortion or damage. Some shapes tend to invite distortion
during the extrusion process (such as a asymmetric profile
or thin details at the end of a long flange). Such tendencies
exert more influence on thin-walled shapes than on those
with normal metal thickness.
Keep Metal Thickness as Uniform as Possible
Extrusion allows you to put extra metal where it is
needed—in high-stress areas, for example—and still save
material by using normal dimensions elsewhere in the
same piece. Adjacent wall thickness ratios of less than
2-to-1 are extruded without difficulty. But large contrasts
between thick and thin areas may create uneven conditions
during extrusion. It is best to maintain near uniform metal
thickness throughout a shape if possible. When a design
combines thick and thin dimensions, streamline the transitions with a radius (a curve, rather than a sharp angle) at
junctions where the thickness changes sharply. Rounded
corners ease the flow of metal.
“An Open Space Dimension” is more
difficult to hold to close tolerances.
Visualize the Die and the Metal Flow
Remember what extrusion die does; while it lets metal
flow through its shaped aperture, it must hold back metal all
around that aperture against great force. When you design
a shape for extrusion, you are simultaneously designing a
die aperture and you must take extrusion forces and metal
flow into account.
For example, a U-shaped channel in an extrusion corresponds to a solid “tongue” in the die, attached at only one
end. Flexibility in this tongue can alter the aperture slightly
under the pressure of extrusion; the deeper you make the
channel, the longer you make the tongue and the more
difficult it becomes to regulate the extruded dimensions.
On the other hand, rounding corners at the base and tip
III-38
A “Metal Dimension” can be
extruded to close tolerances.
January 2005
Smooth All Transitions
Transitions should be
streamlined by a generous
radius at any thick-thin
junction.
Instead
of This
Consider
This
Keep Wall Thickness
Uniform
The preceding shape
can be further improved by
maintaining uniform wall
thickness.
In addition to using more
metal, thick-thin junctions
give rise to distortion, die
breakage or surface defects
on the extrusion.
Ribs Help Straightening
Operation
Wide, thin sections
can be hard to straighten
after extrusion. Ribs help
to reduce twisting, and to
improve flatness.
Symmetry Preferred in
Semi-Hollow Areas
When designing visualize
the die and tongue that will
be necessary to produce
a semi-hollow shape. By
keeping the void symmetrical you lessen the chances
that the die tongue may
break.
January 2005
III-39
7.4 Design For Assembly
Aluminum extrusions can be designed for joining by a
wide variety of methods such as riveting, bolting, welding,
brazing, soldering and adhesive bonding.
They can also be designed to fit, hook or snap together
mating with melting parts. Hinges or slides can often by
“designed-in” as integral parts of extrusions, eliminating
the need for additional assembly and moving parts.
Eight types of extruded joints are discussed in this section:
• Nesting Joints
• Interlocking Joints
• Snap-Fit Joints
• Three-Piece, Blind-Fastened Joints
• Combination Joints
• Slip-Fit Joints: Dovetails and Hinges
• Key-Locked Joints
• Screw Slots
Nesting Joints
Nesting joints, which include “lap joints” and “tongueand-groove” joints, have mating elements that are shaped
to be assembled with little or no self-locking action.
They serve primarily to align adjoining parts, and they
usually depend on rivets, bolts, adhesives, confinement
within a rigid frame, or other fasteners, to hold them
together.
Lap joints, shown here, are the simplest nesting joints.
Interlocking Joints
The interlocking joint is, in effect, a modified tongueand-groove. But instead of being straight, the two mating
elements are curved and so cannot be assembled or (more
to the point) disassembled by simple straight-line motion.
They are assembled by a rotating motion and will not separate without a corresponding counter-rotation. As long as
the parts are held in their assembled position, they strongly
resist separation and misalignment in both the horizontal
and the vertical directions.
The amount of rotation required for interlocking assembly depends on the geometry of the design. It can be made
more or less than 45 degrees, as long as the design allows
enough clearance for the required rotation.
Interlocking joints can be secured after assembly in at
least five ways, all based on preventing counter-rotation.
• Fastening the elements to structural cross-members.
• Restraining the assembly within a rigid frame.
• Restraining the assembly with channel end-closures.
• Fastening the joint with rivets, welds, adhesives or other
devices.
• Providing a folding, locking flange as shown below.
III-40
January 2005
Snap-Fit Joints
Screw Slots
A “snap-fit” or “snap-lock” joint is one which is selflocking and requires no additional fasteners to hold the
joint together.
The mating parts of a snap-fit joint exert a cam action
on each other, flexing until one part slips past a raised lip
on the other part. Once past this lip, the flexed parts snap
back to their normal shape and the lip prevents them from
separating. After it is snapped together, this joint cannot be
disassembled unintentionally.
The strength of this joint can be increased by applying adhesive to the mating surfaces before assembly. Even
short lengths of an adhesively bonded snap-fit joint cannot
be easily slid apart.
Precise dimensions are critical in a snap-fit joint. The
dimensions of a snap-fit joint should only be referenced
on drawings. Experienced extrusion designers who are
fully conversant with snap-fit production requirements can
determine the precise final dimensions.
Screw slots are often used to facilitate the assembly of
aluminum extrusions. Standard screw slots are illustrated
here and should always be used with self tapping screws.
The screw slot should be designed so that the area of the
void and the metal thickness surrounding it is symmetrical
about the center line of the gap.
The type F self tapping screw is recommended for use
with the extruded screw slot. This screw has threads which
approximate machine screw threads . . . plus a blunt point
that will stay within the screw slot.
“Sheet metal” type screws are not recommended since
their thread projects to the very point and thereby can
“walk” through the slot opening.
Self Tapping Screw Type F
NF
Screw OD
(in.)
A DIA. (in.)
4–401
4–481
0.120
0.099 ± 0.006
1
6–32
6–401
0.138
0.120 ± 0.006
8–32
8–36
0.164
0.147 ± 0.007
NC
10–24
10–32
0.190
0.169 ± 0.007
12–24
12–28
0.216
0.190 ± 0.007
¼ × 20
¼ × 28
0.250
0.228 ± 0.007
Not recommended for incorporation on inside wall of hollow or
semihollow shapes.
2The recommended location for screw slots on the inside of hollow
or semihollow shapes is at the corners. When not located at corners dimension “B” must be at least 0.250 in.
1
January 2005
III-41
8.0 Prevention of Corrosion
A great deal of technology and experience exist for successful prevention of corrosion in assemblies and structures. Documentation of the technology and experience
is scattered throughout the open literature. The following
information has been adapted from Reference 28.
The seven types of measures listed below can be used
individually or in combinations to address aluminum corrosion prevention.
• Alloy and temper selection
• Design
• Coatings and sealants
• Inhibitors
• Cathodic protection
• Enhanced protective oxide films
• Modification of environment
The following paragraphs in this section will provide
guidelines for each of these types of measures. It is important to note that these guidelines are general in nature and
may not apply to all cases.
Alloy and temper selection are based on many factors.
From the standpoint of corrosion prevention, the selection
process should consider the following guidelines. Alloys
of the 1XXX, 3XXX, 5XXX, and 6XXX series generally
have very good corrosion resistance in natural environments and can be used without supplemental corrosion
protection. Temper selection for the 1XXX, 3XXX, and
6XXX series alloys may be based on other-than corrosion
factors. Temper selection for the 5XXX series alloys containing up to 3% magnesium (e.g. 5005, 5050, 5052, and
5454) may be based on other-than corrosion factors. However, temper selection for the 5XXX series alloys containing more than 3% magnesium (e.g. 5456, 5083, and 5086)
for applications with service temperatures exceeding 150oF
or in marine environments should be limited to –H116 or
–H321 as a precaution against intergranular forms of corrosion. Alloys of the 2XXX and 7XXX series alloys have
poor corrosion resistance and require supplemental corrosion protection. Temper selection for the 2XXX and 7XXX
series alloys can be a significant factor in the exfoliation
and stress corrosion resistances.
During the design phase of a project utilizing aluminum,
a number of factors that may impact on corrosion resistance can be conveniently considered. Often such considerations as part of this phase are much more cost effective
than they are after the design is finalized. While a number
of the following factors can, if adopted, prevent corrosion,
it is recognized that there are times that such situations are
unavoidable. Consequently, the subsequent paragraphs will
discuss remedial actions.
• Avoid contacts with dissimilar metals (galvanic corrosion
prevention discussed below).
III-42
• Avoid crevices, especially at joints (crevice corrosion
prevention discussed below).
• Avoid skip welding by using continuous welding.
• Avoid standing fluid and poultice catchments.
• Avoid placement of absorbent materials, such as gaskets,
insulation, and soundproofing, against aluminum.
• Avoid direct impingement by fluid stream, especially
sharp pipe bends.
• Avoid heat transfer hot spots.
• Avoid corrosive conditions when locating and orienting
equipment and joints.
• Avoid sharp edges when coating will be used.
During the design phase of a project that involves aluminum, one of the key areas for corrosion prevention consideration is joints between parts. Joints may involve aluminum
and other metallic materials. Galvanic corrosion can occur
when aluminum is joined to other metals and the joint is covered by an aqueous, conductive fluid. Joints made in such a
way that they are dry or the dissimilar metals are not electrically connected, even by a remote path, will be free from
galvanic corrosion. Because galvanic couples are inevitable,
it is important to be able to predict which metal will corrode (anode) in a given couple. A common tool for making
this prediction is the galvanic series, which is environmentspecific (see Table 8.0-1 for example in sodium chloride
solution). In Table 8.0-1 the metal in a galvanic couple that is
toward the active end of the galvanic series will corrode, and
the other metal in the couple which is toward the noble end
of the series will not corrode. It is important to remember
that the galvanic series is useful only as a predictive tool as
to location of corrosion in a galvanic couple, not rate of corrosion. However, as a general suggestion, selection of couple
members that are close together in the galvanic series will
tend to minimize galvanic corrosion. Based on the galvanic
series and experience gained over many years, aluminum
can be coupled to magnesium, zinc, cadmium, and passive
stainless steel in most environments without the threat of
galvanic corrosion. In most other galvanic couples aluminum will experience galvanic corrosion.
In cases where dissimilar metals must be joined, creating an undesirable galvanic couple, there are several steps
that can be taken to minimize the galvanic corrosion. The
exposed area of the more noble or cathodic metal should
be minimized by design and by application of protective
coatings (e.g. paint, gasket, tape, etc.). At bolted or riveted galvanic joints (e.g. aluminum to steel) the fasteners (the smaller exposed surface area) should be the more
noble material, such as steel or 3XX series stainless steel
rather than aluminum. A further step with steel would be
to coat the fasteners with an organic coating or with zinc
(galvanizing).
In cases where galvanic couples have only a few points
of electrical contact, it may be possible to control corrosion
January 2005
by electrical insulation. Insulation can be effective only
when all points of electrical contact are broken. Insulation
can be achieved by inserting nonmetallic, non-wicking
bushings, gaskets, sleeves, tapes, etc., into all aluminum
to other metal joints. Such insulation is difficult to achieve
in large, complex structures where remote electrical paths
may exist.
Table 8.0-1
GALVANIC SERIES IN SODIUM
CHLORIDE SOLUTION
(similar to sea water)
Active
Noble
Magnesium
Zinc
Aluminum alloy 7072 (Alcladding)
5XXX aluminum alloys
7XXX structural aluminum alloys
1XXX, 3XXX, 6XXX aluminum alloys
Cadmium
2XXX aluminum alloys
Iron and steel
Lead
Tin
Brass
Copper
Stainless steel (3XX, passive)
Nickel
In fluid-carrying systems where piping of aluminum
and other metals must be joined, a thick-walled, replaceable aluminum nipple should be used at the joint. In closed
loop mixed metal fluid-carrying systems, such as automotive cooling systems, it may be possible to control galvanic
corrosion by using a mixed metal corrosion inhibitor package. Mixed metal fluid-carrying systems, which include
aluminum and cannot be treated with inhibitors, should not
contain copper-based materials.
Crevices are inevitable in the assembly of structures.
When crevices trap or retain fluids, accelerated corrosion
January 2005
may result. Often the location and orientation of crevices
(joints) can be considered during design in order to minimize moisture ingress and retention. The use of adhesives,
caulks, nonabsorbent gaskets, and sealants can prevent the
ingress of moisture into crevices. Continuous welds are
desirable because they leave no crevices, whereas skip or
intermittent welds are undesirable because they do leave
crevices. A type of crevice corrosion known as poultice
corrosion can occur under deposited materials, such as
mud, paper, or cloth. Poultice corrosion can often be minimized by avoiding catchments and pockets during design
of a structure.
When surface treatments, such as anodizing, organic
coating, or plating, are used on aluminum to provide consistent appearance or improved corrosion resistance, the
quality of the treatment is extremely important. If flaws or
points of damage occur which expose the substrate aluminum surface, accelerated localized pitting corrosion may
result. All steps of the treatment process must be controlled
in order to obtain the desired durability.
For aluminum structures that are buried or immersed in
aqueous environments, it may be feasible to control corrosion by application of the electrochemical process known
as cathodic (noncorroding) electrode in an electrochemical corrosion cell. Expert assistance should be utilized in
applying this corrosion control process.
In cases involving 2XXX and 7XXX series aluminum
alloys, consideration should be given to stress corrosion
cracking (SCC). SCC can be a problem when residual or
assembly stresses can occur in the through-the-thickness or
short transverse direction. This can be minimized by giving
consideration to temper selection, residual stresses from
fabrication (e.g. forming, machining, and thermal treatments), and fitup details.
Thus, when aluminum’s inherently good corrosion resistance is compromised by environmental conditions, galvanic
couples, crevices, etc., there are approaches available to prevent problems.
III-43
9.0 Fire Protection
There is limited information available on the behavior
of aluminum in fires. Some of the similarities and differences in the behavior of aluminum and steel members are
provided below.
1. Both aluminum and steel members are noncombustible.
2. The cross sectional areas of the aluminum members
usually will be about 40% larger than those of steel.
3. The thermal conductivity of aluminum is about 2.7
times that of steel.
4. Strength properties of aluminum degrade at much
lower temperature compared to those of steel.
All of the above items have an effect on the relative performance of the two materials in a fire. Generally the aluminum parts would be expected to reach a lower temperature but the strength properties relative to those at room
temperature would be more degraded compared to those
for steel. The aluminum members thus need more insulation compared to steel members.
Some guidance has been published on fire protection for
aluminum members (29). The criteria for establishing the
amounts of fire protection for aluminum were as follows.
1. To ensure strengths at least equal to the design allowable stresses during the test exposure, the limiting
temperature for aluminum would be 500oF.
2. To ensure that there will be no substantial change in
properties at room temperature as a result of the test
exposure, the limiting temperature would be 375oF.
Light weight vermiculate plaster was used in the tests
and specimens were as indicated on Figure 9.0-1. The relative thicknesses of protection required for various periods
of time are shown below (29).
RELATIVE THICKNESS OF VERMICULITE
REQUIRED FOR FIRE PROTECTION OF STRUCTURAL ALUMINUM MEMBERS
Fire Protection Period, hours
Ratio
Thickness for Aluminum Member
Thickness for Steel Member
1
1.7
2
1.9
3
1.8
4
1.7
Numbers designate materials as
follows:
(1) 8 WF 10.72 column
(2) Vermiculite plaster
(3) Lath
(4) Keystone key corner beads
Figure 9.0-1
SPECIMENS FOR FIRE PROTECTION TESTS
III-44
January 2005
10.0 References
The following references apply the information presented
in Sections 3.0 through 9.0 of this part of the manual.
1. Sharp, Maurice L., Behavior and Design of Aluminum
Structures, McGraw-Hill Inc., New York, New York,
1993.
2. The Aluminum Association Position on Fracture Toughness Requirements and Quality Control Testing 1987,
T-5, Aluminum Association, Washington, DC, 1987.
3. Menzemer, Craig C., Fatigue Behavior of Welded Aluminum Structures, Dissertation in partial fulfillment of
the requirements for the degree of Doctor of Philosophy, Lehigh University, Bethlehem, PA, July 1992.
4. Galambos, Theodore V., editor, Guide to Stability
Design Criteria for Metal Structures, 5th edition John
Wiley & Sons, 1998.
17. Thrall, Edward W. and Shannon, Raymond W., Adhesive Bonding of Aluminum Alloys, Marcel Dekkar,
New York, New York, 1984.
18. Kinloch, A.J., Adhesion and Adhesives, Science and
Technology, Chapman and Hall, New York, NY, 1987.
19. Hart-Smith, A.J., “Design of Adhesively Bonded Joints,”
Joining Fibre-Reinforced Plastics, F.L. Mathews, editor,
Elsevier Applied Science Publishing, New York, NY,
1987.
20. Annual Book of ASTM Standards, Vol. 08.01, “Plastics,” American Society for Testing and Materials,
Philadelphia, 1992.
21. Drieger, R.B., “Analyzing Joint Stresses Using an Extensometer,” Adhesive Age, pp 26-28, October, 1985.
5. Torsional Analysis of Steel Members, American Institute of Steel Construction, Chicago, IL, 1983.
22. Annual Book of ASTM Standards, Vol. 15.06, “Adhesives,” American Society for Testing and Materials,
Philadelphia, PA, 1992.
6. Davis, J.M. and Bryan, E.R., Manual of Stressed Skin
Diaphragm Design, Granada Publishing, Great Britain,
1982.
23. Minford, J. Dean, Handbook of Aluminum Bonding
Technology and Data, Marcel Dekker, Inc., New York,
1993.
7. Sooi, Took Kowng, “Behavior of Component Elements
of Aluminum Members,” Research Report No. 93-1,
Teoman Peköz, Project Director, Cornell University,
1993.
24. Preliminary European Recommendations Sandwich
Panels, Part I Design and Part II Good Practice, ECCS
Technical Committee 7-Working Group 7.4-Design
and Application of Sandwich Panels, 1991.
8. Sharp, Maurice L., Nordmark, Glenn E. and Menzemer,
Craig C., Fatigue Design of Aluminum Components and
Structures, McGraw-Hill, Inc., New York, New York,
1996.
25. Davis, J.M., “Sandwich Panels,” Thin-Walled Structures, 16 (1993), pp. 179-198.
26. Structural Performance, Poured and Debridged Framing Systems, AAMA, TIR-A8-90, Schaumberg, IL.
9. Marsh, Cedric, “Tear-out Failures of Bolt Groups,”
Technical Notes, Journal of the Structural Division,
Proceedings of the American Society of Civil Engineers, October, 1979.
27. The Aluminum Extrusion Manual, Aluminum Association, Washington, DC and the Aluminum Extruders
Council, 1998.
10. Structural use of Aluminum Part I. Code of Practice
for Design, British Standard BS 8118, 1991.
28. Aluminum—Properties and Physical Metallurgy, Edited
by John E. Hatch, American Society for Metals, 1984,
pp. 300-309.
11. Metal Curtain Wall Fasteners, AAMA TIR-A9-91
(with 2000 adendum), American Architectural Manufacturers Association, Schaumberg, IL.
12. Welding Aluminum, Theory and Practice, Aluminum
Association, Washington, DC, 2002.
13. Angermayer, Karl, Structural Aluminum Design, CPE
Corporation, Richmond, VA, 1987.
14. Structural Welding Code-Aluminum, AWS D1.2/D1.2M:
2003, American Welding Society, Miami, FL, 2003.
15. Adhesives, 4th Edition, D.A.T.A., Inc., 1986.
16. Shields, J., Adhesives Handbook, CRC Press, 1970.
January 2005
29. Kaufman, J.G. and Kasser, R.C., “Fire Protection for
Aluminum Alloy Structural Shapes,” Civil Engineering, March, 1963.
30. Sharp, M.L., Nordmark, G.E., and Menzemer, C.C.,
“Hot-Spot Fatigue Design of Aluminum Joints,” Proceedings of the 1996 ASCE Materials Engineering
Conference, Washington, DC.
31. Kissell, J.R. and Ferry, R.L., “Aluminum Friction Connections”, Proceedings of Structures Congress XV,
April, 1997.
32. Kissell, J.R. and Ferry, R.L., Aluminum Structures,
2nd edition, John Wiley, New York, 2002.
III-45
Aluminum Design Manual
PART IV
Materials
The Aluminum Association, Inc.
1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
Third Edition, January 2005
IV
Materials
TABLE OF CONTENTS
1.0
Features of Aluminum-General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.0
Features of Aluminum/Metallurgical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.0
Designation System for Wrought Aluminum and Aluminum Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1 Aluminum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Aluminum Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3 Experimental Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.4 National Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.0
Cast Aluminum and Aluminum Alloy Designation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.1 Aluminum Castings and Ingot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.2 Aluminum Alloy Castings and Ingot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.3 Experimental Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.0
Effect of Alloying Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
6.0 Temper Designation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
6.1 Basic Temper Designations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
6.2 Subdivision of Basic Tempers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
6.2.1 Subdivisions of H Temper: Strain-hardened . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
6.2.2 Subdivisions of T Temper: Thermally Treated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
6.3 Variations of O Temper: Annealed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Table 1 Comparative Characteristics and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Table 2 Historical Foreign Alloy Designations and Similar AA Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
January 2005
IV-3
1.0 Features of Aluminum-General
Light Weight – The specific gravity of aluminum is
about 2.7 and its mass (“weight”) is roughly 35% that of
iron and 30% that of copper.
A Range of Useful Strengths – The usefulness of
“commercially pure” aluminum as a structural material is
limited by its tensile strength of about 13 ksi. By working the metal, such as by cold rolling, its strength can be
approximately doubled. Much larger increases in strength
are obtained, however, by alloying aluminum with small
percentages of one or more other metals such as manganese,
silicon, copper, magnesium or zinc. Many alloys can also
be strengthened by heat treatments so that tensile strengths
approaching 100 ksi are possible.
Aluminum and its alloys lose part of their strength at
elevated temperatures, although some alloys retain good
strength at temperatures from 300 to 400oF (150 to 200oC). At
sub-freezing temperatures, however, their strength increases
without loss of ductility so that aluminum is a particularly
useful metal for low temperature applications.
Good Corrosion Resistance – When aluminum surfaces are exposed to the atmosphere, a thin, invisible oxide
skin forms immediately which protects the metal from
further oxidation. This self-protecting characteristic gives
aluminum its high resistance to corrosion. Unless exposed
to some substance or condition which destroys this protective oxide coating, the metal remains resistant to corrosion.
Aluminum is highly resistant to weathering, even in many
industrial atmospheres which often corrode other metals. It
is also resistant to many acids.
Direct contact with certain other metals should be
avoided in the presence of an electrolyte: otherwise, galvanic corrosion of the aluminum may take place in the
vicinity of the contact area. Where these other metals must
be fastened to aluminum, the use of a protective insulating
coating is recommended.
High Electrical Conductivity – Aluminum is one of
the two common metals having electrical conductivity high
enough for use as an electric conductor. The conductivity
of electric conductor grade (Alloy 1350) is about 62% of
the International Annealed Copper Standard. Because aluminum has less than one third the specific gravity of copper, a kilogram of aluminum will go about twice as far as a
kilogram of copper when used for this purpose.
High Thermal Conductivity – The high thermal conductivity of aluminum is important wherever the transfer
of thermal energy from one medium to another is involved,
either heating or cooling. Thus, aluminum heat exchangers
are widely used in automotive air conditioning systems and
aluminum radiators are also becoming the standard for this
application.
January 2005
Useful Reflector of Radiant Energy – Aluminum is
an excellent reflector of radiant energy through the entire
range of wave lengths from ultraviolet, through the visible
spectrum, to infrared and heat waves. It also reflects electromagnetic wave lengths in the radio and radar range. Aluminum has a light reflectivity of over 80% which has led to
its wide use in automotive trim and in lighting fixtures.
Nonmagnetic and Resistance to Sparking – These
properties are of great importance for some uses. Nonmagnetic properties of aluminum make it useful in electronics,
as well as delicate moving parts, where various components must be shielded from electromagnetic disturbances
that would upset their operation. The advantages of using
a material of low sparking sensitivity around flammable or
explosive substances are obvious.
Ease of Fabrication – The forming and fabrication
characteristics of aluminum are perhaps among its most
important assets. Often it can compete successfully with
less expensive materials having a lower degree of workability. Aluminum can be rolled to any desired thickness
down to foil thinner than paper: it can be stamped, drawn,
spun or roll-formed. Aluminum may also be hammered or
forged. Aluminum wire may be stranded into cable of any
desired size and type. There is almost no limit to the different shapes in which the metal may be extruded.
Good Machinability – The ease and speed with which
many aluminum alloys may be machined is one of the
important factors contributing to the low cost of finished
aluminum parts. The metal may be turned, milled, bored, or
machined at the maximum speeds of which most machines
are capable. An example of this is aluminum rod and bar
employed in the high speed manufacture of parts of automatic screw machines.
Joining Flexibility – Almost any joining method is
applicable to aluminum: riveting, welding, brazing or soldering. A wide variety of mechanical aluminum fasteners
simplifies the assembly of many products. Adhesive bonding of aluminum parts is widely employed in aircraft components and is being used increasingly for automotive body
panels.
Adaptability to Finishing – Aluminum needs no protective coating for many applications. Mechanical finishes
such as polishing, sandblasting or wire brushing will be
sufficient to meet many needs. In many instances, the surface finish supplied is entirely adequate without further finishing. Where the plain aluminum surface does not suffice,
or where decorating or additional protection is required, a
wide variety of surface finishes such as chemical, electrochemical and paint finishes may be applied.
Chemical conversion coatings are available for additional corrosion protection. They also provide an excellent
base for paint. Electroplating procedures have been develIV-5
oped to give aluminum an attractive, durable finish. Anodic
coatings are used for both decorative and functional applications. Hardcoat anodized aluminum surfaces can provide
wear resistance similar to case hardened steel. Vitreous
enamels have also been developed for aluminum.
Environmental Compatibility-Recycling – Aluminum
is very suitable for recycling. Recycled aluminum makes
up more than 30% of the aluminum used in the United
States, and its use saves nearly 95% of the energy needed
for production from bauxite. Life cycle costs should be
considered when designing with aluminum versus other
materials. In general, aluminum has the advantage of having a high recycling value.
2.0 Features of Aluminum/
Metallurgical Aspects
In high purity form aluminum is soft and ductile and has
relatively low strength. Most commercial uses, however,
require greater strength than pure aluminum affords. This is
achieved in aluminum first by the addition of other elements
to produce various alloys, which singly or in combination
impart strength to the metal. The numerical alloy designation system adopted by the aluminum industry is based
on the principal alloying elements in each class of alloy.
Further strengthening is possible by means that classify the
alloys roughly into two categories: non-heat-treatable and
heat-treatable.
Non-heat-treatable Alloys – The initial strength of alloys
in this group depends upon the hardening effect provided by
manganese, silicon, iron and magnesium, singly or in various combinations. The non-heat-treatable alloys are usually
designated as the 1xxx, 3xxx, 4xxx or 5xxx series. Since
these alloys are work-hardenable, strengthening is achieved
by various degrees of cold working, denoted by the “H”
series of tempers. Alloys containing appreciable amounts of
magnesium when supplied in strain-hardened tempers are
usually given a final elevated-temperature treatment called
stabilizing to insure stability of properties.
Heat-treatable Alloys – The initial strength of alloys in
this group is enhanced by the addition of alloying elements
such as copper, magnesium, zinc, silicon and lithium.
Since these elements singly or in various combinations
show increasing solid solubility in aluminum with increasing temperature, it is possible to subject them to thermal
treatments which will cause pronounced strengthening.
These alloys are usually designated as the 2xxx, 6xxx and
7xxx series.
The first step, called heat treatment or solution heat treatment, is an elevated-temperature process designed to put the
soluble element or elements in solid solution. This is followed
by rapid quenching, usually in water, which momentarily
“freezes” the structure and renders the alloy very workable
for a period of time. For a few cases some fabricators retain
IV-6
this more workable structure by storing the alloys at below
freezing temperatures until they are ready to form them. At
room temperature alloys age with time which changes their
mechanical properties. This change varies with alloy and is
not typically relied on in design.
By heating for a controlled time at slightly elevated temperatures, even further strengthening is possible and properties are stabilized. This is called artificial aging or precipitation hardening. By the proper combination of solution heat treatment, quenching, cold working and artificial
aging, the highest strengths are obtained.
Clad Alloys – The heat-treatable alloys in which copper or zinc are major alloying constituents are less resistant
to corrosive attack than the majority of non-heat-treatable
alloys. To increase the corrosion resistance of these alloys
in sheet and plate form they are often clad with high-purity
aluminum, a low magnesium-silicon alloy, or an alloy
containing 1% zinc. The cladding, usually from 2.5 to 5%
of the total thickness on each side, not only protects the
composite due to its own inherently excellent corrosion
resistance but also exerts a galvanic effect which further
protects the core material.
Special composites may be obtained, such as clad nonheat-treatable alloys, for extra corrosion protection, for brazing purposes, or for special surface finishes. Some alloys in
wire and tubular form are clad for similar reasons, and on an
experimental basis extrusions also have been clad.
Annealing Characteristics – All wrought aluminum
alloys are available in annealed form. In addition, it may be
desirable to anneal an alloy from any other initial temper,
after working, or between successive stages of working
such as in deep drawing.
3.0 Designation System for Wrought
Aluminum and Aluminum Alloys
The Aluminum Association is the registrar for the composition designation system under ANSI H35.1.
Aluminum, 99.00% and greater
Aluminum alloys grouped by
major alloying elements
Copper
Manganese
Silicon
Magnesium
Magnesium and Silicon
Zinc
Other element
Unused series
Designation No.
1xxx
2xxx
3xxx
4xxx
5xxx
6xxx
7xxx
8xxx
9xxx
A system of four-digit numerical designations is used to
identify wrought aluminum and wrought aluminum alloys.
The first digit indicates the alloy group. The last two digits identify the aluminum alloy or indicate the aluminum
January 2005
purity. The second digit indicates modifications of the original alloy or impurity limits.
3.1 Aluminum
In the 1xxx group for minimum aluminum purities of
99.00% and greater, the last two of the four digits in the
designation indicate the minimum aluminum percentage.
These digits are the same as the two digits to the right of
the decimal point in the minimum aluminum percentage
when it is expressed to the nearest 0.01%. The second digit
in the designation indicates modification in impurity limits. If the second digit in the designation is zero, it indicates unalloyed aluminum having natural impurity limits;
integers 1 through 9, which are assigned consecutively as
needed, indicate special control of one or more individual
impurities or alloying elements.
3.2 Aluminum Alloys
In the alloy groups 2xxx through 8xxx, the last two of the
four digits in the designation have no special significance
but serve only to identify the different alloys in the group.
The second digit in the alloy designation indicates alloy
modifications. If the second digit in the designation is zero,
it indicates the original alloy; integers 1 through 9, which are
assigned consecutively, indicate alloy modifications.
3.3 Experimental Alloys
Experimental alloys are also designated in accordance
with this system but they are indicated by the prefix X. The
prefix is dropped when the alloy is no longer experimental.
During development and before they are designated as
experimental, new alloys are identified by serial numbers
assigned by their originators. Use of the serial number is
discontinued when the X number is assigned.
3.4 National Variations
National variations of wrought aluminum and wrought
aluminum alloys registered by another country in accordance with this system are identified by a serial letter following the numerical designation. The serial letters are
assigned internationally in alphabetical sequence starting
with A but omitting I, O, and Q.
A national variation has composition limits which are
similar but not identical to those registered by another
country.
January 2005
4.0 Cast Aluminum and Aluminum Alloy
Designation System
Aluminum, 99.00% and greater
Aluminum alloys grouped by major
alloying elements
Copper
Silicon, with Copper
and/or Magnesium
Silicon
Magnesium
Zinc
Tin
Other element
Unused series
Designation No.
1xx.x
2xx.x
3xx.x
4xx.x
5xx.x
7xx.x
8xx.x
9xx.x
6xx.x
A system of four-digit numerical designations is used
to identify aluminum and aluminum alloys in the form of
castings and foundry ingot. The first digit indicates the
alloy group. The second two digits identify the aluminum
alloy or indicate the aluminum purity. The last digit, which
is separated from the others by a decimal point, indicates
the product form: i.e., casting or ingot. A modification of
the original alloy or impurity limits is indicated by a serial
letter before the numerical designation. The serial letters
are assigned in alphabetical sequence starting with A but
omitting I, O, Q, and X, the X being reserved for experimental alloys.
4.1 Aluminum Castings and Ingot
In the 1xx.x group for minimum aluminum purities of
99.00% and greater, the second two of the four digits in the
designation indicate the minimum aluminum percentage.
These digits are the same as the two digits to the right
of the decimal point in the minimum aluminum percentage
when it is expressed to the nearest 0.01%. The last digit,
which is to the right of the decimal point, indicates the
product form: 1xx.0 indicates castings, and 1xx.1 indicates
ingot.
4.2 Aluminum Alloy Castings and Ingot
In the 2xx.x through 9xx.x alloy groups the second two
of the four digits in the designation have no special significance but serve only to identify the different aluminum
alloys in the group. The last digit, which is to the right of
the decimal point, indicates the product form: xxx.0 indicates castings, xxx.1 indicates ingot.
IV-7
4.3 Experimental Alloys
Experimental alloys are also designated in accordance
with this system but they are indicated by the prefix X. The
prefix is dropped when the alloy is no longer experimental.
During development and before they are designated as
experimental, new alloys are identified by serial numbers
assigned by their originators. Use of the serial number is
discontinued when the X number is assigned.
5.0 Effect of Alloying Elements
1xxx series – Aluminum of 99% or higher purity has
many applications, especially in the electrical and chemical fields. These alloys are characterized by excellent corrosion resistance, high thermal and electrical conductivity, low
mechanical properties and excellent workability. Moderate
increases in strength may be obtained by strain-hardening.
Iron and silicon are the major impurities.
2xxx series – Copper is the principal alloying element
in this group. These alloys require solution heat-treatment
to obtain optimum properties. In the heat treated and naturally aged condition alloys have mechanical properties that
are similar to, and sometimes exceed, those of mild steel.
Artificial aging can be employed to further increase the
mechanical properties. This treatment materially increases
tensile yield strength, with attendant loss in elongation; its
effect on tensile (ultimate) strength is not as great. 2xxx
series alloys have been used extensively for aircraft components and for cryogenic tanks.
3xxx series – Manganese is the major alloying element of
alloys in this group, which are generally non-heat-treatable.
Because only a limited percentage of manganese, up to
about 1.5%, can be effectively added to aluminum, it is used
as a major element in only a few instances. One of these,
however, is the popular alloy 3003, which is widely used as
a general-purpose alloy for moderate strength applications
requiring good workability. Alloy 3004 which contains
magnesium as well as manganese for higher strength, is
used widely for beverage container bodies.
4xxx series – The major alloying element of this group
is silicon, which can be added in sufficient quantities to
cause substantial lowering of the melting point without producing brittleness in the resulting alloys. For these reasons
aluminum-silicon alloys are used in welding wire and as
brazing alloys where a lower melting point than that of the
parent metal is required. Most alloys in this series are nonheat-treatable. When used in welding heat-treatable alloys
they will pick up some of the alloying constituents of the
latter and respond to heat treatment to a limited extent.
5xxx series – Magnesium is one of the most effective
and widely used alloying elements for aluminum. When it
is used as the major alloying element or with manganese,
the result is a moderate to high strength non-heat-treatable
IV-8
alloy. Magnesium is considerable more effective than manganese as a hardener, about 0.8% magnesium being equal
to 1.25% manganese, and it can be added in considerably
higher quantities. Alloys in this series possess good welding
characteristics and good resistance to corrosion in marine
atmospheres. These alloys are used in cryogenic applications. Certain limitations, however, should be placed on the
amount of cold work and the safe operating temperature
permissible for the higher magnesium content alloys (over
about 3.0%) is about 150°F (66°C) to avoid susceptibility
to intergranular forms of corrosion.
6xxx series – Alloys in this group contain silicon and
magnesium in appropriate proportions to form magnesium
silicide, thus making them heat-treatable. A major alloy in
this series is 6061, one of the most versatile of the heat
treatable alloys. Though less strong than most of the 2000
or 7000 alloys, the magnesium-silicon (or magnesium
silicide) alloys possess good formability, weldability and
corrosion resistance, with medium strength. Alloys in this
heat-treatable group may be formed in the T4 temper (solution heat-treated but not artificially aged) and then reach full
T6 properties by artificial aging.
7xxx series – Zinc is the major alloying element and
when coupled with a smaller percentage of magnesium,
results in heat-treatable alloys of very high strength. Other
elements such as copper and chromium may also be added.
Alloys in this series include those used for automotive
bumpers and bumper reinforcements and aircraft applications. Alloys without copper are weldable and have been
used for armor plate.
6.0 Temper Designation System⑥
The temper designation system is used for all forms of
wrought and cast aluminum and aluminum alloys except
ingot. It is based on the sequences of basic treatments used
to produce the various tempers. The temper designation
follows the alloy designation, the two being separated by
a hyphen. Basic temper designations consist of letters. Subdivisions of the basic tempers, where required, are indicated
by one or more digits following the letter. These designate
specific sequences of basic treatments, but only operations
recognized as significantly influencing the characteristics
of the product are indicated. Should some other variation
of the same sequence of basic operations be applied to the
same alloy, resulting in different characteristics, then additional digits are added to the designation.
⑥ Temper designations conforming to this standard for wrought aluminum
and wrought aluminum alloys, and aluminum alloy castings may be registered
with the Aluminum Association provided: (1) the temper is used or is available
for use by more than one user, (2) mechanical property limits are registered,
(3) the characteristics of the temper are significantly different from those of all
other tempers that have the same sequence of basic treatments and for which
designations already have been assigned for the same alloy and product, and
(4) the following are also registered if characteristics other than mechanical
properties are considered significant: (a) test methods and limits for the characteristics or (b) the specific practices used to produce the temper.
January 2005
6.1 Basic Temper Designations
F
as fabricated. Applies to the products of shaping processes in which no special control over thermal conditions or strain hardening is employed. For wrought
products, there are no mechanical property limits.
O
annealed. Applies to wrought products that are
annealed to obtain the lowest strength temper, and to
cast products that are annealed to improve ductility
and dimensional stability. The O may be followed by
a digit other than zero.
H
strain-hardened (wrought products only). Applies
to products that have their strength increased by strainhardening, with or without supplementary thermal treatments to produce some reduction in strength. The H is
always followed by two or more digits.
W
solution heat-treated. An unstable temper applicable only to alloys that spontaneously age at room
temperature after solution heat-treatment. This designation is specific only when the period of natural
aging is indicated; for example: W ½ hr.
T
thermally treated to produce stable tempers other
than F, O, or H. Applies to products that are thermally treated, with or without supplementary strainhardening, to produce stable tempers. The T is always
followed by one or more digits.
6.2 Subdivisions of Basic Tempers
6.2.1 Subdivision of H Temper: Strain-hardened
6.2.1.1 The first digit following the H indicates the specific combination of basic operations, as follows:
H1
strain-hardened only. Applies to products that are
strain-hardened to obtain the desired strength without supplementary thermal treatment. The number
following this designation indicates the degree of
strain-hardening.
H2
strain-hardened and partially annealed. Applies
to products that are strain-hardened more than the
desired final amount and then reduced in strength
to the desired level by partial annealing. For alloys
that age-soften at room temperature, the H2 tempers
have the same minimum ultimate tensile strength
as the corresponding H3 tempers. For other alloys,
the H2 tempers have the same minimum ultimate
tensile strength as the corresponding H1 tempers
and slightly higher elongation. The number following this designation indicates the degree of strainhardening remaining after the product has been
partially annealed.
January 2005
H3
strain-hardened and stabilized. Applies to products
that are strain-hardened and whose mechanical properties are stabilized either by a low temperature thermal treatment or as a result of heat introduced during
fabrication. Stabilization usually improves ductility.
This designation is applicable only to those alloys
that, unless stabilized, gradually age-soften at room
temperature. The number following this designation
indicates the degree of strain-hardening remaining
after the stabilization treatment.
H4
strain-hardened and lacquered or painted. Applies
to products which are strain-hardened and which are
subjected to some thermal operation during the subsequent painting or lacquering operation. The number following this designation indicates the degree of
strain-hardening remaining after the product has been
thermally treated, as part of painting/lacquering cure
operation. The corresponding H2X or H3X mechanical property limits apply.
6.2.1.2 The digit following the designation H1, H2, H3,
and H4 indicates the degree of strain-hardening as identified by the minimum value of the ultimate tensile strength.
Numeral 8 has been assigned to the hardest tempers normally produced. The minimum tensile strength of tempers
HX8 may be determined from Table 1 and is based on the
minimum tensile strength of the alloy in the annealed temper. However, temper registrations prior to 1992 that do not
conform to the requirements of Table 1 shall not be revised
and registrations of intermediate or modified tempers for
such alloy/temper systems shall conform to the registration
requirements that existed prior to 1992.
Table 1
Minimum tensile strength
in annealed temper
ksi
up to 6
7 to 9
10 to 12
13 to 15
16 to 18
19 to 24
25 to 30
31 to 36
37 to 42
43 and over
Increase in tensile strength
to HX8 temper
ksi
8
9
10
11
12
13
14
15
16
17
Tempers between O (annealed) and HX8 are designated by
numerals 1 through 7.
—Numeral 4 designates tempers whose ultimate tensile
strength is approximately midway between that of the
O temper and that of the HX8 tempers;
IV-9
—Numeral 2 designates tempers whose ultimate tensile
strength is approximately midway between that of the
O temper and that of the HX4 tempers;
—Numeral 6 designates tempers whose ultimate tensile
strength is approximately midway between that of the
HX4 tempers and that of the HX8 tempers;
the effect of cold work in flattening or straightening is
recognized in mechanical property limits.
T3
solution heat-treated,⑨ cold worked, and naturally aged to a substantially stable condition.
Applies to products that are cold worked to improve
strength after solution heat-treatment, or in which the
effect of cold work in flattening or straightening is
recognized in mechanical property limits.
T4
solution heat-treated⑨ and naturally aged to a
substantially stable condition. Applies to products
that are not cold worked after solution heat-treatment,
or in which the effect of cold work in flattening or
straightening may not be recognized in mechanical
property limits.
T5
cooled from an elevated temperature shaping process and then artificially aged. Applies to products
that are not cold worked after cooling from an elevated
temperature shaping process, or in which the effect of
cold work in flattening or straightening may not be
recognized in mechanical property limits.
T6
solution heat-treated⑨ and then artificially aged.
Applies to products that are not cold worked after
solution heat-treatment, or in which the effect of cold
work in flattening or straightening may not be recognized in mechanical property limits.
T7
solution heat-treated⑨ and overaged/stabilized.
Applies to wrought products that are artificially aged
after solution heat-treatment to carry them beyond a
point of maximum strength to provide control of some
significant characteristic⑩. Applies to cast products
that are artificially aged after solution heat-treatment
to provide dimensional and strength stability.
T8
solution heat-treated,⑨ cold worked, and then
artificially aged. Applies to products that are cold
worked to improve strength, or in which the effect of
cold work in flattening or straightening is recognized
in mechanical property limits.
T9
solution heat-treated,⑨ artificially aged, and then
cold worked. Applies to products that are cold
worked to improve strength.
—Numerals 1, 3, 5 and 7 designate, similarly, tempers
intermediate between those defined above.
—Numeral 9 designates tempers whose minimum
ultimate tensile strength exceeds that of the HX8 tempers by 2 ksi or more.
The ultimate tensile strength of the odd numbered intermediate (-HX1, -HX3, -HX5, and HX7) tempers, determined
as described above, shall be rounded to the nearest multiple
of 0.5 ksi.
6.2.1.3 The third digit, when used, indicates a variation
of a two-digit temper. It is used when the degree of control
of temper or the mechanical properties or both differ from,
but are close to, that (or those) for the two-digit H temper designation to which it is added, or when some other
characteristic is significantly affected. (See Appendix for
assigned three-digit H tempers.) NOTE: The minimum ultimate tensile strength of a three-digit H temper must be at
least as close to that of the corresponding two-digit H temper as it is to the adjacent two-digit H tempers. Products in
the H temper whose mechanical properties are below H__1
shall be variations of H__1.
⑦
6.2.2 Subdivision of T Temper:
Thermally Treated
6.2.2.1 Numerals 1 through 10 following the T indicate
specific sequences of basic treatments, as follows:⑧
T1
T2
cooled from an elevated temperature shaping
process and naturally aged to a substantially stable condition. Applies to products that are not cold
worked after cooling from an elevated temperature
shaping process, or in which the effect of cold work
in flattening or straightening may not be recognized
in mechanical property limits.
cooled from an elevated temperature shaping process, cold worked, and naturally aged to a substantially stable condition. Applies to products that are
cold worked to improve strength after cooling from
an elevated temperature shaping process, or in which
⑦ Numerals 1 through 9 may be arbitrarily assigned as the third digit and
registered with the Aluminum Association for an alloy and product to indicate a variation of a two-digit H temper (see note ⑥).
⑧ A period of natural aging at room temperature may occur between or after
the operations listed for the T tempers. Control of this period is exercised
when it is metallurgically important.
IV-10
⑨ Solution heat treatment is achieved by heating cast or wrought products
to a suitable temperature, holding at that temperature long enough to allow
constituents to enter into solid solution and cooling rapidly enough to hold
the constituents in solution. Some 6xxx series alloys attain the same specified mechanical properties whether furnace solution heat treated or cooled
from an elevated temperature shaping process at a rate rapid enough to
hold constituents in solution. In such cases the temper designations T3,
T4, T6, T7, T8, and T9 are used to apply to either process and are appropriate designations.
⑩ For this purpose, characteristic is something other than mechanical
properties. The test method and limit used to evaluate material for this
characteristic are specified at the time of the temper registration.
January 2005
T10 cooled from an elevated temperature shaping
process, cold worked, and then artificially aged.
Applies to products that are cold worked to improve
strength, or in which the effect of cold work in flattening or straightening is recognized in mechanical
property limits.
6.2.2.2 Additional digits,⑪ the first of which shall not be
zero, may be added to designations T1 through T10 to
indicate a variation in treatment that significantly alters the
product characteristics that are or would be obtained using
the basic treatment. (See Appendix for specific additional
digits for T tempers.)
6.3 Variations of O Temper: Annealed
6.3.1 A digit following the O, when used, indicates a product in the annealed condition having special characteristics.
NOTE: As the O temper is not part of the strain-hardened
(H) series, variations of O temper shall not apply to products that are strain-hardened after annealing and in which
the effect of strain-hardening is recognized in the mechanical properties or other characteristics.
APPENDIX
A1 Three-Digit H Tempers
A1.1 The following three-digit H temper designations
have been assigned for wrought products in all alloys:
H_11 Applies to products that incur sufficient strain hardening after the
final anneal that they fail to qualify as annealed but not so much
or so consistent an amount of strain hardening that they qualify as
H_1.
H112 Applies to products that may acquire some temper from working at an elevated temperature and for which there are mechanical
property limits.
A1.2 The following three-digit H temper designations
have been assigned for
pattern or
embossed
sheet
fabricated from
H114
H124, H224, H324
H134, H234, H334
H144, H244, H344
H154, H254, H354
H164, H264, H364
H174, H274, H374
H184, H284, H384
H194, H294, H394
H195, H295, H395
O temper
H11, H21, H31 temper, respectively
H12, H22, H32 temper, respectively
H13, H23, H33 temper, respectively
H14, H24, H34 temper, respectively
H15, H25, H35 temper, respectively
H16, H26, H36 temper, respectively
H17, H27, H37 temper, respectively
H18, H28, H38 temper, respectively
H19, H29, H39 temper, respectively
A1.3 The following three-digit H temper designations
have been assigned only for wrought products in the 5xxx
series, for which the magnesium content is 3% nominal or
more:
H116 Applies to products manufactured from alloys in the 5xxx series,
for which the magnesium content is 3% nominal or more. Products are normally strain hardened at the last operation to specified
stable tensile property limits and meet specified levels of corrosion resistance in accelerated type corrosion tests. They are suitable for continuous service at temperature no greater than 150o F.
Corrosion tests include inter-granular and exfoliation
H321 Applies to products from alloys in the 5xxx series, for which the
magnesium content is 3% nominal or more. Products are normally
thermally stabilized at the last operation to specified stable tensile
property limits and meet specified levels of corrosion resistance in
accelerated type corrosion tests. They are suitable for continuous
service at temperatures no greater than 150o F. Corrosion tests
include inter-granular and exfoliation.
A2 Additional Digits for T Tempers
A2.1 The following specific additional digits have been
assigned for stress-relieved tempers of wrought products:
Stress relieved by stretching.
T_51 Applies to plate and rolled or cold-finished rod or bar, die or ring
forgings and rolled rings when stretched the indicated amounts
after solution heat treatment or after cooling from an elevated temperature shaping process. The products receive no further straightening after stretching.
Plate . . . . . . . . . . . . . . . . . . . . . . . . . .1½% to 3% permanent set.
Rolled or
Cold-Finished
Rod and Bar . . . . . . . . . . . . . . . . . . . . 1% to 3% permanent set.
Die or Ring
Forgings and
Rolled Rings . . . . . . . . . . . . . . . . . . . . 1% to 5% permanent set.
T_510 Applies to extruded rod, bar, profiles (shapes) and tube and to drawn
tube when stretched the indicated amounts after solution heat treatment or after cooling from an elevated temperature shaping process.
These products receive no further straightening after stretching.
Extruded Rod
Bar, Profiles (Shapes)
and Tube . . . . . . . . . . . . . . . . . . . . . . . 1% to 3% permanent set.
Drawn Tube . . . . . . . . . . . . . . . . . . . . .½% to 3% permanent set.
T_511 Applies to extruded rod, bar, profiles (shapes) and tube and to
drawn tube when stretched the indicated amounts after solution
heat treatment or after cooling from an elevated temperature shaping process. These products may receive minor straightening after
stretching to comply with standard tolerances.
Extruded Rod,
Bar, Profiles (Shapes)
and Tube . . . . . . . . . . . . . . . . . . . . . . . 1% to 3% permanent set.
Drawn Tube . . . . . . . . . . . . . . . . . . . . .½% to 3% permanent set.
Stress relieved by compressing.
⑪ Additional digits may be arbitrarily assigned and registered with The
Aluminum Association for an alloy and product to indicate a variation of
tempers T1 through T10 even though the temper representing the basic
treatment has not been registered (see note ⑥). Variations in treatment
that do not alter the characteristics of the product are considered alternate
treatments for which additional digits are not assigned.
January 2005
T_52 Applies to products that are stress-relieved by compressing after
solution heat treatment or cooling from an elevated temperature shaping process to produce a permanent set of 1 percent to
5 percent.
Stress relieved by combined stretching and compressing.
IV-11
T_54 Applies to die forgings that are stress relieved by restriking cold in
the finish die.
• “-T351 to -T42 Capability Demonstration for response
to re-solution heat-treatment”.
NOTE: The same digits (51, 510, 511, 52, 54) may be
added to the designation W to indicate unstable
solution heat-treated and stress-relieved tempers.
A2.4 Temper Designation for Purchaser/User
Heat-treatment
A2.2 Temper Designations for Producer/Supplier Laboratory Demonstration
of Response to Heat-treatment:
The following temper designations have been assigned for
wrought products test material, furnace heat-treated from
annealed (O, O1, etc.) or F temper, to demonstrate response
to heat-treatment.
T42
Solution heat-treated from annealed or F temper and naturally
aged to a substantially stable condition.
T62
Solution heat-treated from annealed or F temper and artificially aged.
T7_2 Solution heat-treated from annealed or F temper and artificially
overaged to meet the mechanical properties and corrosion resistance limits of the T7_ temper.
A2.3 Temper Designations for Producer/Supplier
Demonstration of Response to Temper
Conversion:
Temper designation T_2 shall be used to indicate wrought
product test material, which has undergone furnace heattreatment for capability demonstration of temper conversion. When the purchaser requires capability demonstrations from T-temper, the seller shall note “Capabilitiy
Demonstration” adjacent to the specified and ending tempers. Some examples are:
• “-T3 to -T82 Capability Demonstration for response to
aging”;
• “-T4 to -T62 Capability Demonstration for response to
aging”;
Temper designation T_2 should also be applied to wrought
products heat-treated by the purchaser/user, in accordance
with the applicable heat treatment specification, to achieve
the properties applicable to the final temper.
A3 Assigned O Temper Variations
A3.1 The following temper designation has been assigned
for wrought products high temperature annealed to accentuate ultrasonic response and provide dimensional stability.
O1 Thermally treated at approximately same time and temperature
required for solution heat treatment and slow cooled to room temperature. Applicable to products that are to be machined prior to
solution heat treatment by the user. Mechanical property limits are
not applicable.
A4 Designation of Unregistered Tempers
A4.1 The letter P has been assigned to denote H, T and O
temper variations that are negotiated between manufacturer
and purchaser. The letter P immediately follows the temper
designation that most nearly pertains. Specific examples where
such designation may be applied include the following:
A4.1.1 The use of the temper is sufficiently limited so as
to preclude its registration. (Negotiated H temper variations
were formerly indicated by the third digit zero.)
A4.1.2 The test conditions (sampling location, number
of samples, test specimen configuration, etc.) are different
from those required for registration with The Aluminum
Association.
• “-T4 to -T762 Capability Demonstration for response to
overaging”;
A4.1.3 The mechanical property limits are not established
on the same basis as required for registration with The Aluminum Association.
• “-T6 to -T732 Capability Demonstration for response to
overaging”;
A4.1.4 For products such as Aluminum Metal Matrix Composites which are not included in any registration records.
IV-12
January 2005
Table 1
COMPARATIVE CHARACTERISTICS AND APPLICATIONS
StressCorrosion
Cracking ②
Workability
(Cold) ⑤
Machinability ⑤
Brazeability ⑥
Gas
Arc
Resistance
Spot and
Seam
WELDABILITY ⑥
General ①
RESISTANCE
TO
CORROSION
1060-O
H12
H14
H16
H18
A
A
A
A
A
A
A
A
A
A
A
A
A
B
B
E
E
D
D
D
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
B
A
A
A
A
Chemical equipment, railroad tank cars
1100-O
H12
H14
H16
H18
A
A
A
A
A
A
A
A
A
A
A
A
A
B
C
E
E
D
D
D
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
B
A
A
A
A
Sheet metal work, spun hollowware,
fin stock
1350-O
H12, H111
H14, H24
H16, H26
H18
A
A
A
A
A
A
A
A
A
A
A
A
A
B
B
E
E
D
D
D
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
B
A
A
A
A
Electrical conductors
2011-T3
T4, T451
T8
D③
D③
D
D
D
B
C
B
D
A
A
A
D
D
D
D
D
D
D
D
D
D
D
D
Screw machine products
2014-O
T3, T4, T451
T6, T651, T6510, T6511
..
D③
D
..
C
C
..
C
D
D
B
B
D
D
D
D
D
D
D
B
B
B
B
B
Truck frames, aircraft structures
2017-T4, T451
D③
C
C
B
D
D
B
B
Screw machine products, fittings
2018-T61
..
..
..
B
D
D
C
B
Aircraft engine cylinders, heads and
pistons
2024-O
T4, T3, T351, T3510, T3511
T361
T6
T861, T81, T851, T8510, T8511
T72
..
D③
D③
D
D
..
..
C
C
B
B
..
..
C
D
C
D
..
D
B
B
B
B
B
D
D
D
D
D
D
D
C
D
D
D
D
D
B
C
C
C
C
D
B
B
B
B
B
Truck wheels, screw machine products,
aircraft structures
2025-T6
D
C
..
B
D
D
B
B
Forgings, aircraft propellers
2036-T4
C
..
B
C
D
C
B
B
Auto body panel sheet
2117-T4
C
A
B
C
D
D
B
B
Rivets
2124-T851
D
B
D
B
D
D
C
B
Aircraft structures
2218-T61
T72
D
D
C
C
..
..
..
B
D
D
D
D
C
C
B
B
Jet engine impellers and rings
2219-O
T31, T351, T3510, T3511
T37
T81, T851, T8510, T8511
T87
..
D③
D③
D
D
..
C
C
B
B
..
C
D
D
D
..
B
B
B
B
D
D
D
D
D
D
A
A
A
A
A
A
A
A
A
B
A
A
A
A
Structural uses at high temperatures
(to 600°F)
High strength weldments
2618-T61
D
C
..
B
D
D
C
B
Aircraft engines
3003-O
H12
H14
H16
H18
H25
A
A
A
A
A
A
A
A
A
A
A
A
A
A
B
C
C
B
E
E
D
D
D
D
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
B
A
A
A
A
A
Cooking utensils, chemical equipment,
pressure vessels, sheet metal work,
builder’s hardware, storage tanks
3004-O
H32
H34
H36
H38
A
A
A
A
A
A
A
A
A
A
A
B
B
C
C
D
D
C
C
C
B
B
B
B
B
A
A
A
A
A
A
A
A
A
A
B
A
A
A
A
Sheet metal work, storage tanks
3105-O
H12
H14
H16
H18
H25
A
A
A
A
A
A
A
A
A
A
A
A
A
B
B
C
C
B
E
E
D
D
D
D
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
B
A
A
A
A
A
Residential siding, mobile homes, rain
carrying goods, sheet metal work
ALLOY AND TEMPER
SOME
APPLICATIONS
OF ALLOYS
For all numbered footnotes, see page IV-15.
January 2005
IV-13
Table 1
COMPARATIVE CHARACTERISTICS AND APPLICATIONS (Continued)
StressCorrosion
Cracking ②
Workability
(Cold) ⑤
Machinability ⑤
Brazeability ⑥
Gas
Arc
Resistance
Spot and
Seam
WELDABILITY ⑥
General ①
RESISTANCE
TO
CORROSION
4032-T6
C
B
..
B
D
D
B
C
Pistons
5005-O
H12
H14
H16
H18
H32
H34
H36
H38
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
B
C
C
A
B
C
C
E
E
D
D
D
E
D
D
D
B
B
B
B
B
B
B
B
B
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
B
A
A
A
A
A
A
A
A
Appliances, utensils, architectural,
electrical conductor
5050-O
H32
H34
H36
H38
A
A
A
A
A
A
A
A
A
A
A
A
B
C
C
E
D
D
C
C
B
B
B
B
B
A
A
A
A
A
A
A
A
A
A
B
A
A
A
A
Builder’s hardware, refrigerator trim,
coiled tubes
5052-O
H32
H34
H36
H38
A
A
A
A
A
A
A
A
A
A
A
B
B
C
C
D
D
C
C
C
C
C
C
C
C
A
A
A
A
A
A
A
A
A
A
B
A
A
A
A
Sheet metal work, hydraulic tube,
appliances
5056-O
H111
H12, H32
H14, H34
H18, H38
H192
H392
A④
A④
A④
A④
A④
B④
B④
B④
B④
B④
B④
C④
D④
D④
A
A
B
B
C
D
D
D
D
D
C
C
B
B
D
D
D
D
D
D
D
C
C
C
C
C
C
C
A
A
A
A
A
A
A
B
A
A
A
A
A
A
Cable sheathing, rivets for magnesium,
screen wire, zipper
5083-O
H321 ⑧
H111
H116 ⑧
A④
A④
A④
A④
A④
A④
B④
A④
B
C
C
C
D
D
D
D
D
D
D
D
C
C
C
C
A
A
A
A
B
A
A
A
5086-O
H32 ⑧
H34
H36
H38
H111
H116 ⑧
A④
A④
A④
A④
A④
A④
A④
A④
A④
B④
B④
B④
A④
A④
A
B
B
C
C
B
B
D
D
C
C
C
D
D
D
D
D
D
D
D
D
C
C
C
C
C
C
C
A
A
A
A
A
A
A
B
A
A
A
A
A
A
Unfired, welded pressure vessels,
marine, auto aircraft cryogenics,
TV towers, drilling rigs, transportation
equipment, missile components
5154-O
H32
H34
H36
H38
A④
A④
A④
A④
A④
A④
A④
A④
A④
A④
A
B
B
C
C
D
D
C
C
C
D
D
D
D
D
C
C
C
C
C
A
A
A
A
A
B
A
A
A
A
Welded structures, storage tanks,
pressure vessels, salt water service
5252-H24
H25
H28
A
A
A
A
A
A
B
B
C
D
C
C
C
C
C
A
A
A
A
A
A
A
A
A
Automotive and appliance trim
5254-O
H32
H34
H36
H38
A④
A④
A④
A④
A④
A④
A④
A④
A④
A④
A
B
B
C
C
D
D
C
C
C
D
D
D
D
D
C
C
C
C
C
A
A
A
A
A
B
A
A
A
A
Hydrogen peroxide and chemical
storage vessels
5454-O
H32
H34
H111
A
A
A
A
A
A
A
A
A
B
B
B
D
D
C
D
D
D
D
D
C
C
C
C
A
A
A
A
B
A
A
A
Welded structures, pressure vessels,
marine service
5456-O
H321 ⑧
H116 ⑧
A④
A④
A④
B④
B④
B④
B
C
C
D
D
D
D
D
D
C
C
C
A
A
A
B
A
A
High strength welded structures,
pressure vessels, marine applications,
storage tanks
5457-O
A
A
A
E
B
A
A
B
5652-O
H32
H34
H36
H38
A
A
A
A
A
A
A
A
A
A
A
B
B
C
C
D
D
C
C
C
C
C
C
C
C
A
A
A
A
A
A
A
A
A
A
B
A
A
A
A
ALLOY AND TEMPER
SOME
APPLICATIONS
OF ALLOYS
Hydrogen peroxide and chemical
storage vessels
For all numbered footnotes, see page IV-15.
IV-14
January 2005
Table 1
COMPARATIVE CHARACTERISTICS AND APPLICATIONS (Continued)
Brazeability ⑥
Gas
Arc
Resistance
Spot and
Seam
A
A
A
A
A
A
A
A
A
B
B
C
D
D
D
D
B
B
B
B
A
A
A
A
A
A
A
A
A
A
A
A
6005-T1, T5
..
..
..
..
A
A
A
A
6053-O
T6, T61
..
A
..
A
..
..
E
C
B
B
A
A
A
A
B
A
Wire and rod for rivets
6061-O
T4, T451, T4510, T4511
T6, T651, T652, T6510, T6511
B
B
B
A
B
A
A
B
C
D
C
C
A
A
A
A
A
A
A
A
A
B
A
A
Heavy-duty structures requiring good
corrosion resistance, truck and marine,
railroad cars, furniture, pipelines
6063-T1
T4
T5, T452
T6
T83, T831, T832
A
A
A
A
A
A
A
A
A
A
B
B
B
C
C
D
D
C
C
C
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
Pipe railing, furniture, architectural
extrusions
6066-O
T4, T4510, T4511
T6, T6510, T6511
C
C
C
A
B
B
B
C
C
D
C
B
D
D
D
D
D
D
B
B
B
B
B
B
Forgings and extrusion for welded
structures
6070-T4, T4511
T6
B
B
B
B
B
C
C
C
D
D
A
A
A
A
A
A
Heavy duty welded structures, pipelines
6101-T6, T63
T61, T64
A
A
A
A
C
B
C
D
A
A
A
A
A
A
A
A
High strength bus conductors
6151-T6, T652
..
..
..
..
B
..
..
..
Moderate strength, intricate forgings
for machine and auto parts
StressCorrosion
Cracking ②
5657-H241
H25
H26
H28
ALLOY AND TEMPER
General ①
Machinability ⑤
WELDABILITY ⑥
Workability
(Cold) ⑤
RESISTANCE
TO
CORROSION
SOME
APPLICATIONS
OF ALLOYS
Anodized auto and appliance trim
6201-T81
A
A
..
C
A
A
A
A
High strength electric conductor wire
6262-T6, T651, T6510, T6511
T9
B
B
A
A
C
D
B
B
B
B
B
B
B
B
A
A
Screw machine products
6351-T1
T4
T5
T6
..
A
A
A
..
..
..
..
C
C
C
C
C
C
C
C
C
C
C
C
B
B
B
B
A
A
A
A
B
B
A
A
Extruded shapes, structurals, pipe and
tube
6463-T1
T5
T6
A
A
A
A
A
A
B
B
C
D
C
C
A
A
A
A
A
A
A
A
A
A
A
A
Extruded architectural and trim sections
6951-T42, T62
..
..
..
..
A
A
A
A
7005-T53
..
..
..
..
B
C
A
A
7049-T73, T7352
C
B
D
B
D
D
D
B
Aircraft forgings
7050-T73510, T73511
T74 ⑦, T7451 ⑦, T74510 ⑦,
T74511 ⑦, T7452 ⑦, T7651,
T76510, T76511
C
B
D
B
D
D
D
B
Aircraft and other structures
7075-O
T6, T651, T652, T6510, T6511
T73, T7351
..
C③
C
..
C
B
..
D
D
D
B
B
D
D
D
D
D
D
D
D
D
B
B
B
Aircraft and other structures
7175-T74, T7452, T7454
C
B
D
B
D
D
C
B
7178-O
T6, T651, T6510, T6511
..
C③
..
C
..
D
..
B
D
D
D
D
D
D
B
B
Aircraft and other structures
7475-O
7475-T61, -T651
7475-T761, T7351
..
C
C
..
C
B
..
D
D
..
B
B
D
D
D
D
D
D
D
B
D
B
B
B
Shell Casings
Aircraft & Other
Structures
8017-H12, H22, H221
A
A
A
D
A
A
A
A
Electrical conductors
8030-H12, H221
A
A
A
E
A
A
A
A
Electrical conductors
8176-H14, H24
A
A
A
D
A
A
A
A
Electrical conductors
For all numbered footnotes, see page IV-15.
January 2005
IV-15
Notes for Table 1
① Ratings A through E are relative ratings in decreasing order of merit, based
on exposures to sodium chloride solution by intermittent spraying or immersion. Alloys with A and B ratings can be used in industrial and seacoast
atmospheres without protection. Alloys with C, D and E ratings generally
should be protected at least on faying surfaces.
② Stress-corrosion cracking ratings are based on service experience and on
laboratory tests of specimens exposed to the 3.5% sodium chloride alternate
immersion test.
A = No known instance of failure in service or in laboratory tests.
B = No known instance of failure in service; limited failures in laboratory
tests of short transverse specimens.
C = Service failures with sustained tension stress acting in short transverse direction relative to grain structure; limited failures in laboratory
tests of long transverse specimens.
D = Limited service failures with sustained longitudinal or long transverse
areas.
These ratings are neither product specific nor test direction specific and
therefore indicate only the general level of stress-corrosion cracking resistance. For more specific information on certain alloys, see ASTM G64.
③ In relatively thick sections the rating would be E.
IV-16
④ This rating may be different for material held at elevated temperature for
long periods.
⑤ Ratings A through D for Workability (cold), and A through E for Machinability, are relative ratings in decreasing order of merit.
⑥ Ratings A through D for Weldability and Brazeability are relative ratings
defined as follows:
A = Generally weldable by all commercial procedures and methods.
B = Weldable with special techniques or for specific applications that justify preliminary trials or testing to develop welding procedure and weld
performance.
C = Limited weldability because of crack sensitivity or loss in resistance to
corrosion and mechanical properties.
D = No commonly used welding methods have been developed.
⑦ T74 type tempers, although not previously registered, have appeared in
various literature and specifications as T736 type tempers.
⑧ 5xxx products in the -H116 and H32X tempers have similar mechanical
properties; however, production methods and testing requirements differ,
and these tempers are not interchangeable. The -H116 temper is typically
used in marine and other applications requiring demonstration of exfoliation
resistance.
January 2005
Table 2
HISTORICAL FOREIGN ALLOY DESIGNATIONS AND SIMILAR AA ALLOYS
Foreign Alloy
Designation
Al99
Al99,5
E-Al
AlCuMg1
AlCuMg2
AlCuMg0,5
AlMg5
AlMgSi0,5
E-AlMgSi
AlZnMgCu1,5
990C
CB60
CG30
CG42
CG42 Alclad
CM41
CN42
CS41N
CS41N Alclad
CS41P
GM31N
GM41
GM50P
GM50R
GR20
GS10
GS11N
GS11P
MC10
S5
SG11P
SG121
ZG62
ZG62 Alclad
A5/L
A45
A-G1
A-G0.6
A-G4MC
A-GS
A-GS/L
A-M1
A-M1G
A-U4G
A-U2G
A-U2GN
A-U4G1
A-U4N
A-U4SG
A-S12UN
A-Z5GU
Designating
Country
Austria
(Önorm) ①
Canada
(CSA) ②
France
(NF) ③
Equivalent or
Similar AA Alloy
1200
1050
1350
2017
2024
2117
5056
6063
6101
7075
1100
2011
2117
2024
Alclad 2024
2017
2018
2014
Alclad 2014
2025
5454
5083
5356
5056
5052
6063
6061
6053
3003
4043
6151
4032
7075
Alclad 7075
1350
1100
5050
5005
5086
6063
6101
3003
3004
2017
2117
2618
2024
2218
2014
4032
7075
Foreign Alloy
Designation
E-A1995 ④
3.0257 ⑤
AlCuBiPb ④
3.1655 ⑤
AlCuMg0.5 ④
3.1305 ⑤
AlCuMg1 ④
3.1325 ⑤
AlCuMg2 ④
3.1355 ⑤
AlCuSiMn ④
3.1255 ⑤
AlMg4.5Mn ④
3.3547 ⑤
AlMgSi0.5 ④
3.3206 ⑤
AlSi5 ④
3.2245 ⑤
E-AlMgSi0.5 ④
3.3207 ⑤
AlZnMgCu1.5 ④
3.4365 ⑤
Designating
Country
}
}
}
}
}
}
}
}
}
}
}
1E
91E
H14
H19
H20
L.80, L.81
L.86
L.87
L.93, L.94
L.95, L.96
L.97, L.98
2L.55, 2L.56
2L.58
3L.44
5L.37
6L.25
N8
N21
150A
324A
372B
717, 724, 731A
745, 5014, 5084
5090
5100
Equivalent or
Similar AA Alloy
1350
2011
2117
2017
2024
Germany
2014
5083
6063
4043
6101
7075
1350
6101
2017
6063
6061
5052
2117
2117
2014A
7075
2024
5052
5056
5050
2017
2218
5083
4043
Great Britain
(BS) ⑥
}
Great Britain
(DTD) ⑦
}
2017
4032
6063
2618
2024
Alclad 2024
For all numbered footnotes, see next page.
January 2005
IV-17
Table 2
HISTORICAL FOREIGN ALLOY DESIGNATIONS AND SIMILAR AA ALLOYS (Continued)
Foreign Alloy
Designation
Designating
Country
Equivalent or
Similar AA Alloy
P-AlCu4MgMn
P-AlCu4.5MgMn
P-AlCu4.5MgMnplacc.
P-AlCu2.5MgSi
P-AlCu4.4SiMnMg
Italy
P-AlCu4.4SiMnMgplacc. (UNI) ⑧
P-AlMg0.9
P-AlMg1.5
P-AlMg2.5
P-AlSi0.4Mg
P-AlSi0.5Mg
2017
2024
Alclad 2024
2117
2014
Alclad 2014
5657
5050
5052
6063
6101
Al99.5E
L-313
L-314
L-315
L-371
1350
2014
2024
2218
7075
Spain
(UNE) ⑨
① Austrian Standard M3430.
② Canadian Standards Association.
③ Normes Françaises.
④ Deutsche Industrie-Norm.
⑤ Werkstoff-Nr.
⑥ British Standard.
IV-18
Foreign Alloy
Designation
Al-Mg-Si
Al1.5Mg
Al-Cu-Ni
Al3.5Cu0.5Mg
Al4Cu1.2Mg
Al-Zn-Mg-Cu
Al-Zn-Mg-Cu-pl
Al99.0Cu
AlCu2Mg
AlCu4Mg1
AlCu4SiMg
AlCu4MgSi
AlMg1
AlMg1.5
AlMg2.5
AlMg3.5
AlMg4
AlMg5
AlMn1Cu
AlMg3Mn
AlMg4.5Mn
AlMgSi
AlMg1SiCu
AIZn6MgCu
Designating
Country
Switzerland
(VSM) ⑩
ISO ⑪
Equivalent or
Similar AA Alloy
6101
5050
2218
2017
2027
7075
Alclad 7075
1100
2117
2024
2014
2017
5005
5050
5052
5154
5086
5056
3003
5454
5083
6063
6061
7075
⑦ Directorate of Technical Development.
⑧ Unificazione Nazionale Italiana.
⑨ Una Norma Espanol.
⑩ Verein Schweizerischer Maschinenindustrieller.
⑪ International Organization for Standardization.
January 2005
Aluminum Design Manual
PART V
Material Properties
The Aluminum Association, Inc.
1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
Third Edition, January 2005
V
Material Properties
TABLE OF CONTENTS
1.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.0 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Table 1
Table 1M
Table 2
Table 2M
Table 3
Table 3M
Table 4
Table 4M
Table 5
Table 5M
Table 6
Table 6M
Table 7
Table 7M
Table 8
Table 9
Table 9M
Minimum Mechanical Properties for Aluminum Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Minimum Mechanical Properties for Aluminum Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Minimum Mechanical Properties for Welded Aluminum Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Minimum Mechanical Properties for Welded Aluminum Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Mechanical Property Limits for Aluminum Sand Casting Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Mechanical Property Limits for Aluminum Sand Casting Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Mechanical Property Limits for Aluminum Permanent Mold Casting Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Mechanical Property Limits for Aluminum Permanent Mold Casting Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Mechanical Property Limits of Fastener Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Mechanical Property Limits of Fastener Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Typical Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Typical Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Typical Physical Properties-Thermal and Electrical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Typical Physical Properties-Thermal and Electrical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Typical Physical Properties-Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Typical Tensile Properties at Various Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Typical Tensile Properties at Various Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
January 2005
V-3
1.0 Introduction
The mechanical properties intended to be used for structural design in accordance with the Design Guide and the
Specification for Aluminum Structures included in this
manual are listed in Tables 1 and 2 of this Part.
In Table 1, the tensile strength (Ftu) and tensile yield
strength (Fty) are equal to specified minimum properties,
and are based on producer analysis of data accumulated
from standard procedures (Reference 1). The limits are
established after sufficient test data have been accumulated to adequately determine the form of the frequency
distribution curve and to provide a reliable estimate of the
population mean and standard deviation. In most instances
the distribution is normal in form and properties are based
on the results of a minimum of 100 tests from at least
10 different lots of material. In some instances, however,
limits may be derived through their known relationship
with another limit or property having sufficient data and
meeting the above data base criteria. The standard mechanical property limits are subsequently established at levels
at which 99% of the material is expected to conform at a
confidence level of 0.95.
The compressive yield strength (Fcy), and shear ultimate strength (Fsu) in Table 1 are “expected minimum”
properties, strengths which 99% of the population would
be expected, but are not guaranteed, to equal or exceed;
individual lots of material may not be accepted or rejected
based upon these properties. They are derived values established by multiplying values of these properties from tests
of representative lots of material by the ratio of the specified minimum tensile yield or ultimate strength to the tensile yield or ultimate strength of the lot tested. While every
effort is made to base these values on test data for at least
5 to 10 lots of each alloy, temper and product, there are
instances where insufficient data are available, and the
derived properties are based on data for similar products.
Minimum mechanical properties for welded material
are shown in Table 2. Values of tensile strength (Ftuw) are
weld qualification properties required by AWS D1.2. For
non-heat-treatable alloys, the values of tensile strength
(Ftuw) are the minimum properties of the parent metal in the
annealed (O) temper.
The tensile ultimate strengths (Ftuw) of heat-treatable
alloys and the tensile yield strengths (Ftyw) of all the alloys
listed are based, where possible, on the statistical analysis
of test data. Minimum values are those that 99% of the
population would be expected to equal or exceed with a
confidence level of 0.75. There are instances where insuf-
January 2005
ficient data are available, and in those cases the minimum
properties are based on data for similar combinations of
filler and parent material.
Generally, the compressive and shear properties in Table
2 are derived from the relationships among those properties of the parent alloys and tempers. None of the minimum mechanical properties of welds are specified (guaranteed) values upon which individual lots of material may be
accepted or rejected. All values are based on the assumption
that recommended weld procedures are employed, with the
realization that variations in these procedures could alter the
values obtained.
Tables 3 and 4 show minimum mechanical properties
for aluminum sand and permanent mold casting alloys
respectively. Table 5 has minimum mechanical properties
of threaded fastener alloys.
As a resource for comparing alloys and tempers, Table 6
gives typical mechanical properties which include not only
tensile ultimate and yield, but also hardness, shear, fatigue,
and modulus. These typical properties are not guaranteed
and are averages for various sizes, product forms, and
methods of manufacture. The data should not be specified
as engineering requirements or used for design purposes.
Table 7 similarly shows typical physical properties, both
thermal and electrical and can be used as a basis for comparing alloys and tempers. Densities for alloys are shown in
Table 8, while Table 9 displays tensile properties at various
temperatures. As stated earlier, properties shown in Tables
6 and 9 are not to be used for design purposes.
Other material properties and material properties of other
alloys and tempers may be found in References 1 through 3.
2.0 References
1. Aluminum Association, Aluminum Standards and
Data, The Aluminum Association, Washington, DC,
2003.
2. DOT/FAA/AR-MMPDS-01, Metallic Materials Properties Development and Standardization (MMPDS),
(formerly MIL Handbook 5) Chapter 3, January, 2003,
U.S. Department of Transportation, Federal Aviation
Administration, Washington, D.C. Copies available
through the National Technical Information Service
(NTIS), 5285 Port Royal Road, Springfield VA 221610001; www.ntis.gov or downloadable from http://www.
tc.faa.gov/its/worldpac/techrpt/ar-mmpds-01.pdf
3. Bruhn, E.F., Analysis and Design of Flight Vehicle
Structures, Tristate Offset Co., Cincinnati, OH, 1965.
V-5
Table 1
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
1100-H12
-H14
2014-T6
-T651
-T6, T6510, T6511
-T6, T651
Alclad
2014-T6
-T6
-T651
3003-H12
-H14
-H16
-H18
-H12
-H14
-H16
-H18
Alclad
3003-H12
-H14
-H16
-H18
-H14
-H18
3004-H32
-H34
-H36
-H38
-H34
-H36
Alclad
3004-H32
-H34
-H36
-H38
-H131, H241, H341
-H151, H261, H361
3005-H25
-H28
3105-H25
5005-H12
-H14
-H16
-H32
-H34
-H36
5050-H32
-H34
-H32
-H34
THICKNESS
RANGE
in.
Ftu
ksi
Fty
ksi
Fcy
ksi
Fsu
ksi
All
All
0.040 to 0.249
0.250 to 2.000
All
All
14
16
66
67
60
65
11
14
58
59
53
55
10
13
59
58
52
53
9
10
40
40
35
38
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (ksi)
10,100
10,100
10,900
10,900
10,900
10,900
Sheet
Sheet
Plate
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Drawn Tube
Drawn Tube
0.025 to 0.039
0.040 to 0.249
0.250 to 0.499
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.006 to 0.128
All
All
All
All
63
64
64
17
20
24
27
17
20
24
27
55
57
57
12
17
21
24
12
17
21
24
56
58
56
10
14
18
20
11
16
19
21
38
39
39
11
12
14
15
11
12
14
15
10,800
10,800
10,800
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.006 to 0.128
0.025 to 0.259
0.010 to 0.500
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.006 to 0.128
0.018 to 0.450
0.018 to 0.450
16
19
23
26
19
26
28
32
35
38
32
35
11
16
20
23
16
23
21
25
28
31
25
28
9
13
17
19
15
20
18
22
25
29
24
27
10
12
14
15
12
15
17
19
20
21
19
20
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Sheet
Cold Fin. Rod & Bar
Drawn Tube
Cold Fin. Rod & Bar
Drawn Tube
0.017 to 0.249
0.009 to 0.249
0.006 to 0.162
0.006 to 0.128
0.024 to 0.050
0.024 to 0.050
0.013 to 0.050
0.006 to 0.080
0.013 to 0.080
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.017 to 2.000
0.009 to 1.000
0.006 to 0.162
0.017 to 2.000
0.009 to 0.249
All
27
31
34
37
31
34
26
31
23
18
21
24
17
20
23
22
25
22
20
24
27
30
26
30
22
27
19
14
17
20
12
15
18
16
20
16
17
21
24
28
22
28
20
25
17
13
15
18
11
14
16
14
18
15
16
18
19
21
18
19
15
17
14
11
12
14
11
12
13
14
15
13
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
All
25
20
19
15
10,100
PRODUCT
Plate, Drawn Tube,
)
( Sheet,
Rolled Rod & Bar
Sheet
Plate
Extrusions
Cold Finished Rod & Bar,
Drawn Tube
For all footnotes, see last page of this Table.
V-6
January 2005
Table 1
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
5052-O
-H32
-H34
-H36
5083-O
-H111
-H111
-O
-H116
-H32, H321
-H116
-H32, H321
5086-O
-H111
-H111
-O
-H112
-H112
-H112
-H112
-H116
-H32
-H34
5154-H38
5454-O
-H111
-H111
-H112
-O
-H32
-H34
5456-O
-H116
-H32, H321
-H116
-H32, H321
-H116
-H32, H321
6005-T5
6061-T6, T651
-T6, T6510, T6511
-T6, T651
-T6
-T6
6063-T5,
-T52
-T5
-T6
6066-T6, T6510, T6511
6070-T6, T62
6105-T5
6351 -T5
6351 -T6
6463-T6
7005-T53
PRODUCT
Sheet & Plate
Sheet & Plate
Cold Fin. Rod & Bar
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Extrusions
Extrusions
Extrusions
Sheet & Plate
Plate
Plate
Plate
Plate
Sheet & Plate
Sheet & Plate
Drawn Tube
Sheet & Plate
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Plate
Plate
Extrusions
Sheet & Plate
Extrusions
Cold Fin. Rod & Bar
Drawn Tube
Pipe
Extrusions
Extrusions
Extrusions
Extrusions & Pipe
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
(
)
THICKNESS
RANGE
in.
Ftu
ksi
Fty
ksi
Fcy
ksi
Fsu
ksi
0.006 to 3.000
All
All
25
31
34
9.5
23
26
9.5
21
24
16
19
20
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (ksi)
10,200
10,200
10,200
0.006 to 0.162
up thru 5.000
up thru 0.500
0.501 to 5.000
0.051 to 1.500
0.188 to 1.500
0.188 to 1.500
1.501 to 3.000
1.501 to 3.000
up thru 5.000
up thru 0.500
0.501 to 5.000
0.020 to 2.000
0.025 to 0.499
0.500 to 1.000
1.001 to 2.000
2.001 to 3.000
All
All
37
39
40
40
40
44
44
41
41
35
36
36
35
36
35
35
34
40
40
29
16
24
24
18
31
31
29
29
14
21
21
14
18
16
14
14
28
28
26
16
21
21
18
26
26
24
24
14
18
18
14
17
16
15
15
26
26
22
24
24
23
25
26
26
24
24
21
21
21
21
22
21
21
21
24
24
10,200
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
All
44
34
32
26
10,400
0.006 to 0.128
up thru 5.000
up thru 0.500
0.501 to 5.000
up thru 5.000
0.020 to 3.000
0.020 to 2.000
0.020 to 1.000
0.051 to 1.500
0.188 to 1.250
0.188 to 1.250
1.251 to 1.500
1.251 to 1.500
1.501 to 3.000
1.501 to 3.000
up thru 1.000
0.010 to 4.000
All
up thru 8.000
0.025 to 0.500
All
up thru 0.500
up thru 1.000
0.500 to 1.000
All
All
up thru 2.999
up thru 0.500
up thru 1.000
up thru 0.750
up thru 0.500
up thru 0.750
45
31
33
33
31
31
36
39
42
46
46
44
44
41
41
38
42
38
42
42
38
22
22
21
30
50
48
38
38
42
30
50
35
12
19
19
12
12
26
29
19
33
33
31
31
29
29
35
35
35
35
35
35
16
16
15
25
45
45
35
35
37
25
44
33
12
16
16
13
12
24
27
19
27
27
25
25
25
25
35
35
35
35
35
35
16
16
15
25
45
45
35
35
37
25
43
24
19
20
19
19
19
21
23
26
27
27
25
25
25
25
24
27
24
25
27
24
13
13
12
19
27
29
24
24
27
19
28
10,300
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,400
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,100
10,500
1. Ftu and Fty are minimum specified values (except Fty for 1100-H12, H14 Cold Finished Rod and Bar and Drawn Tube, Alclad 3003-H18 Sheet and
5050-H32, H34 Cold Finished Rod and Bar which are minimum expected values); other strength properties are corresponding minimum expected
values.
2. Typical values. For deflection calculations an average modulus of elasticity is used; this is 100 ksi lower than values in this column.
May 2005
V-7
Table 1M
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
1100-H12
-H14
2014-T6
-T651
-T6, T6510, T6511
-T6, T651
Alclad
2014-T6
-T6
-T651
3003-H12
-H14
-H16
-H18
-H12
-H14
-H16
-H18
Alclad
3003-H12
-H14
-H16
-H18
-H14
-H18
3004-H32
-H34
-H36
-H38
-H34
-H36
Alclad
3004-H32
-H34
-H36
-H38
-H131, H241, H341
-H151, H261, H361
3005-H25
-H28
3105-H25
5005-H12
-H14
-H16
-H32
-H34
-H36
5050-H32
-H34
-H32
-H34
THICKNESS
RANGE
mm
Ftu
MPa
Fty
MPa
Fcy
MPa
Fsu
MPa
All
All
1.00 to 6.30
6.30 to 50.00
All
All
95
110
455
460
415
450
75
95
400
405
365
380
70
90
405
400
360
365
62
70
275
275
240
260
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (MPa)
69,600
69,600
75,200
75,200
75,200
75,200
Sheet
Sheet
Plate
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Drawn Tube
Drawn Tube
0.63 to 1.00
1.00 to 6.30
6.30 to 12.50
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.15 to 3.20
All
All
All
All
435
440
440
120
140
165
185
120
140
165
185
380
395
395
85
115
145
165
85
115
145
165
385
400
385
70
95
125
140
75
110
130
145
260
270
270
75
85
95
105
75
85
95
105
74,500
74,500
74,500
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Drawn Tube
Drawn Tube
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.15 to 3.20
0.63 to 6.30
0.25 to 12.50
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.15 to 3.20
0.45 to 11.50
0.45 to 11.50
115
135
160
180
135
180
190
220
240
260
220
240
80
110
140
160
110
160
145
170
190
215
170
190
62
90
115
130
105
140
125
150
170
200
165
185
70
85
95
105
85
105
115
130
140
145
130
140
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Sheet
Cold Fin. Rod & Bar
Drawn Tube
Cold Fin. Rod & Bar
Drawn Tube
0.40 to 6.30
0.20 to 6.30
0.15 to 4.00
0.15 to 3.20
0.60 to 1.20
0.60 to 1.20
0.32 to 1.20
0.15 to 2.00
0.32 to 2.00
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.40 to 50.00
0.20 to 25.00
0.15 to 4.00
0.40 to 6.30
0.20 to 6.30
All
185
215
235
255
215
235
180
215
160
125
145
165
120
140
160
150
170
150
140
165
185
205
180
205
150
185
130
95
115
135
85
105
125
110
140
110
115
145
165
195
150
195
140
170
115
90
105
125
75
95
110
95
125
105
110
125
130
145
125
130
105
115
95
75
85
95
75
85
90
95
105
90
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
All
170
140
130
105
69,600
PRODUCT
Plate, Drawn Tube,
)
( Sheet,
Rolled Rod & Bar
Sheet
Plate
Extrusions
Cold Finished Rod & Bar,
Drawn Tube
For all footnotes, see last page of this Table.
V-8
January 2005
Table 1M
MINIMUM MECHANICAL PROPERTIES FOR ALUMINUM ALLOYS
ALLOY AND TEMPER
5052-O
-H32
-H34
-H36
5083-O
-H111
-H111
-O
-H116
-H32, H321
-H116
-H32, H321
5086-O
-H111
-H111
-O
-H112
-H112
-H112
-H116
-H32
-H34
5154 -H38
5454-O
-H111
-H111
-H112
-O
-H32
-H34
5456-O
-H116
-H32, H321
-H116
-H32, H321
-H116
-H32, H321
6005-T5
6061-T6, T651
-T6, T6510, T6511
-T6, T651
-T6
-T6
6063-T5,
-T52
-T5
-T6
6066-T6, T6510, T6511
6070-T6, T62
6105 -T5
6351-T5
6351-T6
6463-T6
7005-T53
PRODUCT
Sheet & Plate
Sheet & Plate
Cold Fin. Rod & Bar
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Plate
Plate
Sheet & Plate
Sheet & Plate
Drawn Tube
Sheet & Plate
Drawn Tube
Sheet
Extrusions
Extrusions
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Sheet & Plate
Plate
Plate
Plate
Plate
Extrusions
Sheet & Plate
Extrusions
Cold Fin. Rod & Bar
Drawn Tube
Pipe
Extrusions
Extrusions
Extrusions
Extrusions & Pipe
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
Extrusions
(
)
THICKNESS
RANGE
mm
Ftu
MPa
Fty
MPa
Fcy
MPa
Fsu
MPa
0.15 to 80.00
All
All
170
215
235
65
160
180
66
145
165
110
130
140
COMPRESSIVE
MODULUS OF
ELASTICITY2
E (MPa)
70,300
70,300
70,300
0.15 to 4.00
up thru 13.00
up thru 12.70
12.70 to 130.00
1.20 to 6.30
4.00 to 40.00
4.00 to 40.00
40.00 to 80.00
40.00 to 80.00
up thru 130.00
up thru 12.70
12.70 to 130.00
0.50 to 50.00
4.00 to 12.50
12.50 to 40.00
40.00 to 80.00
1.60 to 50.00
All
255
270
275
275
275
305
305
285
285
240
250
250
240
250
240
235
275
275
200
110
165
165
125
215
215
200
200
95
145
145
95
125
105
95
195
195
180
110
145
145
125
180
180
165
165
95
125
125
95
115
110
105
180
180
150
165
165
160
170
180
180
165
165
145
145
145
145
150
145
145
165
165
70,300
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
All
300
235
220
180
71,700
0.15 to 3.20
up thru 130.00
up thru 12.70
12.70 to 130.00
up thru 130.00
0.50 to 80.00
0.50 to 50.00
0.50 to 25.00
1.20 to 6.30
4.00 to 12.50
4.00 to 12.50
12.50 to 40.00
12.50 to 40.00
40.00 to 80.00
40.00 to 80.00
up thru 25
0.25 to 100.00
All
up thru 200
0.63 to 12.50
All
up thru 12.50
up thru 25.00
12.50 to 25.00
All
All
up thru 80.00
up thru 12.50
up thru 25.00
up thru 20.00
up thru 12.50
up thru 20.00
310
215
230
230
215
215
250
270
290
315
315
305
305
285
285
260
290
260
290
290
260
150
150
145
205
345
330
260
260
290
205
345
240
85
130
130
85
85
180
200
130
230
230
215
215
200
200
240
240
240
240
240
240
110
110
105
170
310
310
240
240
255
170
305
230
85
110
110
90
85
165
185
130
185
185
170
170
170
170
240
240
240
240
240
240
110
110
105
170
310
310
240
240
255
170
295
165
130
140
130
130
130
145
160
180
185
185
170
170
170
170
165
185
165
170
185
165
90
90
85
130
185
200
165
165
185
130
195
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
71,700
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
69,600
72,400
1. Ftu and Fty are minimum specified values (except Fty for 1100-H12, H14 Cold Finished Rod and Bar and Drawn Tube, Alclad 3003-H18 Sheet and
5050-H32, H34 Cold Finished Rod and Bar which are minimum expected values); other strength properties are corresponding minimum expected
values.
2. Typical values. For deflection calculations an average modulus of elasticity is used; this is 700 MPa lower than values in this column.
January 2005
V-9
Table 2
MINIMUM MECHANICAL PROPERTIES FOR WELDED ALUMINUM ALLOYS
All
All
TENSION
Ftuw1
Ftyw2
ksi
ksi
11
3.5
14
5
All
All
13
22
4.5
4.5
8.5
8.5
All
Sheet
All
All
All
Extrusions
Sheet & Plate
Plate
Extrusions
Plate
Sheet & Plate
Sheet
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Plate
Extrusions
All
All
All
Extrusions
Extrusions
Extrusions
Extrusions
21
17
15
18
25
39
40
39
35
35
35
30
31
31
31
42
41
24
24
24
17
24
24
17
40
8
6.5
5
6
9.5
16
18
17
14
14
14
11
12
12
12
19
18
13
15
11
8
15
11
8
24
8
6.5
5
6
9.5
15
18
17
13
14
14
11
11
12
12
18
17
13
15
11
8
15
11
8
24
ALLOY AND TEMPER
1100-H12, H14
3003-H12, H14, H16, H18
Alclad
3003-H12, H14, H16, H18
3004-H32, H34, H36, H38
Alclad
3004-H32, H34, H36, H38
3005-H25
5005-H12, H14, H32, H34
5050-H32, H34
5052-O, H32, H34
5083-O, H111
5083-O, H116, H32, H321
5083-O, H116, H32, H321
5086-O, H111
5086-H112
5086-O, H32, H34, H116
5154-H38
5454-O, H111
5454-H112
5454-O, H32, H34
5456-O, H116, H32, H321
5456-O, H116, H32, H321
6005-T5
6061-T6, T651, T6510, T65113
6061-T6, T651, T6510, T65114
6063-T5, T52, T6
6351-T5, T63
6351-T5, T64
6463-T6
7005-T53
PRODUCT
THICKNESS
RANGE
in.
0.188-1.500
1.501-3.000
0.250-2.000
0.188-1.500
1.501-3.000
up thru 0.250
over 0.375
over 0.375
0.125-0.500
up thru 0.750
COMPRESSION
Fcyw2
ksi
SHEAR
Fsuw
ksi
3.5
5
8
10
10
14
13
12
9
12
16
23
24
24
21
21
21
19
19
19
19
25
25
15
15
15
11
15
15
11
22
1. Filler wires are listed in Table 7.1-1. Values of Ftuw are AWS D1.2 weld qualification values.
2. 0.2% offset in 2 in. gage length across a groove weld.
3. Values when welded with 5183, 5356, or 5556 alloy filler wire, regardless of thickness. Values also apply to thicknesses less than or equal
to 0.375 in. when welded with 4043, 5554, or 5654 alloy filler wire.
4. Values when welded with 4043, 5554, or 5654 alloy filler wire.
V-10
January 2005
Table 2M
MINIMUM MECHANICAL PROPERTIES FOR WELDED ALUMINUM ALLOYS
All
All
TENSION
Ftuw †
Ftyw ‡
MPa
MPa
75
25
95
35
All
All
90
150
30
60
30
60
70
95
All
Sheet
All
All
All
Extrusions
Sheet & Plate
Plate
Extrusions
Plate
Sheet & Plate
Sheet
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
Plate
Extrusions
All
All
All
Extrusions
Extrusions
Extrusions
Extrusions
145
115
105
125
170
270
270
270
240
240
240
205
215
215
215
285
285
165
165
165
115
165
165
115
275
55
45
35
40
65
110
115
115
95
95
95
75
85
85
85
125
125
90
105
80
55
105
80
55
165
55
45
35
40
65
110
115
115
85
95
95
75
85
85
85
125
120
90
105
80
55
105
80
55
165
90
85
62
85
110
160
165
165
145
145
145
130
130
130
130
170
170
105
105
105
75
105
105
75
155
ALLOY AND TEMPER
1100-H12, H14
3003-H12, H14, H16, H18
Alclad
3003-H12, H14, H16, H18
3004-H32, H34, H36, H38
Alclad
3004-H32, H34, H36, H38
3005-H25
5005-H12, H14, H32, H34
5050-H32, H34
5052-O, H32, H34
5083-O, H111
5083-O, H116, H32, H321
5083-O, H116, H32, H321
5086-O, H111
5086-H112
5086-O, H32, H34, H116
5154-H38
5454-O, H111
5454-H112
5454-O, H32, H34
5456-O, H116, H32, H321
5456-O, H116, H32, H321
6005-T5
6061-T6, T651, T6510, T6511*
6061-T6, T651, T6510, T6511**
6063-T5, T52, T6
6351-T5, T6*
6351-T5, T6**
6463-T6
7005-T53
PRODUCT
THICKNESS
RANGE
mm
6.30-38.00
38.00-80.00
6.30-50.00
6.30-38.00
38.00-80.00
up thru 12.50
over 9.50
over 9.50
3.20-12.50
up thru 20.00
COMPRESSION
Fcyw ‡
MPa
SHEAR
Fsuw
MPa
25
35
55
70
† Filler wires are listed in Table 7.1-1. Values of Ftuw are AWS D1.2 weld qualification values.
‡ 0.2% offset in 50 mm gage length across a groove weld.
* Values when welded with 5183, 5356, or 5556 alloy filler wire, regardless of thickness. Values also apply to thicknesses less than or equal to
9.5 mm when welded with 4043, 5554, or 5654 alloy filler wire.
** Values when welded with 4043, 5554, or 5654 alloy filler wire.
January 2005
V-11
Table 3
MECHANICAL PROPERTY LIMITS FOR ALUMINUM SAND CASTING ALLOYS
ALLOY
TEMPER
MINIMUM
TENSILE
ULTIMATE
STRENGTH
(ksi)
MINIMUM
TENSILE YIELD
STRENGTH
(ksi)
MINIMUM %
ELONGATION
in 2 in. or 4D
TYPICAL BRINNELL
HARDNESS
(500 kgf load 10 mm ball)
–
201.0
T7
60.0
50.0
3.0
204.0
T4
45.0
28.0
6.0
–
242.0
O
23.0
A
A
70
242.0
T61
32.0
20.0
A
105
A242.0
T75
29.0
A
1.0
75
295.0
T4
29.0
13.0
6.0
60
295.0
T6
32.0
20.0
3.0
75
295.0
T62
36.0
28.0
A
95
295.0
T7
29.0
16.0
3.0
70
319.0
F
23.0
13.0
1.5
70
319.0
T5
25.0
A
A
80
319.0
T6
31.0
20.0
1.5
80
355.0
T51
25.0
18.0
A
65
355.0
T6
32.0
20.0
2.0
80
355.0
T71
30.0
22.0
A
75
C355.0
T6
36.0
25.0
2.5
–
356.0
F
19.0
9.5
2.0
55
356.0
T51
23.0
16.0
A
60
356.0
T6
30.0
20.0
3.0
70
356.0
T7
31.0
A
A
75
356.0
T71
25.0
18.0
3.0
60
A356.0
T6
34.0
24.0
3.5
80
A356.0
T61
35.0
26.0
1.0
–
443.0
F
17.0
7.0
3.0
40
B443.0
F
17.0
6.0
3.0
40
512.0
F
17.0
10.0
–
50
514.0
F
22.0
9.0
6.0
50
520.0
T4
42.0
22.0
12.0
75
535.0
F
35.0
18.0
9.0
70
705.0
T5
30.0
17.0 B
5.0
65
707.0
T7
37.0
30.0 B
1.0
80
710.0
T5
32.0
20.0
2.0
75
712.0
T5
34.0
25.0 B
4.0
75
713.0
T5
32.0
22.0
3.0
75
771.0
T5
42.0
38.0
1.5
100
771.0
T51
32.0
27.0
3.0
85
771.0
T52
36.0
30.0
1.5
85
771.0
T6
42.0
35.0
5.0
90
771.0
T71
48.0
45.0
2.0
120
850.0
T5
16.0
A
5.0
45
851.0
T5
17.0
A
3.0
45
852.0
T5
24.0
18.0
A
60
A = not required; B = to be determined only when specified by the purchaser
V-12
January 2005
Table 3M
MECHANICAL PROPERTY LIMITS FOR ALUMINUM SAND CASTING ALLOYS
ALLOY
TEMPER
MINIMUM
TENSILE
ULTIMATE
STRENGTH
(MPa)
MINIMUM
TENSILE YIELD
STRENGTH
(MPa)
MINIMUM %
ELONGATION
in 5D
TYPICAL BRINNELL
HARDNESS
(500 kgf load 10 mm ball)
201.0
T7
415
345
3.0
–
204.0
T4
310
195
6.0
–
242.0
O
160
A
A
70
242.0
T61
220
140
A
105
A242.0
T75
200
A
1.0
75
295.0
T4
200
90
6.0
60
295.0
T6
220
140
3.0
75
295.0
T62
250
195
A
95
295.0
T7
200
110
3.0
70
319.0
F
160
90
1.5
70
319.0
T5
170
A
A
80
319.0
T6
215
140
1.5
80
355.0
T51
170
125
A
65
355.0
T6
220
140
2.0
80
355.0
T71
205
150
A
75
C355.0
T6
250
170
2.5
–
356.0
F
130
65
2.0
55
356.0
T51
160
110
A
60
356.0
T6
205
140
3.0
70
356.0
T7
215
A
A
75
356.0
T71
170
125
3.0
60
A356.0
T6
235
165
3.5
80
A356.0
T61
245
180
1.0
–
443.0
F
115
50
3.0
40
B443.0
F
115
40
3.0
40
512.0
F
115
70
–
50
514.0
F
150
60
6.0
50
520.0
T4
290
150
12.0
75
535.0
F
240
125
9.0
70
705.0
T5
205
115 B
5.0
65
707.0
T7
255
205 B
1.0
80
710.0
T5
220
140
2.0
75
712.0
T5
235
170
B
4.0
75
713.0
T5
220
150
3.0
75
771.0
T5
290
260
1.5
100
771.0
T51
220
185
3.0
85
771.0
T52
250
205
1.5
85
771.0
T6
290
240
5.0
90
771.0
T71
330
310
2.0
120
850.0
T5
110
A
5.0
45
851.0
T5
115
A
3.0
45
852.0
T5
165
125
A
60
January 2005
V-13
A = not required; B = to be determined only when specified by the purchaser
Table 4
MECHANICAL PROPERTY LIMITS FOR ALUMINUM
PERMANENT MOLD CASTING ALLOYS
ALLOY
TEMPER
204.0
242.0
242.0
319.0
332.0
333.0
333.0
333.0
333.0
336.0
336.0
354.0
354.0
354.0
354.0
354.0
354.0
355.0
355.0
355.0
355.0
C355.0
C355.0
C355.0
356.0
356.0
356.0
A356.0
A356.0
A356.0
357.0
A357.0
A357.0
A357.0
359.0
359.0
359.0
359.0
359.0
359.0
443.0
B443.0
A444.0
A444.0
513.0
535.0
705.0
707.0
707.0
711.0
713.0
850.0
851.0
851.0
852.0
T4 separately cast specimens
T571
T61
F
T5
F
T5
T6
T7
T551
T65
T61 separately cast specimens
T61 castings, designated area
T61 castings, no location designated
T62 separately cast specimens
T62 castings, designated area
T62 castings, no location designated
T51
T62
T7
T71
T61 separately cast specimens
T61 castings, designated area
T61 castings, no location designated
F
T6
T71
T61 separately cast specimens
T61 castings, designated area
T61 castings, no location designated
T6
T61 separately cast specimens
T61 castings, designated area
T61 castings, no location designated
T61 separately cast specimens
T61 castings, designated area
T61 castings, no location designated
T62 separately cast specimens
T62 castings, designated area
T62 castings, no location designated
F
F
T4 separately cast specimens
T4 castings, designated area
F
F
T1 or T5
T1
T7
T1
T1 or T5
T5
T5
T6
T5
MINIMUM
TENSILE
ULTIMATE
STRENGTH
(ksi)
48.0
34.0
40.0
27.0
31.0
28.0
30.0
35.0
31.0
31.0
40.0
48.0
47.0
43.0
52.0
50.0
43.0
27.0
42.0
36.0
34.0
40.0
40.0
37.0
21.0
33.0
25.0
38.0
33.0
28.0
45.0
45.0
46.0
41.0
45.0
45.0
40.0
47.0
47.0
40.0
21.0
21.0
20.0
20.0
22.0
35.0
37.0
42.0
45.0
28.0
32.0
18.0
17.0
18.0
27.0
MINIMUM
TENSILE
YIELD
STRENGTH
(ksi) B
29.0
–
–
14.0
–
–
–
–
–
–
–
37.0
36.0
33.0
42.0
42.0
33.0
–
–
–
27.0
30.0
30.0
30.0
10.0
22.0
–
26.0
26.0
26.0
–
36.0
36.0
31.0
34.0
34.0
30.0
38.0
38.0
30.0
7.0
6.0
–
–
12.0
18.0
17.0
25.0
35.0
18.0
22.0
–
–
–
–
MINIMUM %
ELONGATION in
2 in. or 4D
8.0
A
A
2.5
A
A
A
A
A
A
A
3.0
3.0
2.0
2.0
2.0
2.0
A
A
A
A
3.0
3.0
1.0
3.0
3.0
3.0
5.0
5.0
3.0
3.0
3.0
3.0
3.0
4.0
4.0
3.0
3.0
3.0
3.0
2.0
2.5
20
20
2.5
8.0
10.0
4.0
3.0
7.0
4.0
8.0
3.0
8.0
3.0
TYPICAL
BRINNELL
HARDNESS
(500 kgf load
10 mm ball)
–
105
110
95
105
90
100
105
90
105
125
75
105
90
80
85 – 90
85
85
70
80 – 90
–
100
–
–
90
100
45
45
–
–
60
–
70
A = not required
B = to be determined only when specified by the purchaser
V-14
January 2005
Table 4M
MECHANICAL PROPERTY LIMITS FOR ALUMINUM
PERMANENT MOLD CASTING ALLOYS
ALLOY
TEMPER
204.0
242.0
242.0
319.0
332.0
333.0
333.0
333.0
333.0
336.0
336.0
354.0
354.0
354.0
354.0
354.0
354.0
355.0
355.0
355.0
355.0
C355.0
C355.0
C355.0
356.0
356.0
356.0
A356.0
A356.0
A356.0
357.0
A357.0
A357.0
A357.0
359.0
359.0
359.0
359.0
359.0
359.0
443.0
B443.0
A444.0
A444.0
513.0
535.0
705.0
707.0
707.0
711.0
713.0
850.0
851.0
851.0
852.0
T4 separately cast specimens
T571
T61
F
T5
F
T5
T6
T7
T551
T65
T61 separately cast specimens
T61 castings, designated area
T61 castings, no location designated
T62 separately cast specimens
T62 castings, designated area
T62 castings, no location designated
T51
T62
T7
T71
T61 separately cast specimens
T61 castings, designated area
T61 castings, no location designated
F
T6
T71
T61 separately cast specimens
T61 castings, designated area
T61 castings, no location designated
T6
T61 separately cast specimens
T61 castings, designated area
T61 castings, no location designated
T61 separately cast specimens
T61 castings, designated area
T61 castings, no location designated
T62 separately cast specimens
T62 castings, designated area
T62 castings, no location designated
F
F
T4 separately cast specimens
T4 castings, designated area
F
F
T1 or T5
T1
T7
T1
T1 or T5
T5
T5
T6
T5
MINIMUM
TENSILE
ULTIMATE
STRENGTH
(MPa)
331
234
276
186
214
193
207
241
214
214
276
331
324
297
359
344
297
186
290
248
234
276
276
255
145
228
172
262
228
193
310
310
317
283
310
310
276
324
324
276
145
145
138
138
152
241
255
290
310
193
221
124
117
124
186
MINIMUM
TENSILE
YIELD
STRENGTH
(MPa) B
200
–
–
97
–
–
–
–
–
–
–
255
248
228
290
290
228
–
–
–
186
207
207
207
69
152
–
179
179
179
–
248
248
214
234
234
207
262
262
207
49
41
–
–
83
124
117
173
241
124
152
–
–
–
–
MINIMUM %
ELONGATION in
50 mm or 4D
8.0
A
A
2.5
A
A
A
A
A
A
A
3.0
3.0
2.0
2.0
2.0
2.0
A
A
A
A
3.0
3.0
1.0
3.0
3.0
3.0
5.0
5.0
3.0
3.0
3.0
3.0
3.0
4.0
4.0
3.0
3.0
3.0
3.0
2.0
2.5
20
20
2.5
8.0
10.0
4.0
3.0
7.0
4.0
8.0
3.0
8.0
3.0
TYPICAL BRINNELL
HARDNESS
(500 kgf load
10 mm ball)
–
105
110
95
105
90
100
105
90
105
125
75
105
90
80
85 – 90
85
85
70
80 – 90
–
100
–
–
90
100
45
45
–
–
60
–
70
A = not required
B = to be determined only when specified by the purchaser
January 2005
V-15
Table 5
MECHANICAL PROPERTY LIMITS OF FASTENER ALLOYS ①
ALLOY AND
TEMPER
2017-T4
2024-T42
2117-T4
2219-T6
6053-T61
6061-T6
7050-T7
7075-T6
7075-T73
7178-T6
YIELD ②
ELONGATION ②
percent
min. in.
2 in. or 4D ③
ULTIMATE
SHEARING
STRENGTH
ksi min.
32.0
..
40.0
18.0
35.0
20.0
35.0
58.0
66.0
56.0
73.0
12
..
10
18
6
14
10
10
7
10
5
33.0
37.0
37.0
26.0
30.0
20.0
25.0
39.0
42.0
41.0
46.0
TENSILE STRENGTH
ksi min.
SPECIFIED
DIAMETER
in.
ULTIMATE
0.063–1.000
0.063–0.124
0.125–1.000
0.063–1.000
0.063–1.000
0.063–1.000
0.063–1.000
0.063–1.000
0.063–1.000
0.063–1.000
0.063–1.000
55.0
62.0
62.0
38.0
55.0
30.0
42.0
70.0
77.0
68.0
84.0
① Rivet and cold heading wire and rod, and the fasteners produced from it, shall upon proper heat treatment (T4 and T42 tempers) or heat treatment and aging
(T6, T61, T7 and T73 tempers) be capable of developing the properties presented in Table 5. Tensile tests are preferred for the rivet and cold heading wire and
rod, and shear tests for the fasteners made from it.
② The measurement of elongation and yield strength is not required for wire less than 0.125 inch in thickness or diameter.
③ D represents specimen diameter.
Table 5M
MECHANICAL PROPERTY LIMITS OF FASTENER ALLOYS ①
ALLOY AND
TEMPER
2017-T4
2024-T42
2117-T4
2219-T6
6053-T61
6061-T6
7050-T7
7075-T6
7075-T73
7178-T6
SPECIFIED
DIAMETER
mm
ULTIMATE
YIELD ②
50 mm
5D (5.65 √A )
ULTIMATE
SHEARING
STRENGTH
MPa min
1.60–25.00
1.60–3.15
3.15–25.00
1.60–25.00
1.60–25.00
1.60–25.00
1.60–25.00
1.60–25.00
1.60–25.00
1.60–25.00
1.60–25.00
380
425
425
260
380
205
290
485
530
470
580
220
..
255
125
240
135
240
400
455
385
500
12
..
10
18
6
14
10
10
7
10
5
10
..
9
16
5
12
9
9
6
9
4
225
255
255
180
205
135
170
270
290
280
315
TENSILE STRENGTH
MPa min
ELONGATION ②
percent min
__
① Rivet and cold heading wire and rod, and the fasteners produced from it, shall upon proper heat treatment (T4 and T42 tempers) or heat treatment and aging
(T6, T61, T7 and T73 tempers) be capable of developing the properties presented in Table 5. Tensile tests are preferred for the rivet and cold heading wire and
rod, and shear tests for the fasteners made from it.
② The measurement of elongation and yield strength is not required for wire 3.2 mm and less in thickness or diameter.
V-16
January 2005
Table 6
TYPICAL MECHANICAL PROPERTIES ① ②
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particu-
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
TENSION
ALLOY
AND
TEMPER
STRENGTH
ksi
HARDNESS
SHEAR
FATIGUE
MODULUS
BRINNELL
NUMBER
ULTIMATE
SHEARING
STRENGTH
ENDURANCE ③
Limit
MODULUS ④
OF
ELASTICITY
ELONGATION
percent in 2 in.
YIELD
1
⁄16 in.
Thick
Specimen
1
⁄2 in.
Diameter
Specimen
500 kg load
10 mm ball
ksi
ksi
ksi × 103
1060-O
1060-H12
1060-H14
1060-H16
1060-H18
10
12
14
16
19
4
11
13
15
18
43
16
12
8
6
..
..
..
..
..
19
23
26
30
35
7
8
9
10
11
3
4
5
6.5
6.5
10.0
10.0
10.0
10.0
10.0
1100-O
1100-H12
1100-H14
1100-H16
1100-H18
13
16
18
21
24
5
15
17
20
22
35
12
9
6
5
23
28
32
38
44
9
10
11
12
13
5
6
7
9
9
10.0
10.0
10.0
10.0
10.0
1350-O
1350-H12
1350-H14
1350-H16
1350-H19
12
14
16
18
27
4
12
14
16
24
..
..
..
..
..
45
25
20
17
15
..⑤
..
..
..
..⑥
..
..
..
..
..
8
9
10
11
15
..
..
..
..
7
10.0
10.0
10.0
10.0
10.0
2011-T3
2011-T8
55
59
43
45
..
..
15
12
95
100
32
35
18
18
10.2
10.2
2014-O
2014-T4, T451
2014-T6, T651
27
62
70
14
42
60
..
..
..
18
20
13
45
105
135
18
38
42
13
20
18
10.6
10.6
10.6
25
63
61
68
10
40
37
60
21
20
22
10
..
..
..
..
..
..
..
..
18
37
37
41
..
..
..
..
10.5
10.5
10.5
10.5
2017-O
2017-T4, T451
26
62
10
40
45
105
18
38
13
18
10.5
10.5
2018-T61
61
46
IG
ES
D
R
22
22
..
12
120
39
17
10.8
FO
Alclad 2014-O
Alclad 2014-T3
Alclad 2014-T4, T451
Alclad 2014-T6, T651
N
ULTIMATE
27
70
68
72
11
50
47
57
20
18
20
13
22
..
19
..
47
120
120
130
18
41
41
42
13
20
20
18
10.6
10.6
10.6
10.6
26
65
64
67
65
70
11
45
42
63
60
66
20
18
19
11
6
6
..
..
..
..
..
..
..
..
..
..
..
..
18
40
40
41
40
42
..
..
..
..
..
..
10.6
10.6
10.6
10.6
10.6
10.6
2025-T6
58
37
..
19
110
35
18
10.4
2036-T4
49
28
24
..
..
..
18 ⑨
10.3
2024-O
2024-T3
2024-T4, T351
2024-T361 ⑦
O
T
Alclad 2024-O
Alclad 2024-T3
Alclad 2024-T4, T351
Alclad 2024-T361 ⑦
Alclad 2024-T81, T851
Alclad 2024-T861 ⑦
..
..
43
24
..
27
70
28
14
10.3
70
64
..
8
..
..
..
10.6
N
2117-T4
2124-T851
2218-T72
48
37
..
11
95
30
..
10.8
2219-O
2219-T42
2219-T31, T351
2219-T37
2219-T62
2219-T81, T851
2219-T87
25
52
52
57
60
66
69
11
27
36
46
42
51
57
18
20
17
11
10
10
10
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
15
15
15
10.6
10.6
10.6
10.6
10.6
10.6
10.6
2618-T61
64
54
..
10
115
38
18
10.8
3003-O
3003-H12
3003-H14
3003-H16
3003-H18
16
19
22
26
29
6
18
21
25
27
30
10
8
5
4
40
20
16
14
10
28
35
40
47
55
11
12
14
15
16
7
8
9
10
10
10.0
10.0
10.0
10.0
10.0
For all numbered footnotes, see last page of this Table.
January 2005
V-17
Table 6
TYPICAL MECHANICAL PROPERTIES ① ② (Continued)
TENSION
ALLOY
AND
TEMPER
STRENGTH
ksi
ELONGATION
percent in 2 in.
HARDNESS
SHEAR
FATIGUE
MODULUS
BRINNELL
NUMBER
ULTIMATE
SHEARING
STRENGTH
ENDURANCE ③
Limit
MODULUS ④
OF
ELASTICITY
YIELD
1
⁄16 in.
Thick
Specimen
1
⁄2 in.
Diameter
Specimen
500 kg load
10 mm ball
ksi
ksi
ksi × 103
16
19
22
26
29
6
18
21
25
27
30
10
8
5
4
40
20
16
14
10
..
..
..
..
..
11
12
14
15
16
..
..
..
..
..
10.0
10.0
10.0
10.0
10.0
26
31
35
38
41
10
25
29
33
36
20
10
9
5
5
25
17
12
9
6
45
52
63
70
77
16
17
18
20
21
14
15
15
16
16
10.0
10.0
10.0
10.0
10.0
26
31
35
38
41
10
25
29
33
36
20
10
9
5
5
25
17
12
9
6
..
..
..
..
..
16
17
18
20
21
..
..
..
..
..
10.0
10.0
10.0
10.0
10.0
3105-O
3105-H12
3105-H14
3105-H16
3105-H18
3105-H22
3105-H24
3105-H25
3105-H26
3105-H28
17
22
25
28
31
24
26
26
24
26
8
19
22
25
28
20
22
23
24
26
24
7
5
4
3
11
10
8
9
8
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
12
14
15
16
17
14
15
15
16
17
..
..
..
..
..
..
..
..
..
..
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
4032-T6
55
46
..
5005-O
5005-H12
5005-H14
5005-H16
5005-H18
5005-H32
5005-H34
5005-H36
5005-H38
18
20
23
26
29
20
23
26
29
6
19
22
25
28
17
20
24
27
25
10
6
5
4
11
8
6
5
Alclad 3003-O
Alclad 3003-H12
Alclad 3003-H14
Alclad 3003-H16
Alclad 3003-H18
3004-O
3004-H32
3004-H34
3004-H36
3004-H38
38
16
11.4
28
..
..
..
..
36
41
46
51
11
14
14
15
16
14
14
15
16
..
..
..
..
..
..
..
..
..
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
5050-O
5050-H32
5050-H34
5050-H36
5050-H38
FO
R
120
21
25
28
30
32
8
21
24
26
29
24
9
8
7
6
..
..
..
..
..
36
46
53
58
63
15
17
18
19
20
12
13
13
14
14
10.0
10.0
10.0
10.0
10.0
O
T
9
..
..
..
..
..
..
..
..
..
5052-O
5052-H32
5052-H34
5052-H36
5052-H38
28
33
38
40
42
13
28
31
35
37
25
12
10
8
7
30
18
14
10
8
47
60
68
73
77
18
20
21
23
24
16
17
18
19
20
10.2
10.2
10.2
10.2
10.2
N
Alclad 3004-O
Alclad 3004-H32
Alclad 3004-H34
Alclad 3004-H36
Alclad 3004-H38
D
ES
IG
N
ULTIMATE
5056-O
5056-H18
5056-H38
42
63
60
22
59
50
..
..
..
35
10
15
65
105
100
26
34
32
20
22
22
10.3
10.3
10.3
5083-O
5083-H116 ⑪
5083-H321
42
46
46
21
33
33
..
..
..
22
16
16
..
..
..
25
..
..
..
23
23
10.3
10.3
10.3
5086-O
5086-H32
5086-H116 ⑪
5086-H34
5086-H112
38
42
42
47
39
17
30
30
37
19
22
12
12
10
14
..
..
..
..
..
..
..
..
..
..
23
..
..
27
..
..
..
..
..
..
10.3
10.3
10.3
10.3
10.3
5154-O
5154-H32
5154-H34
5154-H36
5154-H38
5154-H112
35
39
42
45
48
35
17
30
33
36
39
17
27
15
13
12
10
25
..
..
..
..
..
..
58
67
73
78
80
63
22
22
24
26
28
..
17
18
19
20
21
17
10.2
10.2
10.2
10.2
10.2
10.2
For all numbered footnotes, see last page of this Table.
V-18
January 2005
Table 6
TYPICAL MECHANICAL PROPERTIES ① ② (Continued)
TENSION
ALLOY
AND
TEMPER
STRENGTH
ksi
ELONGATION
percent in 2 in.
HARDNESS
SHEAR
FATIGUE
MODULUS
BRINNELL
NUMBER
ULTIMATE
SHEARING
STRENGTH
ENDURANCE ③
Limit
MODULUS ④
OF
ELASTICITY
YIELD
1
⁄16 in.
Thick
Specimen
1
⁄2 in.
Diameter
Specimen
500 kg load
10 mm ball
ksi
ksi
ksi × 103
5252-H25
5252-H38, H28
34
41
25
35
11
5
..
..
68
75
21
23
..
..
10.0
10.0
5254-O
5254-H32
5254-H34
5254-H36
5254-H38
5254-H112
35
39
42
45
48
35
17
30
33
36
39
17
27
15
13
12
10
25
..
..
..
..
..
..
58
67
73
78
80
63
22
22
24
26
28
..
17
18
19
20
21
17
10.2
10.2
10.2
10.2
10.2
10.2
5454-O
5454-H32
5454-H34
5454-H111
5454-H112
36
40
44
38
36
17
30
35
26
18
22
10
10
14
18
..
..
..
..
..
62
73
81
70
62
23
24
26
23
23
..
..
..
..
..
10.2
10.2
10.2
10.2
10.2
5456-O
5456-H25
5456-H116 ⑪
5456-H321 ⑪
45
45
51
51
23
24
37
37
..
..
..
..
24
22
16
16
..
..
90
90
..
..
30
30
..
..
..
..
10.3
10.3
10.3
10.3
5457-O
5457-H25
5457-H38, H28
19
26
30
7
23
27
22
12
6
..
..
..
32
48
55
12
16
18
..
..
..
10.0
10.0
10.0
5652-O
5652-H32
5652-H34
5652-H36
5652-H38
28
33
38
40
42
13
28
31
35
37
25
12
10
8
7
30
18
14
10
8
47
60
68
73
77
18
20
21
23
24
16
17
18
19
20
10.2
10.2
10.2
10.2
10.2
5657-H25
5657-H38, H28
23
28
20
24
12
7
..
..
40
50
12
15
..
..
10.0
10.0
6061-O
6061-T4, T451
6061-T6, T651
18
35
45
8
21
40
25
22
12
30
25
17
30
65
95
12
24
30
9
14
14
10.0
10.0
10.0
17
33
42
7
19
37
25
22
12
..
..
..
..
..
..
11
22
27
..
..
..
10.0
10.0
10.0
13
22
25
27
35
37
30
42
7
13
13
21
31
35
27
39
..
20
22
12
12
9
10
12
..
..
..
..
..
..
..
..
25
42
..
60
73
82
70
95
10
14
..
17
22
22
18
27
8
9
..
10
10
..
..
..
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
22
52
57
12
30
52
..
..
..
18
18
12
43
90
120
14
29
34
..
..
16
10.0
10.0
10.0
6070-T6
55
51
10
..
..
34
14
10.0
6101-H111
6101-T6
14
32
11
28
..
15 ⑧
..
..
..
71
..
20
..
..
10.0
10.0
6063-O
6063-T1
6063-T4
6063-T5
6063-T6
6063-T83
6063-T831
6063-T832
O
T
6066-O
6066-T4, T451
6066-T6. T651
FO
R
Alclad 6061-O
Alclad 6061-T4, T451
Alclad 6061-T6, T651
D
ES
IG
N
ULTIMATE
58
55
..
10
120
35
13
10.0
36
45
22
41
20
14
..
..
..
95
..
29
..
13
10.0
10.0
6463-T1
6463-T5
6463-T6
22
27
35
13
21
31
20
12
12
..
..
..
42
60
74
14
17
22
10
10
10
10.0
10.0
10.0
7049-T73
7049-T7352
75
75
65
63
..
..
12
11
135
135
44
43
..
..
10.4
10.4
7050-T73510,
T73511
7050-T7451 ⑩
7050-T7651
72
76
80
63
68
71
..
..
..
12
11
11
..
..
..
..
44
47
..
..
..
10.4
10.4
10.4
7075-O
7075-T6, T651
33
83
15
73
17
11
16
11
60
150
22
48
..
23
10.4
10.4
N
6262-T9
6351-T4
6351-T6
For all numbered footnotes, see last page of this Table.
January 2005
V-19
Table 6
TYPICAL MECHANICAL PROPERTIES ① ② (Continued)
TENSION
ALLOY
AND
TEMPER
STRENGTH
ksi
ELONGATION
percent in 2 in.
HARDNESS
SHEAR
FATIGUE
MODULUS
BRINNELL
NUMBER
ULTIMATE
SHEARING
STRENGTH
ENDURANCE ③
Limit
MODULUS ④
OF
ELASTICITY
YIELD
1
⁄16 in.
Thick
Specimen
1
⁄2 in.
Diameter
Specimen
500 kg load
10 mm ball
ksi
ksi
ksi × 103
32
76
14
67
17
11
..
..
..
..
22
46
..
..
10.4
10.4
7175-T74
76
66
..
11
135
42
23
10.4
7178-O
7178-T6, T651
7178-T76, T7651
33
88
83
15
78
73
15
10
..
16
11
11
..
..
..
..
..
..
..
..
..
10.4
10.4
10.3
Alclad 7178-O
Alclad 7178-T6, T651
32
81
14
71
16
10
..
..
..
..
..
..
..
..
10.4
10.4
7475-T61
7475-T651
7475-T7351
7475-T761
7475-T7651
82
85
72
75
77
71
74
61
65
67
11
..
..
12
..
..
13
13
..
12
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
10.2
10.4
10.4
10.2
10.4
Alclad 7475-T61
Alclad 7475-T761
75
71
66
61
11
12
..
..
..
..
..
..
..
..
10.2
10.2
8176-H24
17
14
15
..
10
..
10.0
Alclad 7075-O
Alclad 7075-T6, T651
D
ES
IG
N
ULTIMATE
..
⑦ Tempers T361 and T861 were formerly designated T36 and T86,
respectively.
⑧ Based on ¼ in. thick specimen.
⑨ Based on 107 cycles using flexural type testing of sheet specimens.
⑩ T7451, although not previously registered, has appeared in literature and
in some specifications as T73651.
⑪ 5xxx products in the -H116 and -H32X tempers have similar mechanical
properties; however, production methods and testing requirements differ,
and these tempers are not interchangeable. The -H116 temper is typically
used in marine and other applications requiring demonstrations of exfoliation resistance.
N
O
T
FO
R
① The mechanical property limits are listed by major product in the “Standards Section” of Aluminum Standards and Data 2003.
② The indicated typical mechanical properties for all except O temper
material are higher than the specified minimum properties. For O temper
products typical ultimate and yield values are slightly lower than specified
(maximum) values.
③ Based on 500,000,000 cycles of completely reversed stress using the
R.R. Moore type of machine and specimen.
④ Average of tension and compression moduli. Compression modulus is
about 2% greater than tension modulus.
⑤ 1350-O wire will have an elongation of approximately 23% in 10 inches.
⑥ 1350-H19 wire will have an elongation of approximately 1½% in 10 inches.
V-20
January 2005
Table 6M
TYPICAL MECHANICAL PROPERTIES ① ②
TENSION
N
in 5D
SHEAR
FATIGUE
BRINNELL
NUMBER
ULTIMATE
SHEARING
STRENGTH
ENDURANCE ③
LIMIT
MPa
MPa
50
55
60
70
75
60
70
75
85
90
55
60
70
75
105
220
240
125
260
290
125
255
255
285
125
260
270
125
285
285
290
125
275
275
285
275
290
240
205
195
..
205
..
..
..
..
..
..
..
260
75
85
95
105
110
20
30
35
45
45
35
40
50
60
60
..
..
..
..
50
125
125
90
140
125
ULTIMATE
YIELD
1.60 mm
Thick
Specimen
12.5 mm
Diameter
Specimen
500 kgf load
10 mm ball
70
85
100
115
130
90
110
125
145
165
85
95
110
125
185
380
405
185
425
485
170
435
421
470
180
425
420
185
485
472
495
180
450
440
460
450
485
400
340
295
485
330
170
360
360
395
415
455
475
440
110
130
150
175
200
30
75
90
105
125
35
105
115
140
150
30
85
95
110
165
295
310
95
290
415
70
275
255
415
70
275
315
75
345
325
395
75
310
290
365
415
455
255
195
165
440
255
75
185
250
315
290
350
395
370
40
125
145
170
185
43
16
12
8
6
35
12
9
6
5
..
..
..
..
..
..
..
..
..
..
21
20
22
10
..
..
..
20
18
20
13
20
18
19
11
6
6
..
24
..
..
..
18
20
17
11
10
10
10
..
30
10
8
5
4
..
..
..
..
..
42
22
18
15
13
. .⑤
..
..
..
. .⑥
19
23
26
30
35
23
28
32
38
44
..
..
..
..
..
95
100
45
105
135
..
..
..
..
45
105
120
47
120
120
130
..
..
..
..
..
..
110
..
70
..
95
..
..
..
..
..
..
..
115
28
35
40
47
55
O
T
Alclad 2024-O
Alclad 2024-T3
Alclad 2024-T4, T351
Alclad 2024-T361 ⑦
Alclad 2024-T81, T851
Alclad 2024-T861 ⑦
2025-T6
2036-T4
2117-T4
2124-T851
2218-T72
2219-O
2219-T42
2219-T31, T351
2219-T37
2219-T62
2219-T81, T851
2219-T87
2618-T61
3003-O
3003-H12
3003-H14
3003-H16
3003-H18
in 50 mm
HARDNESS
D
ES
IG
N
1060-O
1060-H12
1060-H14
1060-H16
1060-H18
1100-O
1100-H12
1100-H14
1100-H16
1100-H18
1350-O
1350-H12
1350-H14
1350-H16
1350-H19
2011-T3
2011-T8
2014-O
2014-T4, T451
2014-T6, T651
Alclad 2014-O
Alclad 2014-T3
Alclad 2014-T4, T451
Alclad 2014-T6, T651
2017-O
2017-T4, T451
2018-T61
2024-O
2024-T3
2024-T4, T351
2024-T361 ⑦
ELONGATION
percent
FO
R
ALLOY
AND
TEMPER
STRENGTH
MPa
13
10
16
18
11
..
..
..
..
20
20
10
20
..
17
..
..
..
..
..
..
..
17
..
24
8
9
..
..
..
..
..
..
..
10
37
18
14
12
9
..
..
..
..
90
125
115
90
140
140
125
..
..
..
..
..
..
125
125 ⑨
95
..
..
..
..
..
..
105
105
105
90
50
55
60
70
70
MODULUS
MODULUS ④
OF
ELASTICITY
MPa × 103
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
70
70
73
73
73
73
73
73
73
73
73
74
73
73
73
73
73
73
73
73
73
73
72
71
71
73
74
73
73
73
73
73
73
73
73
69
69
69
69
69
For all numbered footnotes, see last page of this Table.
January 2005
V-21
Table 6M
TYPICAL MECHANICAL PROPERTIES ① ② (Continued)
TENSION
ALLOY
AND
TEMPER
STRENGTH
MPa
ELONGATION
percent
in 50 mm
in 5D
HARDNESS
SHEAR
FATIGUE
BRINNELL
NUMBER
ULTIMATE
SHEARING
STRENGTH
ENDURANCE ③
LIMIT
MPa
MPa
MODULUS
MODULUS ④
OF
ELASTICITY
MPa × 103
YIELD
1.60 mm
Thick
Specimen
12.5 mm
Diameter
Specimen
500 kgf load
10 mm ball
Alclad 3003-O
Alclad 3003-H12
Alclad 3003-H14
Alclad 3003-H16
Alclad 3003-H18
110
130
150
175
200
40
125
145
170
185
30
10
8
5
4
37
18
14
12
9
..
..
..
..
..
75
85
95
105
110
..
..
..
..
..
69
69
69
69
69
3004-O
3004-H32
3004-H34
3004-H36
3004-H38
180
215
240
260
285
70
170
200
230
250
20
10
9
5
5
22
15
10
8
5
45
52
63
70
77
110
115
125
140
145
95
105
105
110
110
69
69
69
69
69
Alclad 3004-O
Alclad 3004-H32
Alclad 3004-H34
Alclad 3004-H36
Alclad 3004-H38
180
215
240
260
285
70
170
200
230
250
20
10
9
5
5
22
15
10
8
5
..
..
..
..
..
110
115
125
140
145
..
..
..
..
..
69
69
69
69
69
3105-O
3105-H12
3105-H14
3105-H16
3105-H18
3105-H22
3105-H24
3105-H25
3105-H26
3105-H28
115
150
170
195
215
165
180
185
195
205
55
130
150
170
195
140
150
160
165
180
24
7
5
4
3
11
10
9
9
8
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
85
95
105
110
115
95
105
105
110
115
..
..
..
..
..
..
..
..
..
..
69
69
69
69
69
69
69
69
69
69
4032-T6
380
315
..
5005-O
5005-H12
5005-H14
5005-H16
5005-H18
5005-H32
5005-H34
5005-H36
5005-H38
125
140
160
180
200
140
160
180
200
40
130
150
170
195
115
140
165
185
25
10
6
5
4
11
8
6
5
5050-O
5050-H32
5050-H34
5050-H36
5050-H38
145
170
190
205
220
55
145
165
180
200
5052-O
5052-H32
5052-H34
5052-H36
5052-H38
195
230
260
275
290
5056-O
5056-H18
5056-H38
D
ES
IG
N
ULTIMATE
120
260
110
79
28
..
..
..
..
36
41
46
51
75
95
95
105
110
95
95
105
110
..
..
..
..
..
..
..
..
..
69
69
69
69
69
69
69
69
69
24
9
8
7
6
..
..
..
..
..
36
46
53
58
63
105
115
125
130
140
85
90
90
95
95
69
69
69
69
69
90
195
215
240
255
25
12
10
8
7
27
16
12
9
7
47
60
68
73
77
125
140
145
160
165
110
115
125
130
140
70
70
70
70
70
290
435
415
150
405
345
..
..
..
32
9
13
65
105
100
180
235
220
140
150
150
71
71
71
5083-O
5083-H116 ⑪
5083-H321
290
315
315
145
230
230
..
..
..
20
14
14
..
..
..
170
..
..
..
160
160
71
71
71
5086-O
5086-H32
5086-H116 ⑪
5086-H34
5086-H112
260
290
290
325
270
115
205
205
255
130
22
12
12
10
14
..
..
..
..
..
..
..
..
..
..
165
..
..
185
..
..
..
..
..
..
71
71
71
71
71
N
O
T
FO
R
9
..
..
..
..
..
..
..
..
..
For all numbered footnotes, see last page of this Table.
V-22
January 2005
Table 6M
TYPICAL MECHANICAL PROPERTIES ① ② (Continued)
TENSION
N
in 50 mm
in 5D
HARDNESS
SHEAR
FATIGUE
MODULUS
BRINNELL
NUMBER
ULTIMATE
SHEARING
STRENGTH
ENDURANCE ③
LIMIT
MPa
MPa
MODULUS ④
OF
ELASTICITY
MPa × 103
YIELD
1.60 mm
Thick
Specimen
12.5 mm
Diameter
Specimen
500 kgf load
10 mm ball
240
270
290
310
330
240
235
285
240
270
290
310
330
240
250
275
305
260
250
115
205
230
250
270
115
170
240
115
205
230
250
270
115
115
205
240
180
125
27
15
13
12
10
25
11
5
27
15
13
12
10
25
22
10
10
14
18
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
58
67
73
78
80
63
68
75
58
67
73
78
80
63
62
73
81
70
62
150
150
165
180
195
..
145
160
150
150
165
180
195
..
160
165
180
160
160
115
125
130
140
145
115
..
..
115
125
130
140
145
115
..
..
..
..
..
70
70
70
70
70
70
69
69
70
70
70
70
70
70
70
70
70
70
70
310
310
350
160
165
255
..
..
..
22
20
14
..
..
90
..
..
205
..
..
..
71
71
71
130
180
205
195
230
260
275
290
160
195
125
240
310
115
230
290
90
150
170
185
240
255
205
290
150
360
395
380
95
220
400
250
310
150
185
240
50
160
185
90
195
215
240
255
140
165
55
145
275
50
130
255
50
90
90
145
215
240
185
270
85
205
360
350
75
195
380
150
285
90
145
215
22
12
6
25
12
10
8
7
12
7
25
22
12
25
22
12
..
20
22
12
12
9
10
12
..
..
..
10
..
15 ⑧
..
20
14
20
12
12
..
..
..
27
16
12
9
7
..
..
27
22
15
..
..
..
..
..
..
..
..
..
..
..
16
16
10
..
..
..
9
..
..
..
..
..
32
48
55
47
60
68
73
77
40
50
30
65
95
..
..
..
25
42
..
60
73
82
70
95
43
90
120
..
..
71
120
..
95
42
60
74
85
110
125
125
140
145
160
165
95
105
85
165
205
75
150
185
70
95
..
115
150
150
125
185
95
200
235
235
..
140
240
..
200
95
115
150
..
..
..
110
115
125
130
140
..
..
60
95
95
..
..
..
55
60
..
70
70
..
..
..
..
..
110
95
..
..
90
..
90
70
70
70
69
69
69
70
70
70
70
70
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
D
ES
IG
N
ULTIMATE
O
T
5154-O
5154-H32
5154-H34
5154-H36
5154-H38
5154-H112
5252-H25
5252-H38, H28
5254-O
5254-H32
5254-H34
5254-H36
5254-H38
5254-H112
5454-O
5454-H32
5454-H34
5454-H111
5454-H112
5456-O
5456-H25
5456-H321,
H116
5457-O
5457-H25
5457-H38, H28
5652-O
5652-H32
5652-H34
5652-H36
5652-H38
5657-H25
5657-H38, H28
6061-O
6061-T4, T451
6061-T6, T651
Alclad 6061-O
Alclad 6061-T4, T451
Alclad 6061-T6, T651
6063-O
6063-T1
6063-T4
6063-T5
6063-T6
6063-T83
6063-T831
6063-T832
6066-O
6066-T4, T451
6066-T6. T651
6070-T6
6101-H111
6101-T6
6262-T9
6351-T4
6351-T6
6463-T1
6463-T5
6463-T6
ELONGATION
percent in 2 in.
FO
R
ALLOY
AND
TEMPER
STRENGTH
ksi
For all numbered footnotes, see last page of this Table.
January 2005
V-23
Table 6M
TYPICAL MECHANICAL PROPERTIES ① ② (Continued)
TENSION
ALLOY
AND
TEMPER
STRENGTH
MPa
ELONGATION
percent in 2 in.
in 50 mm
in 5D
HARDNESS
SHEAR
FATIGUE
BRINNELL
NUMBER
ULTIMATE
SHEARING
STRENGTH
ENDURANCE ③
LIMIT
MPa
MPa
MODULUS
MODULUS ④
OF
ELASTICITY
MPa × 103
YIELD
1.60 mm
Thick
Specimen
12.5
Diameter
Specimen
500 kgf load
10 mm ball
7049-T73
7049-T7352
515
515
450
435
..
..
10
9
135
135
305
295
..
..
72
72
7050-T73510,
T73511
7050-T7451 ⑩
7050-T7651
495
525
550
435
470
490
..
..
..
11
10
10
..
..
..
..
305
325
..
..
..
72
72
72
7075-O
7075-T6, T651
230
570
105
505
17
11
14
9
60
150
150
330
..
160
72
72
Alclad 7075-O
Alclad 7075-T6, T651
220
525
95
460
17
11
..
..
..
..
150
315
..
..
72
72
7175-T74
525
455
..
7178-O
7178-T6, T651
7178-T76, T7651
230
605
570
105
540
505
15
10
..
220
560
95
460
16
10
7475-T61
7475-T651
7475-T7351
7475-T761
7475-T7651
565
585
495
515
530
490
510
420
450
460
11
..
..
12
..
Alclad 7475-T61
Alclad 7475-T761
515
490
455
420
11
12
8176-H24
160
95
15
Alclad 7178-O
Alclad 7178-T6, T651
D
ES
IG
N
ULTIMATE
135
290
160
160
72
..
..
..
..
..
..
..
..
..
72
72
71
..
..
..
..
..
..
..
..
72
72
..
13
13
..
12
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
70
72
72
70
72
..
..
..
..
..
..
..
..
70
70
..
..
70
..
69
⑦ Tempers T361 and T861 were formerly designated T36 and T86, respectively.
⑧ Based on 6.3 mm. thick specimen.
⑨ Based on 107 cycles using flexural type testing of sheet specimens.
⑩ T7451, although not previously registered, has appeared in literature and
in some specifications as T73651.
⑪ 5xxx products in the -H116 and -H32X tempers have similar mechanical
properties; however, production methods and testing requirements differ,
and these tempers are not interchangeable. The -H116 temper is typically
used in marine and other applications requiring demonstrations of exfoliation resistance.
N
O
T
FO
R
① The mechanical property limits are listed by major product in the “Standards Section” of Aluminum Standards and Data, 2003.
② The indicated typical mechanical properties for all except O temper
material are higher than the specified minimum properties. For O temper
products typical ultimate and yield values are slightly lower than specified
(maximum) values.
③ Based on 500,000,000 cycles of completely reversed stress using the
R.R. Moore type of machine and specimen.
④ Average of tension and compression moduli. Compression modulus is
about 2% greater than tension modulus.
⑤ 1350-O wire will have an elongation of approximately 23% in 250 mm.
⑥ 1350-H19 wire will have an elongation of approximately 1½% in 250 mm.
10
14
9
9
V-24
January 2005
Table 7
TYPICAL PHYSICAL PROPERTIES—
THERMAL AND ELECTRICAL
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuAVERAGE ①
COEFFICIENT
OF THERMAL
EXPANSION
MELTING
RANGE ② ③
APPROX.
68° TO 212°F
per °F
°F
1060
13.1
1195–1215
1100
13.1
1190–1215
ALLOY
TEMPER
lar product or size. These data are intended only as a
basis for comparing alloys and tempers and should not
be specified as engineering requirements or used for
design purposes.
THERMAL
CONDUCTIVITY
AT 77°F
ELECTRICAL
CONDUCTIVITY
AT 68°F
Percent of International
Annealed Copper Standard
ELECTRICAL
RESISTIVITY
AT 68°F
English
Units ④
Equal
Volume
Equal
Weight
Ohm—Cir.
Mil/Foot
O
H18
O
H18
All
1625
1600
1540
1510
1625
62
61
59
57
62
204
201
194
187
204
17
17
18
18
17
T3
T8
O
T4
T6
O
T4
1050
1190
1340
930
1070
1340
930
39
45
50
34
40
50
34
123
142
159
108
127
159
108
27
23
21
31
26
21
31
T61
O
T3, T4, T361
T6, T81, T861
T6
T4
1070
1340
840
1050
1070
1100
40
50
30
38
40
41
127
160
96
122
128
135
26
21
35
27
26
25
13.2
1195–1215
12.7
1005–1190 ⑥
2014
12.8
945–1180 ⑤
2017
13.1
955–1185 ⑤
2018
2024
12.4
12.9
945–1180 ⑥
935–1180 ⑤
2025
2036
12.6
13.0
970–1185 ⑤
1030–1200 ⑥
2117
2124
2218
2219
13.2
12.7
12.4
12.4
1030–1200 ⑥
935–1180 ⑤
940–1175 ⑤
1010–1190 ⑤
T4
T851
T72
O
T31, T37
T6, T81, T87
1070
1055
1070
1190
780
840
40
38
40
44
28
30
130
122
126
138
88
94
26
27
26
24
37
35
2618
3003
12.4
12.9
1020–1180
1190–1210
T6
O
H12
H14
H18
All
1020
1340
1130
1100
1070
1130
37
50
42
41
40
42
120
163
137
134
130
137
28
21
25
25
26
25
All
1190
45
148
23
O
T6
O
All
1070
960
1130
1190
40
35
42
45
132
116
140
151
26
30
25
23
13.3
13.1
4032
10.8
4043
4045
12.3
11.7
12.0
13.2
13.2
13.2
13.4
5083
5086
1165–1210
1175–1210
990–1060 ⑤
1065–1170
1065–1110
1070–1135
All
1250
47
158
25
1170–1210
1155–1205
1125–1200
1055–1180
All
All
All
O
H38
1390
1340
960
810
750
52
50
35
29
27
172
165
116
98
91
20
21
30
36
38
13.2
13.2
1095–1180
1085–1185
O
All
810
870
29
31
98
104
36
33
5154
5252
5254
5356
13.3
13.2
13.3
13.4
1100–1190
1125–1200
1100–1190
1060–1175
All
All
All
O
870
960
870
810
32
35
32
29
107
116
107
98
32
30
32
36
5454
13.1
1115–1195
5456
5457
5652
5657
13.3
13.2
13.2
13.2
1055–1180
1165–1210
1125–1200
1180–1215
O
H38
O
All
All
All
930
930
810
1220
960
1420
34
34
29
46
35
54
113
113
98
153
116
180
31
31
36
23
30
19
6005
13.0
1125–1210 ⑥
T1
T5
1250
1310
47
49
155
161
22
21
N
O
T
4343
5005
5050
5052
5056
FO
R
3004
3105
D
ES
IG
N
1350
2011
For all numbered footnotes, see last page of this Table.
January 2005
V-25
Table 7
TYPICAL PHYSICAL PROPERTIES—
THERMAL AND ELECTRICAL (Continued)
AVERAGE ①
COEFFICIENT
OF THERMAL
EXPANSION
MELTING
RANGE ② ③
APPROX.
68° TO 212°F
per °F
°F
6053
12.8
1070–1205 ⑥
6061
13.1
6063
6066
ALLOY
TEMPER
ELECTRICAL
CONDUCTIVITY
AT 68°F
Percent of International
Annealed Copper Standard
ELECTRICAL
RESISTIVITY
AT 68°F
Equal
Volume
Equal
Weight
Ohm—Cir.
Mil/Foot
O
T4
T6
1190
1070
1130
45
40
42
148
132
139
23
26
25
1080–1205 ⑥
O
T4
T6
1250
1070
1160
47
40
43
155
132
142
22
26
24
13.0
1140–1210
O
T1
T5
T6, T83
1510
1340
1450
1390
58
50
55
53
191
165
181
175
18
21
19
20
12.9
1045–1195 ⑤
6070
..
1050–1200 ⑤
O
T6
T6
1070
1020
1190
40
37
44
132
122
145
26
28
24
6101
13.0
1150–1210
T6
T61
T63
T64
T65
1510
1540
1510
1570
1510
57
59
58
60
58
188
194
191
198
191
18
18
18
17
18
6105
13.0
1110–1200 ⑥
6151
12.9
1090–1200 ⑥
T1
T5
O
T4
T6
1220
1340
1420
1130
1190
46
50
54
42
45
151
165
178
138
148
23
21
19
25
23
6201
6262
6351
13.0
13.0
13.0
1125–1210 ⑥
1080–1205 ⑥
1030–1200
T81
T9
T6
1420
1190
1220
54
44
46
180
145
151
19
24
23
6463
13.0
1140–1210
6951
13.0
T1
T5
T6
O
T6
1340
1450
1390
1480
1370
50
55
53
56
52
165
181
175
186
172
21
19
20
19
20
7049
7050
7072
7075
13.0
12.8
13.1
13.1
T73
T74 ⑧
O
T6
1070
1090
1540
900
40
41
59
33
132
135
193
105
26
25
18
31
7175
7178
7475
13.0
13.0
12.9
890–1175
910–1165
1185–1215
890–1175 ⑦
890–1175 ⑦
890–1165 ⑦
890–1175
T74
T6
T61, T651
T76, T761
T7351
1080
870
960
1020
1130
39
31
35
40
42
124
98
116
132
139
26
33
30
26
25
8017
13.1
1190–1215
8030
8176
13.1
13.1
1190–1215
1190–1215
H12, H22
H212
H221
H24
..
..
1600
59
61
61
61
193
200
201
201
18
17
17
17
FO
R
D
ES
IG
N
English
Units ④
O
T
1140–1210
N
① Coefficient to be multiplied by 10−6. Example: 12.2 × 10−6 = 0.0000122.
② Melting ranges shown apply to wrought products of ¼ inch thickness or
greater.
③ Based on typical composition of the indicated alloys.
④ English units = btu-in./ft2hr°F.
⑤ Eutectic melting is not eliminated by homogenization.
V-26
THERMAL
CONDUCTIVITY
AT 77°F
⑥ Eutectic melting can be completely eliminated by homogenization.
⑦ Homogenization may raise eutectic melting temperature 20–40°F but
usually does not eliminate eutectic melting.
⑧ Although not formerly registered, the literature and some specifications
have used T736 as the designation for this temper.
January 2005
Table 7M
TYPICAL PHYSICAL PROPERTIES—
THERMAL AND ELECTRICAL
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuMELTING
RANGE ② ③
APPROX.
20° TO 100°C
per °C
°C
1060
23.6
645–655
1100
23.6
640–655
ALLOY
23.6
645–655
2011
22.9
540–645 ⑤
2014
23.0
505–635 ④
2017
23.6
510–640 ④
2018
2024
22.3
23.2
505–640 ⑤
500–635 ④
2025
2036
22.7
23.4
2117
2124
2218
2219
23.8
22.9
22.3
22.3
520–640 ④
555–650 ⑤
550–650 ⑤
500–635 ④
505–635 ④
545–645 ④
2618
3003
22.3
23.2
550–640
640–655
3004
23.9
630–655
3105
23.6
4032
19.4
4043
4045
22.0
21.1
4343
21.6
5005
5050
5052
5056
23.8
23.8
23.8
24.1
5083
5086
ELECTRICAL
RESISTIVITY
AT 20°C
W/m •K
Equal
Volume
Equal
Mass
Ohm • mm2/m
O
H18
O
H18
All
234
230
222
218
234
36
35
34
33
36
118
117
113
108
118
0.028
0.029
0.029
0.030
0.028
T3
T8
O
T4
T6
O
T4
151
172
193
134
155
193
134
23
26
29
20
23
29
20
71
82
92
63
74
92
63
0.043
0.038
0.034
0.050
0.043
0.034
0.050
T61
O
T3, T4, T361
T6, T81, T861
T6
T4
155
193
121
151
155
159
23
29
17
22
23
24
74
74
93
56
71
74
78
0.043
0.034
0.059
0.045
0.043
0.042
T4
T851
T72
O
T31, T37
T6, T81, T87
155
152
155
172
113
121
23
22
23
26
16
17
75
71
73
80
57
58
0.043
0.045
0.043
0.038
0.062
0.059
T6
O
H12
H14
H18
All
146
193
163
159
155
163
21
29
24
24
23
24
70
92
78
78
74
79
0.048
0.034
0.042
0.042
0.043
0.042
FO
R
1350
TEMPER
ELECTRICAL
CONDUCTIVITY
AT 20°C
MS/m ⑧
THERMAL
CONDUCTIVITY
AT 25°C
D
ES
IG
N
AVERAGE ①
COEFFICIENT
OF THERMAL
EXPANSION
lar product or size. These data are intended only as a
basis for comparing alloys and tempers and should not
be specified as engineering requirements or used for
design purposes.
635–655
All
172
26
86
0.038
530–570 ④
O
T6
O
All
155
138
163
171
23
20
24
26
77
67
81
88
0.043
0.050
0.041
0.038
575–630
575–600
All
180
27
92
0.037
All
All
All
O
H38
201
193
138
117
109
30
29
20
17
16
100
96
67
57
53
0.033
0.034
0.050
0.059
0.062
23.8
23.8
580–640
585–640
O
All
117
126
17
18
57
60
0.059
0.056
5154
5252
5254
5356
23.9
23.8
23.9
24.1
590–645
605–650
590–645
575–635
All
All
All
O
126
138
126
117
19
20
19
17
62
67
62
57
0.053
0.050
0.053
0.059
5454
23.6
600–645
5456
5457
5652
5657
23.9
23.8
23.8
23.8
570–640
630–655
605–650
635–655
O
H38
O
All
All
All
134
134
117
176
138
205
20
20
17
27
20
31
66
66
57
89
69
104
0.050
0.050
0.059
0.037
0.050
0.032
6005
23.6
605–655 ⑤
T1
T5
180
188
27
28
90
93
0.037
0.036
N
O
T
575–615
630–655
625–650
605–650
565–640
For all numbered footnotes, see last page of this Table.
January 2005
V-27
Table 7M
TYPICAL PHYSICAL PROPERTIES—
THERMAL AND ELECTRICAL (Continued)
AVERAGE ①
COEFFICIENT
OF THERMAL
EXPANSION
MELTING
RANGE ② ③
APPROX.
20° TO 100°C
per °C
°C
6053
23.0
575–650 ⑤
6061
23.6
6063
6066
ALLOY
TEMPER
ELECTRICAL
RESISTIVITY
AT 20°C
Equal
Volume
Equal
Mass
Ohm • mm2/m
O
T4
T6
172
155
167
26
23
24
86
77
81
0.038
0.042
0.041
580–650 ⑤
O
T4
T6
180
155
167
27
23
25
90
77
82
0.037
0.043
0.040
23.4
615–655
O
T1
T5
T6, T83
218
193
209
201
34
29
32
31
111
96
105
102
0.029
0.034
0.031
0.032
23.2
560–645 ④
6070
..
565–650 ④
O
T6
T6
155
146
172
23
21
26
77
71
84
0.043
0.048
0.038
6101
23.4
620–655
T6
T61
T63
T64
T65
218
222
218
226
218
33
34
34
35
34
109
113
111
115
111
0.030
0.029
0.029
0.029
0.029
6105
23.4
600–650 ⑥
6151
23.2
590–650 ⑤
T1
T5
O
T4
T6
176
193
205
163
172
27
29
31
24
26
88
96
103
80
86
0.037
0.034
0.032
0.042
0.038
6201
6262
6351
23.4
23.4
23.4
T81
T9
T6
205
172
176
31
26
27
104
84
88
0.032
0.038
0.038
6463
23.4
610–655 ⑤
580–650 ⑤
555–650
615–655 ⑤
6951
23.4
615–655
T1
T5
T6
O
T6
193
209
201
213
197
29
32
31
32
30
96
105
102
108
100
0.034
0.031
0.032
0.031
0.033
7049
7050
7072
7075
23.4
23.0
23.6
23.6
T73
T74 ⑦
O
T6
155
157
222
130
23
24
34
19
77
78
112
61
0.043
0.042
0.029
0.053
7175
7178
7475
23.4
23.4
23.2
475–635
490–630
640–655
475–635 ⑥
475–635 ⑥
475–630 ⑥
475–635
T74
T6
T61, T651
T76, T761
T7351
157
126
138
146
163
23
18
20
23
24
72
57
69
77
81
0.043
0.056
0.050
0.043
0.041
8017
23.6
645–655
8030
8176
23.6
23.6
645–655
645–655
H12, H22
H212
H221
H24
..
..
230
230
34
35
35
35
113
117
117
117
0.029
0.029
0.029
0.029
O
T
FO
R
D
ES
IG
N
W/m • K
N
① Coefficient to be multiplied by 10–6. Example: 23.6 × 10–6 = 0.0000236.
② Melting ranges shown apply to wrought products of 6 mm thickness or
greater.
③ Based on typical composition of the indicated alloys.
④ Eutectic melting is not eliminated by homogenization.
⑤ Eutectic melting can be completely eliminated by homogenization.
V-28
ELECTRICAL
CONDUCTIVITY
AT 20°C
MS/m ⑧
THERMAL
CONDUCTIVITY
AT 25°C
⑥ Homogenization may raise eutectic melting temperature 10–20°C but
usually does not eliminate eutectic melting.
⑦ Although not formerly registered, the literature and some specifications
have used T736 as the designation for this temper.
⑧ MS/m = 0.58 × % IACS.
January 2005
Table 8
TYPICAL PHYSICAL PROPERTIES—DENSITY
Density and specific gravity are dependent upon
composition, and variations are discernible from one
cast to another for most alloys. The nominal values
shown below should not be specified as engineering
requirements but are used in calculating typical values for weight per unit length, weight per unit area,
Alloy
Density
(lbs/cu. in.)
Specific
Gravity
1050
1060
1100
1145
1175
1200
1230
1235
1345
1350
2011
2014
2017
2018
2024
2025
2036
2117
2124
2218
2219
2618
3003
3004
3005
3105
4032
4043
4045
4047
4145
4343
4643
5005
5050
5052
5056
5083
5086
5154
5183
.0975
.0975
.098
.0975
.0975
.098
.098
.0975
.0975
.0975
.102
.101
.101
.102
.100
.101
.100
.099
.100
.101
.103
.100
.099
.098
.098
.098
.097
.097
.096
.096
.099
.097
.097
.098
.097
.097
.095
.096
.096
.096
.096
2.705
2.705
2.71
2.700
2.700
2.70
2.70
2.705
2.705
2.705
2.83
2.80
2.79
2.82
2.78
2.81
2.75
2.75
2.78
2.81
2.84
2.76
2.73
2.72
2.73
2.72
2.68
2.69
2.67
2.66
2.74
2.68
2.69
2.70
2.69
2.68
2.64
2.66
2.66
2.66
2.66
January 2005
covering area, etc. The density values are derived
from the metric and subsequently rounded. These
values are not to be converted to the metric. X.XXX0
and X.XXX5 density values and X.XX0 and X.XX5
specific gravity values are limited to 99.35 percent or
higher purity aluminum.
Alloy
Density
(lbs/cu. in.)
Specific
Gravity
5252
5254
5356
5454
5456
5457
5554
5556
5652
5654
5657
6003
6005
6053
6061
6063
6066
6070
6101
6105
6151
6162
6201
6262
6351
6463
6951
7005
7008
7049
7050
7072
7075
7175
7178
7475
8017
8030
8176
8177
.096
.096
.096
.097
.096
.097
.097
.096
.097
.096
.097
.097
.097
.097
.098
.097
.098
.098
.097
.097
.098
.097
.097
.098
.098
.097
.098
.100
.100
.103
.102
.098
.101
.101
.102
.101
.098
.098
.098
.098
2.67
2.66
2.64
2.69
2.66
2.69
2.69
2.66
2.67
2.66
2.69
2.70
2.70
2.69
2.70
2.70
2.72
2.71
2.70
2.69
2.71
2.70
2.69
2.72
2.71
2.69
2.70
2.78
2.78
2.84
2.83
2.72
2.81
2.80
2.83
2.81
2.71
2.71
2.71
2.70
V-29
Table 9
TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES ①
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuTENSILE STRENGTH,
ksi
°F
ULTIMATE
YIELD ②
2024-T3
(Sheet)
–320
–112
–18
75
212
300
400
500
600
700
85
73
72
70
66
55
27
11
7.5
5
62
52
51
50
48
45
20
9
6
4
18
17
17
17
16
11
23
55
75
100
45
24
20
20
20
23
26
75
80
85
2024-T4, T351
(plate)
–320
–112
–18
75
212
300
400
500
600
700
84
71
69
68
63
45
26
11
7.5
5
61
49
47
47
45
36
19
9
6
4
19
19
19
19
19
17
27
55
75
100
30
16
15
15
15
20
65
75
80
85
2024-T6, T651
–320
–112
–18
75
212
300
400
500
600
700
84
72
70
69
65
45
26
11
7.5
5
68
59
58
57
54
36
19
9
6
4
11
10
10
10
10
17
27
55
75
100
43
34
19
11
3.8
1.8
1.4
15
16
25
35
45
90
125
2024-T81, T851
84
74
72
70
63
40
16
9.5
6.5
4.3
72
65
62
60
57
35
13
7.5
5
3.5
14
13
13
13
15
20
38
52
65
72
–320
–112
–18
75
212
300
400
500
600
700
85
74
73
70
66
55
27
11
7.5
5
78
69
68
65
62
49
20
9
6
4
8
7
7
7
8
11
23
55
75
100
2024-T861
80
65
64
62
57
40
16
9
6
4.3
53
42
41
40
39
30
13
7.5
5
3.5
28
24
23
22
18
15
35
45
65
70
–320
–112
–18
75
212
300
400
500
600
700
92
81
78
75
70
54
21
11
7.5
5
85
77
74
71
67
48
17
9
6
4
5
5
5
5
6
11
28
55
75
100
2117-T4
–320
–112
–18
75
212
300
400
500
600
700
56
45
44
43
36
30
16
7.5
4.7
2.9
33
25
24
24
21
17
12
5.5
3.3
2
30
29
28
27
16
20
35
55
80
110
ULTIMATE
YIELD ②
1100-O
–320
–112
–18
75
212
300
400
500
600
700
25
15
14
13
10
8
6
4
2.9
2.1
6
5.5
5
5
4.6
4.2
3.5
2.6
2
1.6
50
43
40
40
45
55
65
75
80
85
1100-H14
–320
–112
–18
75
212
300
400
500
600
700
30
20
19
18
16
14
10
4
2.9
2.1
20
18
17
17
15
12
7.5
2.6
2
1.6
1100-H18
–320
–112
–118
75
212
300
400
500
600
700
34
26
25
24
21
18
6
4
2.9
2.1
26
23
23
22
19
14
3.5
2.6
2
1.6
2011-T3
75
212
300
400
500
600
700
55
47
28
16
6.5
3.1
2.3
2014-T6, T651
–320
–112
–18
75
212
300
400
500
600
700
FO
R
O
T
N
2017-T4, T451
–320
–112
–18
75
212
300
400
500
600
700
ALLOY AND
TEMPER
TEMP.
D
ES
IG
N
°F
TEMP.
TENSILE STRENGTH,
ksi
ELONGATION
IN 2 IN.,
PERCENT
ELONGATION
IN 2 IN.,
PERCENT
ALLOY AND
TEMPER
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
For all numbered footnotes, see last page of table.
V-30
January 2005
Table 9
TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES ① (Continued)
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuTENSILE STRENGTH,
ksi
ULTIMATE
YIELD ②
2124-T851
–452
–320
–112
–18
75
212
300
400
500
600
700
102
86
76
73
70
66
54
27
11
7.5
5.5
90
79
71
68
64
61
49
20
8
6
4.1
10
9
8
8
9
9
13
28
60
75
100
2218-T61
–320
–112
–18
75
212
300
400
500
600
700
72
61
59
59
56
41
22
10
5.5
4
52
45
44
44
42
35
16
6
3
2.5
15
14
13
13
15
17
30
70
85
100
2219-T62
–320
–112
–18
75
212
300
400
500
600
700
73
63
60
58
54
45
34
27
10
4.4
49
44
42
40
37
33
25
20
8
3.7
16
13
12
12
14
17
20
21
40
75
2219-T81, T851
–320
–112
–18
75
212
300
400
500
600
700
83
71
69
66
60
49
36
29
7
4.4
61
54
52
50
47
40
29
23
6
3.7
15
13
12
12
15
17
20
21
55
75
2618-T61
–320
–12
–18
75
212
300
400
500
600
700
78
67
64
64
62
50
32
13
7.5
5
61
55
54
54
54
44
26
9
4.5
3.5
12
11
10
10
10
14
24
50
80
120
33
20
17
16
13
11
8.5
6
4
2.8
8.5
7
6.5
6
5.5
5
4.3
3.4
2.4
1.8
46
42
41
40
43
47
60
65
70
70
N
FO
R
O
T
TEMP.
3003-O
–320
–112
–18
75
212
300
400
500
600
700
TENSILE STRENGTH,
ksi
°F
ULTIMATE
YIELD ②
ELONGATION
IN 2 IN.,
PERCENT
3003-H14
–320
–112
–18
75
212
300
400
500
600
700
35
24
22
22
21
18
14
7.5
4
2.8
25
22
21
21
19
16
9
4
2.4
1.8
30
18
16
16
16
16
20
60
70
70
3003-H18
–320
–112
–18
75
212
300
400
500
600
700
41
32
30
29
26
23
14
7.5
4
2.8
33
29
28
27
21
16
9
4
2.4
1.8
23
11
10
10
10
11
18
60
70
70
3004-O
–320
–112
–18
75
212
300
400
500
600
700
42
28
26
26
26
22
14
10
7.5
5
13
11
10
10
10
10
9.5
7.5
5
3
38
30
26
25
25
35
55
70
80
90
3004-H34
–320
–112
–18
75
212
300
400
500
600
700
52
38
36
35
34
28
21
14
7.5
5
34
30
29
29
29
25
15
7.5
5
3
26
16
13
12
13
22
35
55
80
90
3004-H38
–320
–112
–18
75
212
300
400
500
600
700
58
44
42
41
40
31
22
12
7.5
5
43
38
36
36
36
27
15
7.5
5
3
20
10
7
6
7
15
30
50
80
90
4032-T6
–320
–112
–18
75
212
300
400
500
600
700
66
58
56
55
50
37
13
8
5
3.4
48
46
46
46
44
33
9
5.5
3.2
2
11
10
9
9
9
9
30
50
70
90
ALLOY AND
TEMPER
TEMP.
D
ES
IG
N
°F
ELONGATION
IN 2 IN.,
PERCENT
ALLOY AND
TEMPER
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
For all numbered footnotes, see last page of table.
January 2005
V-31
Table 9
TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES ① (Continued)
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuTENSILE STRENGTH,
ksi
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
TENSILE STRENGTH,
ksi
°F
ULTIMATE
YIELD ②
ELONGATION
IN 2 IN.,
PERCENT
°F
ULTIMATE
YIELD ②
ELONGATION
IN 2 IN.,
PERCENT
5050-O
–320
–112
–18
75
212
300
400
500
600
700
37
22
21
21
21
19
14
9
6
3.9
10
8.5
8
8
8
8
7.5
6
4.2
2.6
..
..
..
..
..
..
..
..
..
..
5083-O
–320
–112
–18
75
212
300
400
500
600
700
59
43
42
42
40
31
22
17
11
6
24
21
21
21
21
19
17
11
7.5
4.2
36
30
27
25
36
50
60
80
110
130
5050-H34
–320
–112
–18
75
212
300
400
500
600
700
44
30
28
28
28
25
14
9
6
3.9
30
25
24
24
24
22
7.5
6
4.2
2.6
..
..
..
..
..
..
..
..
..
..
5086-O
–320
–112
–18
75
212
300
400
500
600
700
55
39
38
38
38
29
22
17
11
6
19
17
17
17
17
16
15
11
7.5
4.2
46
35
32
30
36
50
60
80
110
130
5050-H38
–320
–112
–18
75
212
300
400
500
600
700
46
34
32
32
31
27
14
9
6
3.9
36
30
29
29
29
25
7.5
6
4.2
2.6
..
..
..
..
..
..
..
..
..
..
5154-O
–320
–112
–18
75
212
300
400
500
600
700
52
36
35
35
35
29
22
17
11
6
19
17
17
17
17
16
15
11
7.5
4.2
46
35
32
30
36
50
60
80
110
130
5052-O
–320
–112
–18
75
212
300
400
500
600
700
44
29
28
28
28
23
17
12
7.5
5
16
13
13
13
13
13
11
7.5
5.5
3.1
46
35
32
30
36
50
60
80
110
130
5254-O
–320
–112
–18
75
212
300
400
500
600
700
52
36
35
35
35
29
22
17
11
6
19
17
17
17
17
16
15
11
7.5
4.2
46
35
32
30
36
50
60
80
110
130
5052-H34
–320
–112
–18
75
212
300
400
500
600
700
55
40
38
38
38
30
24
12
7.5
5
36
32
31
31
31
27
15
7.5
5.5
3.1
28
21
18
16
18
27
45
80
110
130
5454-O
–320
–112
–18
75
212
300
400
500
600
700
54
37
36
36
36
29
22
17
11
6
19
17
17
17
17
16
15
11
7.5
4.2
39
30
27
25
31
50
60
80
110
130
60
44
42
42
40
34
25
12
7.5
5
44
38
37
37
36
28
15
7.5
5.5
3.1
25
18
15
14
16
24
45
80
110
130
5454-H32
–320
–112
–18
75
212
300
400
500
600
700
59
42
41
40
39
32
25
17
11
6
36
31
30
30
29
26
19
11
7.5
4.2
32
23
20
18
20
37
45
80
110
130
N
5052-H38
–320
–112
–18
75
212
300
400
500
600
700
ALLOY AND
TEMPER
TEMP.
D
ES
IG
N
FO
R
TEMP.
O
T
ALLOY AND
TEMPER
For all numbered footnotes, see last page of table.
V-32
January 2005
Table 9
TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES ① (Continued)
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuTENSILE STRENGTH,
ksi
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
TENSILE STRENGTH,
ksi
°F
ULTIMATE
YIELD ②
ELONGATION
IN 2 IN.,
PERCENT
°F
ULTIMATE
YIELD ②
ELONGATION
IN 2 IN.,
PERCENT
5454-H34
–320
–112
–18
75
212
300
400
500
600
700
63
46
44
44
43
34
26
17
11
6
41
36
35
35
34
28
19
11
7.5
4.2
30
21
18
16
18
32
45
80
110
130
6061-T6, T651
–320
–112
–18
75
212
300
400
500
600
700
60
49
47
45
42
34
19
7.5
4.6
3
47
42
41
40
38
31
15
5
2.7
1.8
22
18
17
17
18
20
28
60
85
95
5456-O
–320
–112
–18
75
212
300
400
500
600
700
62
46
45
45
42
31
22
17
11
6
26
23
23
23
22
20
17
11
7.5
4.2
32
25
22
20
31
50
60
80
110
130
6063-T1
–320
–112
–18
75
212
300
400
500
600
700
34
26
24
22
22
21
9
4.5
3.2
2.3
16
15
14
13
14
15
6.5
3.5
2.5
2
44
36
34
33
18
20
40
75
80
105
5652-O
–320
–112
–18
75
212
300
400
500
600
700
44
29
28
28
28
23
17
12
7.5
5
16
13
13
13
13
13
11
7.5
5.5
3.1
46
35
32
30
30
50
60
80
110
130
6063-T5
–320
–112
–18
75
212
300
400
500
600
700
37
29
28
27
24
20
9
4.5
3.2
2.3
24
22
22
21
20
18
6.5
3.5
2.5
2
28
24
23
22
18
20
40
75
80
105
5652-H34
–320
–112
–18
75
212
300
400
500
600
700
55
40
38
38
38
30
24
12
7.5
5
36
32
31
31
31
27
15
7.5
5.5
3.1
28
21
18
16
18
27
45
80
110
130
6063-T6
–320
–112
–18
75
212
300
400
500
600
700
47
38
36
35
31
21
9
4.5
3.3
2.3
36
33
32
31
28
20
6.5
3.5
2.5
2
24
20
19
18
15
20
40
75
80
105
5652-H38
–320
–112
–18
75
212
300
400
500
600
700
60
44
42
42
40
34
25
12
7.5
5
44
38
37
37
36
28
15
7.5
5.5
3.1
25
18
15
14
16
24
45
80
110
130
6101-T6
–320
–112
–18
75
212
300
400
500
600
700
43
36
34
32
28
21
10
4.8
3
2.5
33
30
29
28
25
19
7
3.3
2.3
1.8
24
20
19
19
20
20
40
80
100
105
37
32
25
13
5.5
4
2.9
32
28
24
12
4
2.7
2
13
13
13
25
70
80
90
6151-T6
–320
–112
–18
75
212
300
400
500
600
700
57
50
49
48
43
28
14
6.5
5
4
50
46
45
43
40
27
12
5
3.9
3.2
20
17
17
17
17
20
30
50
43
35
N
6053-T6, T651
75
212
300
400
500
600
700
ALLOY AND
TEMPER
TEMP.
D
ES
IG
N
FO
R
TEMP.
O
T
ALLOY AND
TEMPER
For all numbered footnotes, see last page of table.
January 2005
V-33
Table 9
TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES ① (Continued)
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuALLOY AND
TEMPER
TEMP.
°F
TENSILE STRENGTH,
ksi
ULTIMATE YIELD ②
ELONGATION
IN 2 IN.,
PERCENT
–320
–112
–18
75
212
300
60
49
47
45
42
34
47
42
41
40
38
31
22
18
17
17
18
20
6262-T9
–320
–112
–18
75
212
300
400
500
600
700
74
62
60
58
53
38
15
8.5
4.6
3
67
58
56
55
52
37
13
6
2.7
1.8
14
10
10
10
10
14
34
48
85
95
–320
–112
–18
75
212
300
400
500
600
700
102
90
86
83
70
31
16
11
8
6
92
79
75
73
65
27
13
9
6.5
4.6
–320
–112
–18
75
212
300
400
500
600
700
92
79
76
73
63
31
16
11
8
6
72
67
65
63
58
27
13
9
6.5
4.6
106
90
87
80
72
35
18
98
83
80
73
69
31
13
7075-T73,
T7351
–320
–112
–18
75
212
300
400
O
T
7175-T74
9
11
11
11
14
30
55
65
70
70
14
14
13
13
15
30
55
65
70
70
FO
R
7075-T6,
T651
TENSILE STRENGTH,
ksi
ULTIMATE YIELD ②
13
14
16
14
17
30
65
TEMP.
7178-T6, T651
–320
–112
–18
75
212
300
400
500
600
700
106
94
91
88
73
31
15
11
8.5
6.5
94
84
81
78
68
27
12
9
7
5.5
5
8
9
11
14
40
70
76
80
80
7178-T76,
T7651
–320
–112
–18
75
212
300
400
500
600
700
106
91
88
83
69
31
15
11
8.5
6.5
89
78
76
73
64
27
12
9
7
5.5
10
10
10
11
17
40
70
76
80
80
7475-T61 Sheet
–320
–112
–18
75
212
300
400
500
600
700
99
88
84
80
70
30
14
9.5
6.5
5
87
79
75
72
65
26
11
7
5.5
3.8
10
12
12
12
14
28
55
70
80
85
7475-T761
–320
–112
–18
75
212
300
400
500
600
700
95
84
80
76
64
30
14
9.5
6.5
5
82
73
70
67
61
26
11
7
5.5
3.8
11
12
12
12
14
38
55
70
80
85
°F
perature and time, the application of heat will adversely affect certain other
properties of some alloys.
② Offset equals 0.2 percent.
N
① These data are based on a limited amount of testing and represent the
lowest strength during 10,000 hours of exposure at testing temperature
under no load; stress applied at 5,000 psi/min to yield strength and then
at strain rate of 0.05 in./in./min to failure. Under some conditions of tem-
ELONGATION
IN 2 IN.,
PERCENT
ALLOY AND
TEMPER
D
ES
IG
N
6262-T651
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
V-34
January 2005
Table 9M
TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES ①
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuALLOY
AND
TEMPER
TEMP.
°C
TENSILE STRENGTH,
MPa
ULTIMATE
YIELD ②
ELONGATION
IN 50 mm
PERCENT
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
ALLOY
AND
TEMPER
TEMP.
°C
TENSILE STRENGTH,
MPa
ULTIMATE
YIELD ②
ELONGATION
IN 50 mm
PERCENT
–195
–80
–30
25
100
150
205
260
315
370
170
105
95
90
70
55
41
28
20
14
41
38
34
34
32
29
24
18
14
11
50
43
40
40
45
55
65
75
80
85
2024-T3
(Sheet)
–195
–80
–30
25
100
150
205
260
315
370
585
505
495
485
455
380
185
75
50
34
425
360
350
345
330
310
140
60
41
28
18
17
17
17
16
11
23
55
75
100
1100-H14
–195
–80
–30
25
100
150
205
260
315
370
205
140
130
125
110
95
70
28
20
14
140
125
115
115
105
85
50
18
14
11
45
24
20
20
20
23
26
75
80
85
2024-T4, T351
(plate)
–195
–80
–30
25
100
150
205
260
315
370
580
490
475
470
435
310
180
75
50
34
420
340
325
325
310
250
130
60
41
28
19
19
19
19
19
17
27
55
75
100
1100-H18
–195
–80
–30
25
100
150
205
260
315
370
235
180
170
165
145
125
41
28
20
14
180
160
160
150
130
95
24
18
14
11
30
16
15
15
15
20
65
75
80
85
2024-T6, T651
–195
–80
–30
25
100
150
205
260
315
370
580
495
485
475
450
310
180
75
50
34
470
405
400
395
370
250
130
60
41
28
11
10
10
10
10
17
27
55
75
100
2011-T3
25
100
150
205
260
315
370
380
325
195
110
45
21
16
295
235
130
75
26
12
10
15
16
25
35
45
90
125
2024-T81, T851
2014-T6, T651
–195
–80
–30
25
100
150
205
260
315
370
580
510
495
485
435
275
110
65
45
30
495
450
425
415
395
240
90
50
34
24
14
13
13
13
15
20
38
52
65
72
–195
–80
–30
25
100
150
205
260
315
370
585
510
505
485
455
380
185
75
50
34
540
475
470
450
425
340
140
60
41
28
8
7
7
7
8
11
23
55
75
100
2024-T861
550
450
440
425
395
275
110
60
41
30
365
290
285
275
270
205
90
50
34
24
28
24
23
22
18
15
35
45
65
70
–195
–80
–30
25
100
150
205
260
315
370
635
560
540
515
485
370
145
75
50
34
585
530
510
490
460
330
115
60
41
28
5
5
5
5
6
11
28
55
75
100
2117-T4
–195
–80
–30
25
100
150
205
260
315
370
385
310
305
295
250
205
110
50
32
20
230
170
165
165
145
115
85
38
23
14
30
29
28
27
16
20
35
55
80
110
FO
R
O
T
N
2017-T4, T451
–195
–80
–30
25
100
150
205
260
315
370
For all numbered footnotes, see last page of table.
January 2005
D
ES
IG
N
1100-O
V-35
Table 9M
TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES ① (Continued)
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuTEMP.
°C
TENSILE STRENGTH,
MPa
ULTIMATE
YIELD ②
ELONGATION
IN 50 mm
PERCENT
ALLOY
AND
TEMPER
TEMP.
°C
TENSILE STRENGTH,
MPa
ULTIMATE
YIELD ②
–195
–80
–30
25
100
150
205
260
315
370
240
165
150
150
145
125
95
50
28
19
170
150
145
145
130
110
60
28
17
12
30
18
16
16
16
16
20
60
70
70
3003-H18
–195
–80
–30
25
100
150
205
260
315
370
285
220
205
200
180
160
95
50
28
19
230
200
195
185
145
110
60
28
17
12
23
11
10
10
10
11
18
60
70
70
3004-O
–195
–80
–30
25
100
150
205
260
315
370
290
195
180
180
180
150
95
70
50
34
90
75
70
70
70
70
65
50
34
21
38
30
26
25
25
35
55
70
80
90
3004-H34
–195
–80
–30
25
100
150
205
260
315
370
360
260
250
240
235
195
145
95
50
34
235
205
200
200
200
170
105
50
34
21
26
16
13
12
13
22
35
55
80
90
3004-H38
–195
–80
–30
25
100
150
205
260
315
370
400
305
290
285
275
215
150
85
50
34
295
260
250
250
250
185
105
50
34
21
20
10
7
6
7
15
30
50
80
90
4032-T6
–195
–80
–30
25
100
150
205
260
315
370
455
400
385
380
345
255
90
55
34
23
330
315
315
315
305
230
60
38
22
14
11
10
9
9
9
9
30
50
70
90
705
595
525
505
485
455
370
185
75
50
38
620
545
490
470
440
420
340
140
55
41
28
10
9
8
8
9
9
13
28
60
75
100
2218-T61
–195
–80
–30
25
100
150
205
260
315
370
495
420
405
405
385
285
150
70
38
28
360
310
305
305
290
240
110
41
21
17
15
14
13
13
15
17
30
70
85
100
2219-T62
–195
–80
–30
25
100
150
205
260
315
370
505
435
415
400
370
310
235
185
70
30
340
305
290
275
255
230
170
140
55
26
16
13
12
12
14
17
20
21
40
75
2219-T81, T851
–195
–80
–30
25
100
150
205
160
315
370
570
490
475
455
415
340
250
200
48
30
420
370
360
345
325
275
200
160
41
26
15
13
12
12
15
17
20
21
55
75
2618-T61
–195
–80
–30
25
100
150
205
260
315
370
540
460
440
440
425
345
220
90
50
34
420
380
370
370
370
305
180
60
31
24
12
11
10
10
10
14
24
50
80
120
230
140
115
110
90
75
60
41
28
19
60
50
45
41
38
34
30
23
17
12
46
42
41
40
43
47
60
65
70
70
N
O
T
FO
R
–268
–195
–80
–30
25
100
150
205
260
315
370
3003-O
–195
–80
–30
25
100
150
205
260
315
370
ELONGATION
IN 50 mm
PERCENT
3003-H14
2124-T851
D
ES
IG
N
ALLOY
AND
TEMPER
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
For all numbered footnotes, see last page of table.
V-36
January 2005
Table 9M
TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES ① (Continued)
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuALLOY
AND
TEMPER
TEMP.
°C
TENSILE STRENGTH,
MPa
ULTIMATE
YIELD ②
ELONGATION
IN 50 mm
PERCENT
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
ALLOY
AND
TEMPER
TEMP.
°C
TENSILE STRENGTH,
MPa
ULTIMATE
YIELD ②
ELONGATION
IN 50 mm
PERCENT
–195
–80
–30
25
100
150
205
260
315
370
255
150
145
145
145
130
95
60
41
27
70
60
55
55
55
55
50
41
29
18
..
..
..
..
..
..
..
..
..
..
5083-O
–195
–80
–30
25
100
150
205
260
315
370
405
295
290
290
275
215
150
115
75
41
165
145
145
145
145
130
115
75
50
29
36
30
27
25
36
50
60
80
110
130
5050-H34
–195
–80
–30
25
100
150
205
260
315
370
305
205
195
195
195
170
95
60
41
27
205
170
165
165
165
150
50
41
29
18
..
..
..
..
..
..
..
..
..
..
5086-O
–195
–80
–30
25
100
150
205
260
315
370
380
270
260
260
260
200
150
115
75
41
130
115
115
115
115
110
105
75
50
29
46
35
32
30
36
50
60
80
110
130
5050-H38
–195
–80
–30
25
100
150
205
260
315
370
315
235
220
220
215
185
95
60
41
27
250
205
200
200
200
170
50
41
29
18
..
..
..
..
..
..
..
..
..
..
5154-O
–195
–80
–30
25
100
150
205
260
315
370
360
250
240
240
240
200
150
115
75
41
130
115
115
115
115
110
105
75
50
29
46
35
32
30
36
50
60
80
110
130
5052-O
–195
–80
–30
25
100
150
205
260
315
370
305
200
195
195
195
160
115
85
50
34
110
90
90
90
90
90
75
50
38
21
46
35
32
30
36
50
60
80
110
130
5254-O
–195
–80
–30
25
100
150
205
260
315
370
360
250
240
240
240
200
150
115
75
41
130
115
115
115
115
110
105
75
50
29
46
35
32
30
36
50
60
80
110
130
5052-H34
–195
–80
–30
25
100
150
205
260
315
370
380
275
260
260
260
205
165
85
50
34
250
220
215
215
215
185
105
50
38
21
28
21
18
16
18
27
45
80
110
130
5454-O
–195
–80
–30
25
100
150
205
260
315
370
370
255
250
250
250
200
150
115
75
41
130
115
115
115
115
110
105
75
50
29
39
30
27
25
31
50
60
80
110
130
415
305
290
290
275
235
170
85
50
34
305
260
255
255
250
195
105
50
38
21
25
18
15
14
16
24
45
80
110
130
5454-H32
–195
–80
–30
25
100
150
205
260
315
370
405
290
285
275
270
220
170
115
75
41
250
215
205
205
200
180
130
75
50
29
32
23
20
18
20
37
45
80
110
130
FO
R
O
T
N
5052-H38
–195
–80
–30
25
100
150
205
260
315
370
D
ES
IG
N
5050-O
For all numbered footnotes, see last page of table.
January 2005
V-37
Table 9M
TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES ① (Continued)
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuALLOY
AND
TEMPER
TEMP.
°C
TENSILE STRENGTH,
MPa
ULTIMATE
YIELD ②
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
ELONGATION
IN 50 mm
PERCENT
ALLOY
AND
TEMPER
TEMP.
°C
TENSILE STRENGTH,
MPa
ULTIMATE
YIELD ②
ELONGATION
IN 50 mm
PERCENT
–195
–80
–30
25
100
150
205
260
315
370
435
315
305
305
295
235
180
115
75
41
285
250
240
240
235
195
130
75
50
29
30
21
18
16
18
32
45
80
110
130
6061-T6, T651
–195
–80
–30
25
100
150
205
260
315
370
415
340
325
310
290
235
130
50
32
21
325
290
285
275
260
215
105
34
19
12
22
18
17
17
18
20
28
60
85
95
5456-O
–195
–80
–30
25
100
150
205
260
315
370
425
315
310
310
290
215
150
115
75
41
180
160
160
160
150
140
115
75
50
29
32
25
22
20
31
50
60
80
110
130
6063-T1
–195
–80
–30
25
100
150
205
260
315
370
235
180
165
150
150
145
60
31
22
16
110
105
95
90
95
105
45
24
17
14
44
36
34
33
18
20
40
75
80
105
5652-O
–195
–80
–30
25
100
150
205
260
315
370
305
200
195
195
195
160
115
85
50
34
110
90
90
90
90
90
75
50
38
21
46
35
32
30
30
50
60
80
110
130
6063-T5
–195
–80
–30
25
100
150
205
260
315
370
255
200
195
185
165
140
60
31
22
16
165
150
150
145
140
125
45
24
17
14
28
24
23
22
18
20
40
75
80
105
5652-H34
–195
–80
–30
25
100
150
205
260
315
370
380
275
260
260
260
205
165
85
50
34
250
220
215
215
215
185
105
50
38
21
28
21
18
16
18
27
45
80
110
130
6063-T6
–195
–80
–30
25
100
150
205
260
315
370
325
260
250
240
215
145
60
31
23
16
250
230
220
215
195
140
45
24
17
14
24
20
19
18
15
20
40
75
80
105
5652-H38
–195
–80
–30
25
100
150
205
260
315
370
415
305
290
290
275
235
170
85
50
34
305
260
255
255
250
195
105
50
38
21
25
18
15
14
16
24
45
80
110
130
6101-T6
–195
–80
–30
25
100
150
205
260
315
370
295
250
235
220
195
145
70
33
21
17
230
205
200
195
170
130
48
23
16
12
24
20
19
19
20
20
40
80
100
105
255
220
170
90
38
28
20
220
195
165
85
28
19
14
13
13
13
25
70
80
90
6151-T6
–195
–80
–30
25
100
150
205
260
315
370
395
345
340
330
295
195
95
45
34
28
345
315
310
295
275
185
85
34
27
22
20
17
17
17
17
20
30
50
43
35
FO
R
O
T
N
6053-T6, T651
25
100
150
205
260
315
370
For all numbered footnotes, see last page of table.
V-38
D
ES
IG
N
5454-H34
January 2005
Table 9M
TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES ① (Continued)
The following typical properties are not guaranteed,
since in most cases they are averages for various
sizes, product forms and methods of manufacture
and may not be exactly representative of any particuALLOY
AND
TEMPER
TEMP.
°C
TENSILE STRENGTH,
MPa
ULTIMATE
YIELD ②
ALLOY
AND
TEMPER
TEMP.
7178-T6, T651
–195
–80
–30
25
100
150
205
260
315
370
730
650
625
605
505
215
105
75
60
45
650
580
560
540
470
185
85
60
48
38
5
8
9
11
14
40
70
76
80
80
7178-T76,
T7651
–195
–80
–30
25
100
150
205
260
315
370
730
625
605
570
475
215
105
75
60
45
615
540
525
505
440
185
85
60
48
38
10
10
10
11
17
40
70
76
80
80
7475-T61 Sheet
–195
–80
–30
25
100
150
205
260
315
370
685
605
580
550
485
205
95
65
45
34
600
545
515
495
450
180
75
50
38
26
10
12
12
12
14
28
55
70
80
85
7475-T761 Sheet
–195
–80
–30
25
100
150
205
260
315
370
655
580
550
525
440
205
95
65
45
34
565
505
485
460
420
180
75
50
38
26
11
12
12
12
14
38
55
70
80
85
415
340
325
310
290
235
325
290
285
275
260
215
22
18
17
17
18
20
6262-T9
–195
–80
–30
25
100
150
205
260
315
370
510
425
415
400
365
260
105
60
32
21
460
400
385
380
360
255
90
41
19
12
14
10
10
10
10
14
34
48
85
95
–195
–80
–30
25
100
150
205
260
315
370
705
620
595
570
485
215
110
75
55
41
635
545
515
505
450
185
90
60
45
32
–195
–80
–30
25
100
150
205
260
315
370
635
545
525
505
435
215
110
75
55
41
495
460
450
435
400
185
90
60
45
32
730
620
600
550
495
240
125
675
570
550
505
475
215
90
9
11
11
11
14
30
55
65
70
70
14
14
13
13
15
30
55
65
70
70
FO
R
–195
–80
–30
25
100
150
205
O
T
7175-T74
°C
D
ES
IG
N
–195
–80
–30
25
100
150
7075-T73,
T7351
TENSILE STRENGTH,
MPa
ULTIMATE
YIELD ②
ELONGATION
IN 50 mm
PERCENT
6262-T651
7075-T6,
T651
lar product or size. These data are intended only as
a basis for comparing alloys and tempers and should
not be specified as engineering requirements or used
for design purposes.
13
14
16
14
17
30
65
Under some conditions of temperature and time, the application of heat will
adversely affect certain other properties of some alloys.
② Offset equals 0.2 percent.
N
① These data are based on a limited amount of testing and represent
the lowest strength during 10,000 hours of exposure at testing temperature under no load; stress applied at approximately 0.58 MPa/s in to yield
strength and then at strain rate of approximately 0.001mm/mm/s in to failure.
ELONGATION
IN 50 mm
PERCENT
January 2005
V-39
Aluminum Design Manual
PART VI
Section Properties
The Aluminum Association, Inc.
1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
Third Edition, January 2005
VI
Section Properties
TABLE OF CONTENTS
Table 1
Table 2
Table 3
Table 4
Table 5
Table 6
Table 7
Table 8
Table 9
Table 10
Table 11
Table 12
Table 13
Table 14
Table 15
Table 16
Table 17
Table 18
Table 19
Table 20
Table 21
Table 22
Table 23
Table 24
Table 25
Table 26
Table 27
Table 28
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Section Designations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Weights Per Square Foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Aluminum Association Standard Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
American Standard Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Car and Ship Building Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Canadian Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Aluminum Association Standard I Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Wide Flange Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Army-Navy Wide Flange Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
American Standard I Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Canadian I Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Canadian Wide Flange Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Angles – Equal Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Square End Angles – Equal Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Angles – Unequal Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Square End Angles – Unequal Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Tees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Army-Navy and Special Tees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Zees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Round Tubes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Square Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Rectangular Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Roofing And Siding – Dimensions and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Roofing and Siding – Section Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Decimal Equivalents in Inches of Sheet Metal and Wire Gauges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Geometric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
January 2005
VI-3
TABLE 1 – NOMENCLATURE
Symbol
Property
Units
A
Area
in2
b
width
in.
Cw
warping constant
in6
d
depth
in.
I
moment of inertia
in4
J
torsion constant
in4
r
radius of gyration
in.
r0
polar radius of gyration about the shear center
in.
R
fillet radius
in.
Rb
mid-thickness radius of a pipe or tube
in.
S
section modulus
in3
t
thickness
in.
in.
tf
flange thickness
tw
web thickness
in.
Wt
weight per length
lb/ft
x
location of the y axis
in.
x0
x coordinate of shear center
in.
y
location of the x axis
in.
x and y subscripts denote the axis about which the property is taken.
The x axis is the major axis. The y axis is the minor axis.
VI-4
January 2005
TABLE 2 – SECTION DESIGNATIONS
Section
Designation
Example
Description
Channels
CS Depth × Wt
CS 4 × 2.33
C shapes with flat flanges; includes Canadian
Channels
Car and Ship Building
Channels
CS Depth × Wt
CS 3 × 2.23
C shapes; some have a slope on the inner surface of
the flanges
American Standard
Channels
C Depth × Wt
C 2 × 1.22
C shapes with flanges with a 1:6 slope on the inner
surface
I-Beams
I Depth × Wt
I 12 × 11.7
I shapes with flat flanges; includes Canadian
I-Beams
American Standard IBeams
S Depth × Wt
S 10 × 12.1
I shapes with flanges with a 1:6 slope on the inner
surface
Wide Flange Beams
WF Nominal Depth × Wt
WF 12 × 13.8
I shapes with a flange width approximately equal to
the depth
Army-Navy Wide Flange
Beams
WF(A-N) Depth × Wt
WF(A-N) 4 × 4.14
I shapes with flat flanges and a radius on the inside
corner of the flanges
Angles
L long leg × short leg ×
thickness
L3×2×¼
L shaped product with a fillet at the junction of the
legs and radii on the inside tips of the legs
Square End Angles
LS long leg × short leg ×
thickness
LS 3 × 3 × 1/8
L shaped product with small radii at the corners
Tees
T Depth × Width × Wt
T 2.50 × 2.50 × 1.91
T shapes
Zees
Z Depth × Width × Wt
Z 4.00 × 3.19 × 4.32
Z shapes
Plates
PL Thickness × Width
PL 0.375 × 60
Rolled product with a rectangular cross section at
least 0.25 in. thick
Rods
RD Diameter
RD 0.500
Solid product with a circular cross section at least
0.375 in. in diameter
Square Bars
SQ Side dimension
SQ 4
Solid product with a square cross section at least
0.375 in. on a side
Pipes
NPS size × SCH
schedule no.
NPS 4 × SCH 40
Tube in standardized outside diameters and wall
thicknesses
Round Tubes
Outside diameter OD × wall
thickness WALL
4 OD × 0.125 WALL
Hollow product with a circular cross section
Rectangular Tubes
RT short side × long side
× wall thickness
RT 4 × 6 × ¼
Hollow product with a rectangular cross
section (including square tube)
January 2005
VI-5
TABLE 3 – WEIGHTS PER SQUARE FOOT
The weight per square foot for an alloy with density of 0.100 lb/in3 is shown for each thickness. The weights for other alloys
can be calculated using the density given in Part V Table 8.
Commonly used thicknesses are shown BOLD.
Thickness – in.
Decimal
.006
.007
.008
.009
.010
.011
.012
.013
.014
.016
.018
.019
.020
.021
.022
.024
.025
.026
.028
.030
.032
.034
.036
.038
.040
.042
.045
.048
.050
.053
.056
.060
.063
.067
.071
.075
.080
.085
.090
.095
.100
.106
.112
.118
.125
.132
.140
.150
.160
.170
.180
.1875
.190
.200
.212
.224
VI-6
Fraction
1/64
1/16
1/8
3/16
Weight (lb/ft2)
0.086
0.101
0.115
0.130
0.144
0.158
0.173
0.187
0.202
0.230
0.259
0.274
0.288
0.302
0.317
0.346
0.360
0.374
0.403
0.432
0.461
0.490
0.518
0.547
0.576
0.605
0.648
0.691
0.720
0.763
0806
0.864
0.907
0.965
1.02
1.08
1.15
1.22
1.30
1.37
1.44
1.53
1.61
1.70
1.80
1.90
2.02
2.16
2.30
2.45
2.59
2.70
2.74
2.88
3.05
3.23
Thickness – in.
Decimal
Fraction
.236
.250
¼
.266
17/64
.281
9/32
.297
19/64
5/16
.313
.328
21/64
.344
11/32
.359
23/64
.375
3/8
.391
25/64
.406
13/32
.422
27/64
.438
7/16
.453
29/64
.469
15/32
.484
31/64
.500
½
.531
17/32
.562
9/16
.594
19/32
.625
5/8
.656
21/32
.688
11/16
.719
23/32
.750
¾
.812
13/16
.875
7/8
.938
15/16
1.000
1
1 1/8
1.125
1¼
1.250
1 3/8
1.375
1½
1.500
1 5/8
1.625
1¾
1.750
1 7/8
1.875
2.000
2
2.125
2 1/8
2.250
2¼
2.375
2 3/8
2.500
2½
2.625
2 5/8
2.750
2¾
2.875
2 7/8
3.000
3
3.250
3¼
3.500
3½
3.750
3¾
4.000
4
4.250
4¼
4.500
4½
4.750
4¾
5.000
5
5.250
5¼
5.500
5½
5.750
5¾
6.000
6
Weight (lb/ft2)
3.40
3.60
3.83
4.05
4.28
4.51
4.72
4.95
5.17
5.40
5.63
5.85
6.08
6.31
6.52
6.75
6.97
7.20
7.65
8.09
8.55
9.00
9.45
9.91
10.35
10.80
11.69
12.60
13.51
14.40
16.20
18.00
19.80
21.60
23.40
25.20
27.00
28.80
30.60
32.40
34.20
36.00
37.80
39.60
41.40
43.20
46.80
50.40
54.00
57.60
61.20
64.80
68.40
72.00
75.60
79.20
82.80
86.40
January 2005
January 2005
VI-7
1.000
1.250
1.500
1.750
2.000
2.250
2.250
2.750
2.500
2.000
2.000
3.000
3.000
4.000
4.000
5.000
5.000
6.000
CS 2 × 0.577
CS 2 × 1.07
CS 3 × 1.14
CS 3 × 1.60
CS 4 × 1.74
CS 4 × 2.33
CS 5 × 2.21
CS 5 × 3.09
CS 6 × 2.83
0.620
4.000
5.000
6.000
12.000
12.000
14.000
CS 12 × 8.27
CS 12 × 11.8
0.640
0.500
0.320
0.350
0.290
0.310
0.250
0.290
0.230
0.250
0.190
0.210
0.170
0.210
0.170
0.190
0.150
0.190
0.150
0.170
0.130
0.170
0.130
Web
Thickness
tw
in.
0.450
0.450
0.400
0.400
0.350
0.350
0.350
0.350
0.300
0.300
0.300
0.300
0.300
0.300
0.300
0.250
0.250
0.250
0.250
0.150
0.100
Fillet
Radius
R
in.
11.8
10.1
7.04
7.11
5.22
5.93
4.24
4.92
3.53
4.01
2.73
3.43
2.41
2.63
1.88
1.98
1.48
1.36
0.965
0.911
0.490
Area
A
in2
1. New shape; check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
CS 14 × 13.9
0.470
4.250
10.000
CS 10 × 8.36
0.410
0.440
0.350
0.410
3.500
3.250
9.000
CS 9 × 4.98
4.000
3.750
8.000
CS 8 × 5.79
0.350
9.000
3.000
8.000
CS 8 × 4.15
0.380
10.000
3.500
7.000
CS 7 × 4.72
0.290
0.350
CS 10 × 6.14
2.750
CS 7 × 3.21
0.290
0.320
0.260
0.290
0.230
0.260
0.200
0.260
0.130
CS 9 × 6.97
3.250
6.000
7.000
CS 6 × 4.03
1
Designation
Width
b
in.
Depth
d
in.
Flange
Thickness
tf
in.
401
240
160
116
83.2
78.3
54.4
52.7
37.4
33.8
22.1
21.0
14.4
11.1
7.88
5.21
3.91
1.97
1.41
0.546
0.288
Ix
in4
57.3
39.9
26.6
23.2
16.6
17.4
12.1
13.2
9.35
9.65
6.31
7.01
4.78
4.45
3.15
2.60
1.95
1.31
0.940
0.546
0.288
Sx
in3
Axis x-x
TABLE 4 – ALUMINUM ASSOCIATION STANDARD CHANNELS
5.82
4.88
4.77
4.04
3.99
3.63
3.58
3.27
3.26
2.90
2.85
2.48
2.44
2.06
2.05
1.62
1.63
1.20
1.21
0.774
0.766
rx
in.
44.7
25.7
11.0
13.0
6.33
9.60
4.40
7.12
3.25
5.13
2.10
3.76
1.53
2.05
0.975
1.02
0.601
0.417
0.217
0.139
0.0450
Iy
in4
11.2
7.59
3.85
4.46
2.55
3.49
1.89
2.82
1.57
2.23
1.10
1.76
0.896
1.14
0.642
0.692
0.446
0.368
0.215
0.178
0.0639
Sy
in3
ry
in.
1.94
1.60
1.25
1.35
1.10
1.27
1.02
1.20
0.959
1.13
0.878
1.05
0.798
0.884
0.720
0.717
0.638
0.554
0.474
0.390
0.303
Axis y-y
2.00
1.61
1.14
1.34
1.02
1.25
0.928
1.22
0.934
1.20
0.842
1.12
0.788
0.955
0.731
0.775
0.653
0.617
0.494
0.471
0.296
x
in.
4.25
3.40
2.47
2.84
2.20
2.68
2.02
2.59
1.99
2.52
1.81
2.34
1.67
1.98
1.54
1.60
1.38
1.25
1.02
0.904
0.626
xo
in.
1510
639
281
226
111
135
62.8
78.5
36.0
43.0
17.8
23.1
9.52
8.70
4.17
2.76
1.65
0.626
0.332
0.0894
0.0324
Cw
in6
1.19
0.948
0.367
0.444
0.209
0.293
0.127
0.210
0.102
0.147
0.0552
0.109
0.0495
0.0700
0.0314
0.0444
0.0202
0.0246
0.00990
0.0171
0.00274
J
in4
7.46
6.16
5.51
5.12
4.69
4.69
4.24
4.34
3.94
4.01
3.49
3.57
3.06
2.99
2.66
2.39
2.22
1.82
1.65
1.25
1.03
r0
in.
VI-8
January 2005
1.410
1.498
1.596
3.000
3.000
3.000
4.000
4.000
4.000
5.000
5.000
5.000
6.000
6.000
6.000
6.000
7.000
7.000
7.000
7.000
Designation
C 2 × 1.22
C 3 × 1.42
C 3 × 1.73
C 3 × 2.07
C 4 × 1.85
C 4 × 2.16
C 4 × 2.50
C 5 × 2.32
C 5 × 3.11
C 5 × 3.97
C 6 × 2.83
C 6 × 3.00
C 6 × 3.63
C 6 × 4.50
C 7 × 3.54
C 7 × 4.23
C 7 × 5.10
C 7 × 5.96
2.110
2.194
2.299
2.404
1.920
1.945
2.034
2.157
1.750
1.885
2.032
1.580
1.647
1.720
Width
b
in.
1.410
Depth
d
in.
2.000
0.210
0.210
0.210
0.210
0.200
0.200
0.200
0.200
0.190
0.190
0.190
0.180
0.180
0.180
0.170
0.170
0.170
Flange Tip
Thickness
tf
in.
0.170
0.367
0.367
0.367
0.367
0.343
0.343
0.343
0.343
0.320
0.320
0.320
0.297
0.297
0.297
0.273
0.273
0.273
Average
Flange
Thickness
t
in.
0.273
0.230
0.314
0.419
0.524
0.200
0.225
0.314
0.438
0.190
0.325
0.472
0.180
0.247
0.320
0.170
0.258
0.356
Web
Thickness
tw
in.
0.170
TABLE 5 – AMERICAN STANDARD CHANNELS
0.310
0.310
0.310
0.310
0.300
0.300
0.300
0.300
0.290
0.290
0.290
0.280
0.280
0.280
0.270
0.270
0.270
Fillet
Radius
R1
in.
0.270
0.130
0.130
0.130
0.130
0.120
0.120
0.120
0.120
0.110
0.110
0.110
0.110
0.110
0.110
0.100
0.100
0.100
Tip
Radius
R2
in.
0.100
5.50
5.50
5.50
5.50
4.50
4.50
4.50
4.50
3.75
3.75
3.75
2.75
2.75
2.75
1.75
1.75
1.75
d1
in.
0.75
3.01
3.60
4.33
5.07
2.40
2.55
3.09
3.83
1.97
2.64
3.38
1.57
1.84
2.13
1.21
1.47
1.76
Area
A
in2
1.04
21.8
24.2
27.2
30.3
13.1
13.6
15.2
17.4
7.49
8.90
10.4
3.83
4.19
4.58
1.66
1.85
2.07
Ix
in4
0.622
6.24
6.93
7.78
8.64
4.37
4.52
5.06
5.80
3.00
3.56
4.17
1.92
2.10
2.29
1.10
1.24
1.38
Sx
in3
0.622
Axis x-x
2.69
2.60
2.51
2.44
2.34
2.31
2.22
2.13
1.95
1.83
1.76
1.56
1.51
1.47
1.17
1.12
1.08
rx
in.
0.774
1.01
1.17
1.38
1.59
0.69
0.73
0.87
1.05
0.48
0.63
0.81
0.32
0.37
0.43
0.20
0.21
0.31
Iy
in4
0.172
0.64
0.70
0.78
0.86
0.49
0.51
0.56
0.64
0.38
0.45
0.53
0.28
0.31
0.34
0.20
0.21
0.27
Sy
in3
0.188
Axis y-y
0.58
0.57
0.56
0.56
0.54
0.54
0.50
0.52
0.49
0.49
0.49
0.45
0.45
0.45
0.40
0.41
0.42
ry
in.
0.407
0.54
0.52
0.53
0.55
0.51
0.51
0.50
0.51
0.48
0.48
0.51
0.46
0.45
0.46
0.44
0.44
0.46
y-axis
Location
x
in.
0.49
January 2005
VI-9
9.000
9.000
9.000
9.000
10.000
10.000
10.000
10.000
12.000
12.000
12.000
12.000
15.000
15.000
C 9 × 4.60
C 9 × 5.19
C 9 × 6.91
C 9 × 8.65
C 10 × 5.28
C 10 × 6.91
C 10 × 8.64
C 10 × 10.4
C 12 × 7.41
C 12 × 8.64
C 12 × 10.4
C 12 × 12.1
C 15 × 11.7
C 15 × 17.3
3.400
3.716
2.960
3.047
3.170
3.292
2.600
2.739
2.886
3.033
2.430
2.485
2.648
2.812
2.290
2.343
2.435
2.527
0.400
0.400
0.280
0.280
0.280
0.280
0.240
0.240
0.240
0.240
0.230
0.230
0.230
0.230
0.220
0.220
0.220
0.220
0.650
0.650
0.502
0.502
0.502
0.502
0.437
0.437
0.437
0.437
0.413
0.413
0.413
0.413
0.390
0.390
0.390
0.390
0.400
0.716
0.300
0.387
0.510
0.632
0.240
0.379
0.526
0.673
0.230
0.285
0.448
0.612
0.250
0.303
0.395
0.487
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
8.000
8.000
8.000
8.000
C 8 × 4.25
C 8 × 4.75
C 8 × 5.62
C 8 × 6.48
0.500
0.500
0.380
0.380
0.380
0.380
0.340
0.340
0.340
0.340
0.330
0.330
0.330
0.330
0.320
0.320
0.320
0.320
0.240
0.240
0.170
0.170
0.170
0.170
12.4
12.4
10.0
10.0
10.0
10.0
8.25
8.25
8.25
8.25
7.25
7.25
7.25
7.25
0.140
0.140
0.140
0.140
0.140
0.140
0.140
0.140
6.25
6.25
6.25
6.25
0.130
0.130
0.130
0.130
9.96
14.7
6.30
7.35
8.82
10.3
315
404
132
144
162
180
67.4
79.0
91.2
104
47.7
51.0
60.9
70.9
3.91
4.41
5.88
7.35
4.49
5.88
7.35
8.82
33.9
36.1
40.0
44.0
3.62
4.04
4.78
5.51
42.0
53.8
22.0
24.1
27.0
29.9
13.5
15.8
18.2
20.7
10.6
11.3
13.5
15.8
8.46
9.03
10.0
11.0
5.62
5.24
4.57
4.43
4.29
4.18
3.87
3.66
3.52
3.43
3.49
3.40
3.22
3.11
3.06
2.99
2.90
2.82
8.13
11.0
3.99
4.47
5.14
5.82
2.28
2.81
3.36
3.95
1.75
1.93
2.42
2.94
1.40
1.53
1.75
1.98
3.11
3.78
1.76
1.89
2.06
2.24
1.16
1.32
1.48
1.66
0.96
1.01
1.17
1.34
0.81
0.85
0.93
1.01
0.90
0.87
0.80
0.78
0.76
0.75
0.71
0.69
0.68
0.67
0.67
0.66
0.64
0.63
0.62
0.61
0.61
0.60
0.79
0.80
0.69
0.67
0.67
0.69
0.63
0.61
0.62
0.65
0.60
0.59
0.58
0.61
0.56
0.55
0.55
0.57
VI-10
January 2005
3.000
3.000
4.000
5.000
6.000
6.000
8.000
8.000
10.000
10.000
10.000
Designation
CS 3 × 2.23
CS 3 × 2.70
CS 4 × 3.32
CS 5 × 5.82
CS 6 × 5.77
CS 6 × 5.93
CS 8 × 6.59
CS 8 × 7.86
CS 10 × 8.58
CS 10 × 9.32
CS 10 × 10.1
3.500
3.563
3.625
3.000
3.500
3.000
3.500
2.500
2.875
2.000
2.000
Width
b
in.
0.544
0.544
0.544
0.468
0.524
0.375
0.442
0.344
0.562
0.320
0.375
Avg Flange
Thickness
tf
in.
0.375
0.438
0.500
0.380
0.425
0.500
0.375
0.318
0.438
0.250
0.375
Web
Thickness
tw
in.
1:9
1:9
1:9
1:14.43
1:28.5
0
1:49.6
1:34.9
1:9.8
1:12.1
0
Flange
Slope
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth
d
in.
TABLE 6 – CAR AND SHIP BUILDING CHANNELS
0.625
0.625
0.625
0.550
0.525
0.375
0.480
0.375
0.250
0.250
0.188
Fillet
Radius
R1
in.
0.188
0.188
0.188
0.220
0.375
0.250
0.420
0.125
0.094
0
0.375
Tip
Radius
R2
in.
7.50
7.50
7.50
5.75
5.75
4.50
4.00
2.38
3.00
1.75
0.875
d1
in.
7.30
7.93
8.55
5.60
6.68
4.91
5.04
2.82
4.95
1.90
2.30
Area
A
in2
110
115
120
54.2
63.8
24.1
28.2
6.84
18.1
2.61
2.89
Ix
in.4
21.9
24.0
24.0
13.5
15.9
8.02
9.41
3.42
7.25
1.74
1.92
Sx
in.3
Axis x-x
3.88
3.81
3.75
3.11
3.09
2.21
2.37
1.56
1.91
1.17
1.12
rx
in.
7.19
7.73
8.25
4.10
7.06
3.52
5.58
1.62
3.57
0.68
0.78
Iy
in.4
2.80
2.93
3.04
1.88
2.84
1.61
2.31
0.95
1.87
0.52
0.59
Sy
in.3
0.99
0.99
0.98
0.86
1.03
0.85
1.05
0.76
0.85
0.60
0.58
ry
in.
Axis y-y
0.93
0.92
0.91
0.81
1.01
0.81
1.09
0.81
0.96
0.68
0.67
x
in.
January 2005
VI-11
1.500
1.500
2.000
1.620
1.750
2.000
2.000
2.500
3.000
3.000
3.000
4.000
4.000
4.000
4.000
4.000
5.000
5.000
5.000
5.000
6.000
6.000
6.000
7.000
7.000
8.000
8.000
10.000
10.000
10.000
12.000
CS 2 × 0.706
CS 2.25 × 0.86
CS 3 × 1.48
CS 3 × 1.85
CS 3 × 2.18
CS 4 × 1.90
CS 4 × 2.24
CS 4 × 2.02
CS 4 × 2.53
CS 4 × 2.90
CS 5 × 2.51
CS 5 × 3.11
CS 5 × 3.05
CS 5 × 3.55
CS 6 × 3.60
CS 6 × 3.51
CS 6 × 6.42
CS 7 × 3.90
CS 7 × 4.61
CS 8 × 4.65
CS 8 × 5.56
CS 10 × 6.23
CS 10 × 7.58
CS 10 × 19.0
CS 12 × 10.3
0.437
0.500
1.250
0.562
3.000
3.500
4.000
4.000
0.375
0.281
0.312
0.812
0.250
0.281
0.218
0.250
0.281
0.250
0.375
0.188
0.281
0.218
0.250
0.188
0.250
0.188
0.250
0.250
0.188
0.250
0.250
0.125
0.188
Web
Thickness
tw
in.
0.625
0.500
0.562
0.500
0.437
0.500
0.437
0.500
0.437
0.437
0.437
0.375
0.375
0.437
0.437
0.375
0.375
0.375
0.375
0.375
0.312
0.312
0.188
0.125
0.062
Fillet
Radius
R
in.
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
0.375
0.437
0.375
0.375
0.375
0.312
0.500
0.312
0.343
0.312
0.375
0.281
0.281
0.250
0.312
0.312
0.250
0.312
0.312
0.125
0.188
Flange
Thickness
tf
in.
2.750
3.000
2.500
3.000
2.000
2.500
3.500
2.000
2.000
2.500
2.500
1.500
1.000
2.000
2.250
Designation
Width
b
in.
Depth
d
in.
TABLE 7 – CANADIAN CHANNELS
8.74
5.29
6.44
16.2
3.96
4.73
3.32
3.92
3.06
2.99
5.46
2.13
2.64
2.60
3.02
1.62
1.90
1.72
2.15
2.46
1.26
1.57
1.86
0.600
0.730
Area
A
in2
192
79.9
101
223
39.0
47.3
25.8
30.8
15.8
16.4
30.9
8.45
9.59
10.5
12.0
3.95
4.41
4.36
5.21
6.27
1.72
2.03
2.56
0.391
0.505
Ix
in4
4.69
3.89
3.95
3.71
16.0
20.1
44.5
32.0
3.14
3.16
2.79
2.80
2.27
2.34
2.38
1.99
1.90
2.01
1.99
1.56
1.52
1.59
1.56
1.60
1.17
1.14
1.17
0.807
0.832
rx
in.
9.74
11.8
7.37
8.79
5.26
5.47
10.3
3.38
3.84
4.18
4.79
1.98
2.21
2.18
2.60
3.14
1.15
1.35
1.71
0.391
0.449
Sx
in3
Axis x-x
13.1
4.39
7.59
23.3
2.83
4.10
2.02
3.47
1.06
1.74
6.62
0.832
0.942
1.60
1.86
0.396
0.514
0.667
0.810
1.52
0.268
0.321
0.730
0.137
0.062
Iy
in4
4.56
2.01
3.07
8.94
1.44
1.95
1.16
1.67
0.740
0.978
2.87
0.607
0.669
0.944
1.11
0.355
0.417
0.486
0.595
0.919
0.265
0.322
0.568
0.136
0.090
Sy
in3
1.22
0.911
1.09
1.20
0.846
0.931
0.781
0.941
0.588
0.764
1.10
0.625
0.597
0.786
0.784
0.495
0.520
0.623
0.613
0.786
0.461
0.452
0.627
0.477
0.292
ry
in.
Axis y-y
1.13
0.819
1.03
1.39
0.781
0.900
0.759
0.921
0.569
0.719
1.19
0.630
0.592
0.801
0.830
0.504
0.519
0.627
0.638
0.842
0.489
0.502
0.714
0.493
0.303
x
in.
2.38
1.73
2.15
2.49
1.65
1.87
1.57
1.94
1.13
1.52
2.44
1.29
1.20
1.67
1.69
1.01
1.05
1.31
1.30
1.74
0.981
0.971
1.44
1.06
0.605
xo
in.
J
in4
338
79.3
134
402
32.2
46.1
17.3
29.5
7.04
11.2
40.3
3.59
4.27
6.86
7.89
1.11
1.49
1.84
2.25
4.13
0.415
0.501
1.09
0.665
0.234
0.383
6.547
0.134
0.220
0.109
0.138
0.109
0.079
0.380
0.050
0.086
0.066
0.110
0.032
0.044
0.029
0.058
0.068
0.021
0.043
0.053
0.0938 0.0031
0.0589 0.0086
Cw
in6
5.40
4.35
4.63
4.62
3.65
3.79
3.29
3.53
2.61
2.90
3.58
2.45
2.33
2.73
2.73
1.92
1.92
2.15
2.12
2.49
1.59
1.56
1.96
1.42
1.07
r0
in.
VI-12
January 2005
0.350
0.410
0.440
0.410
0.500
0.470
0.620
2.500
2.500
3.000
3.000
3.500
4.000
4.000
4.500
5.000
5.000
5.500
6.000
6.000
7.000
7.000
8.000
3.000
3.000
4.000
4.000
5.000
6.000
6.000
7.000
8.000
8.000
9.000
10.000
10.000
12.000
12.000
14.000
Designation
I 3 × 1.64
I 3 × 2.03
I 4 × 2.31
I 4 × 2.79
I 5 × 3.70
I 6 × 4.03
I 6 × 4.69
I 7 × 5.80
I 8 × 6.18
I 8 × 7.02
I 9 × 8.36
I 10 × 8.65
I 10 × 10.3
I 12 × 11.7
I 12 × 14.3
I 14 × 16.01
0.300
0.250
0.290
0.290
0.310
0.230
0.250
0.270
0.190
0.190
0.210
0.230
0.130
0.150
0.150
0.170
Web
Thickness
tw
in.
0.400
0.400
0.400
0.400
0.400
0.300
0.300
0.300
0.300
0.300
0.300
0.300
0.250
0.250
0.250
0.250
Fillet
Radius
R
in.
1. New shape; check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
0.600
0.320
0.290
0.350
0.380
0.200
0.260
0.230
0.290
Width
b
in.
Depth
d
in.
Flange
Thickness
tf
in.
14.2
7.35
8.75
9.92
12.2
5.26
5.97
7.11
3.15
3.43
3.99
4.93
1.39
1.73
1.96
2.38
Area
A
in2
TABLE 8 – ALUMINUM ASSOCIATION STANDARD I-BEAMS
489
132
156
256
317
59.7
67.8
102
13.9
22.0
25.5
42.9
2.24
2.71
5.62
6.71
Ix
in4
69.9
26.4
31.2
42.6
52.9
14.9
16.9
22.7
5.58
7.33
8.50
12.3
1.49
1.81
2.81
3.36
Sx
in3
Axis x-x
6.00
4.24
4.22
5.07
5.11
3.37
3.37
3.79
2.11
2.53
2.53
2.95
1.27
1.25
1.69
1.68
rx
in.
51.2
14.8
18.0
26.9
35.5
7.30
8.55
12.2
2.29
3.10
3.74
5.78
0.522
0.679
1.04
1.31
Iy
in4
12.8
4.93
6.01
7.69
10.1
2.92
3.42
4.44
1.31
1.55
1.87
2.57
0.418
0.543
0.691
0.872
Sy
in3
Axis y-y
1.94
1.42
1.44
1.65
1.71
1.18
1.20
1.31
0.853
0.951
0.968
1.08
0.613
0.627
0.727
0.742
ry
in.
2300
340
407
894
1149
107
123
224
12.5
25.3
29.8
63.3
1.02
1.27
3.68
4.50
Cw
in6
1.31
0.360
0.620
0.621
1.26
0.188
0.286
0.386
0.0984
0.0888
0.145
0.206
0.0192
0.0374
0.0333
0.0608
J
in4
6.31
4.47
4.46
5.33
5.39
3.57
3.57
4.01
2.27
2.71
2.71
3.14
1.41
1.40
1.84
1.84
r0
in.
January 2005
VI-13
2.000
4.000
5.000
6.000
6.000
6.000
6.000
6.000
8.000
8.000
8.000
8.000
8.000
8.000
9.750
9.900
11.940
12.060
Designation
WF 2 × 1.43
WF 4 × 4.76
WF 5 × 6.49
WF 6 × 4.16
WF 6 × 5.40
WF 6 × 7.85
WF 6 × 8.30
WF 6 × 9.18
WF 8 × 5.90
WF 8 × 8.32
WF 8 × 10.7
WF 8 × 11.2
WF 8 × 11.8
WF 8 × 13.0
WF 10 × 11.4
WF 10 × 7.30
WF 12 × 13.8
WF 12 × 18.3
8.000
10.000
7.964
5.750
5.250
6.500
8.000
7.940
8.000
8.130
4.000
6.000
5.930
6.000
6.130
2.000
4.000
5.000
Width
b
in.
0.516
0.576
0.433
0.340
0.308
0.398
0.433
0.458
0.458
0.458
0.279
0.269
0.451
0.451
0.451
0.232
0.370
0.415
Avg Flange
Thickness
tf
in.
0.294
0.345
0.292
0.240
0.230
0.245
0.288
0.313
0.375
0.500
0.230
0.240
0.250
0.313
0.438
0.188
0.313
0.313
Web
Thickness
tw
in.
0
0
0
0
0
0
0
1:18.9
1:18.9
1:18.9
0
0
1:15.6
1:15.6
1:15.6
1:11.4
1:11.3
1:13.6
Flange
Slope
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth
d
in.
TABLE 9 – WIDE FLANGE BEAMS
0.600
0.600
0.500
0.312
0.320
0.400
0.400
0.313
0.313
0.313
0.250
0.250
0.313
0.313
0.313
0.188
0.313
0.313
Fillet
Radius
R1
in.
0
0
0
0
0
0
0
0.179
0.179
0.179
0
0
0.180
0.180
0.180
0.094
0.145
0.165
Tip Radius
R2
in.
9.69
9.69
7.88
8.56
6.75
6.38
6.38
6.25
6.25
6.25
4.88
4.88
4.38
4.38
4.38
1.13
2.38
3.38
d1
in.
11.8
15.6
9.71
6.21
5.02
7.08
9.12
9.55
10.1
11.1
3.54
4.59
6.68
7.06
7.81
1.22
4.05
5.52
Area
A
in2
310
426
171
107
56.7
84.2
110
113
116
121
21.8
30.2
44.3
45.4
47.6
0.782
10.8
23.9
Ix
in.4
51.9
70.7
35.1
21.6
14.2
21.0
27.4
28.3
29.0
30.3
7.25
10.1
14.8
15.1
15.9
0.782
5.40
9.58
Sx
in.3
Axis x-x
5.13
5.23
4.20
4.15
3.36
3.44
3.47
3.45
3.40
3.31
2.48
2.56
2.57
2.54
2.47
0.80
1.63
2.08
rx
in.
44.1
96.1
36.5
10.8
7.44
18.2
37.0
33.9
34.7
36.5
2.98
9.69
14.0
14.5
15.5
0.275
3.52
7.73
Iy
in.4
11.0
19.2
9.16
3.75
2.83
5.61
9.24
8.47
8.68
9.13
1.49
3.23
4.67
4.83
5.16
0.275
1.76
3.09
Sy
in.3
Axis y-y
1.94
2.48
1.94
1.32
1.22
1.61
2.01
1.88
1.86
1.82
0.92
1.45
1.45
1.43
1.41
0.47
0.93
1.18
ry
in.
VI-14
January 2005
2.000
2.000
2.000
2.000
3.000
3.500
3.500
4.000
5.000
2.500
3.000
3.000
4.000
4.000
4.000
4.000
4.000
5.000
Designation
WF(A-N) 2 × 0.928
WF(A-N) 3 × 0.769
WF(A-N) 3 × 1.00
WF(A-N) 4 × 1.14
WF(A-N) 4 × 1.79
WF(A-N) 4 × 2.35
WF(A-N) 4 × 3.06
WF(A-N) 4 × 4.14
WF(A-N) 5 × 5.36
0.125
0.094
0.125
0.125
0.156
0.188
0.250
0.312
0.312
0.125
0.094
0.125
0.125
0.156
0.188
0.250
0.312
0.312
Web
Thickness
tw
in.
0.156
0.156
0.156
0.125
0.188
0.188
0.188
0.250
0.312
Fillet
Radius
R1
in.
0.125
0.094
0.125
0.125
0.156
0.188
0.250
0.312
0.125
Tip
Radius
R2
in.
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Width
b
in.
Depth
d
in.
Flange
Thickness
tf
in.
TABLE 10 – ARMY-NAVY WIDE FLANGE BEAMS
2.00
2.50
2.50
3.50
3.25
3.25
3.00
2.75
3.75
d1
in.
0.789
0.654
0.851
0.969
1.52
2.00
2.60
3.52
4.56
Area
A
in2
0.831
0.992
1.26
2.42
4.14
5.52
6.97
9.39
19.7
Ix
in4
0.665
0.661
0.841
1.21
2.07
2.76
3.48
4.70
7.86
Sx
in3
Axis x-x
1.03
1.23
1.22
1.58
1.65
1.66
1.64
1.63
2.08
rx
in.
0.155
0.118
0.155
0.155
0.659
1.26
1.64
3.03
6.43
Iy
in4
0.155
0.118
0.155
0.155
0.439
0.719
0.936
1.51
2.57
Sy
in3
Axis y-y
0.443
0.426
0.426
0.400
0.658
0.793
0.793
0.927
1.19
ry
in.
0.235
0.265
0.344
0.626
2.59
4.88
6.28
11.3
35.7
Cw
in6
0.00407
0.00189
0.00439
0.00505
0.0123
0.0235
0.0547
0.115
0.146
J
in4
1.12
1.30
1.29
1.63
1.78
1.84
1.82
1.88
2.39
r0
in.
January 2005
VI-15
0.290
0.310
0.310
0.310
0.350
0.350
0.460
0.460
0.460
4.000
4.171
4.262
4.330
4.660
4.797
4.944
5.000
5.078
5.250
5.355
5.477
4.000
4.000
5.000
5.000
5.000
6.000
6.000
6.000
7.000
8.000
8.000
8.000
9.000
10.000
10.000
10.000
12.000
12.000
12.000
12.000
12.000
S 3 × 1.96
S 3 × 2.59
S 4 × 2.64
S 4 × 3.28
S 5 × 3.43
S 5 × 4.23
S 5 × 5.10
S 6 × 4.30
S 6 × 5.10
S 6 × 5.96
S 7 × 6.05
S 8 × 6.35
S 8 × 7.96
S 8 × 8.81
S 9 × 7.51
S 10 × 8.76
S 10 × 10.4
S 10 × 12.1
S 12 × 11.0
S 12 × 12.1
S 12 × 14.1
S 12 × 15.6
S 12 × 17.3
0.270
0.270
0.270
0.250
0.230
0.230
0.230
0.210
0.210
0.210
0.190
0.190
0.544
0.544
0.660
0.660
0.660
0.491
0.491
0.491
0.458
0.425
0.425
0.425
0.392
0.359
0.359
0.359
0.326
0.326
0.326
0.293
0.293
0.260
0.260
Avg
Flange
Thickness
t
in.
0.350
0.428
0.460
0.565
0.687
0.310
0.447
0.594
0.290
0.270
0.441
0.532
0.345
0.230
0.343
0.465
0.210
0.347
0.494
0.190
0.326
0.170
0.349
Web
Thickness
tw
in.
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
3.755
3.330
3.443
3.565
3.000
3.137
3.284
2.660
2.796
2.330
2.509
3.000
3.000
Designation
0.170
0.170
Width
b
in.
Depth
d
in.
Flange Tip
Thickness
tf
in.
TABLE 11 – AMERICAN STANDARD I-BEAMS
0.450
0.450
0.560
0.560
0.560
0.410
0.410
0.410
0.390
0.370
0.370
0.370
0.350
0.330
0.330
0.330
0.310
0.310
0.310
0.290
0.290
0.270
0.270
Fillet
Radius
R1
in.
0.210
0.210
0.280
0.280
0.280
0.190
0.190
0.190
0.170
0.160
0.160
0.160
0.150
0.140
0.140
0.140
0.130
0.130
0.130
0.110
0.110
0.100
0.100
Tip Radius
R2
in.
9.75
9.75
9.25
9.25
9.25
8.00
8.00
8.00
7.00
6.25
6.25
6.25
5.25
4.50
4.50
4.50
3.50
3.50
3.50
2.75
2.75
1.75
1.75
d1
in.
9.35
10.3
12.0
13.2
14.7
7.45
8.82
10.3
6.38
5.40
6.77
7.49
5.15
3.66
4.34
5.07
2.92
3.60
4.34
2.25
2.79
1.67
2.21
Area
A
in2
218
229
272
287
305
123
135
147
85.9
57.6
64.9
68.7
39.4
22.1
24.1
26.3
12.3
13.7
15.2
6.06
6.79
2.52
2.93
Ix
in4
36.4
38.2
45.4
47.9
50.8
24.5
27.0
29.4
19.1
14.4
16.2
17.2
11.3
7.36
8.04
8.77
4.90
5.48
6.09
3.03
3.39
1.68
1.95
Sx
in3
Axis x-x
4.83
4.72
4.77
4.66
4.56
4.07
3.91
3.78
3.67
3.27
3.10
3.03
2.77
2.46
2.36
2.28
2.05
1.95
1.87
1.64
1.56
1.23
1.15
rx
in.
9.35
9.87
13.5
14.5
15.7
6.78
7.50
8.36
5.09
3.73
4.31
4.66
2.88
1.82
2.04
2.31
1.21
1.41
1.66
0.76
0.90
0.46
0.59
Iy
in4
3.74
3.89
5.16
5.42
5.74
2.91
3.13
3.38
2.35
1.86
2.07
2.19
1.53
1.09
1.19
1.30
0.81
0.90
1.01
0.57
0.65
0.39
0.47
Sy
in3
Axis y-y
1.00
0.98
1.06
1.05
1.03
0.95
0.92
0.90
0.89
0.83
0.80
0.79
0.75
0.71
0.69
0.68
0.64
0.63
0.62
0.58
0.57
0.52
0.52
ry
in.
VI-16
March 2005
0.375
0.500
0.500
0.500
0.625
0.625
4.000
4.000
5.000
5.000
6.000
5.500
6.500
4.000
5.000
6.000
6.000
6.000
7.000
8.000
8.000
10.000
10.000
12.000
12.000
I 4 × 2.68
I 5 × 4.05
I 6 × 3.92
I 6 × 4.82
I 6 × 5.46
I 7 × 5.79
I 8 × 6.12
I 8 × 8.77
I 10 × 9.83
I 10 × 11.3
I 12 × 12.5
I 12 × 15.5
0.375
0.312
0.375
0.375
0.312
0.250
0.375
0.437
0.343
0.375
0.281
0.312
0.281
0.250
0.250
0.281
0.250
0.188
0.188
Web
Thickness
tw
in.
0.625
0.625
0.562
0.562
0.437
0.562
0.438
0.375
0.438
0.437
0.437
0.375
0.375
Fillet
Radius
R
in.
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
3.000
3.500
4.000
3.500
3.000
0.250
I 3 × 2.16
2.500
3.000
Designation
Flange
Thickness
tf
in.
Depth
d
in.
Width
b
in.
TABLE 12 – CANADIAN I-BEAMS
10.6
13.2
8.36
9.65
5.20
7.46
4.92
3.34
4.10
4.64
3.44
2.28
1.84
Area
A
in2
252
317
139
163
54.6
82.4
40.2
19.2
24.9
28.2
14.5
6.28
2.78
Ix
in4
42.0
52.9
27.8
32.7
13.6
20.6
11.5
6.40
8.28
9.40
5.79
3.14
1.85
Sx
in3
Axis x-x
4.88
4.91
4.08
4.12
3.24
3.32
2.86
2.40
2.46
2.47
2.05
1.66
1.23
rx
in.
15.7
28.7
10.5
18.1
4.02
10.5
4.02
1.42
2.70
4.02
2.24
1.13
0.657
Iy
in4
5.70
8.84
4.19
6.02
2.01
4.18
2.01
0.945
1.54
2.01
1.28
0.754
0.525
Sy
in3
Axis y-y
1.22
1.48
1.12
1.37
0.880
1.18
0.904
0.652
0.811
0.931
0.808
0.705
0.597
ry
in.
513
929
236
408
58.5
147
44.1
11.5
21.3
31.8
12.3
3.98
1.24
Cw
in6
0.193
0.245
0.127
0.140
0.048
0.116
0.048
0.026
0.043
0.048
0.036
0.017
0.017
J
in4
5.03
5.13
4.23
4.34
3.36
3.53
3.00
2.49
2.59
2.64
2.20
1.80
1.37
r0
in.
January 2005
VI-17
4.000
6.000
6.000
8.000
4.000
6.000
6.000
8.000
Designation
WF 4 × 4.12
WF 6 × 7.61
WF 6 × 9.66
WF 8 × 13.1
0.500
0.375
0.500
0.312
Flange
Thickness
tf
in.
0.375
0.312
0.375
0.250
Web
Thickness
tw
in.
0.750
0.625
0.625
0.437
Fillet
Radius
R
in.
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Width
b
in.
Depth
d
in.
TABLE 13 – CANADIAN WIDE FLANGE BEAMS
11.1
6.47
8.21
3.50
Area
A
in2
129
41.5
51.2
9.72
Ix
in4
32.2
13.8
17.1
4.86
Sx
in3
Axis x-x
3.40
2.53
2.50
1.67
rx
in.
42.8
13.5
18.1
3.34
Iy
in4
10.7
4.52
6.02
1.67
Sy
in3
Axis y-y
1.96
1.45
1.48
0.977
ry
in.
601
107
137
11.4
Cw
in6
0.267
0.117
0.176
0.036
J
in4
3.93
2.91
2.91
1.93
r0
in.
VI-18
January 2005
2.500
2.500
2.500
2.500
2.500
2.500
3.000
3.000
3.000
3.000
3.000
1.750
1.750
1.750
2.000
2.000
2.000
2.000
2.000
2.500
2.500
2.500
2.500
2.500
2.500
3.000
3.000
3.000
3.000
3.000
3.500
3.500
3.500
3.500
L 1 1/2 × 1 1/2 × 1/8
L 1 1/2 × 1 1/2 × 1/4
L 1 3/4 × 1 3/4 × 1/8
L 1 3/4 × 1 3/4 × 1/4
L 1 3/4 × 1 3/4 × 3/8
L 2 × 2 × 1/8
L 2 × 2 × 3/16
L 2 × 2 × 1/4
L 2 × 2 × 5/16
L 2 × 2 × 3/8
L 2 1/2 × 2 1/2 × 1/8
L 2 1/2 × 2 1/2 × 3/16
L 2 1/2 × 2 1/2 × 1/4
L 2 1/2 × 2 1/2 × 5/16
L 2 1/2 × 2 1/2 × 3/8
L 2 1/2 × 2 1/2 × 1/2
L 3 × 3 × 3/16
L 3 × 3 × 1/4
L 3 × 3 × 5/16
L 3 × 3 × 3/8
L 3 × 3 × 1/2
L 3 1/2 × 3 1/2 × 1/4
L 3 1/2 × 3 1/2 × 5/16
L 3 1/2 × 3 1/2 × 3/8
L 3 1/2 × 3 1/2 × 1/2
3.500
3.500
3.500
3.500
2.000
2.000
2.000
2.000
2.000
1.750
1.750
1.750
1.500
1.500
1.500
1.500
Designation
Width
b
in.
Depth
d
in.
TABLE 14 – ANGLES – EQUAL LEGS
0.250
0.313
0.375
0.500
0.188
0.250
0.312
0.375
0.500
0.125
0.188
0.250
0.312
0.375
0.500
0.125
0.188
0.250
0.312
0.375
0.125
0.250
0.375
0.125
0.250
Thickness
t
in.
0.375
0.375
0.375
0.375
0.312
0.312
0.312
0.312
0.312
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.188
0.188
0.188
0.188
0.188
Fillet
Radius
R1
in.
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
Tip Radius
R2
in.
1.99
2.47
2.93
3.83
1.28
1.68
2.08
2.47
3.23
0.72
1.07
1.40
1.73
2.05
2.65
0.58
0.85
1.11
1.36
1.61
0.50
0.96
1.38
0.42
0.81
Weight
lb/ft
1.69
2.10
2.49
3.25
1.09
1.43
1.77
2.10
2.74
0.616
0.911
1.19
1.47
1.74
2.26
0.491
0.723
0.944
1.16
1.37
0.423
0.813
1.17
0.360
0.688
Area
A
in2
1.94
2.38
2.79
3.57
0.908
1.19
1.45
1.71
2.17
0.369
0.539
0.695
0.839
0.976
1.22
0.185
0.268
0.342
0.410
0.474
0.121
0.223
0.306
0.0745
0.135
Ix , Iy
in4
0.758
0.942
1.12
1.45
0.412
0.547
0.677
0.804
1.04
0.200
0.297
0.388
0.475
0.560
0.718
0.126
0.186
0.242
0.295
0.346
0.0948
0.182
0.259
0.0684
0.130
Sx , Sy
in3
1.07
1.07
1.06
1.05
0.914
0.912
0.907
0.901
0.889
0.774
0.769
0.763
0.756
0.749
0.735
0.613
0.608
0.602
0.595
0.589
0.535
0.523
0.511
0.455
0.444
rx , ry
in.
Axis x-x, y-y
0.947
0.974
1.00
1.05
0.797
0.826
0.852
0.877
0.924
0.655
0.684
0.710
0.734
0.757
0.802
0.531
0.560
0.585
0.609
0.632
0.473
0.524
0.570
0.411
0.461
x, y
in.
0.739
0.924
1.10
1.45
0.332
0.450
0.563
0.674
0.888
0.143
0.213
0.278
0.341
0.403
0.525
0.071
0.106
0.138
0.169
0.201
0.0462
0.0904
0.132
0.0282
0.0556
Iz
in4
rz
in.
0.661
0.664
0.665
0.667
0.553
0.560
0.564
0.566
0.569
0.483
0.484
0.483
0.482
0.481
0.482
0.381
0.382
0.382
0.383
0.383
0.330
0.333
0.336
0.280
0.284
Axis z-z
January 2005
VI-19
5.000
5.000
5.000
5.000
5.000
5.000
6.000
6.000
6.000
6.000
6.000
8.000
8.000
8.000
8.000
L 5 × 5 × 3/8
L 5 × 5 × 7/16
L 5 × 5 × 1/2
L 5 × 5 × 9/16
L 5 × 5 × 5/8
L 5 × 5 × 3/4
L 6 × 6 × 3/8
L 6 × 6 × 7/16
L 6 × 6 × 1/2
L 6 × 6 × 5/8
L 6 × 6 × 3/4
L 8 × 8 × 1/2
L 8 × 8 × 5/8
L 8 × 8 × 3/4
L8×8×1
8.000
8.000
8.000
8.000
6.000
6.000
6.000
6.000
6.000
5.000
5.000
5.000
5.000
5.000
5.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
0.500
0.625
0.750
1.000
0.375
0.438
0.500
0.625
0.750
0.375
0.438
0.500
0.563
0.625
0.750
0.250
0.313
0.375
0.438
0.500
0.563
0.625
0.688
0.750
0.625
0.625
0.625
0.625
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
L 4 × 4 × 1/4
L 4 × 4 × 5/16
L 4 × 4 × 3/8
L 4 × 4 × 7/16
L 4 × 4 × 1/2
L 4 × 4 × 9/16
L 4 × 4 × 5/8
L 4 × 4 × 11/16
L 4 × 4 × 3/4
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
7.77
9.63
11.5
15.0
4.35
5.06
5.74
7.10
8.43
5.12
5.95
6.75
8.35
9.91
9.14
11.3
13.5
17.7
3.60
4.18
4.74
5.31
5.85
6.93
1.94
2.41
2.86
3.32
3.75
4.19
4.61
5.03
5.44
4.24
4.92
5.58
6.24
6.88
8.15
2.28
2.83
3.37
3.90
4.41
4.93
5.42
5.92
6.40
47.8
58.6
68.9
88.2
14.9
17.2
19.4
23.7
27.7
8.40
9.69
10.9
12.1
13.3
15.4
2.94
3.62
4.26
4.89
5.47
6.04
6.57
7.09
7.58
8.18
10.1
12.0
15.6
3.39
3.94
4.48
5.52
6.53
2.31
2.68
3.04
3.40
3.75
4.42
1.00
1.25
1.48
1.71
1.93
2.15
2.36
2.57
2.77
2.48
2.47
2.45
2.42
1.85
1.84
1.84
1.83
1.81
1.53
1.52
1.52
1.51
1.50
1.49
1.23
1.23
1.22
1.21
1.21
1.20
1.19
1.19
1.18
2.16
2.21
2.26
2.35
1.61
1.64
1.66
1.71
1.76
1.36
1.39
1.41
1.44
1.46
1.51
1.07
1.10
1.12
1.15
1.17
1.20
1.22
1.24
1.27
18.8
23.2
27.5
35.9
5.69
6.65
7.58
9.39
11.1
3.19
3.73
4.25
4.77
5.28
6.27
1.13
1.41
1.68
1.95
2.20
2.46
2.71
2.96
3.21
1.55
1.55
1.55
1.55
1.14
1.15
1.15
1.15
1.15
0.941
0.945
0.947
0.948
0.949
0.951
0.762
0.765
0.766
0.766
0.766
0.766
0.766
0.767
0.768
TABLE 15 – SQUARE END ANGLES – EQUAL LEGS
Designation
LS 1 × 1 × 1/8
LS 1 × 1 × 3/16
LS 1 × 1 × 1/4
Depth
d
in.
Width
b
in.
Thickness
t
in.
Weight
lb/ft
1.000
1.000
1.000
1.000
1.000
1.000
0.125
0.188
0.250
0.28
0.40
0.51
LS 1 1/4 × 1 1/4 × 1/8
LS 1 1/4 × 1 1/4 × 3/16
LS 1 1/4 × 1 1/4 × 1/4
1.250
1.250
1.250
1.250
1.250
1.250
0.125
0.188
0.250
LS 1 1/2 × 1 1/2 × 1/8
LS 1 1/2 × 1 1/2 × 3/16
LS 1 1/2 × 1 1/2 × 1/4
1.500
1.500
1.500
1.500
1.500
1.500
LS 1 3/4 × 1 3/4 × 1/8
LS 1 3/4 × 1 3/4 × 3/16
LS 1 3/4 × 1 3/4 × 1/4
1.750
1.750
1.750
LS 2 × 2 × 1/8
LS 2 × 2 × 3/16
LS 2 × 2 × 1/4
Area
A
in2
Axis x-x, y-y
Axis z-z
0.234
0.341
0.438
Ix , Iy
in4
0.0217
0.0300
0.0369
Sx , Sy
in3
0.0309
0.0440
0.0558
rx , ry
in.
0.304
0.297
0.290
x, y
in.
0.296
0.318
0.339
Iz
in4
0.00896
0.0129
0.0168
rz
in.
0.196
0.195
0.196
0.35
0.51
0.66
0.297
0.435
0.563
0.0439
0.0616
0.0767
0.0493
0.0709
0.0905
0.385
0.377
0.369
0.359
0.381
0.403
0.0179
0.0258
0.0333
0.246
0.244
0.243
0.125
0.188
0.250
0.42
0.62
0.81
0.359
0.529
0.688
0.0778
0.110
0.139
0.0721
0.104
0.134
0.465
0.457
0.449
0.421
0.444
0.466
0.0315
0.0455
0.0586
0.296
0.293
0.292
1.750
1.750
1.750
0.125
0.188
0.250
0.50
0.73
0.96
0.422
0.623
0.813
0.126
0.179
0.227
0.099
0.144
0.186
0.546
0.537
0.529
0.484
0.507
0.529
0.0507
0.0734
0.0947
0.347
0.343
0.341
2.000
2.000
2.000
2.000
2.000
2.000
0.125
0.188
0.250
0.57
0.84
1.10
0.484
0.717
0.938
0.190
0.273
0.348
0.131
0.191
0.247
0.626
0.617
0.609
0.546
0.569
0.592
0.0766
0.111
0.143
0.398
0.394
0.391
LS 2 1/2 × 2 1/2 × 1/8
LS 2 1/2 × 2 1/2 × 3/16
LS 2 1/2 × 2 1/2 × 1/4
LS 2 1/2 × 2 1/2 × 5/16
2.500
2.500
2.500
2.500
2.500
2.500
2.500
2.500
0.125
0.188
0.250
0.312
0.72
1.06
1.40
1.72
0.609
0.905
1.19
1.46
0.378
0.548
0.703
0.847
0.207
0.303
0.394
0.481
0.787
0.778
0.769
0.761
0.671
0.695
0.717
0.739
0.152
0.222
0.287
0.350
0.499
0.495
0.491
0.489
LS 3 × 3 × 1/8
LS 3 × 3 × 3/16
LS 3 × 3 × 1/4
LS 3 × 3 × 5/16
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
0.125
0.188
0.250
0.312
0.86
1.28
1.69
2.09
0.734
1.09
1.44
1.77
0.661
0.964
1.24
1.51
0.300
0.442
0.577
0.706
0.949
0.939
0.930
0.922
0.797
0.820
0.842
0.865
0.265
0.388
0.504
0.616
0.601
0.596
0.592
0.589
LS 3 1/2 × 3 1/2 × 1/8
3.500
3.500
0.125
1.01
0.859
1.06
0.411
1.11
0.922
0.425
0.703
LS 4 × 4 × 1/8
LS 4 × 4 × 1/4
4.000
4.000
4.000
4.000
0.125
0.250
1.16
2.28
0.984
1.94
1.59
3.04
0.539
1.05
1.27
1.25
1.05
1.09
0.638
1.22
0.805
0.795
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
VI-20
January 2005
June 2005
VI-21
Depth
d
in.
1.750
1.750
1.750
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.250
2.500
2.500
2.500
2.500
2.500
2.500
2.500
2.500
2.500
2.500
2.500
3.000
3.000
3.000
3.000
3.000
3.000
Designation
L 1 3/4 × 1 1/4 × 1/8
L 1 3/4 × 1 1/4 × 3/16
L 1 3/4 × 1 1/4 × 1/4
L 2 × 1 × 3/16
L 2 × 1 1/4 × 1/8
L 2 × 1 1/4 × 1/4
L 2 × 1 1/2 × 1/8
L 2 × 1 1/2 × 3/16
L 2 × 1 1/2 × 1/4
L 2 × 1 1/2 × 3/8
L 2 × 1 3/4 × 1/4
L 2 1/4 × 1 1/2 × 1/4
L 2 1/2 × 1 1/4 × 1/8
L 2 1/2 × 1 1/2 × 1/8
L 2 1/2 × 1 1/2 × 3/16
L 2 1/2 × 1 1/2 × 1/4
L 2 1/2 × 1 1/2 × 5/16
L 2 1/2 × 1 1/2 × 3/8
L 2 1/2 × 2 × 1/8
L 2 1/2 × 2 × 3/16
L 2 1/2 × 2 × 1/4
L 2 1/2 × 2 × 5/16
L 2 1/2 × 2 × 3/8
L 3 × 1 1/2 × 1/4
L 3 × 2 × 3/16
L 3 × 2 × 1/4
L 3 × 2 × 5/16
L 3 × 2 × 3/8
L 3 × 2 × 1/2
2.000
2.000
2.000
2.000
2.000
1.500
2.000
2.000
2.000
2.000
2.000
1.500
1.500
1.500
1.500
1.500
1.250
1.500
1.750
1.500
1.500
1.500
1.500
1.250
1.250
1.000
1.250
1.250
1.250
Width
b
in.
0.188
0.250
0.312
0.375
0.500
0.250
0.125
0.188
0.250
0.312
0.375
0.125
0.188
0.250
0.312
0.375
0.125
0.250
0.250
0.125
0.188
0.250
0.375
0.125
0.250
0.188
0.125
0.188
0.250
Thickness
t
in.
0.312
0.312
0.312
0.312
0.312
0.312
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.188
0.250
0.250
0.188
0.188
0.188
0.188
0.188
0.188
0.188
0.188
0.188
0.188
Fillet
Radius
R1
in.
0.188
0.188
0.188
0.188
0.188
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.094
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
Tip
Radius
R2
in.
TABLE 16 – ANGLES – UNEQUAL LEGS
1.07
1.40
1.73
2.05
2.65
1.27
0.65
0.96
1.26
1.54
1.83
0.58
0.85
1.11
1.36
1.61
0.54
1.04
1.04
0.50
0.73
0.96
1.38
0.46
0.88
0.62
0.42
0.62
0.81
Weight
lb/ft
0.910
1.19
1.47
1.74
2.26
1.08
0.554
0.817
1.07
1.31
1.55
0.491
0.723
0.944
1.16
1.37
0.457
0.882
0.882
0.423
0.624
0.813
1.17
0.392
0.751
0.530
0.360
0.530
0.688
Area
A
in2
0.821
1.06
1.29
1.51
1.90
0.980
0.345
0.503
0.646
0.780
0.905
0.314
0.457
0.586
0.705
0.816
0.298
0.435
0.328
0.168
0.243
0.311
0.428
0.158
0.291
0.211
0.109
0.157
0.199
Ix
in4
rx
in.
0.400
0.526
0.647
0.765
0.987
0.510
0.194
0.288
0.375
0.459
0.541
0.186
0.275
0.358
0.437
0.514
0.182
0.292
0.237
0.120
0.178
0.231
0.330
0.117
0.224
0.166
0.949
0.944
0.938
0.931
0.918
0.954
0.789
0.784
0.778
0.770
0.763
0.800
0.794
0.787
0.780
0.773
0.807
0.702
0.610
0.630
0.625
0.618
0.604
0.635
0.623
0.631
0.0901 0.549
0.133 0.544
0.172 0.537
Sx
in3
Axis x-x
0.947
0.976
1.00
1.03
1.08
1.08
0.722
0.752
0.778
0.802
0.826
0.806
0.838
0.864
0.889
0.914
0.867
0.758
0.617
0.605
0.633
0.657
0.704
0.649
0.702
0.728
0.544
0.572
0.596
y
in.
0.292
0.377
0.456
0.529
0.659
0.165
0.197
0.286
0.366
0.440
0.509
0.0860
0.124
0.158
0.188
0.216
0.0515
0.153
0.233
0.0810
0.117
0.148
0.202
0.0477
0.0862
0.0351
0.0460
0.0659
0.0830
Iy
in4
0.190
0.249
0.306
0.361
0.464
0.142
0.129
0.191
0.249
0.304
0.358
0.0728
0.108
0.140
0.170
0.200
0.0516
0.138
0.185
0.0710
0.105
0.136
0.193
0.0492
0.0937
0.0459
0.0484
0.0713
0.0921
Sy
in3
ry
in.
0.567
0.562
0.557
0.551
0.541
0.391
0.596
0.592
0.585
0.579
0.572
0.418
0.414
0.408
0.403
0.398
0.336
0.417
0.514
0.438
0.433
0.427
0.415
0.349
0.339
0.257
0.357
0.353
0.347
Axis y-y
0.459
0.485
0.510
0.534
0.580
0.343
0.478
0.506
0.531
0.555
0.578
0.320
0.347
0.372
0.395
0.419
0.252
0.389
0.494
0.360
0.386
0.410
0.455
0.281
0.330
0.236
0.300
0.326
0.349
x
in.
0.158
0.209
0.257
0.305
0.399
0.106
0.0955
0.142
0.185
0.226
0.267
0.0492
0.0727
0.0946
0.116
0.137
0.0320
0.0877
0.109
0.0407
0.0606
0.0792
0.116
0.0265
0.0515
0.0223
0.0238
0.0355
0.0465
Iz
in4
0.416
0.418
0.419
0.419
0.421
0.313
0.415
0.416
0.416
0.415
0.415
0.316
0.317
0.316
0.316
0.316
0.265
0.315
0.352
0.310
0.312
0.312
0.314
0.260
0.262
0.205
0.257
0.259
0.260
rz
in.
Axis z-z
24.25
23.95
23.64
23.32
22.61
14.59
32.51
32.30
32.09
31.85
31.59
20.43
20.07
19.70
19.29
18.84
15.16
23.46
36.91
29.38
29.00
28.62
27.74
21.87
20.83
14.62
27.12
26.61
26.09
α
(deg)
VI-22
June 2005
Depth
d
in.
3.000
3.000
3.000
3.500
3.500
3.500
3.500
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
5.000
5.000
5.000
5.000
Designation
L 3 × 2 1/2 × 1/4
L 3 × 2 1/2 × 5/16
L 3 × 2 1/2 × 3/8
L 3 1/2 × 3 × 1/4
L 3 1/2 × 3 × 5/16
L 3 1/2 × 3 × 3/8
L 3 1/2 × 3 × 1/2
L 4 × 3 × 1/4
L 4 × 3 × 5/16
L 4 × 3 × 3/8
L 4 × 3 × 7/16
L 4 × 3 × 1/2
L 4 × 3 × 5/8
L 4 × 3 1/2 × 5/16
L 4 × 3 1/2 × 3/8
L 4 × 3 1/2 × 1/2
L 5 × 3 × 1/4
L 5 × 3 × 5/16
L 5 × 3 × 3/8
L 5 × 3 × 1/2
3.000
3.000
3.000
3.000
3.500
3.500
3.500
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
2.500
2.500
2.500
Width
b
in.
0.250
0.312
0.375
0.500
0.312
0.375
0.500
0.250
0.312
0.375
0.438
0.500
0.625
0.250
0.312
0.375
0.500
0.250
0.312
0.375
Thickness
t
in.
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.312
0.312
0.312
Fillet
Radius
R1
in.
0.312
0.312
0.312
0.312
0.312
0.312
0.312
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
Tip
Radius
R2
in.
1.93
2.39
2.85
3.74
2.23
2.66
3.49
2.62
3.13
4.10
2.26
2.81
3.35
4.40
1.69
2.09
2.49
2.88
3.25
3.99
1.57
1.93
2.30
3.00
1.31
1.61
1.92
1.99
2.46
2.93
3.38
3.83
4.69
1.84
2.27
2.71
3.53
1.54
1.90
2.25
Weight
lb/ft
Area
A
in2
TABLE 16 – ANGLES – UNEQUAL LEGS (Continued)
4.90
6.05
7.17
9.26
3.41
4.03
5.18
2.69
3.29
3.88
4.44
4.97
5.96
1.85
2.26
2.66
3.39
1.12
1.37
1.61
Ix
in4
1.45
1.81
2.16
2.83
1.20
1.43
1.88
0.963
1.19
1.42
1.64
1.85
2.26
0.742
0.918
1.09
1.42
0.532
0.659
0.782
Sx
in3
1.60
1.59
1.59
1.57
1.24
1.23
1.22
1.26
1.26
1.25
1.24
1.24
1.22
1.09
1.08
1.08
1.06
0.927
0.922
0.916
rx
in.
Axis x-x
1.62
1.65
1.68
1.73
1.16
1.19
1.24
1.21
1.24
1.27
1.29
1.31
1.36
1.01
1.04
1.07
1.11
0.893
0.919
0.944
y
in.
1.34
1.65
1.95
2.49
2.43
2.87
3.68
1.30
1.59
1.86
2.13
2.37
2.82
1.25
1.53
1.79
2.28
0.704
0.859
1.01
Iy
in4
0.567
0.706
0.843
1.10
0.938
1.12
1.46
0.568
0.703
0.836
0.964
1.09
1.32
0.559
0.692
0.822
1.07
0.380
0.470
0.557
Sy
in3
ry
in.
0.834
0.831
0.827
0.816
1.04
1.04
1.03
0.875
0.871
0.865
0.859
0.853
0.841
0.893
0.888
0.883
0.871
0.734
0.730
0.724
Axis y-y
0.639
0.666
0.692
0.742
0.913
0.940
0.989
0.719
0.746
0.771
0.796
0.819
0.866
0.767
0.793
0.819
0.867
0.647
0.672
0.697
x
in.
0.739
0.930
1.12
1.47
1.06
1.28
1.70
0.651
0.810
0.967
1.12
1.27
1.56
0.562
0.701
0.838
1.10
0.323
0.404
0.484
Iz
in4
0.620
0.624
0.626
0.628
0.691
0.694
0.698
0.620
0.623
0.624
0.624
0.624
0.625
0.599
0.602
0.603
0.605
0.497
0.500
0.503
rz
in.
Axis z-z
20.79
20.54
20.31
19.86
37.33
37.22
37.00
29.39
29.19
29.00
28.81
28.62
28.20
36.17
36.04
35.90
35.63
34.65
34.45
34.25
α
(deg)
June 2005
VI-23
6.000
6.000
6.000
6.000
6.000
6.000
6.000
6.000
6.000
6.000
7.000
8.000
8.000
8.000
L 6 × 3 x 3/8
L 6 × 3 1/2 × 5/16
L 6 × 3 1/2 × 3/8
L 6 × 3 1/2 × 1/2
L 6 × 3 1/2 × 5/8
L 6 × 4 × 3/8
L 6 × 4 × 7/16
L 6 × 4 × 1/2
L 6 × 4 × 5/8
L 6 × 4 × 3/4
L 7 × 4 × 1/2
L 8 × 6 × 5/8
L 8 × 6 × 11/16
L 8 × 6 × 3/4
6.000
6.000
6.000
4.000
4.000
4.000
4.000
4.000
4.000
3.500
3.500
3.500
3.500
3.000
3.500
3.500
3.500
3.500
0.625
0.688
0.750
0.500
0.375
0.438
0.500
0.625
0.750
0.312
0.375
0.500
0.625
0.375
0.312
0.375
0.500
0.625
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.500
0.438
0.438
0.438
0.438
0.312
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.312
0.312
0.312
0.312
0.375
0.312
0.312
0.312
0.312
5.24
8.37
9.15
9.93
6.17
9.84
10.8
11.7
3.60
4.18
4.74
5.85
6.93
2.88
3.43
4.51
5.56
4.24
4.92
5.58
6.88
8.15
3.23
3.39
4.04
5.31
6.54
2.55
3.05
4.00
4.92
3.80
3.00
3.58
4.70
5.79
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
5.000
5.000
5.000
5.000
L 5 × 3 1/2 × 5/16
L 5 × 3 1/2 × 3/8
L 5 × 3 1/2 × 1/2
L 5 × 3 1/2 × 5/8
53.6
58.1
62.6
26.1
13.0
15.1
17.0
20.7
24.1
10.6
12.6
16.4
19.8
11.8
6.39
7.58
9.79
11.8
9.74
10.6
11.5
5.66
3.19
3.70
4.20
5.18
6.12
2.64
3.16
4.15
5.10
3.03
1.86
2.22
2.91
3.57
2.53
2.52
2.51
2.23
1.90
1.90
1.89
1.88
1.87
1.92
1.92
1.90
1.89
1.91
1.58
1.58
1.56
1.55
2.50
2.52
2.55
2.39
1.91
1.93
1.96
2.01
2.06
1.97
2.00
2.06
2.11
2.11
1.56
1.59
1.64
1.69
26.0
28.`0
30.2
6.28
4.66
5.37
6.03
7.30
8.46
2.71
3.21
4.12
4.96
1.99
2.59
3.06
3.93
4.72
5.78
6.27
6.79
2.03
1.51
1.76
1.99
2.45
2.89
0.985
1.18
1.54
1.89
0.842
0.965
1.15
1.51
1.84
1.76
1.75
1.74
1.09
1.14
1.13
1.13
1.12
1.10
0.971
0.967
0.956
0.944
0.786
1.01
1.00
0.991
0.979
1.51
1.53
1.55
0.903
0.920
0.947
0.972
1.02
1.07
0.746
0.773
0.823
0.872
0.630
0.819
0.846
0.895
0.943
13.6
14.7
15.9
3.71
2.50
2.92
3.33
4.12
4.88
1.56
1.87
2.46
3.02
1.21
1.35
1.63
2.14
2.64
1.275
1.266
1.265
0.842
0.834
0.836
0.838
0.839
0.839
0.736
0.738
0.738
0.737
0.612
0.728
0.731
0.732
0.733
29.07
29.03
28.94
18.70
24.33
24.16
24.00
23.68
23.35
19.61
19.43
19.10
18.75
15.24
26.32
26.13
25.78
25.41
VI-24
January 2005
1.000
1.000
1.000
1.500
1.500
1.000
1.500
2.000
2.000
1.000
2.000
2.000
2.000
2.500
1.250
2.000
2.000
3.000
3.000
3.000
4.000
2.250
1.750
2.000
2.000
2.000
2.000
2.500
2.500
2.500
2.500
3.000
3.000
3.000
3.000
3.000
3.500
4.000
4.000
4.000
5.000
5.000
5.000
5.250
LS 1 3/4 × 1 × 1/8
LS 2 × 1 × 1/8
LS 2 × 1 × 3/16
LS 2 × 1 1/2 × 1/8
LS 2 × 1 1/2 × 3/16
LS 2 1/2 × 1 × 1/8
LS 2 1/2 × 1 1/2 × 1/8
LS 2 1/2 × 2 × 1/8
LS 2 1/2 × 2 × 3/16
LS 3 × 1 × 1/8
LS 3 × 2 × 1/8
LS 3 × 2 × 1/4
LS 3 × 2 × 3/8
LS 3 × 2 1/2 × 1/4
LS 3 1/2 × 1 1/4 × 1/8
LS 4 × 2 × 1/8
LS 4 × 2 × 1/4
LS 4 × 3 × 1/8
LS 5 × 3 × 1/8
LS 5 × 3 × 1/4
LS 5 × 4 × 1/8
LS 5 ¼ × 2 ¼ × 1/8
1.08
1.16
2.28
1.30
0.86
1.69
1.01
0.68
0.57
0.72
1.40
2.04
1.54
0.50
0.57
0.64
0.95
0.922
0.984
1.94
1.11
0.734
1.44
0.859
0.578
0.484
0.609
1.19
1.73
1.31
0.422
0.484
0.547
0.811
0.359
0.529
0.422
0.623
0.328
0.39
0.42
0.62
0.50
0.73
0.266
0.297
0.435
0.328
0.266
0.31
0.31
0.35
0.51
0.39
0.203
0.24
Weight
lb/ft
Area
A
in2
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
0.125
0.125
0.250
0.125
0.125
0.250
0.125
0.125
0.125
0.125
0.250
0.375
0.250
0.125
0.125
0.125
0.188
0.125
0.188
0.125
0.188
0.125
0.125
0.125
0.188
0.125
0.750
1.000
1.000
1.250
1.500
1.500
1.500
1.500
0.125
LS 1 1/2 × 3/4 × 1/8
LS 1 1/2 × 1 × 1/8
LS 1 1/2 × 1 × 3/16
LS 1 1/2 × 1 1/4 × 1/8
0.125
0.750
1.000
1.000
1.250
LS 1 × 3/4 × 1/8
LS 1 1/4 × 1 × 1/8
Designation
Thickness
t
in.
Width
b
in.
Depth
d
in.
2.75
2.66
5.11
2.92
1.27
2.41
1.45
0.750
0.456
0.580
1.09
1.53
1.17
0.277
0.319
0.352
0.510
0.150
0.215
0.173
0.248
0.104
0.0613
0.0679
0.0959
0.0733
0.0408
0.0197
Ix
in4
TABLE 17 – SQUARE END ANGLES – UNEQUAL LEGS
0.817
0.784
1.53
0.820
0.484
0.936
0.517
0.347
0.250
0.282
0.542
0.781
0.561
0.178
0.191
0.200
0.294
0.117
0.170
0.125
0.183
0.0909
0.0644
0.0677
0.0979
0.0702
0.0477
0.0295
Sx
in3
rx
in.
1.73
1.64
1.62
1.62
1.31
1.29
1.30
1.14
0.971
0.975
0.957
0.940
0.945
0.811
0.812
0.802
0.793
0.647
0.638
0.641
0.632
0.563
0.480
0.478
0.470
0.473
0.392
0.312
Axis x-x
1.89
1.61
1.66
1.44
1.38
1.43
1.19
1.34
1.18
0.947
0.993
1.04
0.911
0.942
0.829
0.741
0.764
0.715
0.738
0.618
0.641
0.604
0.548
0.497
0.520
0.455
0.393
0.332
y
in.
0.340
0.762
1.44
1.70
0.229
0.421
0.719
0.0570
0.0286
0.213
0.392
0.543
0.743
0.0276
0.0899
0.203
0.292
0.0263
0.0366
0.0847
0.120
0.0255
0.0105
0.0245
0.0340
0.0465
0.0233
0.00947
Iy
in4
0.183
0.319
0.614
0.554
0.141
0.268
0.311
0.0550
0.0347
0.137
0.260
0.371
0.404
0.0342
0.0767
0.135
0.197
0.0335
0.0481
0.0748
0.108
0.0331
0.0183
0.0325
0.0465
0.0505
0.0318
0.0174
Sy
in3
ry
in.
0.607
0.880
0.861
1.24
0.558
0.541
0.914
0.314
0.243
0.592
0.574
0.559
0.753
0.256
0.431
0.609
0.600
0.271
0.263
0.448
0.439
0.279
0.199
0.287
0.280
0.376
0.296
0.216
Axis y-y
0.387
0.610
0.657
0.936
0.382
0.429
0.690
0.215
0.175
0.447
0.493
0.539
0.661
0.192
0.329
0.491
0.514
0.215
0.238
0.368
0.391
0.229
0.173
0.247
0.270
0.330
0.268
0.207
x
in.
0.223
0.447
0.851
0.847
0.144
0.269
0.376
0.0392
0.0201
0.120
0.225
0.320
0.366
0.0187
0.0532
0.102
0.148
0.0168
0.0240
0.0447
0.0645
0.0156
0.00683
0.0140
0.0201
0.0228
0.0119
0.00519
Iz
in4
0.491
0.674
0.663
0.874
0.442
0.432
0.661
0.261
0.204
0.444
0.435
0.430
0.528
0.210
0.331
0.432
0.427
0.216
0.213
0.326
0.322
0.218
0.160
0.217
0.215
0.264
0.212
0.160
rz
in.
Axis z-z
12.17
20.67
20.36
32.63
15.40
14.95
29.45
8.98
7.94
24.28
23.77
23.18
34.37
10.54
20.36
32.46
32.26
14.95
14.45
29.16
28.84
18.50
14.62
23.77
23.18
34.37
32.05
28.49
α
(deg)
TABLE 18 – TEES
Designation
Td × b × Wt
in. in. lb/ft
Thickness
t
in.
t1
in.
t2
in.
R1
in.
Area
A
in2
Ix
in4
Axis x-x
Sx
rx
in3
in.
y
in.
Iy
in4
Axis y-y
Sy
in3
ry
in.
T 1.00 × 1.00 × 0.31
T 1.25 × 1.50 × 0.44
T 1.25 × 1.50 × 0.62
T 1.50 × 1.50 × 0.68
T 1.50 × 1.50 × 0.87
T 2.00 × 1.50 × 0.86
0.125
0.125
0.188
0.188
0.25
0.188
0.156
0.156
0.219
0.219
0.281
0.25
0.156
0.156
0.219
0.219
0.281
0.25
0.125
0.125
0.125
0.188
0.188
0.188
0.27
0.37
0.52
0.58
0.74
0.73
0.023
0.049
0.067
0.114
0.142
0.269
0.032
0.053
0.075
0.108
0.137
0.195
0.293
0.363
0.359
0.433
0.438
0.606
0.292
0.326
0.352
0.437
0.464
0.624
0.011
0.038
0.056
0.056
0.075
0.060
0.023
0.051
0.075
0.075
0.100
0.080
0.206
0.319
0.328
0.312
0.319
0.286
T 2.00 × 2.00 × 1.26
T 2.00 × 2.00 × 1.50
T 2.25 × 2.25 × 1.42
T 1.25 × 2.50 × 1.00
T 2.25 × 2.50 × 1.91
0.25
0.313
0.25
0.188
0.313
0.313
0.375
0.313
0.313
0.375
0.313
0.375
0.313
0.218
0.375
0.25
0.25
0.25
0.188
0.25
1.07
1.28
1.21
0.85
1.62
0.37
0.43
0.53
0.08
0.89
0.26
0.31
0.33
0.09
0.50
0.59
0.58
0.66
0.31
0.74
0.58
0.61
0.64
0.30
0.73
0.18
0.23
0.26
0.285
0.44
0.18
0.23
0.23
0.22
0.35
0.41
0.42
0.46
0.57
0.52
T 3.00 × 2.50 × 2.11
T 2.50 × 3.00 × 2.13
T 3.00 × 3.00 × 2.72
T 2.00 × 4.00 × 2.70
T 3.00 × 4.00 × 2.76
0.313
0.313
0.375
0.375
0.313
0.375
0.375
0.438
0.438
0.375
0.375
0.375
0.438
0.438
0.375
0.25
0.313
0.313
0.25
0.375
1.80
1.81
2.31
2.30
2.34
1.49
0.94
1.83
0.60
1.72
0.72
0.51
0.86
0.40
0.77
0.91
0.72
0.89
0.51
0.86
0.92
0.68
0.88
0.48
0.75
0.44
0.75
0.90
2.10
1.77
0.35
0.50
0.60
1.05
0.89
0.50
0.65
0.63
0.96
0.87
T 4.00 × 4.00 × 3.74
T 5.00 × 4.00 × 4.22
T 5.00 × 4.00 × 5.41
T 3.00 × 4.50 × 2.96
T 3.00 × 5.00 × 4.02
0.375
0.375
0.5
0.313
0.375
0.438
0.438
0.563
0.375
0.625
0.438
0.438
0.563
0.375
0.438
0.5
0.5
0.5
0.375
0.375
3.18
3.59
4.60
2.52
3.42
4.56
8.56
10.8
1.78
2.37
1.58
2.43
3.14
0.78
1.06
1.20
1.54
1.54
0.84
0.83
1.11
1.48
1.54
0.71
0.76
2.12
2.13
2.83
2.52
4.13
1.06
1.06
1.42
1.12
1.65
0.82
0.77
0.79
1.00
1.10
T 1.13 × 1.00 × 0.16
T 1.50 × 1.13 × 0.19
T 1.50 × 1.50 × 0.063
T 1.75 × 1.25 × 0.37
0.063
0.062
0.187
0.109
0.063
0.062
0.187
0.109
0.063
0.062
0.187
0.109
0.094
0.062
0.187
0.062
0.13
0.16
0.54
0.32
0.013
0.018
0.11
0.043
0.017
0.021
0.10
0.045
0.31
0.34
0.45
0.37
0.25
0.26
0.44
0.30
0.007
0.017
0.054
0.049
0.013
0.023
0.072
0.056
0.24
0.33
0.32
0.39
T 2.00 × 3.00 × 0.55
T 2.00 × 1.50 × 0.75
T 2.00 × 2.00 × 1.13
T 2.50 × 2.50 × 1.77
0.094
0.187
0.250
0.312
0.094
0.187
0.250
0.312
0.094
0.187
0.250
0.312
0.157
0.187
0.250
0.312
0.47
0.64
0.96
1.51
0.45
0.12
0.35
0.86
0.22
0.11
0.25
0.49
0.98
0.44
0.60
0.76
0.92
0.39
0.59
0.74
0.063
0.13
0.17
0.42
0.063
0.13
0.17
0.33
0.37
0.45
0.42
0.53
T 3.00 × 3.00 × 2.55
T 4.00 × 2.50 × 2.32
T 4.00 × 4.00 × 3.43
T 5.00 × 3.00 × 3.43
0.375
0.312
0.375
0.375
0.375
0.312
0.375
0.375
0.375
0.312
0.375
0.375
0.375
0.312
0.375
0.375
2.17
1.98
2.92
2.92
1.78
0.93
4.40
2.06
0.84
0.49
1.54
0.90
0.91
0.69
1.23
0.84
0.89
0.60
1.14
0.72
0.86
1.68
2.03
3.93
0.58
0.84
1.01
1.57
0.63
0.92
0.83
1.16
T 6.50 × 10.00 × 10.5(1)
0.500
0.625
0.500
0.625
8.92
89.7
12.7
3.17
2.95
14.4
4.44
1.27
1. t = 0.625 for flange and t = 0.500 for web
2. Users are encouraged to check availability with suppliers.
3. Tolerances for extruded shapes are given in Aluminum Standards and Data.
January 2005
VI-25
TABLE 19 – ARMY – NAVY AND SPECIAL TEES
Designation
T(A-N) d × b × Wt
in. in. lb/ft
Stem
Thickness
ts
in.
Flange
Thickness
tf
in.
Area
A
in2
Axis x-x
Axis y-y
R1
in.
Ix
in4
Sx
in3
rx
in.
y
in.
Iy
in4
Sy
in3
ry
in.
T(A-N) 1.25 × 1.50 × 0.384
T(A-N) 1.63 × 1.75 × 0.476
T(A-N) 1.00 × 2.00 × 0.421
T(A-N) 1.75 × 2.00 × 0.531
T(A-N) 1.25 × 2.50 × 0.652
T(A-N) 2.00 × 2.50 × 0.789
0.125
0.125
0.125
0.125
0.156
0.156
0.125
0.125
0.125
0.125
0.156
0.156
0.326
0.405
0.358
0.451
0.554
0.671
0.125
0.125
0.125
0.125
0.125
0.125
0.045
0.100
0.025
0.128
0.062
0.241
0.049
0.83
0.032
0.098
0.063
0.161
0.371
0.496
0.266
0.532
0.333
0.599
0.327
0.434
0.212
0.451
0.265
0.500
0.032
0.052
0.078
0.078
0.188
0.189
0.043
0.059
0.078
0.078
0.151
0.151
0.314
0.357
0.466
0.415
0.583
0.530
T(A-N) 2.00 × 3.00 × 0.881
T(A-N) 2.50 × 3.00 × 1.17
T(A-N) 3.00 × 4.00 × 1.50
T(A-N) 4.00 × 4.00 × 2.27
T(A-N) 5.00 × 4.00 × 2.57
0.156
0.188
0.188
0.250
0.250
0.156
0.188
0.188
0.250
0.250
0.749
0.995
1.28
1.93
2.18
0.125
0.188
0.188
0.250
0.250
0.254
0.565
1.03
2.98
5.54
0.164
0.302
0.448
1.02
1.57
0.582
0.753
0.897
1.24
1.59
0.456
0.632
0.708
1.08
1.47
0.330
0.393
0.947
1.24
1.24
0.220
0.262
0.474
0.619
0.620
0.663
0.629
0.861
0.801
0.754
T(A-N) 3.00 × 6.00 × 3.24
T(A-N) 4.00 × 6.00 × 3.88
T(A-N) 4.00 × 6.00 × 4.79
T(A-N) 7.50 × 7.50 × 9.46
T(A-N) 7.50 × 7.50 × 14.4
T(A-N) 6.00 × 8.00 × 11.2
0.3121
0.3751
0.3751
0. 5001
1.131
0.5001
0.312
0.313
0.450
0.750
0.750
0.860
2.75
3.30
4.07
8.04
12.3
9.56
0.3121
0.3131
0.3121
0.6251
0.6251
0.5001
1.83
4.78
5.02
40.3
69.3
22.9
0.77
1.59
1.61
7.28
14.5
4.82
0.81
1.20
1.11
2.24
2.38
1.55
0.62
1.00
0.88
1.96
2.71
1.24
5.63
5.65
8.12
13.6
14.4
36.8
1.88
1.88
2.71
4.53
4.80
9.19
1.43
1.31
1.41
1.30
1.08
1.96
1. Both Flange and stem of these shapes have square ends. Fillet radius R1 applies only to juncture of stem and flange.
2. Users are encouraged to check availability with suppliers.
3. Tolerances for extruded shapes are given in Aluminum Standards and Data.
VI-26
January 2005
January 2005
VI-27
1.250
1.250
2.688
2.688
3.062
3.125
3.188
3.062
3.188
3.250
3.312
3.250
2.000
2.375
3.000
3.000
4.000
4.062
4.125
4.000
4.125
5.000
5.062
5.000
Z 1 3/4 × 1 3/4 × 1.09
Z 2 × 1.25 × 0.922
Z 2 3/8 × 1 1/4 × 1.00
Z 3 × 2 11/16 × 2.33
Z 3 × 2 11/16 × 3.38
Z 4 × 3 1/16 × 2.85
Z 4 1/16 × 3 1/8 × 3.57
Z 4 1/8 × 3 3/16 × 4.32
Z 4 × 3 1/16 × 4.78
Z 4 1/8 × 3 3/16 × 6.22
Z 5 × 3 1/4 × 4.01
Z 5 1/16 × 3 5/16 × 4.84
Z 5 × 3 1/4 × 6.19
0.312
0.375
0.500
0.250
0.312
0.375
0.438
0.563
0.250
0.375
0.188
0.188
0.188
Thickness
t
in.
0.312
0.312
0.312
0.312
0.312
0.312
0.312
0.312
0.312
0.312
0.188
0.188
0.188
Fillet
Radius
R1
in.
1. Users are encouraged to check availability with suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
1.750
1.750
Designation
Width
b
in.
Depth
d
in.
TABLE 20 – ZEES
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.250
0.125
0.125
0.125
Tip
Radius
R2
in.
3.41
4.12
5.26
2.42
3.04
3.67
4.07
5.29
1.98
2.87
13.4
16.2
19.2
6.31
7.96
9.66
9.69
12.8
2.89
3.86
0.459
0.695
0.447
0.925
0.784
0.854
lx
in4
Area
A
in2
5.36
6.41
7.69
3.16
3.92
4.69
4.84
6.19
1.92
2.57
0.459
0.586
0.511
Sx
in3
Axis x-x
1.98
1.99
1.91
1.61
1.62
1.62
1.54
1.55
1.21
1.16
0.765
0.902
0.695
rx
in.
5.93
7.40
8.82
4.01
5.23
6.54
6.53
9.06
2.64
3.76
0.186
0.187
0.553
ly
in4
1.92
2.37
2.94
1.36
1.76
2.18
2.30
3.12
1.03
1.50
0.161
0.161
0.334
Sy
in3
Axis y-y
1.32
1.34
1.29
1.29
1.31
1.33
1.27
1.31
1.15
1.14
0.488
0.467
0.773
ry
in.
1.89
2.33
2.82
1.08
1.39
1.72
1.74
2.41
0.590
0.820
0.0630
0.0820
0.101
lz
in4
0.745
0.752
0.732
0.668
0.676
0.684
0.654
0.675
0.545
0.534
0.284
0.310
0.330
rz
in.
Axis z-z
30.67
31.13
31.15
36.78
37.40
37.92
37.83
38.68
43.40
44.52
29.20
23.20
48.82
α
deg
TABLE 21 – ROUND TUBES
Inside
Diameter
in.
Weight
lb/ft
Area
A
in2
I
in4
S
in3
r
in.
J
in4
Rb /t
1.500 OD × 0.062 WALL
1.500 OD × 0.094 WALL
1.500 OD × 0.125 WALL
1.500 OD × 0.156 WALL
1.500 OD × 0.188 WALL
1.500 OD × 0.250 WALL
1.500 OD × 0.375 WALL
1.376
1.312
1.250
1.188
1.124
1.000
0.750
0.329
0.488
0.635
0.775
0.911
1.15
1.56
0.280
0.415
0.540
0.659
0.775
0.982
1.33
0.0725
0.103
0.129
0.151
0.170
0.199
0.233
0.097
0.137
0.172
0.201
0.227
0.266
0.311
0.509
0.498
0.488
0.478
0.469
0.451
0.419
0.145
0.205
0.255
0.297
0.333
0.383
0.419
11.6
7.5
5.5
4.3
3.5
2.5
1.5
1.625 OD × 0.125 WALL
1.625 OD × 0.188 WALL
1.625 OD × 0.250 WALL
1.375
1.249
1.125
0.693
0.998
1.27
0.589
0.849
1.08
0.167
0.223
0.264
0.205
0.274
0.324
0.532
0.512
0.494
0.331
0.438
0.510
6.0
3.8
2.8
1.750 OD × 0.125 WALL
1.750 OD × 0.188 WALL
1.750 OD × 0.250 WALL
1.750 OD × 0.375 WALL
1.500
1.374
1.250
1.000
0.750
1.08
1.39
1.90
0.638
0.923
1.18
1.62
0.212
0.285
0.341
0.411
0.242
0.326
0.389
0.470
0.576
0.556
0.538
0.504
0.421
0.563
0.663
0.766
6.5
4.2
3.0
1.8
1.875 OD × 0.125 WALL
1.875 OD × 0.188 WALL
1.875 OD × 0.250 WALL
1.875 OD × 0.375 WALL
1.625
1.499
1.375
1.125
0.808
1.17
1.50
2.08
0.687
0.996
1.28
1.77
0.264
0.359
0.431
0.528
0.282
0.383
0.460
0.563
0.620
0.600
0.581
0.547
0.526
0.709
0.843
0.994
7.0
4.5
3.3
2.0
2.000 OD × 0.125 WALL
2.000 OD × 0.188 WALL
2.000 OD × 0.250 WALL
2.000 OD × 0.312 WALL
2.000 OD × 0.375 WALL
2.000 OD × 0.500 WALL
1.750
1.624
1.500
1.376
1.250
1.000
0.866
1.26
1.62
1.95
2.25
2.77
0.736
1.07
1.37
1.65
1.91
2.36
0.325
0.444
0.537
0.609
0.666
0.736
0.325
0.444
0.537
0.609
0.666
0.736
0.664
0.644
0.625
0.607
0.590
0.559
0.647
0.878
1.05
1.18
1.26
1.33
7.5
4.8
3.5
2.7
2.2
1.5
2.250 OD × 0.125 WALL
2.250 OD × 0.188 WALL
2.250 OD × 0.250 WALL
2.250 OD × 0.312 WALL
2.250 OD × 0.375 WALL
2.250 OD × 0.500 WALL
2.000
1.874
1.750
1.626
1.500
1.250
0.981
1.43
1.85
2.23
2.60
3.23
0.834
1.22
1.57
1.90
2.21
2.75
0.473
0.653
0.798
0.915
1.01
1.14
0.420
0.580
0.709
0.813
0.897
1.01
0.753
0.732
0.713
0.694
0.676
0.643
0.942
1.29
1.57
1.78
1.94
2.10
8.5
5.5
4.0
3.1
2.5
1.8
2.375 OD × 0.188 WALL
2.375 OD × 0.250 WALL
2.375 OD × 0.375 WALL
2.375 OD × 0.500 WALL
1.999
1.875
1.625
1.375
1.52
1.96
2.77
3.46
1.29
1.67
2.36
2.95
0.778
0.955
1.22
1.39
0.655
0.804
1.03
1.17
0.776
0.756
0.719
0.686
1.54
1.88
2.36
2.59
5.8
4.3
2.7
1.9
2.500 OD × 0.125 WALL
2.500 OD × 0.188 WALL
2.500 OD × 0.250 WALL
2.500 OD × 0.312 WALL
2.500 OD × 0.375 WALL
2.500 OD × 0.500 WALL
2.500 OD × 0.625 WALL
2.500 OD × 0.750 WALL
2.250
2.124
2.000
1.876
1.750
1.500
1.250
1.000
1.10
1.61
2.08
2.52
2.94
3.69
4.33
4.85
0.933
1.37
1.77
2.14
2.50
3.14
3.68
4.12
0.659
0.918
1.13
1.31
1.46
1.67
1.80
1.87
0.528
0.735
0.906
1.05
1.17
1.34
1.44
1.49
0.841
0.820
0.800
0.781
0.763
0.729
0.699
0.673
1.32
1.82
2.24
2.57
2.83
3.14
3.24
3.16
9.5
6.1
4.5
3.5
2.8
2.0
1.5
1.2
2.625 OD × 0.250 WALL
2.125
2.19
1.87
1.33
1.01
0.844
2.63
4.8
Designation
VI-28
January 2005
TABLE 21 – ROUND TUBES (Continued)
Inside
Diameter
in.
Weight
lb/ft
Area
A
in2
I
in4
S
in3
r
in.
J
in4
Rb /t
2.750 OD × 0.125 WALL
2.750 OD × 0.188 WALL
2.750 OD × 0.250 WALL
2.750 OD × 0.312 WALL
2.750 OD × 0.375 WALL
2.750 OD × 0.500 WALL
2.750 OD × 0.625 WALL
2.750 OD × 0.750 WALL
2.500
2.374
2.250
2.126
2.000
1.750
1.500
1.250
1.21
1.78
2.31
2.81
3.29
4.16
4.91
5.54
1.03
1.51
1.96
2.39
2.80
3.53
4.17
4.71
0.890
1.25
1.55
1.80
2.02
2.35
2.56
2.69
0.647
0.908
1.13
1.31
1.47
1.71
1.86
1.95
0.929
0.908
0.888
0.869
0.850
0.815
0.783
0.755
1.78
2.48
3.07
3.55
3.95
4.47
4.71
4.71
10.5
6.8
5.0
3.9
3.2
2.3
1.7
1.3
2.875 OD × 0.250 WALL
2.875 OD × 0.500 WALL
2.375
1.875
2.42
4.39
2.06
3.73
1.79
2.75
1.25
1.91
0.932
0.858
3.55
5.26
5.3
2.4
3.000 OD × 0.125 WALL
3.000 OD × 0.188 WALL
3.000 OD × 0.250 WALL
3.000 OD × 0.375 WALL
3.000 OD × 0.500 WALL
3.000 OD × 0.625 WALL
3.000 OD × 0.750 WALL
3.000 OD × 1.000 WALL
2.750
2.624
2.500
2.250
2.000
1.750
1.500
1.000
1.33
1.95
2.54
3.64
4.62
5.48
6.23
7.39
1.13
1.66
2.16
3.09
3.93
4.66
5.30
6.28
1.17
1.65
2.06
2.72
3.19
3.52
3.73
3.93
0.779
1.10
1.37
1.81
2.13
2.34
2.49
2.62
1.02
0.996
0.976
0.938
0.901
0.868
0.839
0.791
2.33
3.28
4.08
5.33
6.14
6.58
6.71
6.28
11.5
7.5
5.5
3.5
2.5
1.9
1.5
1.0
3.250 OD × 0.250 WALL
3.250 OD × 0.375 WALL
3.250 OD × 0.500 WALL
2.750
2.500
2.250
2.77
3.98
5.08
2.36
3.39
4.32
2.67
3.56
4.22
1.64
2.19
2.60
1.06
1.03
0.988
5.30
7.00
8.17
6.0
3.8
2.8
3.500 OD × 0.125 WALL
3.500 OD × 0.188 WALL
3.500 OD × 0.250 WALL
3.500 OD × 0.312 WALL
3.500 OD × 0.375 WALL
3.500 OD × 0.500 WALL
3.500 OD × 0.750 WALL
3.250
3.124
3.000
2.876
2.750
2.500
2.000
1.56
2.30
3.00
3.67
4.33
5.54
7.62
1.33
1.96
2.55
3.12
3.68
4.71
6.48
1.89
2.69
3.39
4.01
4.56
5.45
6.58
1.08
1.54
1.94
2.29
2.61
3.11
3.76
1.19
1.17
1.15
1.13
1.11
1.08
1.01
3.77
5.36
6.74
7.94
8.99
10.6
12.3
13.5
8.8
6.5
5.1
4.2
3.0
1.8
3.750 OD × 0.125 WALL
3.750 OD × 0.188 WALL
3.750 OD × 0.250 WALL
3.750 OD × 0.375 WALL
3.750 OD × 0.500 WALL
3.500
3.374
3.250
3.000
2.750
1.67
2.47
3.23
4.68
6.00
1.42
2.10
2.75
3.98
5.11
2.34
3.35
4.23
5.73
6.90
1.25
1.78
2.26
3.06
3.68
1.28
1.26
1.24
1.20
1.16
4.68
6.67
8.42
11.3
13.5
14.5
9.5
7.0
4.5
3.3
4.000 OD × 0.125 WALL
4.000 OD × 0.188 WALL
4.000 OD × 0.250 WALL
4.000 OD × 0.312 WALL
4.000 OD × 0.375 WALL
4.000 OD × 0.500 WALL
4.000 OD × 0.625 WALL
4.000 OD × 0.750 WALL
3.750
3.624
3.500
3.376
3.250
3.000
2.750
2.500
1.79
2.65
3.46
4.25
5.02
6.47
7.79
9.01
1.52
2.25
2.95
3.61
4.27
5.50
6.63
7.66
2.86
4.10
5.20
6.19
7.09
8.59
9.76
10.6
1.43
2.05
2.60
3.09
3.54
4.30
4.88
5.32
1.37
1.35
1.33
1.31
1.29
1.25
1.21
1.18
5.71
8.18
10.4
12.3
14.0
16.8
18.9
20.2
15.5
10.1
7.5
5.9
4.8
3.5
2.7
2.2
4.250 OD × 0.125 WALL
4.250 OD × 0.250 WALL
4.250 OD × 0.375 WALL
4.250 OD × 0.500 WALL
4.000
3.750
3.500
3.250
1.90
3.69
5.37
6.93
1.62
3.14
4.57
5.89
3.45
6.31
8.65
10.5
1.62
2.97
4.07
4.96
1.46
1.42
1.38
1.34
6.89
12.6
17.1
20.7
16.5
8.0
5.2
3.8
Designation
January 2005
VI-29
TABLE 21 – ROUND TUBES (Continued)
Inside
Diameter
in.
Weight
lb/ft
Area
A
in2
I
in4
S
in3
r
in.
J
in4
Rb /t
4.500 OD × 0.125 WALL
4.500 OD × 0.188 WALL
4.500 OD × 0.250 WALL
4.500 OD × 0.312 WALL
4.500 OD × 0.375 WALL
4.500 OD × 0.500 WALL
4.500 OD × 0.625 WALL
4.500 OD × 0.750 WALL
4.500 OD × 1.000 WALL
4.250
4.124
4.000
3.876
3.750
3.500
3.250
3.000
2.500
2.02
2.99
3.93
4.83
5.71
7.39
8.95
10.4
12.9
1.72
2.55
3.34
4.10
4.86
6.28
7.61
8.84
11.0
4.11
5.93
7.56
9.05
10.4
12.8
14.7
16.2
18.2
1.83
2.64
3.36
4.02
4.63
5.67
6.51
7.18
8.09
1.55
1.53
1.51
1.48
1.46
1.43
1.39
1.35
1.29
8.22
11.8
15.1
18.0
20.7
25.1
28.6
31.1
33.7
17.5
11.5
8.5
6.7
5.5
4.0
3.1
2.5
1.8
4.750 OD × 0.125 WALL
4.750 OD × 0.188 WALL
4.750 OD × 0.250 WALL
4.750 OD × 0.375 WALL
4.750 OD × 0.500 WALL
4.500
4.374
4.250
4.000
3.750
2.14
3.17
4.16
6.06
7.85
1.82
2.69
3.53
5.15
6.68
4.86
7.02
8.97
12.4
15.3
2.05
2.96
3.78
5.23
6.43
1.64
1.61
1.59
1.55
1.51
9.71
14.0
17.9
24.7
30.1
18.5
12.1
9.0
5.8
4.3
5.000 OD × 0.125 WALL
5.000 OD × 0.188 WALL
5.000 OD × 0.250 WALL
5.000 OD × 0.312 WALL
5.000 OD × 0.375 WALL
5.000 OD × 0.500 WALL
5.000 OD × 0.625 WALL
5.000 OD × 0.750 WALL
5.000 OD × 1.000 WALL
4.750
4.624
4.500
4.376
4.250
4.000
3.750
3.500
3.000
2.25
3.34
4.39
5.40
6.41
8.31
10.1
11.8
14.8
1.91
2.84
3.73
4.60
5.45
7.07
8.59
10.0
12.6
5.69
8.24
10.6
12.7
14.7
18.1
21.0
23.3
26.7
2.28
3.30
4.22
5.07
5.87
7.25
8.39
9.33
10.7
1.72
1.70
1.68
1.66
1.64
1.60
1.56
1.53
1.46
11.4
16.5
21.0
25.2
29.1
35.8
41.1
45.2
50.3
19.5
12.8
9.5
7.5
6.2
4.5
3.5
2.8
2.0
5.500 OD × 0.125 WALL
5.500 OD × 0.188 WALL
5.500 OD × 0.250 WALL
5.500 OD × 0.375 WALL
5.500 OD × 0.500 WALL
5.500 OD × 0.750 WALL
5.500 OD × 1.000 WALL
5.250
5.124
5.000
4.750
4.500
4.000
3.500
2.48
3.69
4.85
7.10
9.24
13.2
16.6
2.11
3.14
4.12
6.04
7.85
11.2
14.1
7.63
11.1
14.2
19.9
24.8
32.4
37.6
2.77
4.03
5.18
7.25
9.01
11.8
13.7
1.90
1.88
1.86
1.82
1.78
1.70
1.63
15.2
22.1
28.4
39.6
49.1
63.1
71.6
21.5
14.1
10.5
6.8
5.0
3.2
2.3
6.000 OD × 0.125 WALL
6.000 OD × 0.188 WALL
6.000 OD × 0.250 WALL
6.000 OD × 0.312 WALL
6.000 OD × 0.375 WALL
6.000 OD × 0.500 WALL
6.000 OD × 0.625 WALL
6.000 OD × 0.750 WALL
6.000 OD × 1.000 WALL
5.750
5.624
5.500
5.376
5.250
5.000
4.750
4.500
4.000
2.71
4.04
5.31
6.56
7.79
10.2
12.4
14.5
18.5
2.31
3.43
4.52
5.58
6.63
8.64
10.6
12.4
15.7
9.96
14.5
18.7
22.6
26.3
32.9
38.6
43.5
51.1
3.32
4.84
6.23
7.54
8.78
11.0
12.9
14.5
17.0
2.08
2.06
2.03
2.01
1.99
1.95
1.91
1.88
1.80
19.9
29.0
37.3
45.1
52.4
65.3
76.2
85.2
98.2
23.5
15.5
11.5
9.1
7.5
5.5
4.3
3.5
2.5
6.500 OD × 0.250 WALL
6.500 OD × 0.375 WALL
6.500 OD × 0.500 WALL
6.500 OD × 0.750 WALL
6.000
5.750
5.500
5.000
5.77
8.49
11.1
15.9
4.91
7.22
9.42
13.5
24.0
34.0
42.7
56.9
7.39
10.5
13.1
17.5
2.21
2.17
2.13
2.05
47.9
67.7
84.8
112
12.5
8.2
6.0
3.8
6.750 OD × 0.500 WALL
6.750 OD × 0.750 WALL
5.750
5.250
11.5
16.6
9.82
14.1
48.2
64.6
14.3
19.1
2.22
2.14
95.9
127
6.3
4.0
Designation
VI-30
January 2005
TABLE 21 – ROUND TUBES (Continued)
Inside
Diameter
in.
Weight
lb/ft
Area
A
in2
I
in4
S
in3
r
in.
J
in4
Rb /t
7.000 OD × 0.250 WALL
7.000 OD × 0.375 WALL
7.000 OD × 0.500 WALL
7.000 OD × 0.750 WALL
7.000 OD × 1.000 WALL
6.500
6.250
6.000
5.500
5.000
6.23
9.18
12.0
17.3
22.2
5.30
7.80
10.2
14.7
18.8
30.2
43.0
54.2
72.9
87.2
8.64
12.3
15.5
20.8
24.9
2.39
2.35
2.30
2.23
2.15
60.4
85.6
108
144
170
13.5
8.8
6.5
4.2
3.0
7.500 OD × 0.250 WALL
7.500 OD × 0.375 WALL
7.500 OD × 0.500 WALL
7.000
6.750
6.500
6.70
9.87
12.9
5.69
8.39
11.0
37.5
53.4
67.7
9.99
14.2
18.1
2.56
2.52
2.48
74.8
107
135
14.5
9.5
7.0
8.000 OD × 0.125 WALL
8.000 OD × 0.250 WALL
8.000 OD × 0.375 WALL
8.000 OD × 0.500 WALL
8.000 OD × 0.625 WALL
8.000 OD × 0.750 WALL
8.000 OD × 1.000 WALL
7.750
7.500
7.250
7.000
6.750
6.500
6.000
3.64
7.16
10.6
13.9
17.0
20.1
25.9
3.09
6.09
8.98
11.8
14.5
17.1
22.0
24.0
45.7
65.4
83.2
99.2
113
137
5.99
11.4
16.4
20.8
24.8
28.4
34.4
2.78
2.74
2.70
2.66
2.62
2.58
2.50
47.9
91.4
131
166
197
224
269
31.5
15.5
10.2
7.5
5.9
4.8
3.5
8.500 OD × 0.250 WALL
8.000
7.62
6.48
55.2
13.0
2.92
110
16.5
9.000 OD × 0.250 WALL
9.000 OD × 0.375 WALL
9.000 OD × 0.500 WALL
8.500
8.250
8.000
8.08
11.9
15.7
6.87
10.2
13.4
65.8
94.7
121
14.6
21.0
26.9
3.09
3.05
3.01
132
189
241
17.5
11.5
8.5
10.000 OD × 0.250 WALL
10.000 OD × 0.375 WALL
10.000 OD × 0.500 WALL
10.000 OD × 0.625 WALL
10.000 OD × 0.750 WALL
10.000 OD × 1.000 WALL
9.500
9.250
9.000
8.750
8.500
8.000
9.01
13.3
17.5
21.6
25.6
33.3
7.66
11.3
14.9
18.4
21.8
28.3
91.1
132
169
203
235
290
18.2
26.3
33.8
40.6
46.9
58.0
3.45
3.41
3.36
3.32
3.28
3.20
182
263
337
404
466
573
19.5
12.8
9.5
7.5
6.2
4.5
10.500 OD × 0.250 WALL
10.500 OD × 0.375 WALL
10.500 OD × 0.500 WALL
10.500 OD × 0.750 WALL
10.000
9.750
9.500
9.000
9.47
14.0
18.5
27.0
8.05
11.9
15.7
23.0
106
153
197
275
20.1
29.2
37.5
52.3
3.63
3.58
3.54
3.46
211
306
393
546
20.5
13.5
10.0
6.5
11.000 OD × 0.375 WALL
11.000 OD × 0.500 WALL
11.000 OD × 0.750 WALL
11.000 OD × 1.000 WALL
10.250
10.000
9.500
9.000
14.7
19.4
28.4
36.9
12.5
16.5
24.2
31.4
177
228
319
397
32.2
41.4
58.0
72.1
3.76
3.72
3.63
3.55
353
455
634
785
14.2
10.5
6.8
5.0
12.000 OD × 0.250 WALL
12.000 OD × 0.375 WALL
12.000 OD × 0.500 WALL
12.000 OD × 0.750 WALL
12.000 OD × 1.000 WALL
11.500
11.250
11.000
10.500
10.000
10.9
16.1
21.2
31.2
40.6
9.23
13.7
18.1
26.5
34.6
159
232
299
421
527
26.6
38.6
49.9
70.2
87.8
4.16
4.11
4.07
3.99
3.91
319
463
597
839
1045
23.5
15.5
11.5
7.5
5.5
Designation
1. Tube can be produced by different methods. Seamless tube is usually required for applications with internal pressure.
2. Users are encouraged to check availability with suppliers. Additional sizes and shapes may be available from suppliers.
3. Tolerances for extruded shapes are given in Aluminum Standards and Data.
January 2005
VI-31
TABLE 22 – PIPES
Schedule
No.
Outside
Diameter
OD
in.
Inside
Diameter
ID
in.
Wall
Thickness
t
in.
Weight2
lb/ft
Area
A
in2
I
in4
S
in3
r
in.
Rb /t
1 1/2
5
10
40
80
160
1.900
1.900
1.900
1.900
1.900
1.770
1.682
1.610
1.500
1.338
0.065
0.109
0.145
0.200
0.281
0.441
0.721
0.940
1.26
1.68
0.375
0.613
0.799
1.07
1.43
0.158
0.247
0.310
0.391
0.482
0.166
0.260
0.326
0.412
0.508
0.649
0.634
0.623
0.605
0.581
14.1
8.2
6.1
4.3
2.9
2
5
10
40
80
160
2.375
2.375
2.375
2.375
2.375
2.245
2.157
2.067
1.939
1.687
0.065
0.109
0.154
0.218
0.344
0.555
0.913
1.26
1.74
2.58
0.472
0.776
1.07
1.48
2.19
0.315
0.499
0.666
0.868
1.16
0.265
0.420
0.561
0.731
0.980
0.817
0.802
0.787
0.766
0.728
17.8
10.4
7.2
4.9
3.0
2 1/2
5
10
40
80
160
2.875
2.875
2.875
2.875
2.875
2.709
2.635
2.469
2.323
2.125
0.083
0.120
0.203
0.276
0.375
0.856
1.22
2.00
2.65
3.46
0.728
1.04
1.70
2.25
2.95
0.710
0.987
1.53
1.92
2.35
0.494
0.687
1.06
1.34
1.64
0.988
0.975
0.947
0.924
0.894
16.8
11.5
6.6
4.7
3.3
3
5
10
40
80
160
3.500
3.500
3.500
3.500
3.500
3.334
3.260
3.068
2.900
2.624
0.083
0.120
0.216
0.300
0.438
1.05
1.50
2.62
3.55
4.95
0.891
1.27
2.23
3.02
4.21
1.30
1.82
3.02
3.89
5.04
0.744
1.04
1.72
2.23
2.88
1.21
1.20
1.16
1.14
1.09
20.6
14.1
7.6
5.3
3.5
3 1/2
5
10
40
80
4.000
4.000
4.000
4.000
3.834
3.760
3.548
3.364
0.083
0.120
0.226
0.318
1.20
1.72
3.15
4.33
1.02
1.46
2.68
3.68
1.96
2.76
4.79
6.28
0.98
1.38
2.39
3.14
1.39
1.37
1.34
1.31
23.6
16.2
8.3
5.8
4
5
10
40
80
120
160
5
10
40
80
120
160
4.500
4.500
4.500
4.500
4.500
4.500
5.563
5.563
5.563
5.563
5.563
5.563
4.334
4.260
4.026
3.826
3.624
3.438
5.345
5.295
5.047
4.813
4.563
4.313
0.083
0.120
0.237
0.337
0.438
0.531
0.109
0.134
0.258
0.375
0.500
0.625
1.35
1.94
3.73
5.18
6.57
7.79
2.20
2.69
5.06
7.19
9.35
11.4
1.15
1.65
3.17
4.41
5.59
6.62
1.87
2.29
4.30
6.11
7.95
9.70
2.81
3.96
7.23
9.61
11.7
13.3
6.95
8.43
15.2
20.7
25.7
30.0
1.25
1.76
3.21
4.27
5.18
5.90
2.50
3.03
5.45
7.43
9.25
10.8
1.56
1.55
1.51
1.48
1.44
1.42
1.93
1.92
1.88
1.84
1.80
1.76
26.6
18.3
9.0
6.2
4.6
3.7
25.0
20.3
10.3
6.9
5.1
4.0
5
10
40
80
120
160
6.625
6.625
6.625
6.625
6.625
6.625
6.407
6.357
6.065
5.761
5.501
5.187
0.109
0.134
0.280
0.432
0.562
0.719
2.62
3.21
6.56
9.88
12.6
15.7
2.23
2.73
5.58
8.40
10.7
13.3
11.8
14.4
28.1
40.5
49.6
59.0
3.58
4.35
8.50
12.2
15.0
17.8
2.30
2.30
2.25
2.19
2.15
2.10
29.9
24.2
11.3
7.2
5.4
4.1
Nominal
Pipe
Size
5
6
VI-32
January 2005
TABLE 22 – PIPES (Continued)
Nominal
Pipe
Size
Schedule
No.
Outside
Diameter
OD
in.
Inside
Diameter
ID
in.
Wall
Thickness
t
in.
Weight2
lb/ft
Area
A
in2
I
in4
S
in3
r
in.
Rb /t
5
10
20
30
40
60
80
100
120
140
160
5
10
20
30
40
60
80
100
5
10
20
30
40
60
80
8.625
8.625
8.625
8.625
8.625
8.625
8.625
8.625
8.625
8.625
8.625
10.750
10.750
10.750
10.750
10.750
10.750
10.750
10.750
12.750
12.750
12.750
12.750
12.750
12.750
12.750
8.407
8.329
8.125
8.071
7.981
7.813
7.625
7.437
7.187
7.001
6.813
10.482
10.420
10.250
10.136
10.020
9.750
9.562
9.312
12.438
12.390
12.250
12.090
11.938
11.626
11.374
0.109
0.148
0.250
0.277
0.322
0.406
0.500
0.594
0.719
0.812
0.906
0.134
0.165
0.250
0.307
0.365
0.500
0.594
0.719
0.156
0.180
0.250
0.330
0.406
0.562
0.688
3.43
4.64
7.74
8.54
9.88
12.3
15.0
17.6
21.0
23.4
25.8
5.26
6.45
9.70
11.8
14.0
18.9
22.3
26.6
7.26
8.36
11.5
15.1
18.5
25.3
30.7
2.92
3.94
6.58
7.26
8.40
10.5
12.8
15.0
17.9
19.9
22.0
4.47
5.49
8.25
10.1
11.9
16.1
19.0
22.7
6.17
7.11
9.82
12.9
15.7
21.5
26.1
26.4
35.4
57.7
63.4
72.5
88.7
106
121
141
154
166
63.0
76.9
114
137
161
212
245
286
122
140
192
248
300
400
476
6.13
8.21
13.4
14.7
16.8
20.6
24.5
28.2
32.6
35.6
38.5
11.7
14.3
21.2
25.6
29.9
39.4
45.6
53.3
19.2
22.0
30.1
39.0
47.1
62.8
74.6
3.01
3.00
2.96
2.95
2.94
2.91
2.88
2.85
2.81
2.78
2.75
3.75
3.74
3.71
3.69
3.67
3.63
3.60
3.56
4.45
4.44
4.42
4.39
4.37
4.31
4.27
39.1
28.6
16.8
15.1
12.9
10.1
8.1
6.8
5.5
4.8
4.3
39.6
32.1
21.0
17.0
14.2
10.3
8.5
7.0
40.4
34.9
25.0
18.8
15.2
10.8
8.8
8
10
12
1. Sizes are In accordance with ASME Standards B36.10M and B36.19M
2. Weights are for 6061, with a density of 0.098 lb/in3
3. Check availability of shaded sizes with suppliers before using. Additional sizes and shapes may be available from suppliers.
4. Tolerances for extruded shapes are given in Aluminum Standards and Data.
January 2005
VI-33
TABLE 23 – SQUARE TUBES
VI-34
Designation
Depth
width
d in.
Thickness
t
in.
RT 1 × 1 × .065
RT 1 × 1 × .095
RT 1 × 1 × .125
1.000
1.000
1.000
RT 1.25 × 1.25 × .065
RT 1.25 × 1.25 × .095
RT 1.25 × 1.25 × .125
Axis x-x, y-y
Weight
lb/ft
Area
A
in2
Ix , Iy
in4
Sx , Sy
in3
rx , ry
in.
J
in4
0.065
0.095
0.125
0.286
0.404
0.515
0.243
0.344
0.438
0.0356
0.0475
0.0570
0.0712
0.0949
0.114
0.383
0.371
0.361
0.0531
0.0704
0.0837
1.250
1.250
1.250
0.065
0.095
0.125
0.362
0.516
0.662
0.308
0.439
0.563
0.0723
0.0982
0.120
0.116
0.157
0.192
0.485
0.473
0.462
0.108
0.146
0.178
RT 1.375 × 1.375 × .125
1.375
0.125
0.735
0.625
0.164
0.239
0.513
0.244
RT 1.5 × 1.5 × .065
RT 1.5 × 1.5 × .078
RT 1.5 × 1.5 × .095
RT 1.5 × 1.5 × .125
RT 1.5 × 1.5 × .250
1.500
1.500
1.500
1.500
1.500
0.065
0.078
0.095
0.125
0.250
0.439
0.522
0.628
0.809
1.47
0.373
0.444
0.534
0.688
1.25
0.128
0.150
0.176
0.218
0.339
0.171
0.200
0.235
0.291
0.451
0.586
0.581
0.575
0.564
0.520
0.192
0.224
0.263
0.325
0.488
RT 1.75 × 1.75 × .125
1.750
0.125
0.956
0.813
0.360
0.411
0.665
0.536
RT 2 × 2 × .095
RT 2 × 2 × .125
RT 2 × 2 × .156
RT 2 × 2 × .188
RT 2 × 2 × .250
2.000
2.000
2.000
2.000
2.000
0.095
0.125
0.156
0.188
0.250
0.851
1.10
1.35
1.60
2.06
0.724
0.938
1.15
1.36
1.75
0.439
0.552
0.657
0.754
0.911
0.439
0.552
0.657
0.754
0.911
0.779
0.767
0.755
0.744
0.722
0.657
0.824
0.978
1.12
1.34
RT 2.25 × 2.25 × .125
2.250
0.125
1.25
1.06
0.802
0.713
0.869
1.20
RT 2.5 × 2.5 × .125
RT 2.5 × 2.5 × .188
RT 2.5 × 2.5 × .250
2.500
2.500
2.500
0.125
0.188
0.250
1.40
2.04
2.65
1.19
1.74
2.25
1.12
1.56
1.92
0.896
1.25
1.54
0.971
0.947
0.924
1.67
2.32
2.85
RT 2.75 × 2.75 × .125
RT 2.75 × 2.75 × .188
2.750
2.750
0.125
0.188
1.54
2.27
1.31
1.93
1.51
2.12
1.10
1.54
1.07
1.05
2.26
3.16
RT 3 × 3 × .095
RT 3 × 3 × .125
RT 3 × 3 × .188
RT 3 × 3 × .250
RT 3 × 3 × .375
3.000
3.000
3.000
3.000
3.000
0.095
0.125
0.188
0.250
0.375
1.30
1.69
2.49
3.23
4.63
1.10
1.44
2.11
2.75
3.94
1.55
1.98
2.80
3.49
4.61
1.04
1.32
1.87
2.33
3.08
1.19
1.17
1.15
1.13
1.08
2.33
2.97
4.18
5.20
6.78
RT 3.5 × 3.5 × .125
RT 3.5 × 3.5 × .250
RT 3.5 × 3.5 × .375
3.500
3.500
3.500
0.125
0.250
0.375
1.98
3.82
5.51
1.69
3.25
4.69
3.21
5.76
7.74
1.83
3.29
4.42
1.38
1.33
1.28
4.81
8.58
11.4
RT 4 × 4 × .125
RT 4 × 4 × .188
RT 4 × 4 × .250
RT 4 × 4 × .375
RT 4 × 4 × .500
4.000
4.000
4.000
4.000
4.000
0.125
0.188
0.250
0.375
0.500
2.28
3.37
4.41
6.39
8.23
1.94
2.87
3.75
5.44
7.00
4.85
6.96
8.83
12.0
14.6
2.43
3.48
4.41
6.02
7.29
1.58
1.56
1.53
1.49
1.44
7.27
10.4
13.2
17.9
21.4
January 2005
TABLE 23 – SQUARE TUBES (Continued)
Designation
Depth
width
d in.
Thickness
t
in.
RT 6 × 6 × .125
RT 6 × 6 × .188
RT 6 × 6 × .250
RT 6 × 6 × .375
RT 6 × 6 × .500
6.000
6.000
6.000
6.000
6.000
RT 8 × 8 × .188
RT 8 × 8 × .250
RT 8 × 8 × .375
RT 8 × 8 × .500
8.000
8.000
8.000
8.000
Axis x-x, y-y
Weight
lb/ft
Area
A
in2
Ix , Iy
in4
Sx , Sy
in3
rx , ry
in.
J
in4
0.125
0.188
0.250
0.375
0.500
3.45
5.14
6.76
9.92
12.9
2.94
4.37
5.75
8.44
11.0
16.9
24.6
31.7
44.7
55.9
5.64
8.21
10.6
14.9
18.6
2.40
2.37
2.35
2.30
2.25
25.3
36.9
47.5
66.7
83.2
0.188
0.250
0.375
0.500
6.91
9.11
13.5
17.6
5.87
7.75
11.4
15.0
59.8
77.7
111
141
14.9
19.4
27.8
35.3
3.19
3.17
3.12
3.07
89.6
116
166
211
1. Users are encouraged to check availability with suppliers. Additional sizes and shapes may be available from
suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
January 2005
VI-35
VI-36
January 2005
1.03
1.10
1.18
1.25
1.32
1.47
1.62
1.76
1.91
2.82
2.21
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.125
0.188
0.125
2.000
2.250
2.500
2.750
3.000
3.500
4.000
4.500
5.000
5.000
6.000
1.750
1.750
1.750
1.750
1.750
1.750
1.750
1.750
1.750
1.750
1.750
RT 1 3/4 × 2 × 1/8
RT 1 3/4 × 2 1/4 × 1/8
RT 1 3/4 × 2 1/2 × 1/8
RT 1 3/4 × 2 3/4 × 1/8
RT 1 3/4 × 3 × 1/8
RT 1 3/4 × 3 1/2 × 1/8
RT 1 3/4 × 4 × 1/8
RT 1 3/4 × 4 1/2 × 1/8
RT 1 3/4 × 5 × 1/8
RT 1 3/4 × 5 × 3/16
RT 1 3/4 × 6 × 1/8
0.882
0.956
1.76
1.10
1.25
1.82
1.54
2.13
0.125
0.125
0.250
0.125
0.125
0.188
0.125
0.125
1.750
2.000
2.000
2.500
3.000
3.000
4.000
6.000
1.500
1.500
1.500
1.500
1.500
1.500
1.500
1.500
RT 1 1/2 × 1 3/4 × 1/8
RT 1 1/2 × 2 × 1/8
RT 1 1/2 × 2 × 1/4
RT 1 1/2 × 2 1/2 × 1/8
RT 1 1/2 × 3 × 1/8
RT 1 1/2 × 3 × 3/16
RT 1 1/2 × 4 × 1/8
RT 1 1/2 × 6 × 1/8
0.882
1.03
1.18
0.125
0.125
0.125
2.000
2.500
3.000
1.250
1.250
1.250
RT 1 1/4 × 2 × 1/8
RT 1 1/4 × 2 1/2 × 1/8
RT 1 1/4 × 3 × 1/8
0.662
0.809
0.956
1.10
1.40
0.125
0.125
0.125
0.125
0.125
1.500
2.000
2.500
3.000
4.000
1.000
1.000
1.000
1.000
1.000
Weight
lb/ft
RT 1 × 1 1/2 × 1/8
RT 1 × 2 × 1/8
RT 1 × 2 1/2 × 1/8
RT 1 × 3 × 1/8
RT 1 × 4 × 1/8
Designation
Thickness
t
in.
Width
b
in.
Depth
d
in.
TABLE 24 – RECTANGULAR TUBES
0.875
0.938
1.00
1.06
1.13
1.25
1.38
1.50
1.63
2.40
1.88
0.750
0.813
1.50
0.938
1.06
1.55
1.31
1.81
0.750
0.875
1.00
0.563
0.688
0.813
0.938
1.19
Area
A
in2
0.401
0.442
0.484
0.525
0.566
0.649
0.732
0.814
0.897
1.23
1.06
0.248
0.278
0.438
0.337
0.396
0.533
0.515
0.752
0.180
0.219
0.259
0.0811
0.105
0.129
0.153
0.201
Ix
in4
0.458
0.506
0.553
0.600
0.647
0.742
0.836
0.931
1.03
1.41
1.21
0.331
0.370
0.583
0.449
0.528
0.711
0.686
1.00
0.288
0.351
0.415
0.162
0.210
0.258
0.307
0.403
Sx
in3
Axis x-x
0.677
0.687
0.696
0.703
0.710
0.721
0.730
0.737
0.743
0.717
0.753
0.575
0.585
0.540
0.599
0.611
0.586
0.626
0.644
0.489
0.501
0.509
0.380
0.391
0.399
0.404
0.412
rx
in.
0.497
0.661
0.855
1.08
1.34
1.96
2.74
3.69
4.83
6.91
7.74
0.318
0.442
0.719
0.767
1.21
1.68
2.51
7.20
0.387
0.678
1.08
0.159
0.332
0.590
0.950
2.04
Iy
in4
0.497
0.588
0.684
0.785
0.892
1.12
1.37
1.64
1.93
2.76
2.58
0.364
0.442
0.719
0.613
0.806
1.12
1.25
2.40
0.387
0.543
0.720
0.212
0.332
0.472
0.633
1.02
Sy
in3
Axis y-y
0.753
0.840
0.925
1.01
1.09
1.25
1.41
1.57
1.72
1.70
2.03
0.652
0.737
0.692
0.904
1.07
1.04
1.38
1.99
0.718
0.881
1.04
0.532
0.695
0.852
1.01
1.31
ry
in.
0.663
0.795
0.931
1.07
1.21
1.50
1.80
2.11
2.41
3.33
3.04
0.416
0.511
0.798
0.711
0.919
1.24
1.35
2.25
0.371
0.510
0.654
0.161
0.245
0.332
0.422
0.605
J
in4
January 2005
VI-37
4.000
5.000
4.000
4.000
4.000
4.000
4.000
5.000
5.000
5.000
6.000
6.000
8.000
5.000
6.000
6.000
6.000
6.000
8.000
8.000
8.000
8.000
8.000
2.500
2.500
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
3.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
4.000
5.000
RT 2 1/2 × 4 × 1/8
RT 2 1/2 × 5 × 1/8
RT 3 × 4 × 1/8
RT 3 × 4 × 3/16
RT 3 × 4 × 1/4
RT 3 × 4 × 3/8
RT 3 × 4 × 1/2
RT 3 × 5 × 1/8
RT 3 × 5 × 3/16
RT 3 × 5 × 1/4
RT 3 × 6 × 1/8
RT 3 × 6 × 3/16
RT 3 × 8 × 1/4
RT 4 × 5 × 1/4
RT 4 × 6 × 1/8
RT 4 × 6 × 3/16
RT 4 × 6 × 1/4
RT 4 × 6 × 1/2
RT 4 × 8 × 3/16
RT 4 × 8 × 1/4
RT 4 × 8 × 3/8
RT 4 × 8 × 1/2
RT 5 × 8 × 3/8
0.375
10.8
5.00
2.87
4.26
5.59
10.6
5.14
6.76
9.92
12.9
1.98
2.93
3.82
5.51
7.06
2.28
3.37
4.41
2.57
3.81
6.17
0.125
0.188
0.250
0.375
0.500
0.125
0.188
0.250
0.125
0.188
0.250
0.250
0.125
0.188
0.250
0.500
0.188
0.250
0.375
0.500
1.84
2.13
1.40
2.65
1.69
2.49
3.23
1.98
2.93
3.82
2.28
3.37
4.41
2.87
0.125
0.125
0.125
0.250
0.125
0.188
0.250
0.125
0.188
0.250
0.125
0.188
0.250
0.125
9.19
4.25
2.44
3.62
4.75
9.00
4.37
5.75
8.44
11.0
1.69
2.49
3.25
4.69
6.00
1.94
2.87
3.75
2.19
3.24
5.25
1.56
1.81
1.19
2.25
1.44
2.11
2.75
1.69
2.49
3.25
1.94
2.87
3.75
2.44
37.0
10.6
6.73
9.69
12.3
20.8
12.4
15.9
21.9
26.9
2.50
3.54
4.44
5.92
7.00
3.02
4.29
5.39
3.53
5.03
8.23
1.65
2.00
0.772
1.30
0.992
1.37
1.68
1.21
1.68
2.07
1.43
1.99
2.45
1.87
14.8
5.29
3.37
4.85
6.17
10.4
6.21
7.93
11.0
13.5
1.67
2.36
2.96
3.94
4.67
2.01
2.86
3.59
2.36
3.35
5.49
1.32
1.60
0.77
1.30
0.992
1.37
1.68
1.21
1.68
2.07
1.43
1.99
2.45
1.87
1. Users are encouraged to check availability with suppliers. Additional sizes and shapes may be available from suppliers.
2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
3.000
3.000
4.000
4.000
4.000
5.000
5.000
5.000
6.000
6.000
6.000
8.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
2.000
RT 2 × 3 × 1/8
RT 2 × 3 × 1/4
RT 2 × 4 × 1/8
RT 2 × 4 × 3/16
RT 2 × 4 × 1/4
RT 2 × 5 × 1/8
RT 2 × 5 × 3/16
RT 2 × 5 × 1/4
RT 2 × 6 × 1/8
RT 2 × 6 × 3/16
RT 2 × 6 × 1/4
RT 2 × 8 × 1/8
2.01
1.58
1.66
1.64
1.61
1.52
1.69
1.66
1.61
1.56
1.22
1.19
1.17
1.12
1.08
1.25
1.22
1.20
1.27
1.25
1.25
1.03
1.05
0.806
0.759
0.831
0.806
0.782
0.847
0.822
0.798
0.860
0.834
0.809
0.876
78.4
15.1
12.6
18.3
23.5
40.8
36.8
47.6
67.5
84.9
3.92
5.59
7.07
9.56
11.5
6.69
9.63
12.3
10.4
15.1
40.1
3.45
5.95
1.47
2.55
2.98
4.23
5.31
5.20
7.45
9.44
8.28
11.9
15.2
17.5
19.6
6.04
4.20
6.09
7.82
13.6
9.21
11.9
16.9
21.2
1.96
2.80
3.53
4.78
5.75
2.68
3.85
4.91
3.48
5.03
10.0
1.72
2.38
0.978
1.70
1.49
2.11
2.65
2.08
2.98
3.78
2.76
3.98
5.07
4.36
2.92
1.88
2.27
2.25
2.22
2.13
2.90
2.88
2.83
2.78
1.52
1.50
1.47
1.43
1.38
1.86
1.83
1.81
2.18
2.16
2.76
1.48
1.81
1.11
1.06
1.44
1.41
1.39
1.76
1.73
1.70
2.07
2.04
2.01
2.68
76.1
18.7
13.3
19.2
24.5
41.2
28.7
36.7
50.9
62.6
4.60
6.52
8.18
10.9
12.8
6.34
9.03
11.4
8.15
11.6
21.6
3.39
4.62
1.53
2.57
2.30
3.19
3.92
3.09
4.32
5.32
3.91
5.47
6.75
5.59
TABLE 25 – ROOFING AND SIDING – DIMENSIONS AND WEIGHTS
VI-38
January 2005
TABLE 26 – ROOFING AND SIDING – SECTION PROPERTIES
January 2005
VI-39
TABLE 27 – DECIMAL EQUIVALENTS IN INCHES OF SHEET METAL AND
WIRE GAUGES
VI-40
January 2005
TABLE 28 – GEOMETRIC SHAPES
January 2005
VI-41
TABLE 28 – GEOMETRIC SHAPES (Continued)
VI-42
January 2005
TABLE 28 – GEOMETRIC SHAPES (Continued)
January 2005
VI-43
TABLE 28 – GEOMETRIC SHAPES (Continued)
ANGLE
x
Z
Y
W
c
X
d
X
y
W
Y
t
a
t
b
Z
z - z axis is axis of minimum I
b + ct
x = _______
2(b + c)
d + at
y = _______
2(b + c)
t(d – y)3 + by3 – a(y – t)3
Ix = ___________________
3
t(b – x)3 + dx3 – c(x – t)3
Iy = ___________________
3
abcdt
K = _______
4(b + c)
2K
α = (1/2)tan-1 _____
Iy – Ix
2
2
(
)
Iz = Ix sin2 α + Iy cos2 α + K sin 2α
Ix + Iy = Iw + Iz
Iw = Ix cos2 α + Iy sin2 α – K sin 2α
xo = x – t/2
yo = y – t/2
wo = yo sin α + xo cos α
zo = yo cos α – xo sin α
b' = d – t/2
d' = b – t/2
( y o – ( yo – b' )4 ) yo
x2
C1 = __o [ y 2o – ( yo – b' )2 ] + _____________ + __ [ x 3o – ( xo – d' )3 ] + y 3o d'
2
4
3
4
( x 4o – ( xo – d' )4 ) x
y2
C2 = __o [ x 2o – ( xo – d' )2 ] + _____________ + __o [ y 3o – ( yo – b' )3 ] + x 3o b'
2
4
3
t(C1 cos α – C2 sin α)
βw = __________________ – 2zo
Iw
VI-44
January 2005
Aluminum Design Manual
PART VII
Design Aids
The Aluminum Association, Inc.
1525 Wilson Boulevard, Suite 600, Arlington, VA 22209
Third Edition, January 2005
VII
Design Aids
TABLE OF CONTENTS
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Compressive Strength Curves
Figure 1-1
1-2
1-3
1-4
1-5
1-6
1-7
1-8
1-9
1-10
1-11
1-12
1-13
1-14
1-15
1-16
1-17
1-18
1-19
1-20
1-21
1-22
1-23
1-24
1-25
1-26
1-27
1-28
1-29
1-30
Section 7
Section 7
Section 8
Section 8
Section 8.1
Section 8.1
Section 9
Section 9
Section 10
Section 10
Section 11
Section 11
Section 12
Section 12
Section 13
Section 14
Section 14
Section 15
Section 15
Section 16
Section 16
Section 17
Section 18
Section 18
Section 19
Section 19
Section 20
Section 20
Section 21
Section 21
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
All Tempers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
All Tempers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Tempers O, H, T1, T2, T3, T4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Tempers T5, T6, T7, T8, T9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Allowable Stress Tables for Building and Similar Type Structures
Table
2-1 Buckling Constants for Aluminum Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2-1W Buckling Constants for Welded Aluminum Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2-2 1100-H14 Sheet, Plate, Drawn Tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2-3 3003-H14 Sheet, Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2-4 3003-H16 Sheet, Drawn Tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2-5 Alclad 3004-H34 Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2-6 5005-H14 Sheet and Plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2-7 5005-H34 Sheet and Plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2-8 5050-H34 Sheet, Drawn Tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2-9 5052-H32 Sheet, Drawn Tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2-10 5052-H34 Sheet, Plate, Drawn Tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2-11 5083-H111 Extrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2-12 5083-H116, -H32, -H321 Sheet and Plate (0.188 to 1.500 in. thick) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2-13 5086-H34 Sheet and Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
January 2005
VII-3
2-14
2-15
2-16
2-17
2-18
2-19
2-20
2-21
2-22
2-23
2-24
2-25
2-26
5086-H111 Extrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5086-H116, -H32 Sheet and Plate, 5086-H32 Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5454-H111 Extrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5454-H32 Sheet and Plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5454-H34 Sheet and Plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5456-H116, -H32, -H321 Sheet and Plate (0.188 to 1.250 in. thick) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6005-T5 Extrusions (up through 1.000 in. thick), 6105-T5 Extrusions (up through 0.500 in. thick) . . . . . . . . 64
6061-T6 Sheet, -T651 Plate (up through 4.000 in. thick), 6061-T6, -T651 Rolled or
Cold Finished Rod and Bar, 6061-T6 Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6061-T6, -T6510, -T6511 Extrusions, 6061-T6 Standard Structural Shapes, Pipe,
6351-T5 Extrusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6063-T5 Extrusions (up through 0.500 in. thick), 6063-T52 Extrusions (up through 1.000 in. thick) . . . . . . . 70
6063-T6 Extrusions and Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6351-T6 Extrusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7005-T53 Extrusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Bending
Table
3-1
3-2
3-3
3-4
Recommended Minimum Bend Radii for 90o Cold Bends of Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Recommended Minimum Inside Radii for 180o Cold Bends, Wire and Rod . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Sheet Thickness for 180o Cold Bending (Metal to Metal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Developed Length of Material for 90o Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Allowable Load Tables
Table
4-1
4-2
4-3
4-4
4-5
Allowable Uniform Beam Loads
Aluminum Association Standard Channels, 6061-T6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Allowable Uniform Beam Loads
Aluminum Association Standard I-Beams, 6061-T6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Allowable Loads on Aluminum Tread Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Maximum Recommended Spans – Commercial Corrugated and V-Beam Roofing and Siding . . . . . . . . . . . . . 86
Maximum Recommended Spans – Commercial Ribbed Siding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Fasteners
Table
5-1
5-2
5-3
5-4
5-5
5-6
5-7
5-8
5-9
5-10
5-11
5-12
5-13
5-14
5-15
5-16
5-17
5-18
5-19
5-20
Load Required to Produce Failure of a Solid Rivet in Single Shear – lb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Reduction in Shear Strength of Rivets Resulting From Their Use in Thin Sheets and Shapes . . . . . . . . . . . . . 89
Tensile and Single-Shear Loads for 2024-T4 and 7075-T73 Machine Screws . . . . . . . . . . . . . . . . . . . . . . . . . 90
Single-Shear Loads for 2024-T4 and 7075-T73 Sheet Metal Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Tensile and Single-Shear Strengths for 2024-T4 and 7075-T73 Bolts and Cap Screws . . . . . . . . . . . . . . . . . . 91
Rivet Head Styles and Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Military Specifications for Aluminum Alloy Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Recommended Hole Sizes for Cold-Driven Solid Rivets with Corresponding Shear and Bearing Areas . . . . . 93
Recommended Hole Sizes for Hot-Driven Solid Rivets with Corresponding Shear and Bearing Areas . . . . . . 94
Approximate Driving Pressures with Squeeze Riveter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Smallest Sizes of Pneumatic Hammers Considered Satisfactory for Driving Aluminum Alloy Rivets . . . . . . . 95
Length of Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Flat Driven Heads - Maximum Rivet Grips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Recommended Hole Sizes for 2024-T4 and 7075-T73 Sheet Metal Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Dimensions for Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Bolt Nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Machine Screw Nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Regular Spring Lock Washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Plain Flat Washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Internal Thread Stripping Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Beam Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
VII-4
January 2005
INTRODUCTION
This part includes information in the form of graphs and tables intended to aid the structural designer. Curves of ultimate
strength in compression (Fc) divided by compressive yield strength (Fcy) for each of the Part I Sections 3.4.7 through 3.4.21 are
given. They are independent of whether allowable stress design or load and resistance factor design is used. These are followed
by allowable stresses determined in accordance with Part IA for Sections 3.4.1 through 3.4.21 for a number of common alloys
for building type structures. Subsequently, allowable load tables for Aluminum Association standard channels and I beams,
tread plate, and roofing and siding are given, also calculated by the allowable stress design Specification in Part IA.
For the fabrication of sheet and plate and wire and rod, minimum bend radii are furnished.
The information given on the strength of some aluminum fasteners, including bolts, rivets, screws, nuts, and washers is based
both on specified shear strengths and test results. Dimensional information is also provided.
Lastly, beam formulas for numerous cases are given.
January 2005
VII-5
Figures 1-1 and 1-2
COMPRESSION IN COLUMNS
January 2005
VII-7
Figures 1-3 and 1-4
COMPRESSION IN ELEMENTS OF COLUMNS:
FLAT ELEMENTS SUPPORTED ON ONE EDGE
VII-8
January 2005
Figures 1-5 and 1-6
COMPRESSION IN ELEMENTS OF COLUMNS:
FLAT ELEMENTS SUPPORTED ON ONE EDGE
January 2005
VII-9
Figures 1-7 and 1-8
COMPRESSION IN ELEMENTS OF COLUMNS:
FLAT ELEMENTS SUPPORTED ON BOTH EDGES
VII-10
January 2005
Figures 1-9 and 1-10
COMPRESSION IN ELEMENTS OF COLUMNS:
CURVED ELEMENTS SUPPORTED ON BOTH EDGES
January 2005
VII-11
Figures 1-11 and 1-12
COMPRESSION IN BEAMS:
SINGLE WEB SHAPES BENT ABOUT STRONG AXIS
VII-12
January 2005
Figures 1-13 and 1-14
COMPRESSION IN BEAMS:
ROUND OR OVAL TUBES
January 2005
VII-13
Figure 1-15
COMPRESSION IN BEAMS:
SOLID RECTANGULAR SHAPES
VII-14
January 2005
Figures 1-16 and 1-17
COMPRESSION IN BEAMS:
TUBULAR SHAPES
January 2005
VII-15
Figures 1-18 and 1-19
COMPRESSION IN ELEMENTS OF BEAMS:
FLAT ELEMENTS SUPPORTED ON ONE EDGE
VII-16
January 2005
Figures 1-20 and 1-21
COMPRESSION IN ELEMENTS OF BEAMS:
FLAT ELEMENTS SUPPORTED ON BOTH EDGES
January 2005
VII-17
Figure 1-22
COMPRESSION IN ELEMENTS OF BEAMS:
FLAT ELEMENTS WITH COMPRESSION EDGE FREE, TENSION EDGE SUPPORTED
VII-18
January 2005
Figures 1-23 and 1-24
COMPRESSION IN ELEMENTS OF BEAMS:
FLAT ELEMENTS SUPPORTED ON BOTH EDGES
January 2005
VII-19
Figures 1-25 and 1-26
COMPRESSION IN ELEMENTS OF BEAMS:
FLAT ELEMENTS WITH HORIZONTAL STIFFENER, BOTH EDGES SUPPORTED
VII-20
January 2005
Figures 1-27 and 1-28
SHEAR IN WEBS:
UNSTIFFENED FLAT WEBS
January 2005
VII-21
Figures 1-29 and 1-30
SHEAR IN WEBS:
STIFFENED FLAT WEBS
VII-22
January 2005
January 2005
VII-23
Product*
Sheet & Plate and
Drawn Tube
Sheet
Plate
Extrusions
Cold-Finished Rod &
Bar, Drawn Tube
Sheet (0.039)
Alclad 2014 T6
Sheet (0.249)
Alclad 2014 T6
Plate
Alclad 2014 T651
Sheet & Plate
3003 H12
3003 H14
Sheet & Plate
3003 H16
Sheet
3003 H18
Sheet
3003 H12
Drawn Tube
3003 H14
Drawn Tube
3003 H16
Drawn Tube
3003 H18
Drawn Tube
Alclad 3003 H12
Sheet & Plate
Alclad 3003 H14
Sheet & Plate
Alclad 3003 H16
Sheet
Alclad 3003 H18
Sheet
Alclad 3003 H14
Drawn Tube
Alclad 3003 H18
Drawn Tube
3004 H32
Sheet & Plate
3004 H34
Sheet & Plate
3004 H36
Sheet
3004 H38
Sheet
3004 H34
Drawn Tube
3004 H36
Drawn Tube
Alclad 3004 H32
Sheet
Alclad 3004 H34
Sheet
Alclad 3004 H36
Sheet
Alclad 3004 H38
Sheet
Alclad 3004 H131,H241,H341 Sheet
Alclad 3004 H151,H261,H361 Sheet
3005 H25
Sheet
3005 H28
Sheet
Sheet
3105 H25
Alloy Temper
1100 H12
1100 H14
2014 T6
2014 T651
2014 T6, T6510, T6511
2014 T6, T651
Dc
ksi
0.044
0.067
0.544
0.529
0.444
0.458
0.502
0.531
0.502
0.044
0.075
0.112
0.133
0.052
0.093
0.123
0.144
0.038
0.067
0.103
0.123
0.084
0.133
0.112
0.155
0.190
0.241
0.178
0.215
0.103
0.144
0.178
0.228
0.155
0.228
0.133
0.190
0.103
Bc
ksi
11.0
14.5
68.6
67.3
59.9
61.1
64.8
67.3
64.8
11.0
15.7
20.4
22.8
12.2
18.0
21.6
24.0
9.9
14.5
19.2
21.6
16.8
22.8
20.4
25.3
29.0
33.9
27.7
31.4
19.2
24.0
27.7
32.7
25.3
32.7
22.8
29.0
19.2
53
52
53
165
138
121
114
157
129
118
112
174
144
125
118
133
114
121
109
102
94
104
98
125
112
104
96
109
96
114
102
125
165
144
52
52
55
55
Cc
74.8
77.7
74.8
12.8
18.4
24.2
27.1
14.2
21.3
25.7
28.6
11.5
17.0
22.8
25.7
19.9
27.1
24.2
30.1
34.6
40.7
33.1
37.7
22.8
28.6
33.1
39.2
30.1
39.2
27.1
34.6
22.8
Bp
ksi
12.8
17.0
79.1
77.7
69.0
70.5
0.622
0.659
0.622
0.056
0.096
0.145
0.172
0.065
0.120
0.159
0.187
0.047
0.086
0.132
0.159
0.108
0.172
0.145
0.201
0.248
0.317
0.232
0.282
0.132
0.187
0.232
0.299
0.201
0.299
0.172
0.248
0.132
Dp
ksi
0.056
0.086
0.674
0.656
0.549
0.567
49
48
49
153
127
111
105
145
119
108
102
162
133
115
108
123
105
111
100
93
86
95
89
115
102
95
87
100
87
105
93
115
153
133
48
49
52
51
Cp
77.6
80.5
77.6
12.7
18.1
23.5
26.3
14.1
20.8
24.9
27.7
11.4
16.7
22.2
24.9
19.4
26.3
23.5
29.0
33.2
38.8
31.8
36.0
22.2
27.7
31.8
37.4
29.0
37.4
26.3
33.2
22.2
Bt
ksi
12.7
16.7
74.3
73.0
65.2
66.5
4.047
4.252
4.047
0.372
0.594
0.843
0.977
0.424
0.715
0.909
1.046
0.321
0.536
0.779
0.909
0.654
0.977
0.843
1.116
1.334
1.643
1.260
1.486
0.779
1.046
1.260
1.564
1.116
1.564
0.977
1.334
0.779
Dt
ksi
0.372
0.536
3.132
3.059
2.629
2.699
Bbr
ksi
17.0
22.6
119.4
117.1
103.6
105.9
Dbr
ksi
0.085
0.131
1.530
1.486
1.238
1.278
98 112.6 1.408
94 117.1 1.493
98 112.6 1.408
17.0 0.085
573
416 24.5 0.147
327 32.2 0.222
295 36.1 0.264
523 18.8 0.100
366 28.3 0.183
310 34.1 0.243
282 38.1 0.286
635 15.2 0.072
446 22.6 0.131
345 30.2 0.202
310 34.1 0.243
389 26.4 0.165
295 36.1 0.264
327 32.2 0.222
269 40.0 0.309
238 46.1 0.381
206 54.2 0.487
247 44.1 0.356
220 50.1 0.433
345 30.2 0.202
282 38.1 0.286
247 44.1 0.356
213 52.2 0.459
269 40.0 0.309
213 52.2 0.459
295 36.1 0.264
238 46.1 0.381
345 30.2 0.202
573
446
94
95
105
103
Ct
Table 2-1
BUCKLING CONSTANTS FOR ALUMINUM ALLOYS
Btb
ksi
19.1
25.1
109.5
109.5
97.8
99.7
Dtb
ksi
0.875
1.260
8.754
8.754
7.523
7.724
53 103.6 8.157
52 107.6 8.571
53 105.6 8.363
133 19.1 0.875
111 27.1 1.397
96 35.3 1.984
91 39.4 2.298
126 21.1 0.999
103 31.2 1.683
94 37.4 2.140
89 41.5 2.461
140
17.1 0.756
115 25.1 1.260
100 33.2 1.832
94 37.4 2.140
107 29.2 1.538
91 39.4 2.298
96 35.3 1.984
86 43.6 2.626
81 49.8 3.140
74 58.2 3.865
82 47.7 2.966
77 54.0 3.497
100 33.2 1.832
89 41.5 2.461
82 47.7 2.966
76 56.1 3.680
86 43.6 2.626
76 56.1 3.680
91 39.4 2.298
81 49.8 3.140
100 33.2 1.832
133
115
52
53
56
55
Cbr
40
39
42
160
127
106
99
150
115
102
96
172
133
111
102
121
99
106
92
85
76
87
80
111
96
87
78
92
78
99
85
111
160
133
39
41
44
44
Ctb
42.6
44.2
44.2
9.1
13.2
16.6
19.2
9.1
13.2
16.6
19.2
8.2
12.4
15.8
18.4
12.4
18.4
16.6
20.1
22.8
25.4
20.1
22.8
15.8
19.2
21.9
24.5
21.0
24.5
17.5
21.9
14.9
Bs
ksi
8.2
10.7
45.1
45.9
40.9
42.6
0.267
0.283
0.283
0.033
0.058
0.083
0.103
0.033
0.058
0.083
0.103
0.029
0.053
0.076
0.096
0.053
0.096
0.083
0.110
0.132
0.156
0.110
0.132
0.076
0.103
0.125
0.148
0.117
0.148
0.089
0.125
0.070
Ds
ksi
0.029
0.043
0.290
0.298
0.250
0.266
65
64
64
182
151
134
125
182
151
134
125
190
156
138
128
156
128
134
122
115
108
122
115
138
125
117
110
119
110
131
117
142
190
167
64
63
67
66
Cs
VII-24
January 2005
5154 H38
5086 H34
5086 H111
5086 H112
5086 H112
5086 H112
5086 H116
5086 H32
Alloy Temper
5005 H12
5005 H14
5005 H16
5005 H32
5005 H34
5005 H36
5050 H32
5050 H34
5050 H32
5050 H34
5052 O
5052 H32
5052 H34
5052 H36
5083 O
5083 H111
5083 O
5083 H116, H321
5083 H116, H321
5086 O
Product*
Sheet & Plate
Sheet & Plate
Sheet
Sheet & Plate
Sheet & Plate
Sheet
Sheet
Sheet
Drawn Tube
Drawn Tube
Sheet & Plate
Sheet & Plate
Drawn Tube
Sheet
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate (1.500)
Plate (3.000)
Extrusions, Sheet &
Plate
Extrusions
Plate (0.500)
Plate (1.000)
Plate (3.000)
Sheet & Plate
Sheet & Plate, Drawn
Tube
Sheet & Plate, Drawn
Tube
Sheet
39.0 0.294
88
90
37.7 0.278
144
133
121
157
138
129
138
121
133
118
170
112
104
100
131
113
123
101
105
140
Cc
123
127
131
135
101
101
Dc
ksi
0.067
0.084
0.112
0.052
0.075
0.093
0.075
0.112
0.084
0.123
0.041
0.143
0.177
0.201
0.092
0.142
0.111
0.199
0.175
0.074
0.111
0.101
0.092
0.083
0.199
0.199
20.4
19.2
18.0
16.8
30.2
30.2
Bc
ksi
14.5
16.8
20.4
12.2
15.7
18.0
15.7
20.4
16.8
21.6
10.4
24.0
27.7
30.2
18.0
24.0
20.4
30.2
27.7
15.7
0.143
0.130
0.118
0.106
0.261
0.261
Dp
ksi
0.086
0.108
0.145
0.065
0.096
0.120
0.096
0.145
0.108
0.159
0.051
0.186
0.231
0.263
0.118
0.184
0.143
0.261
0.229
0.095
46.9 0.388
45.4 0.367
24.2
22.8
21.3
19.9
36.1
36.1
Bp
ksi
17.0
19.9
24.2
14.2
18.4
21.3
18.4
24.2
19.9
25.7
12.1
28.6
33.1
36.1
21.3
28.6
24.2
36.1
33.1
18.4
81
82
113
116
120
125
92
92
133
123
111
145
127
119
127
111
123
108
158
103
96
91
120
104
113
92
96
129
Cp
44.4
43.0
23.5
22.2
20.8
19.4
34.6
34.6
Bt
ksi
16.7
19.4
23.5
14.1
18.1
20.8
18.1
23.5
19.4
24.9
12.1
27.7
31.8
34.6
20.8
27.7
23.5
34.6
31.8
18.1
1.956
1.867
0.835
0.771
0.708
0.647
1.396
1.396
Dt
ksi
0.536
0.654
0.843
0.424
0.594
0.715
0.594
0.843
0.654
0.909
0.345
1.042
1.256
1.405
0.708
1.036
0.835
1.396
1.248
0.588
184
192
336
355
376
400
235
235
446
389
327
523
416
366
416
327
389
310
608
284
250
231
376
289
336
235
254
427
Ct
0.219
0.199
0.181
0.163
0.401
0.401
Dbr
ksi
0.131
0.165
0.222
0.100
0.147
0.183
0.147
0.222
0.165
0.243
0.078
0.285
0.355
0.405
0.181
0.282
0.219
0.401
0.351
0.145
62.6 0.597
60.5 0.565
32.2
30.2
28.3
26.4
48.1
48.1
Bbr
ksi
22.6
26.4
32.2
18.8
24.5
28.3
24.5
32.2
26.4
34.1
16.1
38.1
44.1
48.1
28.3
38.1
32.2
48.1
44.1
24.5
70
71
98
101
104
108
80
80
115
107
96
126
111
103
111
96
107
94
137
89
83
79
104
90
98
80
84
112
Cbr
Table 2-1
BUCKLING CONSTANTS FOR ALUMINUM ALLOYS (Continued)
1.965
1.814
1.667
1.523
3.285
3.285
Dtb
ksi
1.260
1.538
1.984
0.999
1.397
1.683
1.397
1.984
1.538
2.140
0.812
2.453
2.956
3.306
1.667
2.437
1.965
3.285
2.937
1.384
66.7 4.602
64.6 4.394
35.3
33.2
31.2
29.2
51.9
51.9
Btb
ksi
25.1
29.2
35.3
21.1
27.1
31.2
27.1
35.3
29.2
37.4
18.1
41.5
47.7
51.9
31.2
41.5
35.3
51.9
47.7
27.1
71
73
108
113
118
123
84
84
133
121
106
150
127
115
127
106
121
102
167
96
88
83
118
97
108
84
89
129
Ctb
0.081
0.063
0.052
0.042
0.130
0.130
Ds
ksi
0.043
0.058
0.076
0.033
0.048
0.064
0.053
0.076
0.053
0.076
0.023
0.095
0.117
0.139
0.052
0.101
0.063
0.154
0.138
0.042
29.1 0.189
28.2 0.180
16.6
14.1
12.4
10.7
22.8
22.8
Bs
ksi
10.7
13.2
15.8
9.1
11.5
14.1
12.4
15.8
12.4
15.8
7.0
18.4
21.0
23.7
12.4
19.2
14.1
25.4
23.7
10.7
102
105
136
148
158
170
116
116
167
151
138
182
161
146
156
138
156
138
207
128
120
113
158
127
148
110
114
170
Cs
January 2005
VII-25
7005 T53
* maximum thickness (in.) shown in parentheses
Extrusions
6351 T5
6351 T6
6463 T6
48.9 0.334
39.4 0.246
41.7 0.268
27.6 0.145
60
66
64
78
57
51.4 0.366
Extrusions
Extrusions
Extrusions
Extrusions
6070 T6, T62
131
146
105
99
119
99
103
103
66
66
66
66
66
66
66
99
102
99
78
57
18.0
14.5
27.7
31.4
21.6
31.4
29.0
29.0
39.4
39.4
39.4
39.4
39.4
39.4
39.4
17.3
16.2
17.3
27.6
51.4
0.092
0.066
0.175
0.212
0.121
0.212
0.187
0.187
0.246
0.246
0.246
0.246
0.246
0.246
0.246
0.072
0.065
0.072
0.145
0.366
152
13.3 0.058
Sheet & Plate,
Extrusions
5454 H111
Extrusions
5454 H112
Extrusions
5454 H32
Sheet & Plate
5454 H34
Sheet & Plate
5456 O
Sheet & Plate
5456 H116, H321
Sheet & Plate (1.250)
5456 H116, H321
Plate (1.500)
5456 H116, H321
Plate (3.000)
6005 T5
Extrusions
6105 T5
Extrusions
6061 T6, T651
Sheet & Plate
6061 T6, T6510, T6511 Extrusions
6061 T6, T651
Cold-Finished Rod & Bar
6061 T6
Drawn Tube
6061 T6
Pipe
6063 T5
Extrusions (0.500)
6063 T5
Extrusions (1.000)
6063 T52
Extrusions
6063 T6
Extrusions & Pipe
6066 T6, T6510, T6511 Extrusions
5454 O
0.118
0.084
0.229
0.278
0.156
0.278
0.245
0.245
0.301
0.301
0.301
0.301
0.301
0.301
0.301
0.086
0.078
0.086
0.175
0.451
56.2 0.411
45.0 0.301
47.8 0.329
31.4 0.175
59.0 0.451
21.3
17.0
33.1
37.7
25.7
37.7
34.6
34.6
45.0
45.0
45.0
45.0
45.0
45.0
45.0
19.5
18.2
19.5
31.4
59.0
15.6 0.074
56
61
60
74
54
120
135
96
90
110
90
94
94
61
61
61
61
61
61
61
93
96
93
74
54
140
53.5
43.2
45.8
30.5
56.1
20.8
16.7
31.8
36.0
24.9
36.0
33.2
33.2
43.2
43.2
43.2
43.2
43.2
43.2
43.2
19.2
18.0
19.2
30.5
56.1
15.4
2.045
1.558
1.682
0.978
2.207
0.708
0.530
1.248
1.472
0.900
1.472
1.321
1.321
1.558
1.558
1.558
1.558
1.558
1.558
1.558
0.529
0.484
0.529
0.978
2.207
0.474
121
141
134
189
112
376
458
254
227
499
227
244
244
141
141
141
141
141
141
141
275
290
275
189
112
495
1.010
0.181
0.129
0.351
0.426
0.239
0.426
0.376
0.376
0.665
0.665
0.665
0.665
0.665
0.665
0.665
0.183
0.165
0.183
0.381
1.010
83.9 0.918
66.8 0.665
71.0 0.729
46.1 0.381
88.2
28.3
22.6
44.1
50.1
34.1
50.1
46.1
46.1
66.8
66.8
66.8
66.8
66.8
66.8
66.8
28.3
26.4
28.3
46.1
88.2
20.7 0.113
61
67
65
81
58
104
117
84
78
95
78
82
82
67
67
67
67
67
67
67
103
107
103
81
58
122
1.667
1.248
2.937
3.463
2.119
3.463
3.110
3.110
4.458
4.458
4.458
4.458
4.458
4.458
4.458
1.513
1.384
1.513
2.800
6.315
1.116
80.2 5.853
64.8 4.458
68.6 4.815
45.7 2.800
84.1 6.315
31.2
25.1
47.7
54.0
37.4
54.0
49.8
49.8
64.8
64.8
64.8
64.8
64.8
64.8
64.8
28.8
26.9
28.8
45.7
84.1
23.1
49
55
53
70
47
118
136
89
82
104
82
86
86
55
55
55
55
55
55
55
95
99
95
70
47
144
0.069
0.033
0.115
0.138
0.069
0.171
0.154
0.138
0.133
0.133
0.133
0.133
0.133
0.133
0.133
0.038
0.034
0.038
0.077
0.199
33.4 0.189
26.1 0.133
27.7 0.145
18.2 0.077
34.3 0.199
14.9
9.1
21.0
23.7
14.9
27.3
25.4
23.7
26.1
26.1
26.1
26.1
26.1
26.1
26.1
11.3
10.6
11.3
18.2
34.3
9.1 0.033
73
81
78
97
70
144
184
121
114
144
106
110
114
81
81
81
81
81
81
81
122
127
122
97
70
184
VII-26
January 2005
All
All
Extrusions
Sheet & Plate
(1.500)
Plate (3.000)
Extrusions
Plate (2.000)
Sheet & Plate
Sheet
5052- O, H32, H34
5083- O, H111
5083- O, H116, H321
16.8
12.2
8.7
All (2)
All (3)
All
Extrusions (2)
Extrusions (3)
Extrusions
Extrusions
6061- T6, T651, T6510, T6511
6061- T6, T651, T6510, T6511
6063- T5, T52, T6
6351- T5, T6
6351- T5, T6
6463- T6
7005- T53
Bp
ksi
4.2
7.4
6.1
14.2
15.6
15.6
24.2
22.8
17.0
18.4
18.4
14.2
106 33.1
133 19.9
157 14.2
185 10.1
0.084
0.052
0.031
0.174
133 19.9
157 14.2
185 10.1
127 22.8
144 17.0
159
152
152
123
127
146
140
140
158
135 19.9
123 24.2
170 12.1
215
236
236 6.1
250 5.5
180 10.8
185 10.1
206 8.1
284
Cc
0.084
0.052
0.031
0.101
0.067
0.051
0.058
0.058
0.111
0.101
0.066
0.074
0.074
0.051
0.083
0.111
0.041
0.020
0.015
0.015
0.013
0.034
0.031
0.023
Dc
ksi
0.009
0.228
0.108
0.065
0.039
0.108
0.065
0.039
0.130
0.086
0.064
0.074
0.074
0.143
0.130
0.084
0.095
0.095
0.065
0.106
0.143
0.051
0.025
0.018
0.018
0.016
0.043
0.039
0.028
Dp
ksi
0.010
97
123
145
172
123
145
172
116
133
147
140
140
113
116
135
129
129
147
125
113
158
201
221
221
234
167
172
192
267
Cp
31.8
19.4
14.1
10.1
19.4
14.1
10.1
22.2
16.7
14.1
15.4
15.4
23.5
22.2
16.7
18.1
18.1
14.1
19.4
23.5
12.1
7.5
6.2
6.2
5.5
10.7
10.1
8.1
Bt
ksi
4.3
1.244
0.654
0.424
0.273
0.654
0.424
0.273
0.771
0.536
0.420
0.474
0.474
0.835
0.771
0.530
0.588
0.588
0.422
0.647
0.835
0.345
0.183
427
389
523
795
389
523
795
532
446
683
651
651
515
532
622
596
596
680
573
515
732
930
0.142 1065
0.142 1060
0.123 1145
0.297 772
0.273 795
0.204 875
Dt
Ct
ksi
0.087 1375
44.1
26.4
18.8
13.4
26.4
18.8
13.4
30.2
22.6
18.8
20.7
20.7
32.2
30.2
22.6
24.5
24.5
18.8
26.4
32.2
16.1
9.8
8.1
8.1
7.2
14.3
13.4
10.7
Bbr
ksi
5.5
192
203
145
150
167
108
98
101
115
0.350
84
0.165 107
0.100 126
0.060 150
0.165 107
0.100 126
0.060 150
0.199
0.131
0.098 128
0.113 122
0.113 122
0.219
98
0.199 101
0.129 117
0.145 112
0.145 112
0.099 127
0.163
0.219
0.078 137
0.038 175
0.028 192
0.028
0.024
0.066
0.060
0.043
Dbr
Cbr
ksi
0.016 232
47.7
29.2
21.1
15.1
29.2
21.1
15.1
33.2
25.1
21.1
23.1
23.1
35.3
33.2
25.1
27.1
27.1
21.1
29.2
35.3
18.1
11.2
9.3
9.3
8.3
16.1
15.1
12.2
Btb
ksi
6.4
259
279
179
187
216
113
136
129
129
152
2.928
89
1.538 121
0.999 150
0.642 187
1.538 121
0.999 150
0.642 187
1.814 113
1.260 133
0.989 153
1.116 144
1.116 144
1.965 108
1.814
1.248
1.384
1.384
0.992
1.523 123
1.965 108
0.812 167
0.430 228
0.334 259
0.334
0.289
0.698
0.642
0.481
Dtb
Ctb
ksi
0.204 332
(1) Maximum thickness (in.) shown in parentheses.
(2) Values when welded with 5183, 5356, or 5556 filler, regardless of thickness. Values also apply to thicknesses < 0.375 in. when welded with 4043, 5554, or 5654 filler.
(3) Values apply to thicknesses > 0.375 in. when welded with 4043, 5554, or 5654 filler.
27.7
16.8
12.2
8.7
19.2
14.5
5456- O, H116, H321
6005- T5
12.2
13.3
13.3
20.4
Extrusions
Extrusions
Sheet & Plate
Sheet & Plate
(1.500)
Plate (3.000)
Extrusions
19.2
14.5
15.7
15.7
12.2
16.8
20.4
10.4
6.5
5.4
5.4
4.8
9.3
8.7
7.0
Bc
ksi
3.7
5454- O, H111
5454- H112
5454- O, H32, H34
5456- O, H116, H321
5083- O, H116, H321
5086- O, H111
5086- H112
5086- O, H32, H34, H116
5154- H38
All
5050- H32, H34
All
All
All
All
Sheet
Product (1)
All
5005- H12, H14, H32, H34
3003- H12, H14, H16, H18
Alclad 3003- H12, H14, H16, H18
3004- H32, H34, H36, H38
Alclad 3004- H32, H34, H36, H38
3005- H25
Alloy
Temper
1100- H12, H14
Table 2-1W
BUCKLING CONSTANTS FOR WELDED ALUMINUM ALLOYS
19.2
11.5
8.2
5.9
11.5
8.2
5.9
14.1
9.9
9.1
9.1
9.1
14.9
13.2
10.7
10.7
10.7
8.2
12.4
14.1
7.0
4.3
3.5
3.5
3.2
6.3
5.9
4.7
Bs
ksi
2.4
290
307
219
226
253
184
184
184
144
153
170
170
170
192
0.101 127
0.048 161
0.029 190
0.017 226
0.048 161
0.029 190
0.017 226
0.063 148
0.038 174
0.033
0.033
0.033
0.069
0.058
0.042
0.042
0.042
0.029
0.052 158
0.063 148
0.023 207
0.011 264
0.008 290
0.008
0.007
0.019
0.017
0.012
Ds
Cs
ksi
0.005 351
Design Aid Tables 2-2 through 2-26
1. These tables provide allowable stresses for building type structures.
2. Buckling constants used to calculate values in Tables 2-2 through 2-26 are calculated from minimum mechanical properties
given in Part I Tables 3.3-1 and 3.3-2 rather than the rounded buckling constants given in Part VII Tables 2-1 and 2-1W.
3. Unshaded values apply to unwelded members.
4. Shaded values apply to members with the full cross section weld affected and are calculated in accordance with Part IA
Section 7.1.2.
5. For tubes with circumferential welds, equations of 3.4.10, 3.4.12, and 3.4.16.1 apply for Rb /t < 20.
January 2005
VII-27
VII-28
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
1.2
12
2.1
8
2.1
8
2.6
6.6
3.7
3.8
8
2.1
1.2
3.8
8
2.1
0
0
–
–
S1
Allowable
Stress,
S < S1
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
On flat surfaces and pins and on bolts in slotted holes
11.5
Sec.
3.4.
5
2.8
7.5
16
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
2.5
11
11
3
Round or oval tubes
2.1
6
10
2
5.5
Allowable Stress
Flat elements in uniform tension
COMPRESSION
IN COLUMNS, All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
gross section
net section
Sec.
3.4.
8.5
8
8
Type of Member or Element
1
TENSION, axial Any tension member
Type of Stress
125
62
52
26
39
19
280
144
S2
____
2.2 – 0.044 √Rb/t
____
8.6 – 0.275 √Rb/t
1380
450
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
2.2 – 0.0086 b/t
8.7 – 0.070 b/t
2.2 – 0.027 b/t
8.7 – 0.224 b/t
2.2 – 0.027 b/t
8.7 – 0.224 b/t
1.9 – 0.0045 kL/r
7.4 – 0.034 kL/r
Allowable Stress,
S1 < S < S2
____
b
b
____
√Rb/t
1 + _____
( t )( 35 )
√R /t
R
3190 / ( ___ )( 1 + _____ )
t
35
3190 /
Rb
___
135 /(b/t)
271 /(b/t)
1970 /(b/t)2
1970 /(b/t)2
42 /(b/t)
85 /(b/t)
51100 /(kL/r)2
51100 /(kL/r)2
Allowable Stress,
S > S2
2
2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
1100-H14 Sheet, Plate, Drawn Tube
Table 2-2
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
January 2005
VII-29
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber, Solid rectangular and round sections
gross section
11
Single web shapes
42
8.2
2.1
9
12
18
65
93
150
214
49
71
90
167
10
2.8
10
2.8
10
2.8
4.9
1.2
4.9
1.2
4.3
29
8
2.5
13
9.2
8
2.1
221
190
8
2.1
27
2.8
19
10
62
9
129
29
2.1
2.5
26
8
1380
450
125
62
39
19
31500
8070
101
50
460
184
340
172
6.5 – 0.032 h/t
1.5 – 0.0035 h/t
8.9 – 0.044 ae/t
2.0 – 0.0048 ae/t
3.4 – 0.0028 h/t
13.7 – 0.023 h/t
3.4 – 0.0064 h/t
13.7 – 0.053 h/t
3.4 – 0.034 b/t
13.7 – 0.277 b/t
134
280
134
280
600
300
260
129
66
33
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
____
2.6 – 0.0526 √Rb/t
10.1 – 0.325 √Rb/t
____
2.5 – 0.010 b/t
10.3 – 0.083 b/t
2.5 – 0.032 b/t
10.3 – 0.265 b/t
2L___
bSc
2.2 – 0.0084 _____
IyJ
_____
2L___
bSc
8.8 – 0.065 _____
√IyJ
√
√√
_____
Lb
d __
13.7 – 0.182 __
t d
___
Lb
d __
3.4 – 0.022 __
t d
√
√
___
3.9 – 0.124 √Rb/t
____
15.2 – 0.764 √Rb/t
____
2.2 – 0.0044 Lb/ry
8.8 – 0.034 Lb/ry
____
38700 /(h/t)2
38700 /(h/t)2
53200 /(ae/t)2
53200 /(ae/t)2
1010 /(h/t)
2040 /(h/t)
436 /(h/t)
881 /(h/t)
4930 /(b/t)2
b
____
√Rb/t
1 + _____
4930 /(b/t)2
b
Rb
___
2
2
( t )( 35 )
√R /t
R
3780 / ( ___ )( 1 + _____ )
t
35
3780 /
159 /(b/t)
320 /(b/t)
50 /(b/t)
101 /(b/t)
2L___
bSc
23600 / _____
√IyJ
2L___
bSc
23600 / _____
√IyJ
( )
( )
Lb
d 2 __
11400 / __
t d
Lb
d 2 __
11400 / __
t d
Section 3.4.10
Same as
87000 /(Lb/ry)2
87000 /(Lb/ry)2
VII-30
January 2005
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
2.3
12
3.0
8.5
3.0
8.5
3.9
6.8
7.3
3.8
8.5
3.0
2.3
3.8
8.5
3.0
0
0
–
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
14.5
9.5
5
3.9
13.5
21
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
3.5
3.0
6
13.5
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
12
2
7
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
10.5
10.5
10.5
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
104
60
43
25
33
19
236
138
S2
3.2 – 0.073
9.3 – 0.305
√Rb/t
____
____
√Rb/t
1060
420
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
3.1 – 0.015 b/t
9.5 – 0.079 b/t
3.1 – 0.048 b/t
9.5 – 0.252 b/t
3.1 – 0.048 b/t
9.5 – 0.252 b/t
2.7 – 0.0077 kL/r
8.0 – 0.039 kL/r
Allowable Stress,
S1 < S < S2
____
√Rb/t 2
1 + _____
35
b
b
____
2
)
( )(
√R /t
R
3190 /( ___ )( 1 + _____ )
t
35
R
3190 / ___b
t
163 /(b/t)
282 /(b/t)
1970 /(b/t)2
1970 /(b/t)2
51 /(b/t)
89 /(b/t)
51100 /(kL/r)2
51100 /(kL/r)2
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
3003-H14 Sheet, Plate, Drawn Tube
Table 2-3
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
January 2005
VII-31
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
38
8.3
3.0
10
12
16
63
85
147
195
46
65
83
142
11
3.9
11
3.9
11
3.9
6
1.7
6
1.7
5.7
29
8.5
3.5
12
9.0
8.5
3.0
214
188
8.5
3.0
25
3.9
18
11
59
10
106
28
3.0
3.5
26
8.5
___
√Rb/t
____
√Rb/t
1060
420
104
60
33
19
21800
7470
84
48
360
175
280
166
8.0 – 0.044
2.2 – 0.0062
11.0 – 0.061
3.0 – 0.0085
h/t
h/t
ae/t
ae/t
4.9 – 0.0049 h/t
14.8 – 0.026 h/t
4.9 – 0.011 h/t
14.8 – 0.060 h/t
4.9 – 0.059 b/t
14.8 – 0.313 b/t
120
232
120
232
500
290
215
124
55
32
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
____
3.8 – 0.086 √Rb/t
√Rb/t
____
3.7 – 0.018 b/t
11.2 – 0.094 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
_____
3.7 – 0.057 b/t
11.0 – 0.360
___
__ __b
t
Lb
d __
__
11.2 – 0.298 b/t
3.2 – 0.015
9.5 – 0.073
14.8 – 0.206
√d
L
4.9 – 0.039 d √
t d
5.6 – 0.203
16.4 – 0.847
____
3.2 – 0.0076 Lb/ry
9.5 – 0.038 Lb/ry
b
38700
38700
53200
53200
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1220 /(h/t)
2120 /(h/t)
527 /(h/t)
917 /(h/t)
4930 /(b/t)2
4930 /(b/t)2
3780
Rb
___
____
√Rb/t
1 + _____
2
b
____
2
( t )( 35 )
√R /t
R
3780 ( ___ )( 1 + _____ )
t
35
192 /(b/t)
333 /(b/t)
60 /(b/t)
105 /(b/t)
2L___
bSc
23600 / _____
√IyJ
2L___
bSc
23600 / _____
√IyJ
( )
( )
Lb
d 2 __
11400 / __
t d
Lb
d 2 __
11400 / __
t d
Section 3.4.10
Same as
87000 /(Lb/ry)2
87000 /(Lb/ry)2
VII-32
January 2005
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
2.3
13
3.0
11
3.0
11
3.9
7.2
7.3
4.0
11
3.0
2.3
4.0
11
3.0
0
0
–
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
14.5
9.5
5
3.9
16
25
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
3.5
3.0
6
17
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
15
2
7
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
12.5
12.5
12.5
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
3.2 – 0.073
12.1 – 0.432
√Rb/t
____
____
√Rb/t
1060
330
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
104
52
12.4 – 0.119 b/t
3.1 – 0.015 b/t
43
22
33
16
236
121
S2
3.1 – 0.048 b/t
12.4 – 0.380 b/t
3.1 – 0.048 b/t
12.4 – 0.380 b/t
2.7 – 0.0077 kL/r
10.5 – 0.058 kL/r
Allowable Stress,
S1 < S < S2
____
√Rb/t 2
1 + _____
35
b
b
____
2
)
( )(
√R /t
R
3190 /( ___ )( 1 + _____ )
t
35
R
3190 / ___b
t
163 /(b/t)
323 /(b/t)
1970 /(b/t)2
1970 /(b/t)2
51 /(b/t)
101 /(b/t)
51100 /(kL/r)2
51100 /(kL/r)2
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
3003-H16 Sheet, Drawn Tube
Table 2-4
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
January 2005
VII-33
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
16
Flat elements supported on both edges
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
15
Flat elements supported on one edge
Tubular shapes
14
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
38
8.6
3.0
13
√
√
√Rb___
/t
____
√Rb/t
1060
330
104
52
33
16
21800
5730
84
42
360
147
280
145
4.9 – 0.0049 h/t
10.1 – 0.063
2.2 – 0.0062
13.8 – 0.086
3.0 – 0.0085
59
85
136
195
44
65
76
142
14
3.9
14
3.9
7.5
1.7
7.5
1.7
h/t
h/t
ae/t
ae/t
19.5 – 0.039 h/t
4.9 – 0.011 h/t
19.5 – 0.090 h/t
4.9 – 0.059 b/t
16
3.9
19.5 – 0.471 b/t
11
107
232
107
232
500
249
215
108
55
28
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
____
√Rb/t
3.8 – 0.086 √Rb/t
14.3 – 0.511
____
3.7 – 0.018 b/t
14.7 – 0.141 b/t
3.7 – 0.057 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
_____
14.7 – 0.449 b/t
3.2 – 0.015
12.4 – 0.109
Lb
d __
19.5 – 0.310 __
t d
___
Lb
d __
4.9 – 0.039 __
t d
5.6 – 0.203
21.4 – 1.20
____
3.2 – 0.0076 Lb/ry
12.4 – 0.057 Lb/ry
14
5.7
27
11
3.5
12
8.4
11
3.0
214
180
25
3.0
11
3.9
17
14
52
13
106
28
3.0
3.5
26
11
38700
38700
53200
53200
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1220 /(h/t)
2430 /(h/t)
527 /(h/t)
1050 /(h/t)
4930 /(b/t)2
4930 /(b/t)2
b
R
3780 / ___b
____
√Rb/t
1 + _____
2
b
____
2
( t )( 35 )
√R /t
R
3780 /( ___ )( 1 + _____ )
t
35
192 /(b/t)
382 /(b/t)
60 /(b/t)
120 /(b/t)
2L___
bSc
23600 / _____
√IyJ
2L___
bSc
23600 / _____
√IyJ
( )
( )
Section 3.4.10
Lb
d 2 __
11400 / __
t d
Lb
d 2 __
11400 / __
t d
Same as
87000 /(Lb/ry)2
87000 /(Lb/ry)2
VII-34
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
4.8
12.5
5.4
7.4
10
13
12.5
4.8
3.3
4.8
81
48
34
20
25
15
185
112
S2
5.2 – 0.140
14.2 – 0.536
√Rb/t
____
____
√Rb/t
800
280
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
5.2 – 0.032 b/t
14.7 – 0.153 b/t
5.2 – 0.102 b/t
14.7 – 0.488 b/t
4.0
12.5
14.7 – 0.488 b/t
5.2 – 0.102 b/t
4.0
12.5
4.5 – 0.016 kL/r
3.3
0
–
12.3 – 0.074 kL/r
Allowable Stress,
S1 < S < S2
____
√Rb/t 2
1 + _____
35
b
b
____
2
)
( )(
√R /t
R
3190 /( ___ )( 1 + _____ )
t
35
R
3190 / ___b
t
209 /(b/t)
352 /(b/t)
1970 /(b/t)2
1970 /(b/t)2
66 /(b/t)
110 /(b/t)
51100 /(kL/r)2
51100 /(kL/r)2
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
Alclad 3004-H34 Sheet
Table 2-5
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
4.8
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
22
14.5
5
6.5
21
32
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
5.5
4.8
6
19
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
17
2
11
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
14.5
16
14.5
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-35
16
Flat elements supported on both edges
19
20
21
Flat elements supported on both edges
and with a longitudinal stiffener
Unstiffened flat elements supported
on both edges
Stiffened flat elements supported
on both edges
bending in own
plane), gross
section
SHEAR IN
ELEMENTS,
gross section
18
17
16.3
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber, Solid rectangular and round sections
gross section
11
Single web shapes
34
8.7
4.8
15
11
14
56
74
130
172
42
57
71
116
17
6.5
17
6.5
17
6.5
8.5
2.8
8.5
2.8
7.2
26
12.5
5.5
11
8.0
12.5
4.8
203
175
12.5
4.8
22
6.5
16
17
47
15
81
27
4.8
5.5
25
12.5
___
√Rb/t
____
√Rb/t
800
280
81
48
25
15
13400
4860
65
39
260
132
222
134
11.7 – 0.078
3.6 – 0.013
16.0 – 0.107
4.9 – 0.018
h/t
h/t
ae/t
ae/t
8.1 – 0.010 h/t
23.1 – 0.050 h/t
8.1 – 0.024 h/t
23.1 – 0.116 h/t
8.1 – 0.126 b/t
23.1 – 0.607 b/t
100
181
100
181
390
229
167
99
43
25
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
____
√Rb/t
6.1 – 0.165 √Rb/t
16.8 – 0.634
____
6.1 – 0.038 b/t
17.3 – 0.181 b/t
6.1 – 0.121 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
17.3 – 0.577 b/t
5.3 – 0.030
14.6 – 0.139
_____
__ __b
___
Lb
d __
23.1 – 0.399 __
t d
√
L
8.1 – 0.083 d √
t d
9.2 – 0.389
25.1 – 1.49
____
5.3 – 0.016 Lb/ry
14.6 – 0.073 Lb/ry
38700
38700
53200
53200
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1570 /(h/t)
2640 /(h/t)
678 /(h/t)
1140 /(h/t)
4930 /(b/t)2
4930 /(b/t)2
b
R
3780 / ___b
____
√Rb/t
1 + _____
2
b
____
2
( t )( 35 )
√R /t
R
3780 /( ___ )( 1 + _____ )
t
35
247 /(b/t)
415 /(b/t)
77 /(b/t)
130 /(b/t)
2L___
bSc
23600 /_____
√IyJ
2L___
bSc
23600 /_____
√IyJ
( )
( )
Lb
d 2 __
11400 / __
t d
Lb
d 2 __
11400 / __
t d
Section 3.4.10
Same as
87000 /(Lb/ry)2
87000 /(Lb/ry)2
VII-36
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
12
9
3.0
9
3.9
6.9
7
2.3
3.0
3.0
3.9
9
3.9
9
2.3
0
–
3.0
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
15
10.5
5
3.9
14.5
22
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
3.5
3.0
6
13.5
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
12
2
7.5
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
10.5
11
10.5
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
104
58
43
24
33
18
236
133
S2
3.2 – 0.073
10.0 – 0.335
√Rb/t
____
____
√Rb/t
1070
390
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
3.1 – 0.015 b/t
10.2 – 0.089 b/t
3.1 – 0.048 b/t
10.2 – 0.282 b/t
3.1 – 0.048 b/t
10.2 – 0.282 b/t
2.7 – 0.077 kL/r
8.6 – 0.043 kL/r
Allowable Stress,
S1 < S < S2
____
√Rb/t 2
1 + _____
35
b
b
____
2
)
( )(
√R /t
R
3190 /( ___ )( 1 + _____ )
t
35
R
3190 / ___b
t
163 /(b/t)
293 /(b/t)
1970 /(b/t)2
1970 /(b/t)2
51 /(b/t)
92 /(b/t)
51100 /(kL/r)2
51100 /(kL/r)2
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5005-H14 Sheet and Plate
Table 2-6
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
January 2005
VII-37
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
38
8.4
3.0
10.5
12
16
62
85
144
195
46
65
83
142
12
3.9
12
3.9
12
3.9
6
1.7
6
1.7
5.7
28
9
3.5
12
8.8
9
3.0
214
186
9
3.0
25
3.9
18
12
57
10.5
106
28
3.0
3.5
26
9
___
√Rb/t
____
√Rb/t
1070
390
104
58
33
18
21800
6940
84
46
360
167
280
160
8.0 – 0.044
2.2 – 0.0062
11.0 – 0.061
3.0 – 0.0085
h/t
h/t
ae/t
ae/t
4.9 – 0.0049 h/t
16.0 – 0.029 h/t
4.9 – 0.011 h/t
16.0 – 0.067 h/t
4.9 – 0.059 b/t
16.0 – 0.350 b/t
120
232
120
232
500
280
215
119
55
30
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
____
√Rb/t
3.8 – 0.086 √Rb/t
11.8 – 0.396
____
3.7 – 0.018 b/t
12.0 – 0.105 b/t
3.7 – 0.057 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
12.0 – 0.334 b/t
3.2 – 0.015
10.2 – 0.082
_____
__ __b
___
Lb
d __
16.0 – 0.230 __
t d
√
L
4.9 – 0.039 d √
t d
5.6 – 0.203
17.7 – 0.932
____
3.2 – 0.0076 Lb/ry
10.2 – 0.043 Lb/ry
38700
38700
53200
53200
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1220 /(h/t)
2200 /(h/t)
527 /(h/t)
952 /(h/t)
4930 /(b/t)2
4930 /(b/t)2
b
R
3780 / ___b
____
√Rb/t
1 + _____
2
b
____
2
( t )( 35 )
√R /t
R
3780 /( ___ )( 1 + _____ )
t
35
192 /(b/t)
346 /(b/t)
60 /(b/t)
109 /(b/t)
2L___
bSc
23600 /_____
√IyJ
2L___
bSc
23600 /_____
√IyJ
( )
( )
Lb
d 2 __
11400 / __
t d
Lb
d 2 __
11400 __
/
t d
Section 3.4.10
Same as
87000 /(Lb/ry)2
87000 /(Lb/ry)2
VII-38
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
2.3
12
3.0
8.5
3.0
8.5
3.9
6.8
7
3.8
8.5
3.0
2.3
3.8
8.5
3.0
0
0
–
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
15
10.5
5
3.9
13.5
21
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
3.5
3.0
6
12
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
10.5
2
7.5
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
9
10.5
9
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
104
60
43
25
33
19
236
138
S2
3.2 – 0.073
9.3 – 0.305
√Rb/t
____
____
√Rb/t
1070
420
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
3.1 – 0.015 b/t
9.5 – 0.079 b/t
3.1 – 0.048 b/t
9.5 – 0.252 b/t
3.1 – 0.048 b/t
9.5 – 0.252 b/t
2.7 – 0.077 kL/r
8.0 – 0.039 kL/r
Allowable Stress,
S1 < S < S2
____
√Rb/t 2
1 + _____
35
b
b
____
2
)
( )(
√R /t
R
3190 /( ___ )( 1 + _____ )
t
35
R
3190 / ___b
t
163 /(b/t)
282 /(b/t)
1970 /(b/t)2
1970 /(b/t)2
51 /(b/t)
89 /(b/t)
51100 /(kL/r)2
51100 /(kL/r)2
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5005-H34 Sheet and Plate
Table 2-7
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
January 2005
VII-39
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
38
8.3
3.0
10
12
16
63
85
147
195
48
65
88
142
11
3.9
11
3.9
11
3.9
5
1.7
5
1.7
5.7
29
8.5
3.5
12
9.0
8.5
3.0
214
188
8.5
3.0
25
3.9
18
11
59
10
106
28
3.0
3.5
26
8.5
___
√Rb/t
____
√Rb/t
1070
420
104
60
33
19
21800
7470
84
48
360
175
280
166
7.0 – 0.036
2.2 – 0.0062
9.6 – 0.050
3.0 – 0.0085
h/t
h/t
ae/t
ae/t
4.9 – 0.0049 h/t
14.8 – 0.026 h/t
4.9 – 0.011 h/t
14.8 – 0.060 h/t
4.9 – 0.059 b/t
14.8 – 0.313 b/t
129
232
129
232
500
290
215
124
55
32
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
____
√Rb/t
3.8 – 0.086 √Rb/t
11.0 – 0.360
____
3.7 – 0.018 b/t
11.2 – 0.094 b/t
3.7 – 0.057 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
11.2 – 0.298 b/t
3.2 – 0.015
9.5 – 0.073
_____
__ __b
___
Lb
d __
14.8 – 0.206 __
t d
√
L
4.9 – 0.039 d √
t d
5.6 – 0.203
16.4 – 0.847
____
3.2 – 0.0076 Lb/ry
9.5 – 0.038 Lb/ry
38700
38700
53200
53200
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1220 /(h/t)
2120 /(h/t)
527 /(h/t)
917 /(h/t)
4930 /(b/t)2
4930 /(b/t)2
b
R
3780 / ___b
____
√Rb/t
1 + _____
2
b
____
2
( t )( 35 )
√R /t
R
3780 /( ___ )( 1 + _____ )
t
35
192 /(b/t)
333 /(b/t)
60 /(b/t)
105 /(b/t)
2L___
bSc
23600 /_____
√IyJ
2L___
bSc
23600 /_____
√IyJ
( )
( )
Lb
d 2 __
11400 / __
t d
Lb
d 2 __
11400 / __
t d
Section 3.4.10
Same as
87000 /(Lb/ry)2
87000 /(Lb/ry)2
VII-40
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
3.6
11
3.6
4.5
7.2
8.7
94
3.8 – 0.094
12.1 – 0.432
√Rb/t
____
____
√Rb/t
930
330
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
3.8 – 0.020 b/t
52
12.4 – 0.119 b/t
13
11
39
2.7
3.6
22
30
16
215
121
S2
3.8 – 0.065 b/t
12.4 – 0.380 b/t
4.0
11
12.4 – 0.380 b/t
3.8 – 0.065 b/t
4.0
11
3.3 – 0.010 kL/r
2.7
0
–
10.5 – 0.058 kL/r
Allowable Stress,
S1 < S < S2
b
( )(
R
3190 /( ___ )(
t
R
3190 / ___b
t
179 /(b/t)
323 /(b/t)
1970 /(b/t)2
1970 /(b/t)2
56 /(b/t)
101 /(b/t)
51100 /(kL/r)2
51100 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√
Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5050-H34 Sheet, Drawn Tube
Table 2-8
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
3.6
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
18
12.5
5
4.7
17
26
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
4.3
3.6
6
16
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
14
2
9
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
12
13
12
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-41
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
36
8.6
3.6
13
11
15
59
81
136
186
44
62
77
131
14
4.7
14
4.7
14
4.7
7
2.1
7
2.1
6.3
27
11
4.3
11
8.4
11
3.6
210
180
11
3.6
23
4.7
17
14
52
13
95
28
3.6
4.3
26
11
√
√
___
√Rb/t
____
√Rb/t
____
√Rb/t
____
√Rb/t
930
330
94
52
30
16
18100
5730
76
42
310
147
260
145
9.5 – 0.058
2.6 – 0.0083
13.1 – 0.079
3.6 – 0.011
h/t
h/t
ae/t
ae/t
6.0 – 0.0066 h/t
19.5 – 0.039 h/t
6.0 – 0.015 h/t
19.5 – 0.090 h/t
6.0 – 0.080 b/t
19.5 – 0.471 b/t
110
211
110
211
450
249
195
108
50
28
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
4.5 – 0.111
14.3 – 0.511
4.5 – 0.024 b/t
14.7 – 0.141 b/t
4.5 – 0.076 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
14.7 – 0.449 b/t
3.9 – 0.019
12.4 – 0.109
_____
Lb
d __
19.5 – 0.310 __
t d
___
Lb
d __
6.0 – 0.052 __
t d
6.8 – 0.261
21.4 – 1.20
____
3.9 – 0.010 Lb/ry
12.4 – 0.057 Lb/ry
38700
38700
53200
53200
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1340 /(h/t)
2430 /(h/t)
581 /(h/t)
1050 /(h/t)
4930 /(b/t)2
4930 /(b/t)2
b
R
3780 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3780 /( ___ )( 1 + _____ )
t
35
212 /(b/t)
382 /(b/t)
66 /(b/t)
120 /(b/t)
2L___
bSc
23600 /_____
√IyJ
2L___
bSc
23600 /_____
√IyJ
( )
( )
Lb
d 2 __
11400 / __
t d
Lb
d 2 __
11400 / __
t d
Section 3.4.10
Same as
87000 /(Lb/ry)2
87000 /(Lb/ry)2
VII-42
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
6
12.5
6.0
7.4
11
13
12.5
6
3.5
6
74
48
31
20
23
15
170
112
S2
6.2 – 0.177
14.2 – 0.535
√Rb/t
____
____
√Rb/t
730
280
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
6.2 – 0.042 b/t
14.7 – 0.152 b/t
6.2 – 0.134 b/t
14.7 – 0.486 b/t
4.0
12.5
14.7 – 0.486 b/t
6.2 – 0.134 b/t
4.0
12.5
5.3 – 0.021 kL/r
3.5
0
–
12.3 – 0.073 kL/r
Allowable Stress,
S1 < S < S2
b
( )(
R
3230 /( ___ )(
t
R
3230 / ___b
t
230 /(b/t)
353 /(b/t)
1980 /(b/t)2
1980 /(b/t)2
72 /(b/t)
111 /(b/t)
51600 /(kL/r)2
51600 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√
Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5052-H32 Sheet, Drawn Tube
Table 2-9
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
6
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
26
17
5
7.5
21
32
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
6.5
6
6
18
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
16
2
13
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
14
16
14
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-43
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
32
8.8
6
15
11
14
56
71
130
165
43
55
73
108
17
7.5
17
7.5
17
7.5
8
3.3
8
3.3
7.7
26
12.5
6.5
10
8.0
12.5
6
201
177
12.5
6
21
7.5
16
17
48
15
74
27
6
6.5
26
12.5
√
√
___
√Rb/t
____
√Rb/t
____
√Rb/t
____
√Rb/t
730
280
74
48
23
15
11300
4910
60
39
230
133
204
135
103
166
103
166
350
h/t
h/t
ae/t
ae/t
9.7 – 0.014 h/t
11.1 – 0.072
4.3 – 0.017
15.3 – 0.099
5.9 – 0.024
230
153
100
39
25
23.1 – 0.050 h/t
9.7 – 0.032 h/t
23.1 – 0.116 h/t
9.7 – 0.166 b/t
23.1 – 0.604 b/t
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
7.3 – 0.209
16.8 – 0.632
7.4 – 0.050 b/t
17.3 – 0.180 b/t
7.4 – 0.159 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
17.3 – 0.574 b/t
6.3 – 0.040
14.6 – 0.139
_____
Lb
d __
23.1 – 0.397 __
t d
___
Lb
d __
9.7 – 0.109 __
t d
11.0 – 0.492
25.1 – 1.49
____
6.3 – 0.021 Lb/ry
14.6 – 0.072 Lb/ry
39000
39000
53700
53700
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1730 /(h/t)
2660 /(h/t)
747 /(h/t)
1150 /(h/t)
4980 /(b/t)2
4980 /(b/t)2
b
R
3810 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3810 /( ___ )( 1 + _____ )
t
35
272 /(b/t)
418 /(b/t)
85 /(b/t)
131 /(b/t)
2L___
bSc
23800 /_____
√IyJ
2L___
bSc
23800 /_____
√IyJ
( )
( )
Lb
d 2 __
11500 / __
t d
Lb
d 2 __
11500 / __
t d
Section 3.4.10
Same as
87900 /(Lb/ry)2
87900 /(Lb/ry)2
VII-44
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
6
14.5
6
6.0
7.5
11
74
6.2 – 0.177
16.3 – 0.644
√Rb/t
____
____
√Rb/t
730
250
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
6.2 – 0.042 b/t
45
17.0 – 0.190 b/t
13
14.5
31
3.5
6
19
23
14
170
104
S2
6.2 – 0.134 b/t
17.0 – 0.604 b/t
4.0
14.5
17.0 – 0.604 b/t
6.2 – 0.134 b/t
4.0
14.5
5.3 – 0.021 kL/r
3.5
0
–
14.2 – 0.091 kL/r
Allowable Stress,
S1 < S < S2
b
( )(
R
3230 /( ___ )(
t
R
3230 / ___b
t
230 /(b/t)
380 /(b/t)
1980 /(b/t)2
1980 /(b/t)2
72 /(b/t)
119 /(b/t)
51600 /(kL/r)2
51600 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√
Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5052-H34 Sheet, Plate, Drawn Tube
Table 2-10
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
6
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
26
17
5
7.5
23
35
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
6.5
6
6
20
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
18
2
13
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
16
17
16
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-45
16
Flat elements supported on both edges
19
20
21
Flat elements supported on both edges
and with a longitudinal stiffener
Unstiffened flat elements supported
on both edges
Stiffened flat elements supported
on both edges
bending in own
plane), gross
section
SHEAR IN
ELEMENTS,
gross section
18
17
16.3
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
32
8.8
6
17
10
14
54
71
125
165
41
55
69
108
19
7.5
19
7.5
19
7.5
9
3.3
9
3.3
7.7
25
14.5
6.5
10
7.7
14.5
6
201
172
14.5
6
__ __b
21
7.5
730
250
74
45
23
14
11300
4260
60
36
230
121
204
125
96
166
96
166
350
h/t
h/t
ae/t
ae/t
9.7 – 0.014 h/t
12.7 – 0.088
4.3 – 0.017
17.5 – 0.121
5.9 – 0.024
214
153
93
39
24
26.7 – 0.062 h/t
9.7 – 0.032 h/t
26.7 – 0.144 h/t
9.7 – 0.166 b/t
26.7 – 0.752 b/t
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
____
√Rb/t
7.3 – 0.209 √Rb/t
19.3 – 0.761
____
7.4 – 0.050 b/t
20.1 – 0.224 b/t
7.4 – 0.159 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
20.1 – 0.714 b/t
6.3 – 0.040
16.8 – 0.172
_____
___
√
L
9.7 – 0.109 d √
t d
___
Lb
d __
26.7 – 0.494 __
t d
√Rb/t
____
√Rb/t
16
11.0 – 0.492
28.9 – 1.79
19
44
17
____
6.3 – 0.021 Lb/ry
74
27
6
16.8 – 0.089 Lb/ry
6.5
25
14.5
39000
39000
53700
53700
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1730 /(h/t)
2860 /(h/t)
747 /(h/t)
1240 /(h/t)
4980 /(b/t)2
4980 /(b/t)2
b
R
3810 / ___b
____
√Rb/t
1 + _____
2
b
____
2
( t )( 35 )
√R /t
R
3810 /( ___ )( 1 + _____ )
t
35
272 /(b/t)
449 /(b/t)
85 /(b/t)
141 /(b/t)
2L___
bSc
23800 /_____
√IyJ
2L___
bSc
23800 /_____
√IyJ
( )
( )
Lb
d 2 __
11500 / __
t d
Lb
d 2 __
11500 / __
t d
Section 3.4.10
Same as
87900 /(Lb/ry)2
87900 /(Lb/ry)2
VII-46
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
9
12.5
9
7.0
7.5
13
58
10.0 – 0.332
14.2 – 0.531
____
√Rb/t
____
√Rb/t
570
290
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
10.2 – 0.087 b/t
49
14.7 – 0.151 b/t
13
12.5
24
3.9
9
20
18
15
135
113
S2
10.2 – 0.278 b/t
14.7 – 0.481 b/t
4.1
12.5
14.7 – 0.481 b/t
10.2 – 0.278 b/t
4.1
12.5
8.6 – 0.043 kL/r
3.9
0
–
12.3 – 0.073 kL/r
Allowable Stress,
S1 < S < S2
____
b
b
____
b
2
2
√R /t
( )( 1 + _____
35 )
√R /t
R
3290 /( ___ )( 1 + _____ )
t
35
R
3290 / ___b
t
297 /(b/t)
357 /(b/t)
2020 /(b/t)2
2020 /(b/t)2
93 /(b/t)
112 /(b/t)
52600 /(kL/r)2
52600 /(kL/r)2
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5083-H111 Extrusions
Table 2-11
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
9
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
40
27
5
12.5
27
41
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
11.5
9.5
6
19
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
17
2
20
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
14.5
21
14.5
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-47
16
Flat elements supported on both edges
19
20
21
Flat elements supported on both edges
and with a longitudinal stiffener
Unstiffened flat elements supported
on both edges
Stiffened flat elements supported
on both edges
bending in own
plane), gross
section
SHEAR IN
ELEMENTS,
gross section
18
17
16.3
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
29
8.9
9
15
___
√Rb/t
____
√Rb/t
570
290
58
49
18
15
7150
5010
47
39
170
134
162
136
233
280
23.1 – 0.050 h/t
16.0 – 0.029 h/t
57
63
132
146
42
48
72
87
12
17
12
8.5
5.5
8.5
5.5
11.7 – 0.077
7.5 – 0.040
16.0 – 0.105
10.3 – 0.054
h/t
h/t
ae/t
ae/t
16.0 – 0.066 h/t
23.1 – 0.115 h/t
101
126
101
126
121
101
31
17
16.0 – 0.345 b/t
12
26
12
23.1 – 0.598 b/t
11
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
____
√Rb/t
11.8 – 0.392 √Rb/t
16.8 – 0.628
____
12.0 – 0.103 b/t
17.3 – 0.178 b/t
12.0 – 0.329 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
17.3 – 0.568 b/t
10.2 – 0.080
14.6 – 0.137
_____
__ __b
___
Lb
d __
23.1 – 0.393 __
t d
√
L
16.0 – 0.227 d √
t d
17.7 -0.923
25.1 – 1.48
____
10.2 – 0.042 Lb/ry
14.6 – 0.072 Lb/ry
17
8.6
26
12.5
10.5
9.0
8.1
12.5
9
192
180
12.5
9
18
12
17
17
48
15
58
27
9
10.5
26
12.5
39800
39800
54700
54700
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
2230 /(h/t)
2680 /(h/t)
966 /(h/t)
1160 /(h/t)
5080 /(b/t)2
5080 /(b/t)2
b
R
3890 / ___b
____
√Rb/t
1 + _____
2
b
____
2
( t )( 35 )
√R /t
R
3890 /( ___ )( 1 + _____ )
t
35
351 /(b/t)
422 /(b/t)
110 /(b/t)
132 /(b/t)
2L___
bSc
24300 /_____
√IyJ
2L___
bSc
24300 /_____
√IyJ
( )
( )
Lb
d 2 __
11800 / __
t d
Lb
d 2 __
11800 / __
t d
Section 3.4.10
Same as
89600 /(Lb/ry)2
89600 /(Lb/ry)2
VII-48
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
11
16
7.3
7.7
13
13
16
11
4.0
11
53
43
b/t
b/t
22
18
17
14
123
101
b/t
b/t
b/t
b/t
kL/r
kL/r
S2
12.1 – 0.428
17.7 – 0.716
____
√Rb/t
____
√Rb/t
520
235
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
12.4 – 0.117
18.5 – 0.214
12.4 – 0.374
18.5 – 0.682
4.1
16
18.5 – 0.682
12.4 – 0.374
4.1
16
10.5 – 0.057
4.0
0
–
15.5 – 0.102
Allowable Stress,
S1 < S < S2
____
b
b
____
b
2
2
√R /t
( )( 1 + _____
35 )
√R /t
R
3290 /( ___ )( 1 + _____ )
t
35
R
3290 / ___b
t
328 /(b/t)
401 /(b/t)
2020 /(b/t)2
2020 /(b/t)2
103 /(b/t)
126 /(b/t)
52600 /(kL/r)2
52600 /(kL/r)2
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5083-H116, -H32, -H321 Sheet and Plate
(Thickness 0.188 to 1.500 in.)
Table 2-12
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
11
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
41
27
5
14
30
45
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
13
11
6
24
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
22
2
21
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
19
23
19
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-49
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
___
√Rb/t
____
√Rb/t
____
b/t
b/t
b/t
b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
_____
__ __b
t
Lb
d __
__
520
235
53
43
17
14
5900
3990
43
35
150
116
147
121
19.5 – 0.038
15.4 – 0.117
8.5 – 0.048
21.2 – 0.161
11.7 – 0.066
53
60
123
138
39
46
65
82
20
14
20
14
11
6.5
11
6.5
29.2 – 0.070
19.5 – 0.089
29.2 – 0.163
19.5 – 0.465
11
14
29.2 – 0.850
10
88
118
88
118
250
h/t
h/t
h/t
ae/t
ae/t
207
110
90
28
23
h/t
h/t
h/t
b/t
b/t
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
14.3 – 0.506
20
8.8
21.0 – 0.846
9.0
18
13
14.7 – 0.139
27
11
21.9 – 0.253
24
16
14.7 – 0.442
21.9 – 0.806
12.4 – 0.107
18.3 – 0.193
29.2 – 0.559
8.5
7.6
16
___
√Rb/t
____
√Rb/t
____
Lb/ry
Lb/ry
√d
L
19.5 – 0.305 d √
t d
21.4 – 1.19
31.5 – 1.99
12.4 – 0.056
18.3 – 0101
11
186
173
16
11
17
14
16
20
43
18
53
26
11
13
25
16
39800
39800
54700
54700
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
2470 /(h/t)
3020 /(h/t)
1070 /(h/t)
1310 /(h/t)
5080 /(b/t)2
5080 /(b/t)2
b
R
3890 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3890 /( ___ )( 1 + _____ )
t
35
388 /(b/t)
474 /(b/t)
122 /(b/t)
149 /(b/t)
2L___
bSc
24300 /_____
√IyJ
2L___
bSc
24300 /_____
√IyJ
( )
( )
Lb
d 2 __
11800 / __
t d
Lb
d 2 __
11800 / __
t d
Section 3.4.10
Same as
89600 /(Lb/ry)2
89600 /(Lb/ry)2
VII-50
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
3.9
4.0
3.9
13
8.5
19
8.5
19
8.5
19
6.9
7.8
12
23.3 – 0.960 b/t
4.0
19
8.5
9.5 – 0.249 b/t
0
–
2020 /(b/t)2
16
61
9.3 – 0.302
22.1 – 0.958
√Rb/t
____
____
√Rb/t
600
192
see Part IA Section 3.4.9.2
b
( )(
R
3290 /( ___ )(
t
R
3290 / ___b
t
286 /(b/t)
449 /(b/t)
90 /(b/t)
19
39
141 /(b/t)
12
2020 /(b/t)2
52600 /(kL/r)2
140
25
52600 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√
Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
90
S2
see Part IA Section 3.4.9.1
9.5 – 0.078 b/t
23.3 – 0.301 b/t
9.5 – 0.249 b/t
23.3 – 0.960 b/t
8.0 – 0.038 kL/r
0
19.3 – 0.143 kL/r
Allowable Stress,
S1 < S < S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5086-H34 Sheet and Plate, Drawn Tube
Table 2-13
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
36
24
5
11
30
45
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
10
8.5
6
27
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
24
2
18
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
21
23
21
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-51
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
29
9.0
8.5
23
√
√
___
√Rb/t
____
√Rb/t
____
√Rb/t
____
√Rb/t
600
192
61
39
19
12
7690
3190
49
31
178
100
168
108
36.6 – 0.229 h/t
14.8 – 0.059 h/t
36.6 – 0.099 h/t
14.8 – 0.026 h/t
17.1 – 0.136
6.5 – 0.032
23.5 – 0.187
8.9 – 0.044
50
64
115
149
38
50
62
92
25
11
25
11
12
4.9
12
4.9
h/t
h/t
ae/t
ae/t
14.8 – 0.308 b/t
12
11
36.6 – 1.20 b/t
9.5
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
2150 /(h/t)
39800
39800
54700
54700
290
84
136
84
136
3380 /(h/t)
931 /(h/t)
1460 /(h/t)
5080 /(b/t)2
5080 /(b/t)2
b
R
3890 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3890 /( ___ )( 1 + _____ )
t
35
338 /(b/t)
531 /(b/t)
106 /(b/t)
167 /(b/t)
2L___
bSc
24300 /_____
√IyJ
2L___
bSc
24300 /_____
√IyJ
( )
( )
Lb
d 2 __
11800 / __
t d
Lb
d 2 __
11800 / __
t d
Section 3.4.10
Same as
89600 /(Lb/ry)2
89600 /(Lb/ry)2
185
126
80
32
20
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
11.0 – 0.356
26.1 – 1.132
11.2 – 0.092 b/t
27.5 – 0.356 b/t
11.2 – 0.294 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
27.5 – 1.134 b/t
9.5 – 0.072
22.9 – 0.270
_____
Lb
d __
36.6 – 0.787 __
t d
___
Lb
d __
14.8 – 0.203 __
t d
16.4 – 0.839
39.1 – 2.66
____
9.5 – 0.038 Lb/ry
22.9 – 0.141 Lb/ry
25
8.5
23
19
10
9.2
7.1
19
8.5
194
165
19
8.5
19
11
15
25
38
23
60
27
8.5
10
25
19
VII-52
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
8
11
6.8
7.3
12
13
11
8
3.9
8
63
53
26
22
20
8.6 – 0.272
12.1 – 0.428
√Rb/t
____
____
√Rb/t
620
340
see Part IA Section 3.4.9.2
b
( )(
R
3290 /( ___ )(
t
R
3290 / ___b
t
275 /(b/t)
328 /(b/t)
2020 /(b/t)2
2020 /(b/t)2
86 /(b/t)
103 /(b/t)
52600 /(kL/r)2
146
17
52600 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
123
S2
see Part IA Section 3.4.9.1
8.7 – 0.069 b/t
12.4 – 0.117 b/t
8.7 – 0.221 b/t
12.4 – 0.374 b/t
4.0
11
12.4 – 0.374 b/t
8.7 – 0.221 b/t
4.0
11
7.4 – 0.034 kL/r
3.9
0
–
10.5 – 0.057 kL/r
Allowable Stress,
S1 < S < S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5086-H111 Extrusions
Table 2-14
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
8
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
36
24
5
11
25
37
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
10
8.5
6
17
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
15
2
18
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
12.5
18
12.5
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-53
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
30
8.8
8
13
√
√
___
√Rb/t
____
√Rb/t
____
√Rb/t
____
√Rb/t
620
340
63
53
20
17
8310
5900
51
43
188
150
175
147
19.5 – 0.089 h/t
13.7 – 0.052 h/t
19.5 – 0.038 h/t
13.7 – 0.023 h/t
10.1 – 0.062
6.5 – 0.032
13.8 – 0.085
8.9 – 0.044
60
66
138
152
44
50
77
92
14
10
14
10
7.5
4.9
7.5
4.9
h/t
h/t
ae/t
ae/t
13.7 – 0.273 b/t
13
10
19.5 – 0.465 b/t
11
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
2070 /(h/t)
39800
39800
54700
54700
300
109
136
109
136
2470 /(h/t)
894 /(h/t)
1070 /(h/t)
5080 /(b/t)2
5080 /(b/t)2
b
R
3890 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3890 /( ___ )( 1 + _____ )
t
35
325 /(b/t)
388 /(b/t)
102 /(b/t)
122 /(b/t)
2L___
bSc
24300 /_____
√IyJ
2L___
bSc
24300 /_____
√IyJ
( )
( )
Lb
d 2 __
11800 / __
t d
Lb
d 2 __
11800 / __
t d
Section 3.4.10
Same as
89600 /(Lb/ry)2
89600 /(Lb/ry)2
250
131
110
33
28
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
10.1 – 0.321
14.3 – 0.506
10.3 – 0.082 b/t
14.7 – 0.139 b/t
10.3 – 0.261 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
14.7 – 0.442 b/t
8.8 – 0.064
12.4 – 0.107
_____
Lb
d __
19.5 – 0.305 __
t d
___
Lb
d __
13.7 – 0.180 __
t d
15.2 – 0.756
21.4 – 1.19
____
8.8 – 0.033 Lb/ry
12.4 – 0.056 Lb/ry
14
8.4
27
11
9
9
8.5
11
8
196
186
11
8
19
10
17
14
53
13
63
27
8
9
26
11
VII-54
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
8.5
16
6.9
7.7
12
13
16
8.5
3.9
8.5
2020 /(b/t)2
18
61
43
9.3 – 0.302
17.7 – 0.716
√Rb/t
____
____
√Rb/t
600
235
see Part IA Section 3.4.9.2
b
( )(
R
3290 /( ___ )(
t
R
3290 / ___b
t
286 /(b/t)
401 /(b/t)
2020 /(b/t)2
90 /(b/t)
19
25
126 /(b/t)
52600 /(kL/r)2
140
14
52600 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√
Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
101
S2
see Part IA Section 3.4.9.1
9.5 – 0.078 b/t
18.5 – 0.214 b/t
9.5 – 0.249 b/t
18.5 – 0.682 b/t
4.1
16
18.5 – 0.682 b/t
9.5 – 0.249 b/t
4.1
16
8.0 – 0.038 kL/r
3.9
0
–
15.5 – 0.102 kL/r
Allowable Stress,
S1 < S < S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5086-H116, -H32 Sheet and Plate
5086-H32 Drawn Tube
Table 2-15
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
8.5
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
36
24
5
11
27
41
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
10
8.5
6
22
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
20
2
18
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
17
21
17
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-55
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
29
9.0
8.5
18
√
√
___
√Rb/t
____
√Rb/t
____
√Rb/t
____
√Rb/t
600
235
61
43
19
14
7690
3990
49
35
178
116
168
121
29.2 – 0.163 h/t
14.8 – 0.059 h/t
29.2 – 0.070 h/t
14.8 – 0.026 h/t
13.8 – 0.099
6.5 – 0.032
19.0 – 0.136
8.9 – 0.044
53
64
123
149
40
50
67
92
20
11
20
11
10
4.9
10
4.9
h/t
h/t
ae/t
ae/t
14.8 – 0.308 b/t
12
11
29.2 – 0.850 b/t
10
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
2150 /(h/t)
39800
39800
54700
54700
290
93
136
93
136
3020 /(h/t)
931 /(h/t)
1310 /(h/t)
5080 /(b/t)2
5080 /(b/t)2
b
R
3890 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3890 /( ___ )( 1 + _____ )
t
35
338 /(b/t)
474 /(b/t)
106 /(b/t)
149 /(b/t)
2L___
bSc
24300 /_____
√IyJ
2L___
bSc
24300 /_____
√IyJ
( )
( )
Lb
d 2 __
11800 / __
t d
Lb
d 2 __
11800 / __
t d
Section 3.4.10
Same as
89600 /(Lb/ry)2
89600 /(Lb/ry)2
207
126
90
32
23
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
11.0 – 0.356
21.0 – 0.846
11.2 – 0.092 b/t
21.9 – 0.253 b/t
11.2 – 0.294 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
21.9 – 0.806 b/t
9.5 – 0.072
18.3 – 0.193
_____
Lb
d __
29.2 – 0.559 __
t d
___
Lb
d __
14.8 – 0.203 __
t d
16.4 – 0.839
31.5 – 1.99
____
9.5 – 0.038 Lb/ry
18.3 – 0.101 Lb/ry
20
8.5
24
16
10
9.2
7.6
16
8.5
194
173
16
8.5
19
11
16
20
43
18
60
27
8.5
10
25
16
VII-56
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
13
9.5
6.5
9.5
6.4
7.1
12
3.7
6.5
6.5
4.0
9.5
4.0
9.5
3.7
0
–
6.5
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
32
21
5
9.5
23
34
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
8.5
7.5
6
15
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
13.5
2
16
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
11.5
17
11.5
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
69
56
29
24
22
18
159
131
S2
7.2 – 0.216
10.7 – 0.363
√Rb/t
____
____
√Rb/t
680
380
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
7.3 – 0.053 b/t
10.9 – 0.097 b/t
7.3 – 0.168 b/t
10.9 – 0.309 b/t
7.3 – 0.168 b/t
10.9 – 0.309 b/t
6.2 – 0.026 kL/r
9.2 – 0.047 kL/r
Allowable Stress,
S1 < S < S2
b
( )(
R
3290 /( ___ )(
t
R
3290 / ___b
t
251 /(b/t)
308 /(b/t)
2020 /(b/t)2
2020 /(b/t)2
79 /(b/t)
97 /(b/t)
52600 /(kL/r)2
52600 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√
Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5454-H111 Extrusions
Table 2-16
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
January 2005
VII-57
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
31
8.6
6.5
11.5
12
13
62
69
143
159
46
52
80
98
12.5
8.5
12.5
8.5
12.5
8.5
6.5
4.2
6.5
4.2
8.1
28
9.5
8
10
8.8
9.5
6.5
201
189
9.5
6.5
20
8.5
18
12.5
56
11.5
69
27
6.5
8
26
9.5
√
√
___
√Rb/t
____
√Rb/t
____
√Rb/t
____
√Rb/t
680
380
69
56
22
18
9900
6680
56
45
211
162
191
157
9.0 – 0.052
5.5 – 0.025
12.4 – 0.072
7.5 – 0.034
h/t
h/t
ae/t
ae/t
11.4 – 0.017 h/t
17.1 – 0.032 h/t
11.4 – 0.040 h/t
17.1 – 0.073 h/t
11.4 – 0.208 b/t
17.1 – 0.383 b/t
115
148
115
148
330
270
143
117
37
30
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
8.5 – 0.255
12.6 – 0.429
8.6 – 0.062 b/t
12.9 – 0.115 b/t
8.6 – 0.199 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
12.9 – 0.365 b/t
7.4 – 0.049
10.9 – 0.089
_____
Lb
d __
17.1 – 0.252 __
t d
___
Lb
d __
11.4 – 0.137 __
t d
12.8 – 0.599
18.9 – 1.01
____
7.4 – 0.026 Lb/ry
10.9 – 0.046 Lb/ry
39800
39800
54700
54700
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1890 /(h/t)
2310 /(h/t)
817 /(h/t)
1000 /(h/t)
5080 /(b/t)2
5080 /(b/t)2
b
R
3890 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3890 /( ___ )( 1 + _____ )
t
35
297 /(b/t)
364 /(b/t)
93 /(b/t)
114 /(b/t)
2L___
bSc
24300 /_____
√IyJ
2L___
bSc
24300 /_____
√IyJ
( )
( )
Lb
d 2 __
11800 / __
t d
Lb
d 2 __
11800 / __
t d
Section 3.4.10
Same as
89600 /(Lb/ry)2
89600 /(Lb/ry)2
VII-58
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
7.5
14.5
7.5
6.6
7.6
12
66
____
____
√Rb/t
7.9 – 0.243 √Rb/t
16.3 – 0.640
650
250
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
8.0 – 0.061 b/t
45
17.0 – 0.188 b/t
13
14.5
28
3.8
7.5
19
21
14
152
105
S2
8.0 – 0.194 b/t
17.0 – 0.598 b/t
4.1
14.5
17.0 – 0.598 b/t
8.0 – 0.194 b/t
4.1
14.5
6.8 – 0.030 kL/r
3.8
0
–
14.2 – 0.090 kL/r
Allowable Stress,
S1 < S < S2
____
b
b
____
b
2
2
√R /t
( )( 1 + _____
35 )
√R /t
R
3290 /( ___ )( 1 + _____ )
t
35
R
3290 / ___b
t
263 /(b/t)
384 /(b/t)
2020 /(b/t)2
2020 /(b/t)2
83 /(b/t)
120 /(b/t)
52600 /(kL/r)2
52600 /(kL/r)2
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5454-H32 Sheet and Plate
Table 2-17
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
7.5
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
32
21
5
9.5
25
37
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
8.5
7.5
6
20
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
18
2
16
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
16
18
16
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-59
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
30
8.9
7.5
17
10
13
55
67
126
156
41
52
70
98
19
9.5
19
9.5
19
9.5
9
4.2
9
4.2
8.2
25
14.5
8.5
10
7.8
14.5
7.5
198
176
14.5
7.5
20
9.5
16
19
45
17
66
27
7.5
8.5
25
14.5
√
√
___
√Rb/t
____
√Rb/t
____
√Rb/t
____
√Rb/t
650
250
66
45
21
14
9040
4340
53
36
198
122
183
127
12.7 – 0.087
5.5 – 0.025
17.5 – 0.120
7.5 – 0.034
h/t
h/t
ae/t
ae/t
12.5 – 0.020 h/t
26.7 – 0.062 h/t
12.5 – 0.046 h/t
26.7 – 0.143 h/t
12.5 – 0.240 b/t
26.7 – 0.745 b/t
97
148
97
148
320
216
137
94
35
24
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
9.3 – 0.286
19.3 – 0.756
9.5 – 0.072 b/t
20.1 – 0.222 b/t
9.5 – 0.229 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
20.1 – 0.707 b/t
8.1 – 0.057
16.8 – 0.170
_____
Lb
d __
26.7 – 0.490 __
t d
___
Lb
d __
12.5 – 0.158 __
t d
14.0 – 0.677
28.9 – 1.78
____
8.1 – 0.029 Lb/ry
16.8 – 0.089 Lb/ry
39800
39800
54700
54700
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1980 /(h/t)
2890 /(h/t)
856 /(h/t)
1250 /(h/t)
5080 /(b/t)2
5080 /(b/t)2
b
R
3890 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3890 /( ___ )( 1 + _____ )
t
35
311 /(b/t)
453 /(b/t)
98 /(b/t)
142 /(b/t)
2L___
bSc
24300 /_____
√IyJ
2L___
bSc
24300 /_____
√IyJ
( )
( )
Lb
d 2 __
11800 / __
t d
Lb
d 2 __
11800 / __
t d
Section 3.4.10
Same as
89600 /(Lb/ry)2
89600 /(Lb/ry)2
VII-60
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
7.5
16
6.6
7.7
12
13
16
7.5
3.8
7.5
66
42
28
18
21
13
152
99
S2
7.9 – 0.243
18.5 – 0.755
√Rb/t
____
____
√Rb/t
650
227
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
8.0 – 0.061 b/t
19.3 – 0.228 b/t
8.0 – 0.194 b/t
19.3 – 0.726 b/t
4.1
16
19.3 – 0.726 b/t
8.0 – 0.194 b/t
4.1
16
6.8 – 0.030 kL/r
3.8
0
–
16.1 – 0.109 kL/r
Allowable Stress,
S1 < S < S2
b
( )(
R
3290 /( ___ )(
t
R
3290 / ___b
t
263 /(b/t)
409 /(b/t)
2020 /(b/t)2
2020 /(b/t)2
83 /(b/t)
128 /(b/t)
52600 /(kL/r)2
52600 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√
Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5454-H34 Sheet and Plate
Table 2-18
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
7.5
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
32
21
5
9.5
27
40
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
8.5
7.5
6
23
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
21
2
16
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
18
20
18
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-61
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
30
9.0
7.5
19
√
√
___
√Rb/t
____
√Rb/t
____
√Rb/t
____
√Rb/t
650
227
66
42
21
13
9040
3830
53
34
198
113
183
119
12.5 – 0.020 h/t
14.3 – 0.105
5.5 – 0.025
19.7 – 0.144
7.5 – 0.034
53
67
122
156
40
52
66
98
21
9.5
21
9.5
10
4.2
10
4.2
h/t
h/t
ae/t
ae/t
30.4 – 0.075 h/t
12.5 – 0.046 h/t
30.4 – 0.173 h/t
12.5 – 0.240 b/t
13
9.5
30.4 – 0.905 b/t
10
91
148
91
148
320
203
137
88
35
22
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
9.3 – 0.286
21.8 – 0.892
9.5 – 0.072 b/t
22.8 – 0.269 b/t
9.5 – 0.229 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
22.8 – 0.858 b/t
8.1 – 0.057
19.1 – 0.205
_____
Lb
d __
30.4 – 0.594 __
t d
___
Lb
d __
12.5 – 0.158 __
t d
14.0 – 0.677
32.7 – 2.10
____
8.1 – 0.029 Lb/ry
19.1 – 0.107 Lb/ry
21
8.2
24
16
8.5
10
7.5
16
7.5
198
172
16
7.5
20
9.5
15
21
42
19
66
27
7.5
8.5
25
16
39800
39800
54700
54700
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
1980 /(h/t)
3080 /(h/t)
856 /(h/t)
1330 /(h/t)
5080 /(b/t)2
5080 /(b/t)2
b
R
3890 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3890 /( ___ )( 1 + _____ )
t
35
311 /(b/t)
484 /(b/t)
98 /(b/t)
152 /(b/t)
2L___
bSc
24300 /_____
√IyJ
2L___
bSc
24300 /_____
√IyJ
( )
( )
Lb
d 2 __
11800 / __
t d
Lb
d 2 __
11800 / __
t d
Section 3.4.10
Same as
89600 /(Lb/ry)2
89600 /(Lb/ry)2
VII-62
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
11
16
11
7.3
7.7
13
53
12.1 – 0.428
18.5 – 0.755
√Rb/t
____
____
√Rb/t
520
227
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
12.4 – 0.117 b/t
42
19.3 – 0.228 b/t
13
16
22
4.0
11
18
17
13
123
99
S2
12.4 – 0.374 b/t
19.3 – 0.726 b/t
4.1
16
19.3 – 0.726 b/t
12.4 – 0.374 b/t
4.1
16
10.5 – 0.057 kL/r
4.0
0
–
16.1 – 0.109 kL/r
Allowable Stress,
S1 < S < S2
b
( )(
R
3290 /( ___ )(
t
R
3290 / ___b
t
328 /(b/t)
409 /(b/t)
2020 /(b/t)2
2020 /(b/t)2
103 /(b/t)
128 /(b/t)
52600 /(kL/r)2
52600 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√
Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
5456-H116, -H32, -H321 Sheet and Plate
(Thickness 0.188 to 1.250 in.)
Table 2-19
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
11
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
43
29
5
15
31
47
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
13.5
11.5
6
26
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
23
2
22
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
20
24
20
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
January 2005
VII-63
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
27
9.0
11
19
√
√
___
√Rb/t
____
√Rb/t
____
√Rb/t
____
√Rb/t
520
227
53
42
17
13
5900
3830
43
34
150
113
147
119
203
250
30.4 – 0.075 h/t
19.5 – 0.038 h/t
16.5 – 0.129
9.0 – 0.052
22.7 – 0.178
12.4 – 0.072
53
60
122
138
38
46
63
80
14
21
14
11.5
6.5
11.5
6.5
h/t
h/t
ae/t
ae/t
19.5 – 0.089 h/t
30.4 – 0.173 h/t
85
115
85
115
110
88
28
21
19.5 – 0.465 b/t
11
22
14
30.4 – 0.905 b/t
10
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
14.3 – 0.506
21.8 – 0.892
14.7 – 0.139 b/t
22.8 – 0.269 b/t
14.7 – 0.442 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
22.8 – 0.858 b/t
12.4 – 0.107
19.1 – 0.205
_____
Lb
d __
30.4 – 0.594 __
t d
___
Lb
d __
19.5 – 0.305 __
t d
21.4 – 1.19
32.7 – 2.10
____
12.4 – 0.056 Lb/ry
19.1 – 0.107 Lb/ry
21
8.8
24
16
13
9
7.5
16
11
186
172
16
11
17
14
15
21
42
19
53
26
11
13
25
16
39800
39800
54700
54700
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
2470 /(h/t)
3080 /(h/t)
1070 /(h/t)
1330 /(h/t)
5080 /(b/t)2
5080 /(b/t)2
b
R
3890 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3890 /( ___ )( 1 + _____ )
t
35
388 /(b/t)
484 /(b/t)
122 /(b/t)
152 /(b/t)
2L___
bSc
24300 /_____
√IyJ
2L___
bSc
24300 /_____
√IyJ
( )
( )
Lb
d 2 __
11800 / __
t d
Lb
d 2 __
11800 / __
t d
Section 3.4.10
Same as
89600 /(Lb/ry)2
89600 /(Lb/ry)2
VII-64
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
7.6
21
8
21
6.6
1.4
12
3.8
8
8
2.4
21
2.4
21
3.8
0
–
8
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
25
16
5
10
26
39
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
9
8
6
28
3
Round or oval tubes
On flat surfaces and pins and on bolts in slotted holes
24
2
12.5
Allowable Stress
Flat elements in uniform tension
gross section
net section
Sec.
3.4.
21
19
19
Type of Member or Element
1
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
62
33
26
12
19
10
144
66
S2
8.6 – 0.275
22.1 – 0.799
√Rb/t
____
____
√Rb/t
450
141
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
8.7 – 0.070 b/t
23.1 – 0.247 b/t
8.7 – 0.224 b/t
23.1 – 0.787 b/t
8.7 – 0.224 b/t
23.1 – 0.787 b/t
7.4 – 0.034 kL/r
20.2 – 0.126 kL/r
Allowable Stress,
S1 < S < S2
b
( )(
R
3190 /( ___ )(
t
R
3190 / ___b
t
271 /(b/t)
491 /(b/t)
1970 /(b/t)2
1970 /(b/t)2
85 /(b/t)
154 /(b/t)
51100 /(kL/r)2
51100 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
Shaded bars apply to weld-affected metal
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
6005-T5 Extrusions up through 1.000 in. thick
6105-T5 Extrusions up through 0.500 in. thick
Table 2-20
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
January 2005
VII-65
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
29
2.1
8
25
√
√
___
√Rb/t
____
√Rb/t
____
√Rb/t
____
√Rb/t
450
141
62
33
14
10
8070
1680
50
29
184
81
172
79
173
300
40.5 – 0.117 h/t
13.7 – 0.023 h/t
15.8 – 0.101 h/t
6.0 – 0.029 h/t
12
8.2 – 0.039 ae/t
48
65
110
150
36
50
–
93
10
28
10
12
4.5
12
4.5
13.7 – 0.053 h/t
40.5 – 0.270 h/t
64
139
66
139
129
75
33
28
13.7 – 0.277 b/t
12
19
10
40.5 – 1.41 b/t
9.1
see Part IA Section 3.4.16.3
see Part IA Section 3.4.16.2
10.1 – 0.325
26.2 – 0.944
10.3 – 0.083 b/t
27.3 – 0.292 b/t
10.3 – 0.265 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
27.3 – 0.930 b/t
8.8 – 0.065
23.9 – 0.238
_____
Lb
d __
40.5 – 0.927 __
t d
___
Lb
d __
13.7 – 0.182 __
t d
15.2 – 0.764
39.3 – 2.70
____
8.8 – 0.034 Lb/ry
23.9 – 0.124 Lb/ry
28
8.2
21
21
9
9
6.5
21
8
190
123
21
8
19
10
14
28
29
25
62
26
8
9
21
21
38700
38700
53200
53200
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
2040 /(h/t)
3500 /(h/t)
881 /(h/t)
1520 /(h/t)
4930 /(b/t)2
4930 /(b/t)2
b
R
3780 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3780 /( ___ )( 1 + _____ )
t
35
320 /(b/t)
580 /(b/t)
101 /(b/t)
182 /(b/t)
2L___
bSc
23600 /_____
√IyJ
2L___
bSc
23600 /_____
√IyJ
( )
( )
Lb
d 2 __
11400 / __
t d
Lb
d 2 __
11400 / __
t d
Section 3.4.10
Same as
87000 /(Lb/ry)2
87000 /(Lb/ry)2
VII-66
March 2006
Type of Member or Element
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
7.6
21
9
21
6.9
1.4
12
3.9
9
9
2.4
21
2.4
21
3.9
0
–
9
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
16
29
25
12
10.5
9
12.5
6
43
5
On rivets and bolts
On flat surfaces and pins and on bolts in slotted holes
28
4
25
21
22
21
Flat elements in bending in their own plane,
symmetric shapes
2
1
Allowable Stress
3
gross section
net section
Sec.
3.4.
Round or oval tubes
Flat elements in uniform tension
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
58
33
24
12
18
10
133
66
S2
10.0 – 0.335
22.1 – 0.799
____
√Rb/t
____
√Rb/t
390
141
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
10.2 – 0.089 b/t
23.1 – 0.247 b/t
10.2 – 0.282 b/t
23.1 – 0.787 b/t
10.2 – 0.282 b/t
23.1 – 0.787 b/t
8.6 – 0.043 kL/r
20.2 – 0.126 kL/r
Allowable Stress,
S1 < S < S2
____
b
b
____
b
2
2
√R /t
( )( 1 + _____
35 )
√R /t
R
3190 /( ___ )( 1 + _____ )
t
35
R
3190 / ___b
t
293 /(b/t)
491 /(b/t)
1970 /(b/t)2
1970 /(b/t)2
92 /(b/t)
154 /(b/t)
51100 /(kL/r)2
51100 /(kL/r)2
Allowable Stress,
S > S2
Shaded bars apply to all thicknesses with fillers 5183, 5356, or
5556 and thicknesses < 0.375 in. with fillers 4043, 5554, or 5654
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
6061-T6 Sheet, -T651 Plate up through 4.000 in. thick
6061-T6, -T651 Rolled or Cold Finished Rod and Bar
6061-T6 Drawn Tube
Table 2-21
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
January 2005
VII-67
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
28
2.1
9
25
64
129
66
129
280
12
5
12
5
119
75
30
19
15.8 – 0.101 h/t
7.0 – 0.036 h/t
12
9.6 – 0.050 ae/t
12
16.0 – 0.067 h/t
40.5 – 0.270 h/t
16.0 – 0.350 b/t
40.5 – 1.41 b/t
see Part IA Section 3.4.16.3
16.0 – 0.029 h/t
110
28
390
36
48
–
88
62
12
√Rb/t
____
141
144
48
28
____
√Rb/t
58
33
18
10
6940
1680
46
see Part IA Section 3.4.16.2
11.8 – 0.396
26.2 – 0.944
12.0 – 0.105 b/t
27.3 – 0.292 b/t
12.0 – 0.334 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
27.3 – 0.930 b/t
10.2 – 0.082
23.9 – 0.238
_____
29
167
81
160
79
173
12
12
√
√
___
√Rb/t
____
√Rb/t
Lb
d __
40.5 – 0.927 __
t d
___
Lb
d __
16.0 – 0.230 __
t d
17.7 – 0.932
39.3 – 2.70
____
10.2 – 0.043 Lb/ry
23.9 – 0.124 Lb/ry
40.5 – 0.117 h/t
9.1
28
8.4
21
21
10.5
9
6.5
21
9
186
123
21
9
18
12
14
28
29
25
57
26
9
10.5
21
21
38700
38700
53200
53200
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
2200 /(h/t)
3500 /(h/t)
952 /(h/t)
1520 /(h/t)
4930 /(b/t)2
4930 /(b/t)2
b
R
3780 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3780 /( ___ )( 1 + _____ )
t
35
346 /(b/t)
580 /(b/t)
109 /(b/t)
182 /(b/t)
2L___
bSc
23600 /_____
√IyJ
2L___
bSc
23600 /_____
√IyJ
( )
( )
Lb
d 2 __
11400 / __
t d
Lb
d 2 __
11400 / __
t d
Section 3.4.10
Same as
87000 /(Lb/ry)2
87000 /(Lb/ry)2
VII-68
March 2006
Type of Member or Element
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
7.6
21
9
21
6.9
1.4
12
3.9
9
9
2.4
21
2.4
21
3.9
0
–
9
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
16
26
25
12
10.5
9
12.5
6
39
5
On rivets and bolts
On flat surfaces and pins and on bolts in slotted holes
28
4
24
21
19
19
Flat elements in bending in their own plane,
symmetric shapes
2
1
Allowable Stress
3
gross section
net section
Sec.
3.4.
Round or oval tubes
Flat elements in uniform tension
Any tension member
COMPRESSION
IN COLUMNS,
All columns
axial
Type of Stress
BEARING
TENSION
IN BEAMS,
extreme fiber,
net section
TENSION, axial
Type of Stress
58
33
24
12
18
10
133
66
S2
10.0 – 0.335
22.1 – 0.799
√Rb/t
____
____
√Rb/t
390
141
see Part IA Section 3.4.9.2
see Part IA Section 3.4.9.1
10.2 – 0.089 b/t
23.1 – 0.247 b/t
10.2 – 0.282 b/t
23.1 – 0.787 b/t
10.2 – 0.282 b/t
23.1 – 0.787 b/t
8.6 – 0.043 kL/r
20.2 – 0.126 kL/r
Allowable Stress,
S1 < S < S2
b
( )(
R
3190 /( ___ )(
t
R
3190 / ___b
t
293 /(b/t)
491 /(b/t)
1970 /(b/t)2
1970 /(b/t)2
92 /(b/t)
154 /(b/t)
51100 /(kL/r)2
51100 /(kL/r)2
____
)
)
√Rb/t 2
1 + _____
35
____
√Rb/t 2
_____
1+
35
Allowable Stress,
S > S2
Shaded bars apply to all thicknesses with fillers 5183, 5356, or
5556 and thicknesses < 0.375 in. with fillers 4043, 5554, or 5654
For tubes with circumferential welds, Sections 3.4.10, 3.4.12, and
3.4.16.1 apply for Rb / t < 20
White bars apply to unwelded metal
6061-T6 , -T6510, -T6511 Extrusions
6061-T6 Standard Structural Shapes, Pipe
6351-T5 Extrusions
Table 2-22
ALLOWABLE STRESSES FOR
BUILDING TYPE STRUCTURES
January 2005
VII-69
16
Flat elements supported on both edges
SHEAR IN
ELEMENTS,
gross section
20
21
Stiffened flat elements supported
on both edges
19
18
17
16.3
Unstiffened flat elements supported
on both edges
Flat elements supported on tension edge,
COMPRESSION compression edge free
IN BEAM
ELEMENTS,
Flat elements supported on both edges
(element in
bending in own
plane), gross
Flat elements supported on both edges
section
and with a longitudinal stiffener
Flat elements supported on both
edges and with an
intermediate stiffener
16.2
16.1
15
Flat elements supported on one edge
COMPRESSION
IN BEAM
ELEMENTS,
Curved elements supported on both edges
(element in
uniform
compression),
Flat elements supported on
gross section
one edge and with stiffener
on other edge
14
Tubular shapes
13
12
Round or oval tubes
COMPRESSION
IN BEAMS,
extreme fiber,
Solid rectangular and round sections
gross section
11
Single web shapes
28
2.1
9
25
64
129
66
129
280
12
5
12
5
119
75
30
19
15.8 – 0.101 h/t
7.0 – 0.036 h/t
12
9.6 – 0.050 ae/t
12
16.0 – 0.067 h/t
40.5 – 0.270 h/t
16.0 – 0.350 b/t
40.5 – 1.41 b/t
see Part IA Section 3.4.16.3
16.0 – 0.029 h/t
110
28
390
36
48
–
88
62
12
√Rb/t
____
141
144
48
28
____
√Rb/t
58
33
18
10
6940
1680
46
see Part IA Section 3.4.16.2
11.8 – 0.396
26.2 – 0.944
12.0 – 0.105 b/t
27.3 – 0.292 b/t
12.0 – 0.334 b/t
IyJ
2L___
bSc
_____
_____
IyJ
2L___
bSc
_____
√√
√√
27.3 – 0.930 b/t
10.2 – 0.082
23.9 – 0.238
_____
29
167
81
160
79
173
12
12
√
√
___
√Rb/t
____
√Rb/t
Lb
d __
40.5 – 0.927 __
t d
___
Lb
d __
16.0 – 0.230 __
t d
17.7 – 0.932
39.3 – 2.70
____
10.2 – 0.043 Lb/ry
23.9 – 0.124 Lb/ry
40.5 – 0.117 h/t
9.1
28
8.4
21
21
10.5
9
6.5
21
9
186
123
21
9
18
12
14
28
29
25
57
26
9
10.5
21
21
38700
38700
53200
53200
/(h/t)2
/(h/t)2
/(ae/t)2
/(ae/t)2
2200 /(h/t)
3500 /(h/t)
952 /(h/t)
1520 /(h/t)
4930 /(b/t)2
4930 /(b/t)2
b
R
3780 / ___b
t
____
√Rb/t 2
1 + _____
35
b
____
2
)
( )(
√R /t
R
3780 /( ___ )( 1 + _____ )
t
35
346 /(b/t)
580 /(b/t)
109 /(b/t)
182 /(b/t)
2L___
bSc
23600 /_____
√IyJ
2L___
bSc
23600 /_____
√IyJ
( )
( )
Lb
d 2 __
11400 / __
t d
Lb
d 2 __
11400 / __
t d
Section 3.4.10
Same as
87000 /(Lb/ry)2
87000 /(Lb/ry)2
VII-70
March 2006
9
Flat elements supported on both edges
Curved elements supported on both edges
Flat elements supported on both edges
and with an intermediate stiffener
10
9.2
9.1
8.1
Flat elements supported on one edge –
columns not buckling about a symmetry axis
COMPRESSION
IN COLUMN
ELEMENTS,
Flat elements supported
gross section
on one edge and with
stiffener on other edge
8
7
4.6
9.5
4.8
9.5
5.4
0.3
10
3.3
4.8
4.8
1.4
9.5
1.4
9.5
3.3
0
–
4.8
0
–
S1
Allowable
Stress,
S < S1
Sec.
3.4.
Flat elements supported on one edge –
columns buckling about a symmetry axis
Type of Member or Element
17
11.5
5
6.5
15
23
4
Flat elements in bending in their own plane,
symmetric shapes
On rivets and bolts
5.5
4.8
6
12.5
3
Round or oval tubes
On flat sur