SAFE
TM
Integrated
Analysis and Design of Slabs
by
The Finite Element Method
USER’S MANUAL
COMPUTERS &
STRUCTURES
INC.
R
Computers and Structures, Inc.
Berkeley, California, USA
Version 6.0
Revised October 1998
COPYRIGHT
The computer program SAFE and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest
with Computers and Structures, Inc. Unlicensed use of the program or reproduction of the documentation in any form, without prior written
authorization from Computers and Structures, Inc., is explicitly prohibited.
Further information and copies of this documentation may be obtained
from:
Computers and Structures, Inc.
1995 University Avenue
Berkeley, California 94704 USA
Tel: (510) 845-2177
Fax: (510) 845-4096
E-mail: info@csiberkeley.com
Web: www.csiberkeley.com
© Copyright Computers and Structures, Inc., 1978–1998.
The CSI Logo is a registered trademark of Computers and Structures, Inc.
SAFE is a trademark of Computers and Structures, Inc.
Windows is a trademark of Microsoft Corporation.
DISCLAIMER
CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE
INTO THE DEVELOPMENT AND DOCUMENTATION OF SAFE.
THE PROGRAM HAS BEEN THOROUGHLY TESTED AND USED.
IN USING THE PROGRAM, HOWEVER, THE USER ACCEPTS
AND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED OR
IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON
THE ACCURACY OR THE RELIABILITY OF THE PROGRAM.
THIS PROGRAM IS A VERY PRACTICAL TOOL FOR THE DESIGN OF REINFORCED CONCRETE SLABS. HOWEVER, THE
USER MUST THOROUGHLY READ THE MANUAL AND
CLEARLY RECOGNIZE THE ASPECTS OF SLAB DESIGN THAT
THE PROGRAM ALGORITHMS DO NOT ADDRESS.
THE USER MUST EXPLICITLY UNDERSTAND THE ASSUMPTIONS OF THE PROGRAM AND MUST INDEPENDENTLY VERIFY THE RESULTS.
.
Table of Contents
CHAPTER I
Welcome to SAFE
1
CHAPTER II
Getting Started
3
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
What Your SAFE Package Includes . . . . . . . . . . . . . . . . . . . 3
About This Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Single User Installation . . . . . . . . . . . . . . . . . . . . . . . 5
Network Server Installation . . . . . . . . . . . . . . . . . . . . . 6
Network Workstation Installation . . . . . . . . . . . . . . . . . . 7
Installing from CD . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Installing from Disks . . . . . . . . . . . . . . . . . . . . . . . . . 8
Installing from a Network Server . . . . . . . . . . . . . . . . . . 8
Removing SAFE from Your System . . . . . . . . . . . . . . . . . . . 8
Using the Hardware Key Device . . . . . . . . . . . . . . . . . . . . . 9
On a Local Workstation . . . . . . . . . . . . . . . . . . . . . . . 9
On a Local Area Network. . . . . . . . . . . . . . . . . . . . . . 10
Installing the Sentinel Driver . . . . . . . . . . . . . . . . . . . . 11
Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Help Us to Help You . . . . . . . . . . . . . . . . . . . . . . . . 12
Phone and Fax Support . . . . . . . . . . . . . . . . . . . . . . . 12
Online Support . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Upgrading from SAFE V5. . . . . . . . . . . . . . . . . . . . . . . . 13
CHAPTER III SAFE Concepts and Techniques
15
The SAFE Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
i
SAFE User's Manual
The SAFE Plane and Gridline System. . . . .
The SAFE Templates . . . . . . . . . . . . .
The SAFE Layers . . . . . . . . . . . . . . .
The SAFE Finite Element Mesh. . . . . . . .
Slab Element . . . . . . . . . . . . . . .
Beam Element . . . . . . . . . . . . . .
Support Elements . . . . . . . . . . . . .
Slab Element Releases. . . . . . . . . . . . .
Loading . . . . . . . . . . . . . . . . . . . .
SAFE Reinforced Concrete Design . . . . . .
Design Load Combinations . . . . . . . .
Design of Slab . . . . . . . . . . . . . .
Defining Slab Strips . . . . . . . . .
Integrated Strip Moments and Shears
Flexural Design of Slab Strips . . . .
Checking Punching Shear Capacity .
Design of Beam Elements . . . . . . . .
Analysis for No-Tension Surface Supports . .
Analysis for Cracked Deflections . . . . . . .
SAFE Units . . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
CHAPTER IV The Graphical User Interface
Overview. . . . . . . . . . .
The Structural Model . . . .
Coordinate System. . . . . .
The SAFE Screen . . . . . .
Main Window. . . . . .
Menu Bar . . . . . . . .
Toolbar . . . . . . . . .
Display Windows . . . .
Status Line . . . . . . .
Viewing Options. . . . . . .
2-D and 3-D Views . . .
Aerial View . . . . . . .
View Layers of the Slab
Pan, Zoom, and Limits .
Object View Options . .
Other Options . . . . . .
Gridlines . . . . . . . . . . .
Mesh . . . . . . . . . . . . .
Basic Operations. . . . . . .
File Operations . . . . .
ii
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
16
16
17
17
18
18
19
21
22
23
23
24
24
25
26
26
27
28
28
29
31
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
31
31
32
32
33
33
33
34
34
34
34
34
35
35
35
36
36
36
36
37
Table of Contents
Draw . . . . . . . . . . . . . .
Select . . . . . . . . . . . . . .
Edit . . . . . . . . . . . . . . .
Assign . . . . . . . . . . . . . .
Define . . . . . . . . . . . . . .
Analyze . . . . . . . . . . . . .
Display . . . . . . . . . . . . .
Graphical Displays . . . . .
Tabular Displays . . . . . .
Design. . . . . . . . . . . . . .
Undo and Redo . . . . . . . . .
Locking and Unlocking . . . . .
Refreshing the Display Window
Preferences . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
CHAPTER V Quick Tutorial
Overview. . . . . . . . . . . . . . . .
Description of the Model . . . . . . .
Starting the Tutorial . . . . . . . . . .
Setting Up the Geometry . . . . . . .
Checking Slab Properties . . . . . . .
Checking Column Support Properties .
Checking Load Cases . . . . . . . . .
Checking Design Strips . . . . . . . .
Analyzing the Model . . . . . . . . .
Displaying the Deformed Shape. . . .
Displaying Slab Forces . . . . . . . .
Selecting the Design Code. . . . . . .
Checking Load Combinations . . . . .
Starting Design . . . . . . . . . . . .
Displaying Slab Reinforcement . . . .
Displaying Punching Shear Ratios . .
Saving the Model . . . . . . . . . . .
Printing Graphics . . . . . . . . . . .
Displaying Output Tables . . . . . . .
Displaying Design Tables . . . . . . .
Printing/Saving Output Tables . . . .
Printing/Saving Design Tables . . . .
Modifying the Structure . . . . . . . .
Unlocking the Model . . . . . . .
Adding Slab Geometry . . . . . .
37
39
40
40
41
41
42
42
42
43
43
43
43
44
45
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
45
45
46
47
49
51
53
55
56
59
60
61
62
63
64
66
66
66
67
68
70
71
72
72
72
iii
SAFE User's Manual
Adjusting the Coordinate . . . . .
Assigning Slab Property . . . . .
Defining Beam Properties . . . .
Assigning Beam Properties . . . .
Deleting Drop-Panels . . . . . . .
Adding an Opening . . . . . . . .
Assigning Surface Loads . . . . .
Assigning Line Loads. . . . . . .
Modifying the X-Strip Definition.
Re-analyzing the Model . . . . .
Starting Design . . . . . . . . . .
Displaying Beam Forces . . . . .
Displaying Beam Reinforcement .
Saving the Model . . . . . . . . .
Concluding Remarks . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
CHAPTER VI Program Output
Overview. . . . . . . . . . . . . . .
Displacements . . . . . . . . . . . .
Reactions. . . . . . . . . . . . . . .
Integrated Strip Moments and Shears
Beam Moments and Shears . . . . .
Slab Moments and Shears . . . . . .
Slab Reinforcing . . . . . . . . . . .
Beam Reinforcing . . . . . . . . . .
Punching Shear Results . . . . . . .
APPENDIX A Design for ACI 318-95
73
75
76
77
79
80
81
84
85
86
87
88
90
91
92
93
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
93
94
95
95
95
96
96
97
98
99
Design Load Combinations . . . . . . . . . . . . . . . . . . . . . . . 99
Strength Reduction Factors. . . . . . . . . . . . . . . . . . . . . . . 102
Beam Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Design Flexural Reinforcement . . . . . . . . . . . . . . . . . . 103
Determine Factored Moments . . . . . . . . . . . . . . . . 103
Determine Required Flexural Reinforcement . . . . . . . . 103
Design Beam Shear Reinforcement . . . . . . . . . . . . . . . . 109
Determine Shear Force . . . . . . . . . . . . . . . . . . . . 110
Determine Concrete Shear Capacity . . . . . . . . . . . . . 110
Determine Required Shear Reinforcement . . . . . . . . . . 110
Slab Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Design for Flexure. . . . . . . . . . . . . . . . . . . . . . . . . 111
Determine Factored Moments for the Strip. . . . . . . . . . 112
Design Flexural reinforcement for the Strip . . . . . . . . . 112
Check for Punching Shear . . . . . . . . . . . . . . . . . . . . . 112
iv
Table of Contents
Critical Section for Punching Shear
Transfer of Unbalanced Moment . .
Determination of Concrete Capacity
Determination of Capacity Ratio . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
APPENDIX B Design for CSA A23.3-94
Design Load Combinations . . . . . . . . . . . . . .
Strength Reduction Factors. . . . . . . . . . . . . . .
Beam Design . . . . . . . . . . . . . . . . . . . . . .
Design Beam Flexural Reinforcement . . . . . .
Determine Factored Moments . . . . . . . .
Determine Required Flexural Reinforcement
Design Beam Shear Reinforcement . . . . . . . .
Determine Shear Force and Moment . . . . .
Determine Concrete Shear Capacity . . . . .
Determine Required Shear Reinforcement . .
Slab Design. . . . . . . . . . . . . . . . . . . . . . .
Design for Flexure. . . . . . . . . . . . . . . . .
Determine Factored Moments for the Strip. .
Design Flexural reinforcement for the Strip .
Check for Punching Shear . . . . . . . . . . . . .
Critical Section for Punching Shear . . . . .
Transfer of Unbalanced Moment . . . . . . .
Determination of Concrete Capacity . . . . .
Determination of Capacity Ratio . . . . . . .
115
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
APPENDIX C Design for BS 8110-85
Design Load Combinations . . . . . . . . . . . . . .
Design Strength . . . . . . . . . . . . . . . . . . . .
Beam Design . . . . . . . . . . . . . . . . . . . . . .
Design Beam Flexural Reinforcement . . . . . .
Determine Factored Moments . . . . . . . .
Determine Required Flexural Reinforcement
Design Beam Shear Reinforcement . . . . . . . .
Slab Design. . . . . . . . . . . . . . . . . . . . . . .
Design for Flexure. . . . . . . . . . . . . . . . .
Determine Factored Moments for the Strip. .
Design Flexural reinforcement for the Strip .
Check for Punching Shear . . . . . . . . . . . . .
Critical Section for Punching Shear . . . . .
Determination of Concrete Capacity . . . . .
Determination of Capacity Ratio . . . . . . .
APPENDIX D Design for Eurocode 2
113
113
113
114
115
118
118
119
119
119
126
126
126
126
127
128
128
128
129
129
129
130
130
131
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
131
134
134
135
135
135
142
143
143
144
144
145
145
145
146
147
Design Load Combinations . . . . . . . . . . . . . . . . . . . . . . 147
v
SAFE User's Manual
Design Strength . . . . . . . . . . . . . . . . . . . .
Beam Design . . . . . . . . . . . . . . . . . . . . . .
Design Beam Flexural Reinforcement . . . . . .
Determine Factored Moments . . . . . . . .
Determine Required Flexural Reinforcement
Design Beam Shear Reinforcement . . . . . . . .
Slab Design. . . . . . . . . . . . . . . . . . . . . . .
Design for Flexure. . . . . . . . . . . . . . . . .
Determine Factored Moments for the Strip. .
Design Flexural reinforcement for the Strip .
Check for Punching Shear . . . . . . . . . . . . .
Critical Section for Punching Shear . . . . .
Determination of Concrete Capacity . . . . .
Determination of Capacity Ratio . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
APPENDIX E Design for NZS 3101-95
Design Load Combinations . . . . . . . . . . . . . .
Strength Reduction Factors. . . . . . . . . . . . . . .
Beam Design . . . . . . . . . . . . . . . . . . . . . .
Design Beam Flexural Reinforcement . . . . . .
Determine Factored Moments . . . . . . . .
Determine Required Flexural Reinforcement
Design Beam Shear Reinforcement . . . . . . . .
Determine Shear Force and Moment . . . . .
Determine Concrete Shear Capacity . . . . .
Determine Required Shear Reinforcement . .
Slab Design. . . . . . . . . . . . . . . . . . . . . . .
Design for Flexure. . . . . . . . . . . . . . . . .
Determine Factored Moments for the Strip. .
Design Flexural reinforcement for the Strip .
Check for Punching Shear . . . . . . . . . . . . .
Critical Section for Punching Shear . . . . .
Transfer of Unbalanced Moment . . . . . . .
Determination of Capacity Ratio . . . . . . .
Determination of Capacity Ratio . . . . . . .
165
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
APPENDIX F Design for IS 456-78 (R1996)
Design Load Combinations . . . . . . . . . . . . . .
Design Strength . . . . . . . . . . . . . . . . . . . .
Beam Design . . . . . . . . . . . . . . . . . . . . . .
Design Beam Flexural Reinforcement . . . . . .
Determine Factored Moments . . . . . . . .
Determine Required Flexural Reinforcement
Design Beam Shear Reinforcement . . . . . . . .
vi
150
150
151
151
151
159
161
161
162
162
162
163
163
163
165
168
168
169
169
169
175
176
176
176
177
178
178
178
179
179
179
179
180
181
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
181
184
184
185
185
185
192
Table of Contents
Slab Design. . . . . . . . . . . . . . . . . . . . . .
Design for Flexure. . . . . . . . . . . . . . . .
Determine Factored Moments for the Strip.
Design Flexural reinforcement for the Strip
Check for Punching Shear . . . . . . . . . . . .
Critical Section for Punching Shear . . . .
Transfer of Unbalanced Moment . . . . . .
Determination of Concrete Capacity . . . .
Determination of Capacity Ratio . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
196
196
196
196
197
197
197
198
198
References
199
Index
201
vii
.
Chapter I
Welcome to SAFE
Slab systems are a very special class of structures. They are characterized by their
simplicity in geometry and loading. They are typically horizontal plates supported
vertically by beams, columns or walls. The loading in general is comprised of vertical point, line, and surface loads. Basemats share the same characteristics as those
of elevated slabs, with the exception that basemats are supported on soil and loaded
by columns and walls.
Most commercially available finite element programs can be used to model slabs
and basemats. However, such software packages do not recognize the unique characteristics of slab systems resulting in excessive solution times and significant
losses in productivity and man hours. Also, such packages are unnecessarily cumbersome to use and are not integrated with slab design algorithms that would produce information directly usable by the structural engineer.
Recognition of this need, nearly two decades ago, led to the development of the
SAFE System, special purpose software that automates the analysis and design
process for the structural engineer, lending greater sophistication to the engineering
of slab systems. SAFE is designed to minimize engineering man hours and processing time associated with the design of concrete slab systems.
SAFE is a completely integrated product that operates within a Windows 95/NT environment. It features a powerful graphical interface unmatched in terms of
ease-of-use and productivity. Creation and modification of the slab model,
execution of the analysis, checking and optimization of the design and production
of graphical displays of the results are all controlled through this single interface.
1
SAFE User's Manual
New capabilities represent the latest developments in numerical technique, solution
algorithms, and design codes including automatic meshing of complex configurations, a fast equation solver, a large-capacity data management system, very accurate plate bending elements, stress-integration options that guarantee analytical
equilibrium irrespective of the refinement of the finite element mesh, and new
American and international concrete design codes.
The SAFE program is setup on a rectangular grid system but will analyze and design slabs of arbitrary geometry and varying thickness, drop panels, openings with
edge beams and embedded beams subjected to vertical point, line or surface loads.
Column supports, wall supports, or soil supports for basemats can all be modeled.
Optionally, iterations may be performed to obtain no-tension soil surface support
conditions. Discontinuities in the slab system, due to slip joints or differences in
slab elevations, can also be included. The slabs can be modeled with orthotropic
thin or thick plate elements. The thick plate bending element allows for two-way
action with shear deformations. The beam element allows for bending, torsion, and
shear deformations.
The design reinforcing is computed for user defined rectangular design strips using
the latest US, British, Canadian, European, Indian, or New Zealand codes.
2
C h a p t e r II
Getting Started
Overview
This chapter covers the installation, launching, and support procedures for SAFE.
The following topics are discussed in this chapter.
• What Your SAFE Package Includes
• About This Manual
• System Requirements
• Installation
• Removing SAFE from Your System
• Using the Hardware Key Device
• Technical Support
• Upgrading from SAFE 5
What Your SAFE Package Includes
Your SAFE package includes the following:
• A single Compact Disk (CD) containing the Setup program, executable files,
support files, and sample data files
Overview
3
SAFE User's Manual
• Two program manuals in one volume:
– SAFE User’s Manual
– SAFE Verification Manual
• Hardware key device
About This Manual
This manual is designed to help you quickly become productive with SAFE. The
next chapter gives an introduction to the basic concepts underlying the structural
model, the analysis techniques, and the design procedures used by SAFE. It is
required reading. The next two chapters give an introduction to the basic concepts
of the graphical user interface and a quick tutorial on using the program. It is
strongly recommended that you read these chapters and work the tutorial before attempting a real project with SAFE. The last chapter discusses SAFE output capability. The details of design algorithms are provided in the appendices for specific design codes.
Additional information can be found in the on-line Help facility in the SAFE
graphical user interface.
System Requirements
SAFE will work on any Windows-based personal computer with at least the following configuration:
• Intel Pentium, Pentium Pro, or Pentium II processor
• A minimum of 16 MB of RAM
• At least 200 MB of free hard disk space. Program files require about 20 MB.
The remainder is needed for analytical scratch files. Large projects may require
much more disk space
• Microsoft Windows 95 or Windows NT 4.0 operating system
• Windows-compatible graphics card and monitor supporting at least 800 by 600
resolution and 256 colors
4
About This Manual
Chapter II Getting Started
Installation
If you already have SAFE installed on your machine, please uninstall it first before
installing the new version. To do this, follow the directions in the next topic entitled
“Removing SAFE from Your System.”
Three types of installation are available:
• Single User installation installs the entire SAFE program on your local computer. Use this type of installation if you are not connected to a network or you
want your installation to be independent of a network
• Network Server installation copies the entire SAFE program to a network
server. This would typically be performed by a network administrator to make
SAFE available for subsequent installation and execution by network workstations
• Network Workstation installation installs SAFE on a network workstation
using a minimum amount of local disk space. This requires that SAFE already
be installed on a network server that is available to the workstation whenever
the program is used
If you are not sure what to do, choose single-user installation.
The type of program installation you choose is independent of how you access the
hardware key device. For example, a single-user installation can access the key device over the network. Alternatively, a network-workstation installation can access
the key on the local workstation. See Topic “Using the Hardware Key Device” later
in this chapter for more information.
IMPORTANT! After any installation, please read the README.TXT file in the
SAFE directory where you installed the program. This file contains important information that may be more current than the program manuals. You may use any
editor or word-processor to review this file.
Single User Installation
To install the entire SAFE on your local system:
• Turn on your computer and start Windows 95 or Windows NT
• IMPORTANT! No other application should be running during the installation
procedure. Close all other applications before proceeding!
• Follow the instructions below under subtopics “Installing from CD”, “Installing from Disks”, or “Installing from a Network Server”
Installation
5
SAFE User's Manual
• You will be asked to choose the destination folder or directory in which to store
the program and support files on your local machine
• When asked to select the type of Setup, choose “Single User”
• Respond to the remaining prompts from SETUP to complete the installation
The SETUP program will:
• Copy system files to your Windows folder
• Copy program and support files to the folder or directory that you specify on
your local machine
• Copy sample data files to a subfolder called EXAMPLES
• Register SAFE for use with Windows
• Add SAFE to the Start menu for Windows 95 / NT
Network Server Installation
To copy the entire SAFE program to a network server for subsequent installation
and execution by network workstations:
• Turn on your computer and start Windows 95 or Windows NT
• You must perform the installation from a Windows 95 or NT machine, but you
can install it onto any Windows, Novell, or other type of file server that can be
accessed from Windows 95/NT workstations
• You must have sufficient rights to create files on the server
• IMPORTANT! No other application should be running during the installation
procedure. Close all other applications before proceeding!
• Follow the instructions below under subtopics “Installing from CD”, “Installing from Diskette”, or “Installing from a Network Server”
• You will be asked to choose the destination folder or directory in which to store
the setup, system, program, and support files on the network server
• When asked to select the type of Setup, choose “Network Server”
• Respond to the remaining prompts from SETUP to complete the installation
The SETUP program will:
• Copy setup, system, program, and support files to the folder or directory that
you specify on the network server
• Copy sample data files to a subfolder called EXAMPLES
6
Installation
Chapter II Getting Started
You will not be able to run SAFE after this installation. You must still perform
single-user or network-workstation setup from the network server in order to use
the program.
Network Workstation Installation
To install SAFE on your network workstation to run from a network server:
• Turn on your computer and start Windows 95 or Windows NT
• IMPORTANT! No other application should be running during the installation
procedure. Close all other applications before proceeding!
• Follow the instructions below under subtopic “Installing from a Network
Server”; you should not perform this installation from a CD or from Diskettes
• You will be asked to choose the destination folder or directory in which to store
small support files on your local machine
• When asked to select the type of Setup, choose “Network Workstation”
• Respond to the remaining prompts from SETUP to complete the installation
The SETUP program will:
• Copy system files to your Windows folder
• Copy support files to the folder or directory that you specify on your local
machine
• Optionally copy sample data files to a subfolder called EXAMPLES
• Register SAFE for use with Windows
• Add SAFE to the Start menu for Windows 95 / NT
Whenever you run SAFE, your workstation must have access to the network server
from which you installed SAFE.
Installing from CD
To install SAFE from a CD:
• Insert the SAFE CD into your CD-ROM drive
• Wait for the SAFE setup program to start automatically
Then follow the remaining instructions in the subtopics above for the type of installation you are performing.
Installation
7
SAFE User's Manual
Installing from Disks
To install SAFE from Disks:
• Insert SAFE Disk 1 into your disk drive
• Select Run from the Start menu
• For the Command Line in the Run dialog box, type in “A:\SETUP”. If your
disk is in a drive other than A:, substitute the appropriate drive letter for A:
• Click OK in the Run dialog box to start the installation
Then follow the remaining instructions in the subtopics above for the type of installation you are performing.
Installing from a Network Server
To install SAFE from a network server:
• Ask your network administrator for the location of an existing SAFE networkserver installation
• Select Run from the Start menu
• For the Command Line in the Run dialog box, type in the complete path to the
SAFE SETUP program as given to you by your network administrator
• Click OK in the Run dialog box to start the installation
Then follow the remaining instructions in the subtopics above for the type of installation you are performing.
Removing SAFE from Your System
If you need to remove SAFE from your system, or before installing a new version of
SAFE:
• Turn on your computer and start Windows 95 or Windows NT
• IMPORTANT! No other application should be running during this procedure.
Close all other applications before proceeding
• From the Start menu choose Settings > Control Panel > Add Remove Programs, click on SAFE and then the Remove button
• Follow the prompts. When asked, you may safely remove all shared components that reside in the SAFE folder or directory
8
Removing SAFE from Your System
Chapter II Getting Started
Using the Hardware Key Device
Program SAFE is copy-protected with a hardware key device that is provided with
the software. This hardware key device must always be accessible to SAFE whenever you use the program. This is done by attaching the key device to the parallel
port of your local workstation or to that of another workstation on your local area
network, as described below. The same key device may be used in either local or
network access modes.
If SAFE cannot find the hardware key device while you are using the program,
SAFE will enter display-only mode, with the following implications:
• You can use the graphical user interface to display the results of previous
analyses
• You can save your current model
• You cannot make changes to your model
• You cannot perform analysis or design
If the hardware key device inadvertently becomes unavailable while you are using
SAFE, you should save your model, exit the program, then re-attach the key device
before restarting SAFE.
On a Local Workstation
If you are normally going to use SAFE on a single workstation, it is simplest to attach the hardware key device directly to that workstation.
Attach the key device to any parallel printer port on your workstation. The key device should be directly attached to the computer port. Any printers, data switches,
or other devices that use the port may then be attached to the other end of the key device. The hardware key device does not require a printer to be connected or, if connected, for it to be powered.
You may connect an extension cable between the computer port and the hardware
key device, and/or between the key device and any printer or other devices. Use a
straight-through DB-25 male to DB-25 female cable.
Hardware key devices for different programs can usually be attached to the same
parallel port. Contact Computers and Structures, Inc., if you are using multiple key
devices and are experiencing conflicts.
Using the Hardware Key Device
9
SAFE User's Manual
On a Local Area Network
If you are going to use SAFE on multiple workstations, it may be more convenient
to attach the hardware key device to one workstation and access it from other workstations across a local area network.
The workstation to which the hardware key device is attached is called the key
server. The key device is attached to the key server as described above for a local
workstation. The key server must be running either Windows 95 or Windows NT,
and running the key-server program NSRVGX as described below.
The standard, single-user key will allow different workstations to access SAFE at
different times. Multiple-user keys are available that will allow simultaneous use of
SAFE by more than one workstation. Several key devices can exist on the same network by using multiple key servers. Each key server may connect to one or more
key devices on one or more ports. Concurrent usage of SAFE is allowed from different workstations up to the sum of the license limits of all key devices on all key
servers.
Each key server must be running NSRVGX in order for the key device to be accessible across the network. Without NSRVGX, the key device is available locally
only to the key-server workstation itself.
The key device should be attached to the parallel port before starting NSRVGX.
Use the Start menu or Windows Explorer to start NSRVGX.EXE, which is located
in the SAFE folder. After a few seconds of initialization, NSRVGX will run minimized as an icon. You may open the NSRVGX window to see how many other
workstations are currently accessing the hardware key devices attached to the key
server. You may minimize the window, but do not stop NSRVGX or shut down the
key-server workstation while other workstations are accessing the attached key device.
Note that it may take a few moments for SAFE to access a hardware key device
across a network, particularly if the network is busy or if the key server is performing other tasks.
Important note: The present version of NSRVGX is unable to run if it is located
under a folder (directory) whose name contains a space character. By default,
SAFE is installed in a SAFE subfolder under the folder “Program Files”. Since this
folder name contains a space character, NSRVGX will not run. To remedy this
situation, copy NSRVGX.EXE to another folder so that there are no space characters anywhere on the path, and run it from that folder.
10
Using the Hardware Key Device
Chapter II Getting Started
Installing the Sentinel Driver
In order to use the hardware key device on a Windows 95/ NT machine, either in local mode or as a key server, you must install the Sentinel Driver for Windows 95/
NT. This driver is not automatically installed by the SAFE setup program and must
be separately installed. This driver is not required for machines accessing the key
across the network; it is only required for machines with the key device attached.
The Sentinel drivers for the hardware key device are located on the CD in a directory called NETDRIVE. The drivers for both Windows NT and Windows 95 are
contained in this directory.
To install the driver on any machine, insert the CD in the CD drive on that machine
and run
d:\NETDRIVE\SETUP.EXE
where “d:” indicates the drive that contains the CD. The installation takes only a
few seconds. It proceeds quietly, requiring no input from you, and displaying no
messages unless an error occurs. After the installation is done (the hourglass
disappears), you should restart your system. The Sentinel driver will automatically
run every time you start your computer.
The installation of the Sentinel driver is a one-time installation process that needs to
be performed on each machine that may have a hardware key device attached to its
parallel port. This installation is NOT automatically performed when SAFE is installed.
Technical Support
Free technical support is available from Computers and Structures, Inc. (CSI) via
phone, fax, and e-mail for 90 days after the software is purchased. Technical support is available after 90 days if you have a current maintenance agreement with
CSI. Maintenance agreements also provide for free or reduced-cost upgrades to the
program. Please call your dealer to inquire about a maintenance agreement.
Technical support is provided only according to the terms of the Software License
Agreement that comes with the program.
If you are experiencing problems using the software, please:
• Consult the documentation and other printed information included with your
product
Technical Support
11
SAFE User's Manual
• Check the on-line Help facility in the program
If you cannot find a solution, then contact us as described below.
Help Us to Help You
Whenever you contact us with a technical-support question, please provide us with
the following information to help us help you:
• The program name (SAFE) and version number that you are using
• A description of your model, including a picture, if possible
• A description of what happened and what you were doing when the problem
occurred
• The exact wording of any error messages that appeared on your screen
• A description of how you tried to solve the problem
• The computer configuration (make and model, processor, operating system,
hard disk size, and RAM size)
• Your name, your company’s name, and how we may contact you
Phone and Fax Support
Standard phone and fax support is available in the United States, from CSI support
engineers, via a toll call between 8:30 A.M. and 5:00 P.M., Pacific time, Monday
through Friday, excluding holidays.
You may:
• Contact CSI’s offices via phone at (510) 845-2177, or
• Send a fax with questions and information about your model (including a
figure, if possible) to CSI at (510) 845-4096
When you call, please be at your computer and have the program manuals at hand.
Online Support
Online support is available by:
• Sending an e-mail and your model file to support@csiberkeley.com
• Visiting CSI’s web site at http://www.csiberkeley.com to read about frequently
asked questions
12
Technical Support
Chapter II Getting Started
If you send us e-mail, be sure to include all of the information requested above under subtopic “Help Us to Help You.”
Upgrading from SAFE V5
Most modeling and analysis features available in SAFE V5 are also present in
SAFE V6, and many new features have been added. SAFE V5 and SAFERC V5 input data files can be imported directly into the SAFE V6 graphical user interface
and automatically converted to SAFE V6 models. These models can then be modified, analyzed, designed, and displayed. To import SAFERC input files, append
them to the corresponding SAFE input files before importing in SAFE V6.
WARNING! Some imported data may be interpreted differently by SAFE V6 than
by SAFE V5. Be sure to check your imported model carefully! Compare the results
of analyses using both SAFE V6 and SAFE V5 before making further use of the imported SAFE V6 model!
Upgrading from SAFE V5
13
.
C h a p t e r III
SAFE Concepts and Techniques
The purpose of this chapter is to introduce you to the concepts and techniques of
SAFE. These concepts define the basics of the SAFE graphical user interface (GUI)
and the SAFE analysis and design procedures. Therefore a clear understanding of
these concepts is very important for effective application of the software.
The SAFE Objects
A model of a SAFE system may consist of a slab (Area Objects) with embedded
beams (Line Objects) supported by columns (Point Objects), walls (Line Objects)
or soil (Area Objects) and subjected to concentrated loads (Point Objects), wall
loads (Line Objects) or uniformly distributed loads (Area Objects).
In using the SAFE GUI to make a model, the concept is simple. You first draw a series of Point, Line, and Area Objects. These objects are then assigned element, support, or load properties that convert them into structural elements, structural supports, or structural loads respectively. In other words, when an Area Object is assigned a slab property, a structural slab having dimension of the area object and
properties defined by the slab property is introduced into the model. When an Area
Object is assigned a load property, a uniform load applied over the extent of the
Area Object is introduced into the model. A Line Object can be assigned beam
properties to make a structural beam and/or can be assigned load properties to intro-
The SAFE Objects
15
SAFE User's Manual
duce a line load into the model. A Point Object can be assigned load properties to
apply point loads and concentrated moments.
By applying support properties to a Point Object, Line Object or Area Object you
can introduce column supports, wall supports or soil supports (modulus of subgrade reaction), respectively, into the model.
And finally, by applying release properties to any Line Object you can introduce
structural discontinuities into the slabs to model cuts and expansion joints.
An Area Object can be drawn any where on the XY (horizontal) plane as a
quadrilateral. A special option is available for drawing a rectangular Area Object. A
Line Object can be drawn any where on the XY plane. A Point Object can also be
located any where on the XY plane. All objects can be arbitrarily located. No predefinition of gridlines or object nodes is necessary.
The SAFE Plane and Gridline System
The slab is assumed to be flat and horizontal and is located in the XY-plane of the
right-handed X-Y-Z coordinate system. All Area, Line, and Point objects lie in this
plane. The loading and supports are normal to this plane, that is in the Z-direction.
Vertical deflections are associated with the Z-axis. Rotations are measured about
the X- and Y-axes.
In order to facilitate the drawing of the objects, the GUI allows the definition of a
rectangular system of gridlines. These gridlines are the basic construction lines to
aid the drawing of the objects and are not to be confused with the finite element
mesh which is used in the analysis. The finite element mesh is automatically
developed by subdividing the geometry of the objects and the gridline system as
described later. Snap options are available that will cause the cursor to snap to
gridlines and gridline intersections. Drawing constraint options are available to
draw the lines in certain directions.
The SAFE Templates
The built-in SAFE templates are very convenient tools for the immediate generation of models of slabs and basemats that have regular geometries. The templates
require simple control information to define the basic parameters for the structural
geometry and loading from which the complete slab model, including the slab design strips, is created. In many cases the templates can be used as starting points for
the definition of more complex slab systems, which can be obtained by modification of initial models produced by the templates.
16
The SAFE Plane and Gridline System
Chapter III SAFE Concepts and Techniques
The SAFE Layers
To separate the analysis from the design there is a simplified layering system in the
SAFE modeling. The basic layer is the Structural Layer. This layer is used to define
the structural geometry, boundary conditions, and loading. There are two more layers, namely, the X- Direction Strip Layer and the Y-Direction Strip Layer. As the
terminology suggests, these layers are used for defining the design strips associated
with the design of the slab. Only rectangular Area Objects may exist on these design strip layers, and each object is a design strip in the direction corresponding to
the layer.
The SAFE Finite Element Mesh
The finite element mesh used in the analysis is a rectangular mesh that is
automatically generated before the analysis is executed. The mesh is based upon a
maximum acceptable element size. However, extra mesh lines are introduced at all
locations of objects, object boundaries, and gridlines. You can introduce specific
mesh lines by creating additional gridlines at those locations. The mesh lines are
numbered consecutively for output reference purposes. The I-lines are parallel to
the Y-axis and are defined by X-coordinates. The J-lines are parallel to the X-axis
and are defined by Y-coordinates.
After the mesh is generated the program automatically creates slab elements by
subdividing all the area objects that have been assigned slab properties and creates
beam elements by subdividing all the line objects that have been assigned beam
properties.
Support properties are lumped into discrete springs and are assigned to finite element mesh points. Support properties of all Point Objects are assigned directly to
the corresponding finite element mesh point. Support properties of all Line Objects
are discretized and applied to all the mesh points that exist on the line based upon
the tributary length associated with the mesh point. Similarly, support properties of
all Area Objects are discretized and applied to all the mesh points that exist within
the area and on the boundaries of the area, based upon the tributary area associated
with the mesh point.
Point loads of all Point Objects are assigned directly to the corresponding finite
element mesh point. Line loads of all Line Objects are discretized and applied to all
the mesh points that exist on the line based upon the tributary length associated with
the mesh point. Similarly, surface loads of all Area Objects are discretized and applied to all the mesh points that exist within the area and on the boundaries of the
area, based upon the tributary area associated with the mesh point.
The SAFE Layers
17
SAFE User's Manual
Slab Element
Each slab element is an isotropic or orthotropic, thin or thick plate bending element.
The thin plate element is a three to four-node element and is based upon the classical linear thin plate bending theory, neglecting the effects of out-of-plane shear deformations. This element is described in Ibrahimbegovic (1993) and is also used in
the program SAP2000. The thick plate element is also a three to four-node element
and accounts for the effects of out-of-plane shear deformations. This element is
also described in Ibrahimbegovic (1993) modified with shear interpolations described in Morris (1984). The essential features of the plate elements are described
here.
• Each of the element nodes has the three degrees of freedom, ∆ , θ , and θ .
Z
X
Y
• The material properties and thickness within each slab element are constant.
• Optionally, to model orthotropic effects, it is possible to specify three different
effective thicknesses  X-direction bending, Y-direction bending, and twist.
• The slab system must be planar and exist in the XY plane. Changes in slab elevations that cause definite moment discontinuities may be reasonably captured
using the release options.
• In-plane action is not allowed in the XY plane, therefore, membrane stresses in
the plane of the slab system do not exist.
• The calculation of the self-weight of the slab element is based upon the design
thickness, the dimensions between mesh points in the X and Y directions, and
the unit weight of the element. The weight of the slab element is lumped (as
concentrated loads) and distributed equally onto the mesh points into which the
slab element frames.
• Slab element moments and shears are calculated at the mesh points of the element.
Beam Element
The beam element in SAFE is based upon linear elastic beam theory and can have
arbitrary cross section, the cross-sectional properties being defined by the moment
of inertia, torsional constant, and the shear area. The beam element formulation
used in SAFE is described in Zienkiewicz and Chung (1964). The element has two
nodes, each having three degrees of freedom, ∆ , θ , and θ . Other characteristics
of the beam element are as follows:
Z
X
Y
• A beam segment existing between two consecutive mesh points is modeled as
beam element.
18
The SAFE Finite Element Mesh
Chapter III SAFE Concepts and Techniques
• The beam elements are prismatic.
• There is no in-plane action allowed in the XY plane. Therefore, beam axial
forces and other forces associated with such in-plane action do not exist.
• The calculation of the self-weight of the beam is based upon the actual area for
rectangular or general sections and the stem area for T- and L-sections, length
between mesh points, and unit weight of the beam. The weight of the beam element is lumped (as concentrated loads) and distributed equally onto the mesh
points into which the beam element frames.
• The beam moments, shears, and torques are calculated at the two ends of the
element, that is, at each mesh point.
• If any participation of the slab is to be included in the bending of any beam, you
should specify the beam as either a T-beam or an L-beam.
Support Elements
All point supports of the system are modeled as linear elastic spring elements at the
mesh points based on the support properties. The program generates equivalent
mesh point linear elastic springs to model surface and line support conditions. Optionally, you can activate an iterative process to model no-tension surface support
conditions. Typical support elements are shown in Figure III-1. The essential characteristics associated with the support elements are as follows:
• Point Supports have three degrees of freedom, ∆ , θ
springs, K ∆Ζ , K θ , and K θ .
Z
X
X
and θ and associated
Y
Y
• Line supports have two degrees of freedom, vertical (∆ ) and rotation (θ) about
the support line, and associated spring constants K ∆Ζ and K θ . For line supports
along X- and Y-gridlines, the rotational degree of freedoms, θ, and associated
stiffnesses, K θ , are taken about the X- and Y-axes respectively as shown in Figure III-3. For line supports along skewed lines, the rotational degree of freedoms, θ, and the associated stiffnesses, K θ , are resolved about the X- and Yaxes.
Z
• Surface Supports have only one degree of freedom, ∆ , and associated spring
constant, K ∆Ζ .
Z
• The support elements are weightless.
• The support reaction values are produced at every supported mesh point. The
values are the total values associated with the particular mesh point for point
and line supports and the surface pressure at the mesh point for surface supports.
The SAFE Finite Element Mesh
19
SAFE User's Manual
Rotational Springs
X
Y
Translational
Spring
Z
Point Support
Translational and Rotational Point Supports
Generated From Line Support Data and
Tributary Lengths
KθX
KθY
K∆Z
X
Z
Line Support
on X-Line
Z
K∆Z
Line Support
on Y-Line
Y
Line Support
Z
Translational Point Supports
Generated From Surface
Support Data and Tributary
Areas
Y
X
Line Support
K∆Z
Surface Support
Figure III-1
Support Elements
20
The SAFE Finite Element Mesh
Chapter III SAFE Concepts and Techniques
Slab Element Releases
The element release capability of the SAFE program allows convenient modeling
of discontinuity. Releases allow jumps in moment or shear across a specific line of
discontinuity. Figure III-2 demonstrates some practical situations associated with
the joint releases. The releases are specified as a line object. Moment and/or shear
release can be specified. Only the moment and or shear in the slab elements on both
side of the release line are affected. The beam elements are unaffected.
Y
Expansion Joint
1
Moment Release
CASE 1
2
X
Expansion Joint
In Slab
X
Plan
Plan
1
CASE 2
Moment and
Shear Release
Cut In Slab
Y
2
Cut In Slab
Figure III-2
Slab Element Release
Slab Element Releases
21
SAFE User's Manual
Loading
All loading on the slab system is applied as point loads (forces and moments) on the
mesh points. This also applies to line and surface loads, where the program internally generates the point loads based upon the tributary lengths or areas and the
loading intensities supplied by the user. Figure III-3 shows different forms of applied loading in SAFE. Positive direction of all applied vertical loading is downward (−Z axis). Positive direction of applied point moment corresponds to positive
X and Y axes using the right-hand rule for moments. Positive direction of applied
line moments corresponds to positive direction of the line object.
Y
POINT FORCES &
CRANKED-IN MOMENTS
PZ
MY
LINE LOAD
ON Y-LINE
POINT FORCES (NO MOMENTS)
GENERATED FROM SURFACE
LOADING DATA &
TRIBUTARY AREAS
MX
Z
PZ
LINE LOAD
ALONG DIAGONAL
PZ
MX
PZ
POINT FORCES
& CRANKED-IN MOMENTS
GENERATED FROM LINE LOAD DATA
& TRIBUTARY LENGTHS
MOMENT ABOUT DIAGONAL
RESOLVED INTO MX & MY
LINE LOAD
ON X-LINE
FINITE ELEMENT
GRID OF SLAB
X
Figure III-3
Loading Direction
22
Loading
Chapter III SAFE Concepts and Techniques
SAFE Reinforced Concrete Design
This section outlines various aspects of the concrete design and design-check procedures that are used by the SAFE program. The concrete design and check may be
performed in SAFE according to one of the following design codes:
• The 1995 American Concrete Institute “Building Code Requirements for
Structural Concrete,” ACI 318-95 (ACI 1995).
• The 1984 Canadian Standards Association “Design of Concrete Structures for
Buildings,” CSA A23.3-94 (CSA 1994).
• The 1985 British Standards Institution “Structural Use of Concrete,” BS 8110,
(BSI 1985).
• The 1992 European Committee for Standardization “Design of Concrete Structures,” EUROCODE 2 (CEN 1992).
• The 1978 Indian Standard “Code of Practice for Plain and Reinforced Concrete,” IS 456-78 Revision 1996 (IS 1996).
• The 1995 Standards New Zealand “Concrete Structures Standard,” NZS
3101-95 (NZS 1995).
Details of the algorithms associated with each of these codes as implemented in
SAFE are described in the Appendices.
It is assumed that the user has an engineering background in the general area of
structural reinforced concrete design and familiarity with at least one of the above
mentioned design codes.
Design Load Combinations
The design load combinations are the various combinations of the load cases for
which the slab system needs to be designed/checked. The load combination factors
to be used vary with the selected design code. The load combination factors are applied to the forces and moments obtained from the associated load cases and are
then summed to obtain the factored design forces and moments for the load combination.
For normal loading conditions involving static dead load, live load, pattern live
load, wind load, and earthquake load, the program has built-in default loading combinations for each design code. These are based on the code recommendations and
are documented for each code in the corresponding Appendix. For other loading
SAFE Reinforced Concrete Design
23
SAFE User's Manual
conditions, the user must define design loading combinations either in lieu of or in
addition to the default design loading combinations.
The default load combinations assume all static load cases declared as dead load to
be additive. Similarly, all cases declared as live load are assumed additive. However, each static load case declared as pattern live, wind, or earthquake, is assumed
to be non additive with each other. Also wind and static earthquake cases produce
separate loading combinations with the sense (positive or negative) reversed. If
these conditions are not correct, the user must provide the appropriate design combinations.
The default load combinations are included in design if the user requests them to be
included or if no other user defined combination is available for design. If any default combination is included in design, then all default combinations will automatically be updated by the program any time the design code is changed or if static
load cases are modified.
Design of Slab
As is done in conventional design, the flexural design of slabs in SAFE involves
defining sets of strips in two mutually perpendicular directions, integrating strip
moments and shears, and then designing the strips based on a user selected code.
The integrated moments and shear forces are obtained from reactive nodal moments and forces. These reactive moments are obtained by multiplying the slab element stiffness matrices by the element displacement vectors. These moments will
always be in complete static equilibrium with the applied loads, irrespective of the
refinement of the finite element mesh. The details are given in the following subsections.
Defining Slab Strips
For design purposes, the slab system is divided into strips. The strips are in fact rectangular area objects. The extent of the strips is defined by references to the lines of
the SAFE finite element mesh. The strip definition is repeated in two mutually perpendicular directions. The design strips can be overlapped if needed. The locations
of the strips are usually governed by the locations of the slab supports. The strips
can be staggered due to staggered support locations along a particular direction.
Typical slab strips are shown in Figure III-4.
The integration strips can only run parallel to the X- or Y-axis of the SAFE rectangular grid system. Integration in skewed directions is not currently possible.
24
SAFE Reinforced Concrete Design
Chapter III SAFE Concepts and Techniques
Integrated Strip Moments and Shears
The total integrated cross-sectional moments and shears along the length of a design strip are obtained for design and display purposes. The determination of the integrated strip moments and shears for design involves the following. For a particular load combination or load case for each element within the design strip, the program calculates the mesh point reactive moments. The mesh point moments and
shears on one side of the mesh line are then added to get the strip moment and shear.
The positive and negative moments are added separately to get the positive and
negative design moments across the whole strip. The sums are then divided by the
width of the strip to get the average strip moment and shear. This is then repeated
for the other side of the mesh line. The existence of any openings across the strip is
automatically recognized by the program and the dimensions associated with such
elements are not included in the calculation of the strip width. When integrated strip
moments have to be used for display and reporting purposes only, the positive and
negative moments are algebraically added before reporting.
It should be noted that the moments vary linearly between stations, whereas the
shear values are constant between stations.
Y
X
Figure III-4
Design Strips in the Y-Direction
SAFE Reinforced Concrete Design
25
SAFE User's Manual
Flexural Design of Slab Strips
The design of the slab reinforcement for a particular strip is carried out at the mesh
line locations along the length of the strip. Controlling reinforcement is computed
as an average for the width of the strip (reinforcement per unit width) at the mesh
line locations along the length of the strip. For each design strip, for every mesh
line location, the slab flexural design for every load combination involves the following.
For each element within the design strip, the program calculates the mesh point
moments for each load case. The mesh point moments on one side of the mesh line
are then added to get the strip moments. The negative and positive factored design
moments are added separately and then divided by the width of the strip to get the
average strip moments from which the average strip reinforcing is obtained. This is
then repeated for the other side of the mesh line. The existence of any openings
across the strip is automatically recognized by the program and the dimensions associated with such elements are not included in the calculation of the strip width.
The maximum top and bottom average strip reinforcement for each side of a particular mesh line is obtained along with the corresponding controlling load combinations.
The reinforcement design algorithms are different for different codes and are documented in the Appendices. The program provides an option to either consider or
not to consider minimum reinforcement requirements of the specific code. The design is for strength only. Consideration of development length, crack width, maximum bar spacing, etc., are not within the current scope of the SAFE program.
Checking Punching Shear Capacity
The distribution of stresses close to concentrated loads or reaction points in reinforced concrete slabs is quite complex. One particular failure mode recognized by
design codes for which an elastic plate bending analysis may not provide good
enough stress distribution is punching shear. Most codes use empirical methods
based on experimental verification to check against punching shear failures. The
SAFE program automates this check for the more common geometries. The SAFE
procedure for the punching shear check for each column for each design load combination is as follows. It is described below with reference to the ACI 318-95 code.
The procedure for the other codes is similar. Differences are noted in the specific
Appendix for each code.
• Locate the critical section around the column or point load (ACI Section
11.12.1.2). The program reports whether it assumed the column to be an interior, edge, or corner column. This determination is based on minimum area of
26
SAFE Reinforced Concrete Design
Chapter III SAFE Concepts and Techniques
the critical section. The program does not currently account for changes in slab
depth, presence of openings, beams or walls, and other discontinuities. The location of the critical section with respect to the column is code dependent. It is
taken as half the effective slab depth for the ACI code.
• Calculate the reactive force and moments at the column for the load combination (or the applied load)
• Obtain the percentage of moments transferred through eccentricity of shear
(ACI section 11.12.6.1)
• Calculate the distribution of shear stress around the critical section (ACI section 11.12.6.2)
• Obtain the shear capacity of the critical section (ACI section 11.12.2.1)
• Compare the shear stress distribution with the shear capacity (ACI section
11.12.6.2). The comparison is reported as a ratio for the worst load combination. A value above 1.0 indicates failure.
The program currently does not consider any shear reinforcement in slabs or the
presence of any prestressing.
Design of Beam Elements
In the design of concrete beams, SAFE calculates and reports the required areas of
steel for flexure and shear based upon the beam moments, shears, load combination
factors, and other criteria which are described in detail in the code specific
Appendices. The SAFE beam design is executed on an element-by-element basis
considering the moments and shears at each mesh point of the element. The following are some of the basic design assumptions associated with the design process of
SAFE.
• The beams are designed for flexure and shear. Any torsion that may exist in the
beams must be investigated independently by the user.
• The reinforcement requirements reported by the program are based purely
upon strength considerations. Consideration of development lengths, crack
width, minimum bar spacing and sizing, etc. are not within the current scope of
the SAFE program. The program can consider the minimum reinforcement requirements of the specified code if this option is selected.
In designing the flexural reinforcement for the moment at a particular mesh point of
a particular beam element, the steps involve the determination of the maximum factored moments and the determination of the reinforcing steel. The beam section is
designed for the maximum positive and maximum negative factored moment enveSAFE Reinforced Concrete Design
27
SAFE User's Manual
lopes obtained from all of the load combinations. Negative beam moments produce
top steel. In such cases, the beam is always designed as a rectangular section. Positive beam moments produce bottom steel. In such cases the beam may be designed
as a rectangular- or a T-beam. For the design of flexural reinforcement, the beam is
first designed as a singly reinforced beam. If the beam section is not adequate, then
the required compression reinforcement is calculated.
The SAFE beam shear design is also done on an element-by-element basis. The
shear force along the length of any element for a particular SAFE load case is considered constant. In designing the shear reinforcement for a particular element for a
particular set of loading combinations, the steps involve the determination of the
factored shear force, the determination of the shear force that can be resisted by
concrete, and the determination of the reinforcement steel required to carry the balance.
Analysis for No-Tension Surface Supports
SAFE has an option to request nonlinear analysis to consider surface supports (soil
springs) as providing compressive support only. This option requires that load
combinations be defined before an analysis is requested. The nonlinear analysis is
performed only for the loading combinations and not for the individual loading
cases. The program uses iterative procedure using the original stiffness and corrective load vectors to obtain the no-tension results. This procedure converges asymptotically. The iterations for load combinations are stopped either when a user specified number of iterations are reached or when the maximum tension pressure as a
ratio of the maximum compressive pressure falls below a user specified tolerance.
When this option is activated, all program results for loading combinations are for
this nonlinear analysis.
Analysis for Cracked Deflections
In the design of slabs, it is generally recognized that the distributions of moments
obtained from an elastic analysis is good enough for design purposes, however, this
analysis may significantly underestimate the true deflections. The estimation of
true deflections is a complex task. Some guidelines are available in design codes.
For beams the ACI 318-95 Section 9.5 recommends that an effective stiffness be
used to first obtain the cracked deflections and then modification factors be applied
to account for long term deflections. The SAFE program extends the recommendation on effective stiffness to slabs and beams of the floor system to obtain cracked
deflections. The procedure used is as follows:
28
Analysis for No-Tension Surface Supports
Chapter III SAFE Concepts and Techniques
• Perform elastic uncracked analysis
• Design the slab reinforcement
• Calculate cracking moment and cracked moment of inertia for each element for
each direction of moment and for top and bottom reinforcement
• Calculate service level moments as sums of specified dead and live load moments
• Calculate ratio of effective stiffness to gross-section stiffness for both X and Y
directions for the slab elements and for the beam elements
• Reanalyze the structure using effective stiffness calculated for each element
The re-analysis results are only saved for the displacements and are reported as
cracked deflections. All other results are for the original uncracked analysis. The
cracked deflection results should be treated as estimates and need to be modified by
appropriate factors for long term deflections.
SAFE Units
The SAFE GUI will accept English, SI or MKS metric units. However, each design
code is based upon a specific system of units. All equations associated with a particular code as presented in the Appendices correspond to that specific system of
units associated with the code unless otherwise noted. For example, the ACI code is
published in inch-pound-second units. By default, all equations and descriptions
presented in the Appendix “Design for ACI 318-95” correspond to inch-poundsecond units. However, any system of units can be used to define and design the
structure in SAFE.
SAFE Units
29
.
C h a p t e r IV
The Graphical User Interface
Overview
The SAFE graphical user interface (GUI) is used to model, analyze, design, and
display your structure. This chapter introduces you to some of the basic concepts of
the graphical user interface to set the stage for the tutorial described in the next
chapter. More advanced concepts and features are described in the on-line Help facility of the graphical user interface itself. The following topics will be discussed.
• The Structural Model
• Coordinate Systems
• The SAFE Screen
• Viewing Options
• Gridlines
• Mesh
• Basic Operations
The Structural Model
SAFE analyzes and designs your slab structure using a model that you define with
the graphical user interface. The model may include the following features that represent your structure:
• Material and section properties
• Line objects that represent beams
Overview
31
SAFE User's Manual
• Area objects that represent slabs and basemats
• Point objects that represent column supports
• Line objects that represent wall supports
• Area objects that represent soil supports
• Line objects that represent slab discontinuity (releases)
• Area objects that represent openings
• Loads, including self-weight, surface loads, line loads, and point loads modeled as area, line, and point objects
The graphical user interface provides you with many powerful features to create
your model. You can even start with a preliminary model from template, then use
the SAFE design optimization feature to refine your model with little effort.
Coordinate System
All locations in the model are ultimately defined with respect to a single global coordinate system. This is a three-dimensional, right-handed, rectangular (Cartesian)
coordinate system. The three axes X, Y, and Z are mutually perpendicular, and satisfy the right-hand rule. All slabs, beams, and points lie on the XY (horizontal)
plane.
The SAFE Screen
The SAFE graphical user interface appears on your screen and looks similar to the
following:
32
Coordinate System
Chapter IV The Graphical User Interface
Main Title Bar
Display Title Bar
Menu Bar
Display Title Bar
Main Tool Bar
Window Separator
Side Title Bar
Active Display Window
Status Line
Display Window
Pointer Position
Coordinates
Active Units
The various parts of this interface are labeled above and described below.
Main Window
The main window contains the entire graphical user interface. This window may be
moved, resized, maximized, minimized, or closed using standard Windows operations. The main title bar, at the top of the main window, gives the program name and
the model name.
Menu Bar
The menus on the Menu Bar contain most of the operations that you can perform
with SAFE.
Toolbar
There are two toolbars in the SAFE GUI: the Main Toolbar at the top of the window
just below the Menu Bar and the Side Toolbar at the left side of the window. The
Toolbars provides quick access to some commonly used operations, especially
viewing, drawing, selecting, and file operations. Most of the operations available
on the toolbars can also be accessed from the Menu Bar.
The SAFE Screen
33
SAFE User's Manual
Display Windows
Display windows show the geometry of the model, and may also include properties,
loading, analysis or design results. You may have from one to four display windows
present at any time.
Each window may have its own view orientation, selected display object, and display options. For example, the undeformed shape could be displayed in one window, applied loads in another, an animated deformed shape in a third, and design
reinforcement in the fourth window. Alternatively, you could have four different
views of the undeformed shape or other type of display: a plan view and a perspective view, for instance.
Status Line
The status line shows current status information in the message area, a drop down
box that shows or changes the current units, the current pointer location, coordinate
of the last drawn point, and the animation controls when displaying deformed
shapes.
Viewing Options
For each Display Window you may set the view options that affect how the structure appears in that window. These options are available in the View menu and
from the Toolbar. Different view options may apply to different Display Windows.
2-D and 3-D Views
A 2-D view consists of a single plane parallel to the X-Y coordinate plane. Only objects in that plane are visible. This is the default view.
A 3-D view shows the whole model from a vantage point of your choice. Visible
objects are not restricted to a single plane. The view direction is defined by an angle
in the horizontal plane and an angle above the horizontal plane.
Aerial View
The Aerial View displays a full view of the active window’s drawing in a separate
window so that you can quickly zoom into any area of your model without having
to restore the full view first. It can also be used to show you which part of the model
you are zoomed into when working with multiple windows and large models. Each
34
Viewing Options
Chapter IV The Graphical User Interface
time the model is edited the Aerial View is updated. The Aerial View window can
be made visible by selecting Show Aerial View from the Options menu.
View Layers of the Slab
The definition of the slab for analysis and design purposes is done in Layers. There
are three layers in the SAFE model of a slab: Structural Layer, X-Design Strip
Layer, and Y-Design Strip Layer. The Structural Layer is used to define slab geometry, load and boundary conditions which are related to analysis only. The Design Strip Layers are used to define the design strips. The Design Strip Layers hide
all information related to analysis.
Draw operations are affected by the view layer of the slab. For structural elements
and loading, usually the view is set to the Structural Layer. To define strip layers,
you should set your view to Strip Layers.
Pan, Zoom, and Limits
You may zoom-in to a view to see more detail, or zoom-out to see more of the structure. Zooming in and out may be done in predefined increments. You may also
zoom-in to a part of the structure that you define by dragging a window with the
mouse.
Panning allows you to dynamically move the structure around the Display Window
by clicking and moving the mouse.
You may set upper and lower X and Y coordinate limits that restrict the portion of
the structure that is visible in a Display Window. Zooming and panning only apply
to the part of the structure within these limits.
Object View Options
You may set various options that affect how the objects appear in a Display Window. These options primarily affect views of the undeformed shape. Different options are available for the different object types from the Set Object Options... in
the View menu.
Options include whether or not a particular type of object is visible and what object
features are displayed, such as object labels, property labels, etc.
An important option is the shrunken-object view. This shrinks the objects away
from the joints allowing you to better see the connectivity of the model.
Viewing Options
35
SAFE User's Manual
Other Options
You may turn gridlines and the global axes on and off. You may save view parameters under a name of your choice, and recall them later to apply to any Display Window. You can see the automatically generated mesh.
Gridlines
The grid is a set of “construction” lines parallel to the coordinate axes that form a
“framework” to assist you in drawing the model. You may have any number of
gridlines in the X or Y direction with arbitrary spacing that you define. When you
start a new model, you must specify uniform spacing for the grid. Thereafter, you
may add, move, and delete gridlines.
Drawing operations tend to “snap” to gridline intersections unless you turn this feature off. This facilitates accurate construction of your model. When you move a
gridline, you can specify whether or not attached joints should move with it.
Mesh
The mesh is a set of lines parallel to the coordinate axes that form a “framework” to
form the finite element model. The mesh is generated automatically within the program. The user can influence the size of the mesh by setting the maximum mesh dimension in the Set Analysis Options... in the Analysis menu. The following information influences the generation of the mesh:
• The location of the point objects
• The location of the slab elements
• The location of the openings
• The locations and orientation of the beams
• The locations of the loads
• The locations of the soil support
• The locations of the gridlines
Basic Operations
It will be helpful for you to understand the basic types of operations that you can
perform with SAFE. The program responds differently to mouse actions in the dis-
36
Gridlines
Chapter IV The Graphical User Interface
play windows depending upon the type of operation you are performing. Details on
how to actually perform these operations are given in the quick tutorial in the next
chapter, and in the on-line Help facility of the graphical user interface itself.
File Operations
File operations are used to start a new model, to bring in an existing model for display or modification, to save the model that you are currently working on, and to
produce output. File operations are selected from the File menu.
New models can be started from scratch or from predefined templates supplied with
the program.
Models can be saved in a standard SAFE database file (.FDB extension). Existing
models in a standard SAFE database file (.FDB extension) that were created by the
SAFE graphical user interface can be opened.
SAFE allows the user to import existing models in any of the following file formats: SAFE V6 text file (.F2K extension), SAFE V5 text file, or .DXF file (geometry only) created by AutoCAD or other programs.
SAFE allows the user to export SAFE models in any of the following formats:
SAFE V6 text file (.F2K extension), Access Database file, Windows Metafile, or
.DXF file (geometry only) for use by AutoCAD and other programs.
Output that can be produced includes tables of input, analysis results, and design
results in printable format; graphical printout of the active display window; or
video output of animated deflected shapes.
Draw
Drawing is used to add new objects to the model or to modify one object at a time.
Objects include beam elements, slab elements, slab design strips, and other point,
line, and area objects. To draw, you must put the program into Draw Mode by
clicking on one of the seven draw buttons on the Side Toolbar. Alternatively, the
same seven draw operations can be selected from the Draw menu. These operations
are:
• Moving or reshaping existing area, line, and point objects
• Adding new point objects
• Adding new line objects by clicking at their end locations
• Adding new line objects by clicking on a grid segment or space
Basic Operations
37
SAFE User's Manual
• Adding new rectangular area objects by clicking at two diagonal corner locations
• Adding new quadrilateral area objects by clicking at their corner locations
• Adding new rectangular area objects by clicking on a grid space
Once line objects are drawn, they can be assigned beam properties, wall properties
and /or line loads. Point objects can be assigned column properties and /or point
loads. The area objects can be assigned slab properties, soil support properties, surface loads, or can be specified as openings.
In Draw Mode, the left mouse button is used to draw and edit objects, and the right
mouse button is used to query the properties of objects.
In 2-D and 3-D views, cursor placement can be anywhere, since the third (out-ofplane) dimension is always known because of the planar nature of the slab system.
In 2-D views, cursor movements can be controlled by using “snap”, “drawing constraint”, and “location field” tools. This facilitates accurate construction of your
model. These features are available from the Draw menu and the Side Toolbar. The
snap tools can be turned on and off as you draw, so you can snap to different
locations for every point. The area that is searched for snap points is set by the
Screen Snap to Tolerance located in the Preferences dialog box under the
Options menu. Currently there are five snap options:
• Snap to Points
• Snap to Middle and Ends
• Snap to Intersections
• Snap to Perpendicular
• Snap to Lines and Edges
Drawing Constraints provide the capability to constrain the placement of a point
parallel to one of the axes when drawing or reshaping an element. In this manner,
you can quickly draw a frame element parallel to one of the global axes. The
constraint tools can be reached from the Draw menu or by pressing the X, Y, A, or
Spacebar keys on your keyboard while drawing an element. Drawing constraints
Include:
• Constrain X locks the X coordinate of the next point to be drawn
• Constrain Y locks the Y coordinate of the next point to be drawn
• Constrain A locks for a constant angle
• None
38
Basic Operations
Chapter IV The Graphical User Interface
Snaps can optionally be used in conjunction with constraints. Only the
unconstrained component of the selected snap point is used when a constraint has
been selected. Snap tools can also be used when reshaping an element.
Draw operations are also affected by the view layer of the slab. For structural elements and loading, usually the view is set to the Structural Layer. To define design
slab strips, you should set your view to Strip Layers.
Using the Location Fields, the user can explicitly specify the locations of the points
to be drawn. The location can be specified in terms of absolute position and relative
position with respect to the last drawn point in Cartesian or Polar coordinates.
Draw Mode and Select Mode are mutually exclusive. No other operations can be
performed when the program is in Draw Mode.
Select
Selection is used to identify those objects to which the next operation will apply.
SAFE uses a “noun-verb” concept where you first make a selection, and then perform an operation on it. Operations that require you to make a prior selection include certain Editing, Assigning, Printing, and Displaying.
To select, you must put the program into Select Mode by clicking on one of the select buttons on the Toolbar. Alternatively, selecting any action from the Select or
Display menus puts the program into Select Mode.
Many different types of selection are available, including:
• Selecting individual objects
• Drawing a window around objects
• Drawing a line that intersects objects
• Selecting beam or slab objects having the same property type
• Selecting beam or slab by groups
• Selecting all objects
• Selecting previously selected objects again
In Select Mode, the left mouse button is used to select objects, and the right mouse
button is used to query the properties of objects.
Draw Mode and Select Mode are mutually exclusive. Any operation except drawing can be performed when the program is in Select Mode.
Basic Operations
39
SAFE User's Manual
It is possible to select and unselect some objects. It is also possible to reselect the
object which were selected in the previous selection.
Edit
Editing is used to make changes to the model. Most editing operations work with
one or more objects that you have just selected. Editing operations are selected
from the Edit menu, including:
• Cutting and Copying the geometry of selected objects to the Windows clipboard. Geometry information put on the clipboard can be accessed by other
programs, such as spreadsheets
• Pasting object geometry from the Windows clipboard into the model. This
could be edited in a spreadsheet program from a previous Cut or Copy
• Deleting objects
• Moving joints, which also modifies connected elements
• Replicating objects in a linear or radial array or mirroring them
• Aligning line objects or area object edges to be exactly vertical or horizontal
• Changing the drawing order of an area object to determine which slab property
governs
Pasting to the model does not operate on selected objects, and can be done in Draw
or Select Mode. All other operations require a prior selection of objects.
Assign
Assignment is used to assign properties and loads to one or more objects that you
have just selected. Assignment operations are selected from the Assign menu, including:
• Assigning slab properties to area objects
• Assigning opening to area objects
• Assigning beam properties to line objects
• Assigning column support properties to point objects
• Assigning wall support properties to line objects
• Assigning soil support properties to area objects
• Assigning slab discontinuity to line objects
• Assigning point, line, and surface loads
40
Basic Operations
Chapter IV The Graphical User Interface
• Assigning objects to named groups to aid future selection operations
Define
Define is used to create named entities that are not part of the geometry of the
model. These entities include:
• Slab material and section properties and design parameters
• Beam material and section properties and design parameters
• Column support properties
• Wall support properties
• Soil support properties
• Static load cases
• Load combinations
• Object groups
Definition of these entities is performed using the Define menu and does not require
a prior selection of objects.
Analyze
After you have created a complete structural model using the operations above, you
can analyze the model to determine the resulting displacements, stresses, and reactions.
Before analyzing, you may set analysis options from the Analyze menu. These options include:
• Maximum mesh dimension
• Type of analysis and any control parameters
After setting these options, especially, the “maximum element dimension”, you
might want to see the generated finite element mesh. To do this, click the Set
Objects button on the Main Toolbar and check the Show Mesh Option button to
turn it on from the dialog box. If you are satisfied with the mesh, go ahead and run
the analysis. Otherwise, adjust the maximum element size until you are satisfied.
To run the analysis, select Run from the Analyze menu, or click the Run button on
the Main Toolbar.
Basic Operations
41
SAFE User's Manual
The program saves the model in a SAFE database file, then checks and analyzes the
model. During the checking and analysis phases, messages from the analysis engine appear in a monitor window. When the analysis is complete, you may review
the analysis messages using the scroll bar on the monitor window. Click on the OK
button to close the monitor window after you have finished reviewing these messages.
No other SAFE operations may be performed while the analysis is proceeding and
the monitor window is present on the screen. You may, however, run other Windows programs during this time. If you are analyzing a very large model that may
take a while to complete, you may want to activate the run minimized option in the
options menu. This will run the analysis in the background.
Display
Displaying is used to view the model and the results of the analysis. Graphical and
tabular displays are available in SAFE. Most display types may be chosen from the
Display menu. Several of these may also be accessed from the Main Toolbar.
Graphical Displays
You may select different types of graphical display for each Display Window. Each
window may also have its own view orientation and display options.
Available displays of the model input include the undeformed geometry and loads.
Analysis results that can be graphically displayed include deformed shapes;
Beam-element force and moment diagrams; Slab-element moment and shear contour plots; integrated force and moment diagrams for design slab strips; and reactive forces including bearing pressures. Additionally, deformed shape plots may be
animated.
Details of the modeling information can be obtained by clicking on a joint or element with the right mouse button.
Tabular Displays
Tabular information can be displayed for selected joints and elements by choosing
Show Input Tables or Show Output Tables from the Display menu. Tabular information can be printed or saved to a file for selected objects by choosing Print Input
Tables or Print Output Tables from the File menu. If no objects are selected, the tables produced are for the whole model. Tabular input can be displayed at any time.
However, the tabular output can be displayed only after the analysis is complete.
42
Basic Operations
Chapter IV The Graphical User Interface
Design
After analysis is complete, concrete beams and slabs can be designed with respect
to different design code requirements. Design may be performed for the given load
combinations by choosing Start Design from the Design menu. Before designing,
you should properly select the Design Code from the Preferences... menu item in
the Options menu.
Graphical displays of reinforcing steel and other design parameters are available.
Tabular design information can also be displayed from the Design menu. Tabular
design information can be printed or displayed for selected objects by choosing
Print Design Tables from the File menu or by choosing Display Slab Design Info
and Display Beam Design Info from the Design menu.
Undo and Redo
SAFE remembers all drawing, editing, and assignment operations that you perform. It is possible to Undo a series of actions previously performed. If you have
gone too far in the Undo process you may Redo those actions. Undo and Redo are
accessed from the Edit menu or the Toolbar.
Locking and Unlocking
After an analysis is performed, the model is automatically locked to prevent any
changes that would invalidate the analysis results and subsequent design results
that may be obtained. You may also lock the model yourself at any time to prevent
further changes to your model, or unlock the model to permit changes. Lock and
Unlock are accessed from the Main Toolbar.
When you unlock the model after an analysis, you will be warned that the analysis
results will be deleted. If you do not want this to happen, save the model under a different name before unlocking it. Any subsequent changes will then be made to the
new model.
Refreshing the Display Window
After performing certain operations, the Display Window may need to be re-drawn.
In order to save you time, this is not done automatically. Click on the Refresh Window button on the Main Toolbar whenever you would like the active display window to be re-drawn and updated.
Basic Operations
43
SAFE User's Manual
Preferences
SAFE allows custom setting of some of the parameters. Theses includes the preferred design code and the associated overload factor. It also allows definition of
the cross-sectional areas of nominal bars. Also, it allows setting some of the parameters related to tolerances, font, display, and output.
44
Basic Operations
Chapter V
Quick Tutorial
Overview
This tutorial is aimed at giving the first-time user hands-on experience while describing a few of the basic features and capabilities of SAFE. It is assumed that you
have read the previous chapter, “The Graphical User Interface.”
The screens shown in this tutorial may appear slightly different from those on your
computer screen. This may be due to different screen resolution and/or font settings
on your computer.
As you become familiar with the program, you will realize that the order of some of
the steps described here is immaterial. In other words, after some practice, you may
choose to perform the operations in a different order to set up and run the same
model.
We will use the SAFE commands either from the Toolbars or from the menus. This
is done intentionally to familiarize you with both methods. The Toolbar provides
quick access to commonly used features. Most of the features available on the Toolbars can also be accessed from the Menu.
Description of the Model
The model chosen for this tutorial is created, analyzed, designed, and then modified. A simple 2 × 2 span flat plate is selected from the program template, subjected
to both dead and live surface loads, and then analyzed for the two load cases. The
reinforced concrete slab system is designed in accordance with ACI 318-95. The
Overview
45
SAFE User's Manual
geometry of the model is then modified, and the slab system is redesigned. The initial model is shown in Figure V-1. Kip-inch units are used. Concrete strength of 4
ksi and reinforcement of yield strength of 60 ksi are used throughout the model.
Figure V-1
The Tutorial Example
Starting the Tutorial
The following sections describe the step-by-step procedure for creating, analyzing,
designing, and modifying the flat-slab model. It is recommended that you actually
perform these steps using the program while you are reading this chapter.
Start the program by running SAFE from the Start Menu. We will now proceed to
develop the model. The geometry is obtained from a template available in SAFE.
The templates represent a number of common structural configurations for slabs
and basemats. Remember that once the structural geometry has been set up, the order of steps is left to your own discretion.
In the following sections, the phrases “Click”, “Right Click”, and “Left Click” are
used frequently. The phrase “Right Click” is meant to be “Click on the Right
Mouse-Button” and the words “Left Click” is meant to be “Click on the Left
Mouse-Button.” In Windows programming environment, “Left Click” is usually
used for selection and “Right Click” is usually used for inquiring property or de-
46
Starting the Tutorial
Chapter V Quick Tutorial
scription. SAFE follows the same convention. Moreover, the word “Click” is used
to mean “Left Click” for further brevity. The reason for this exclusive use of the
word “Click” rather than “Left Click” is that the word “Click” is used more frequently.
Setting Up the Geometry
When the SAFE program is started, the default units are kip and inch. This is always displayed at the bottom-right corner of the main window. We can modify the
units if desired. For setting up the geometry and defining the surface loading, it is
convenient to define them in the “lb-ft” units.
1. From the drop-down list for units, change the units to lb-ft.
2. From the File menu, choose New Model from Template.... This will display
the Slab Templates dialog box.
2. In this dialog box:
• Click on the Flat Slab template. This will display the Flat Slab dialog box.
The program sets some built-in properties through the use of the templates. We
will use only a 2 × 2 panel, so we will modify the dialog boxes accordingly.
Setting Up the Geometry
47
SAFE User's Manual
• In this dialog box:
– Change the Number of Spans along X-direction to 2
– Change the Number of Spans along Y-direction to 2
– Accept the default slab edge distances from the column centerlines
– Accept the default column spacings in both X- and Y- directions
– Accept the default slab thicknesses and column size and height dimensions
– Accept the default additional dead load and live load
– Check the box Create Live Load Patterns in the Load area to automatically generate pattern loads
– Accept the checked Drop Panel box
– Click the OK button.
From this dialog box, you can start directly with appropriate slab and drop-panel
thicknesses. We will take the default thicknesses now. We can modify them later if
necessary.
The screen will refresh and display 2-D and 3-D views of the model in two
vertically-tiled adjoining windows. The left window shows the X-Y plan view of
the model. The right window shows a 3-D perspective view.
48
Setting Up the Geometry
Chapter V Quick Tutorial
This completes the model geometry. The model includes the support restraints at
nine column points. Each column is represented by three springs  one for vertical
translation and two for rotation. The spring constants are obtained automatically
from the column dimensions.
The units in which the model was started is known as the database units. The program saves data internally in these units. However, the user is free to input data or
review results in any units desired by simply selecting the appropriate units in the
units box.
Checking Slab Properties
In the model created from the template, the main slab is defined as SLAB, the
drop-panels are defined as DROP, and the column areas are defined as COL. We
first want to see which property is assigned to each area, and then want to see the
details of the properties.
1. From the drop-down list for units, change the units to Kip-in. Units are now
Kip-in as shown in the bottom-right status area.
2. On the Main Toolbar, click on the Set Objects. This will display the Set
Objects dialog box. In this dialog box,
– Check the Properties option box in the Area Objects area.
– Click OK.
Checking Slab Properties
49
SAFE User's Manual
This shows the slab properties assigned to the slab areas. The properties are SLAB,
DROP, and COL. We will check properties for SLAB:
3. From the Define menu, choose Slab Properties.... This will display the Slab
Properties dialog box.
Note: In this dialog box, we can add new slab properties, delete old slab properties, and modify existing slab properties if it is necessary.
4. In this dialog box, four slab properties are defined C COL, DROP, NULL, and
SLAB. SLAB is defined for the entire slab itself, the DROP is defined for the
drop-panels, and the COL is defined for the stiffened column areas. We will see
some of the slab properties for SLAB:
• Select SLAB in the Slab Property selection box by clicking on it
• Click the Modify/Show Property button. This will pop up a Slab Property
Data dialog box
• In this dialog box:
– See the name of the property in the top-right corner
– Note the material property data for the slab: Modulus of elasticity,
Poisson’s ratio, and Unit weight
– Note the bending thickness for both X- and Y-directions and the twisting thickness
50
Checking Slab Properties
Chapter V Quick Tutorial
– Note the Design Properties Data
– Click on the Cancel button to quit the dialog box
• Select DROP and COL, consecutively, and check the properties following
the same procedure as done for SLAB. You do not need to change anything
for this tutorial now. Click on the Cancel button to quit the dialog box.
5. Click on the Cancel button to exit the Slab Properties dialog box.
Checking Column Support Properties
In the model created from the template, the slab is supported by column supports at
nine locations. All these nine point supports are assigned to column support property COLUMN. First we want to confirm which property is assigned to which
column and then want to see the details of the COLUMN property. The display
units are currently Kip-in.
1. From the Main Toolbar, click on the Set Objects. This will display the Set
Objects dialog box. In this dialog box,
– Uncheck the Properties option box in the Area Objects area.
– Check the Point Supports option box in the Point Objects area.
– Click OK.
Checking Column Support Properties
51
SAFE User's Manual
This shows the point supports in one color and other points in a different color. Now
we can see the column support property by right clicking on the point support.
2. Put the cursor on one of the columns. If you put the cursor very close to a column support point, the default snap option, Snap to Point, will automatically
force the cursor to move to the column.
3. Right click on the point. This will pop-up a Point Object Information dialog
box. In this dialog box,
– Note the Point Support name as COLUMN in the Specifications area.
– Click Cancel.
Note: You can right-click on any column location to find out the associated
support properties. In this particular model there is only one column support
property defined and named as COLUMN.
Now we will check properties for COLUMN:
4. From the Define menu, choose Column Supports.... This will display the
Support Properties dialog box.
Note: From this dialog box, we can add new support properties, delete old
support properties, and modify existing support properties if it is necessary.
52
Checking Column Support Properties
Chapter V Quick Tutorial
5. In this dialog box, there are already two existing support properties defined C
COLUMN and NULL. COLUMN is defined for all the column supports. We
will look at the column properties for COLUMN:
• Select COLUMN in the Support Props area by clicking on it
• Click the Modify/Show Property button. This will pop up a Column
Support Property Data dialog box
• In this dialog box:
– See the name of the property at the top-right corner
– Note the property has been defined by specifying rectangular column
properties
– Note the material property data for the slab: Modulus of elasticity and
Poisson’s ratio
– Note section dimensions and the column height
– Click on the Cancel button to quit the dialog box
6. Click on the Cancel button to quit the Support Properties dialog box.
Checking Load Cases
Eight load cases will be considered in the analysis. The first load case is for the dead
load which also includes the self-weight of the structure. The second load case is for
the live load. The program’s default names for these load cases are DEAD and
Checking Load Cases
53
SAFE User's Manual
LIVE, respectively. There are also six pattern live load cases created automatically
from the live load value. These pattern load cases are PAT1, PAT2, K, PAT6. The
superimposed dead load is taken to be 20 psf and the superimposed live load for all
other load cases is 80 psf as was defined in the template dialog box. First we will
look at the names of the defined load cases, then the load values for the load cases.
1. From the Define menu, choose Static Load Cases.... This will display the
Static Load Case Names dialog box. This will display the dead load case with
the name DEAD, the type set to DEAD, and the self-weight multiplier set to
unity. Similarly, the live load and the pattern load cases can be seen. Click Cancel to quit this dialog box.
The display units are currently Kip-inch. The superimposed loads are best viewed
in the lb-ft units.
2. From the drop-down list for units, change the units to lb-ft.
3. Click on the Show Loads button on the Main Toolbar. This will pop up the
Show Loads dialog box. In this dialog box, the default load name is DEAD and
only surface load is available for display. In this dialog box:
– Check the Show Loading Values box.
– Click OK.
54
Checking Load Cases
Chapter V Quick Tutorial
This will display the loading values. Similarly, you can select other load cases in the
Show Loads dialog box and display loading magnitudes and locations.
Checking Design Strips
Slabs are usually designed based on design strip forces. SAFE provides a default
definition of design strips. In SAFE, it can be done by first selecting the View as either X-Strip Layer or Y-Strip Layer, then drawing rectangular objects as strips on
the Strip Layers. There is already a default definition for the design strips in the
model which are enough for this tutorial example. There is no limit on how many
strips can be drawn. They can be overlapping. We can skip the following steps.
However, you can follow these steps for the sake of practice.
1. Right now the surface load is shown on the slab. To get a clean view, select
Show Undeformed Shape from the Main Toolbar. This will show the structural layer plan view without the loading.
2. From the View menu, choose Set X-Strip Layer. This will display the X-strip
Layer Plan View with the default strip definitions.
3. We will accept this default definition of the X-strips.
Checking Design Strips
55
SAFE User's Manual
4. Similarly, we can view and accept the Y-strip layer.
5. Go back to the structural layer plan view by selecting Set Structural Layer
from the View menu.
Analyzing the Model
We will now analyze the model. Before analyzing the model, we need to set the parameters for meshing, analysis type, and uplift iterations. The default settings will
suffice for our tutorial example. However, for the sake of practice you can view the
options. To do this:
1. From the Analyze menu, select Set Options.... This will display the Analysis
Options dialog box. In this dialog box,
• Accept the default Maximum Mesh Dimension as 4 feet.
• Accept the other defaults.
• Click OK.
56
Analyzing the Model
Chapter V Quick Tutorial
2. From the Analyze menu, select Run Analysis. This will display the Save
Model File As dialog box.
3. In this dialog box:
• Save the model as Tutor.FDB.
Note: Even if you do not type in the extension .FDB, the program automatically appends this extension to the filename.
• Click on the Save button.
A top window is opened in which various phases of analysis are progressively reported. When the analysis is complete, the screen will display the following:
Analyzing the Model
57
SAFE User's Manual
4. Use the scroll bar on the top window to review the analysis messages and to
check for any error or warning messages (there should be none).
5. Click on the OK button in the top window to close it. SAFE responds by displaying the deformed shape for the DEAD load.
6. Click on the 3D View button on the Main Toolbar to obtain a perspective view
of the model.
58
Analyzing the Model
Chapter V Quick Tutorial
Displaying the Deformed Shape
After the analysis is complete, SAFE automatically displays the deformed shape of
the model for the first load case, DEAD, by default in the active display window.
We will now display the deformed shape for the load case LIVE in the other window.
1. Click in the other window anywhere outside the structural model to activate
this window.
Note: Remember, clicking any time in a window will activate the window.
2. Change the units from “lb-ft” back to “Kip-in” from the drop-down list at the
bottom-right corner of the window.
3. Select the Show Deformed Shape... on the Display menu. This will display
the Deformed Shape dialog box.
4. In this dialog box:
• Select LIVE Load Case from the drop-down list in the Load area.
• Click on the OK button.
You will observe that the two deformed shapes look similar, even though the loads
are different. This is because SAFE automatically scales the deflections for display
Displaying the Deformed Shape
59
SAFE User's Manual
purposes. You can change the scale factors in the dialog box you just used. Note the
differences in the contour ranges between these plots.
You can animate the deformed shape by using the Start Animation button at the
bottom of the screen. Animation speed is controlled by a horizontal scroll bar that
appears next to this button. The animation can be stopped by clicking on the Stop
Animation button.
Note: Results can also be displayed in a tabulated form by choosing Show Output
Tables... from the Display menu and can be printed by choosing Print Output
Tables... from the File menu. The graphical output in the active window can be
printed by choosing Print Graphics from the File menu.
Displaying Slab Forces
As an example, we will plot the M
yy
moment contour for load case DEAD.
1. Click on the Show Slab Forces button on the Main Toolbar. This will display
the Slab Forces dialog box.
2. In this dialog box:
• Accept DEAD Load Case in the Load area.
• Select M
yy
in the Component area.
• Accept the other default values.
60
Displaying Slab Forces
Chapter V Quick Tutorial
• Click on the OK button. The M
yy
diagram for the entire slab is displayed.
• Click on the 2D View button on the Main Toolbar to view it in plan.
Note: Results can also be displayed or printed in a tabulated form by choosing
Show Output Tables... from the Display menu or Print Output Tables... from the
File menu.
Selecting the Design Code
Selection of a design code is activated from Preferences... in the Options menu.
The default design code is ACI 318-95 for reinforced concrete design. Since the default code is used in this tutorial, we can by-pass this step. To confirm, however,
you can:
1. Click on the Preferences... button from the Options menu. This will launch the
Preferences dialog box.
3. Click on the Concrete tab. You can see the currently selected concrete design
code, strength reduction factors, and other parameters. You do not need to
change anything.
3. Click on the Cancel button to close the dialog box.
Selecting the Design Code
61
SAFE User's Manual
Checking Load Combinations
Eight load cases are considered in the analysis. The first load case is for the superimposed dead load and the self-weight of the structure. This load case is named as
DEAD. The second load case is for the live load which is named LIVE. For design,
the dead load is factored by 1.4 and the live load is factored by 1.7 according to the
ACI 318-95 design code. The design combos involving six pattern loads have a factor of 1.4 for dead loads and 1.275 for pattern live loads.
For design, default design combos will automatically be created when you select
the design code from the preference menu. The default design combos depend on
the selected design code. The default combos are named as DCONx. To verify:
• From the Design menu, choose Select Design Combos... . This will show eight
default design combos for the selected ACI 318-95 code. In the dialog box:
– Click on DCON2
– Click on the Show button
– View the default factors for the default combo DCON2
– Click OK
62
Checking Load Combinations
Chapter V Quick Tutorial
Similarly, you can view the other load combinations if you want.
• Click Cancel to quit the Design Load Combinations Selection dialog box.
Starting Design
Before we design, the design code must be selected. We already selected the
“ACI 318-95” design code earlier in this tutorial.
Click on the Start Design button on the Design menu. After processing, the
slab reinforcement for the default design strips (X-strips in this case) is displayed.
Starting Design
63
SAFE User's Manual
Displaying Slab Reinforcement
As an example, we will display Y-strip slab reinforcement.
1. Click on the Display Slab Design Info... button on the Design menu. This will
display the Slab Reinforcing dialog box.
2. In this dialog box:
• Select Y Direction Strip in the Choose Strip Direction area.
• Click on the OK button.
64
Displaying Slab Reinforcement
Chapter V Quick Tutorial
The reinforcement in the Y direction for the entire slab is displayed.
Note: Results can also be displayed or printed in a tabulated form by choosing
Show Design Tables... from the Design menu or Print Design Tables... from the
File menu.
Displaying Slab Reinforcement
65
SAFE User's Manual
Displaying Punching Shear Ratios
Click on the Display Punching Shear Ratios button on the Design menu. The
punching shear capacity ratios for all the columns and point loads for the entire
slab are displayed.
Saving the Model
The model can be saved and retrieved for future use. There are two options to save a
model: Save saves the model with the existing name, and Save as saves the model
with a new name. To save the model:
• Click on the Save button in the File menu.
Printing Graphics
The graphics in the active window can be printed from SAFE. To print the display
in the active window, do this:
• Click on the Print Graphics button on the File menu. It will print the graphics
with the default printer.
As an alternative, you can preview the graphics before printing by selecting Print
Graphics Preview button in the File menu.
66
Displaying Punching Shear Ratios
Chapter V Quick Tutorial
Displaying Output Tables
After the analysis is complete, the results can be displayed in SAFE. To display do
this:
• Click on the Show Output Tables... button on the Display menu. It will pop up
the Output Tables dialog box. In this dialog box:
– Check Displacements
– Check Reactions
– Check Integrated Strip Moments and Shears
– Check Slab Element Moments and Shears
– Click on the Select Loads button. It will pop up a Select Output dialog box.
In this dialog box all the load cases are already selected. Click OK to accept the selections
– Click OK to allow the program to generate the output tables.
After a short pause, a display window pops up with the output quantities tabulated in spreadsheet format. In this window:
– You can display: Displacements, Column Reactions, Soil Pressures, X
Strip Forces, Y Strip Forces, or Slab Forces, selectively.
– You can scroll vertically or horizontally to view desired results.
– Click OK to quit this display window.
Displaying Output Tables
67
SAFE User's Manual
Alternatively, you can print and save the output tables from the File menu. This will
be described later.
Displaying Design Tables
After the design is complete, the design output can be displayed in SAFE. To display do this:
• Click on the Show Design Tables... button on the Design menu. It will pop up
the Design Tables dialog box. In this dialog box:
– Check Slab Strip Reinforcing
– Check Punching Shear
– Check Slab Strip
– Click OK to allow the program to generate the design tables.
68
Displaying Design Tables
Chapter V Quick Tutorial
After a short pause, a display window pops up with the design output quantities
tabulated in spreadsheet format. In this window:
– You can display: X Strip Rebar, Y Strip Rebar, Punching Shear, X Strip
Moments, or Y Strip Moments, selectively.
– You can scroll vertically or horizontally to view desired results.
– Click OK to quit this display window.
Displaying Design Tables
69
SAFE User's Manual
Alternatively, you can print and save the design tables from the File menu. This will
be described next.
Printing/Saving Output Tables
After the analysis is complete, the results can be sent immediately to the printer or
saved to a text file which can be printed later.
Note: Even a small problem can generate large quantities of output, especially if
all nodes and elements and all load cases are included. Note that if no items are selected in the active screen, all items are considered to be selected for output purposes. To print output for specific nodes or elements, select those for which output
is desired.
• Click on the Print Output Tables... button on the File menu.
– When the Output Tables dialog box pops up, check the output types to be
printed. The choices are shown in the screen on this page
– Check Print to File to save the output in a file instead of sending it directly
to the printer. Other options are Selection Only, Envelopes Only and Append (to an existing output file)
– Click on the Select Loads button in this dialog box to choose among the
Load Cases
– Click OK to allow the program to print/save the output tables.
70
Printing/Saving Output Tables
Chapter V Quick Tutorial
Alternatively, you can display the output tables from the Display menu. This has
already been described earlier.
Printing/Saving Design Tables
After the design is complete, the design output can be displayed in SAFE. To display do this:
• Click on the Print Design Tables... button on the File menu. It will pop up the
Design Tables dialog box. In this dialog box:
– Check Slab Strip Reinforcing
– Check Punching Shear
– Check Print to File if you want the design tables to be saved in a file. In
this case you can provide a destination filename. Do not check on the Print
to File if you want to print the design tables with the default printer
– Check Append to add to the existing text file
– Click OK to allow the program to generate the design tables
Alternatively, you can display the design tables from the Design menu. This was
already described earlier.
Printing/Saving Design Tables
71
SAFE User's Manual
Modifying the Structure
Suppose we want to modify the slab to have an opening in the top-left corner panel
and a cantilever extension to the slab at the right. We will also add two beams connecting the columns near the new opening. The final configuration is expected to
look like the following:
Currently, the model is locked to prevent any changes that would invalidate the
analysis and design results we have just obtained. We must first unlock the model,
make the desired changes, re-analyze, and finally re-design.
Unlocking the Model
1. Click on the Lock/Unlock Model button on the Main Toolbar to unlock the
model.
2. You will be warned that unlocking the model will delete analysis results. Click
on OK to acknowledge this.
Adding Slab Geometry
For illustration purposes, we will add the new slab elements first.
1. Click on the Draw Rectangular Area Object on the Side Toolbar.
72
Modifying the Structure
Chapter V Quick Tutorial
2. Turn the snap option ON for the Snap to Middle and Ends from the Side
Toolbar.
3. Click on the existing slab edge of the model where you want to put a corner of
the extension, i.e. at the top-right corner of the slab edge.
4. Move the pointer diagonally to the opposite end of the extension. A rubber
band will show the extent of the rectangle. Move the cursor until it creates a
cantilevered slab on the entire right edge.
5. Release the mouse button and double click. The rectangular area is drawn.
6. Click on the Pointer Button on the Side Toolbar to end the DRAW mode and
to start the SELECTION mode.
If you make any mistakes in drawing the rectangular area, you can select the area
and delete it by using the delete button on the keyboard. Then you can redraw it.
Assuming you drew the rectangle correctly, we now need to select the rectangle,
adjust the coordinates, and assign it to a predefined slab property.
Adjusting the Coordinate
You can adjust the coordinate of any corner. The newly added cantilever extension
of the slab started exactly on the corner because of the snapping option. The bottom
edge was placed close to the bottom-right corner of the original slab. For accurate
placement of the corner, you need to see and modify, if necessary, the coordinates
of the lower two points. To do this:
Modifying the Structure
73
SAFE User's Manual
1. Turn the snap option ON for Snap to Lines and Edges.
2. Place the cursor at the bottom horizontal edge of the slab. Observe the Ycoordinate of the points on this line. It is −300.
3. Right click in the middle of the extension slab. This will pop up a dialog box
Slab Information.
4. In this dialog box, modify Xmax and Ymin, the X and Y coordinates of the corner point, to 400 and −300, respectively, for accurate layout. Click OK.
The slab with cantilever extension now looks like the following.
74
Modifying the Structure
Chapter V Quick Tutorial
Assigning Slab Property
1. Click inside the newly drawn rectangle to select it.
2. Click on the Assign menu and select Slab Properties.... This will display a
Slab Properties dialog box.
3. Select SLAB and click OK.
Modifying the Structure
75
SAFE User's Manual
The response of the program is shown as follows.
Defining Beam Properties
We want to define a new beam property BEAM.
1. From the Define menu, choose Beam Properties.... This will display the Beam
Properties dialog box.
2. In this dialog box:
• Click on the drop-down list of different types of beams. Select Add Rectangular Beam. A new beam property BEAM1 is created and a new dialog
box is displayed to modify the beam property.
• In this dialog box:
– Change the name at the top-right corner from BEAM1 to BEAM.
– Change the width to 10 and depth to 18 in both Analysis Property Data
and Design Property Data
– Accept the other default data.
– Click on the OK button.
76
Modifying the Structure
Chapter V Quick Tutorial
3. Click on the OK button to accept the beam properties and end the definition
process.
Note: We can add additional properties, delete old properties, and edit existing
properties in this dialog box if it is necessary.
Assigning Beam Properties
In this step we will add the edge beams and assign the beam property defined previously to the outside edges of the top-left corner panel connecting the columns in the
floor system. First we will draw two edge beams as line objects. Then we will select
them and assign BEAM to both of them. To do this:
1. Draw line objects along the beam lines. To do this:
• Click the Quick Draw Line Object button on the Side Toolbar. SAFE is
now in the Draw mode.
• Move the pointer to the gridline along the edge beam and click the left
mouse button. This will create a line object on a segment.
• Similarly, point and click on the other segment to complete drawing the
two edge beam line objects.
2. Select the line objects along the beam lines. To do this:
Modifying the Structure
77
SAFE User's Manual
• Click on the Pointer tool button on the Side Toolbar to switch to the
SELECTION mode from the DRAW mode.
Note: Clicking on the Pointer tool button on the Side Toolbar will get
SAFE into the selection mode. If the pointer tool is already selected then it
is in the SELECTION mode and you do not need to click it. SAFE is usually
in the SELECTION mode.
• Move the pointer to one of the two line objects you have just drawn.
• Click on the line object. The line is now dotted to identify itself as a selected line object.
If you do not place the cursor close enough to the beam, your click will be
on the slab and the slab will get selected. If you make this mistake, click on
the slab again to de-select it.
• Similarly, click on the other line object along the beam lines. Both line objects along the beam lines should now be selected.
3. Assign beam property, BEAM, to the selected line objects. To do this:
• From Assign menu, choose Beam Properties.... This will display the
Beam Properties dialog box. This offers the option to assign beam properties for the selected line objects.
• Click on BEAM to choose it for the edge beams. BEAM will get highlighted.
78
Modifying the Structure
Chapter V Quick Tutorial
If BEAM is already highlighted, BEAM does not need to be clicked. But it
will do no harm to click it again.
• Click OK to complete the assignment.
The display window in which the selection process was done is refreshed and the
beam labels are displayed on all selected beam segments. The screen will now show
assignments of all the beam properties.
Deleting Drop-Panels
We have nine drop panels. Since we added two edge-beams, we no longer need a
drop-panel at the top-left corner. We need to delete this drop-panel. To do this we
will select the drop-panel and delete it with the delete key.
1. Select the corner drop-panel. To do this:
• Turn OFF all the snap options
• Move the pointer to the center of the corner drop-panel
• Hold down the control key and click on the drop-panel. This will pop up a
selection list indicating the area objects below the clicked point. Select the
Area DROP7. The selected region is identified by a small dotted rectangle.
2. Now, to delete the selected drop-panel, press the delete key on the key board.
Modifying the Structure
79
SAFE User's Manual
Adding an Opening
Now we need to draw a rectangle, select it, and assign it as an opening.
1. Turn ON the snap options for Snap to Points and Snap to Lines and Edges.
2. Draw a rectangular object as an opening area in the corner of the top-left bay by
using Draw Rectangular Area Object on the Side Toolbar as done before for
the extension.
3. Select the rectangle by changing to the Selection mode and using the pointing
and clicking as done before for the extension.
4. Adjust the Xmin to -288, Xmax to -96, Ymin to 192, and Ymax to 288 for the
most recently drawn rectangle by using right click.
80
Modifying the Structure
Chapter V Quick Tutorial
5. Select Opening from the Assign menu.
The opening is shown, labeled OPENING.
Assigning Surface Loads
Dead and live loads are to be applied as surface load to the cantilever extension part
of the slab. The magnitudes of superimposed dead and live surface loads are taken
to be 20 psf and 80 psf, respectively. Since the current setting of the units are kip
and inch, we need to change the units to lb-ft to facilitate the input process.
1. Change the units from “Kip-in” to “lb-ft” from the drop-down list at the
bottom-right corner of the window.
2. If any selections are showing then click on the Clear Selection button to clear
all the previous selections.
3. Select the cantilever part of the slab by “pointing and clicking”.
4. From the Assign menu, choose Surface Loads.... This will display the Surface
Loads dialog box.
5. In this dialog box:
• Accept the default load case name as DEAD.
• Enter 20 in the Load per Area box in the Loads area.
Modifying the Structure
81
SAFE User's Manual
• Click on the Replace existing loads in the Options area.
• Click on the OK button.
This will create a surface load of 20 psf for the DEAD load case. The Replace existing loads option deletes the existing definition of the load of that kind for that region and for that load case and helps to create a load data base as a fresh start for
each load case. The Add to existing loads option will add the new load to any corresponding existing value.
This will show the surface load on the slab. The value of the surface load will also
be printed on it.
82
Modifying the Structure
Chapter V Quick Tutorial
To assign LIVE load, we need to select the slab again and then assign the load. We
will now enter the live load.
6. Draw the undeformed shape by clicking on the Show Undeformed Shape button on the Main Toolbar.
7. Click on the Restore Previous Selection button from the Toolbar. This will
re-select the slab again.
8. From the Assign menu, choose Surface Loads... . This will again display the
Surface Loads dialog box.
9. In this dialog box:
• Change the load case name to LIVE from the drop-down list.
• Enter 80 in the Load per Area box in the Loads area.
• Click on the Replace existing loads in the Options area.
• Click the OK button.
If you would like to add additional loads for the pattern load cases, you can do that
similarly.
Modifying the Structure
83
SAFE User's Manual
Assigning Line Loads
Suppose we want to add a line load of a magnitude 2 kips per foot as dead load and 1
kip per foot as live load along the right edge at the right side of the opening as a representative load for a stair.
1. Change the units from “lb-ft” to “Kip-ft” from the drop-down list at the
bottom-right corner of the window.
2. Click on the Show Undeformed Shape button on the Main Toolbar.
3. Draw a line object at the end of the stair at the right side of the opening.
– Click on the Draw Line Object button on the Side Toolbar
– Click on the top-right corner point of the opening
– Move the cursor to the bottom-right corner of the opening
– Double click
4. Go to the SELECTION mode by clicking on the Pointer Tool and select the
line object by “pointing and clicking.”
5. From the Assign menu, choose Line Loads.... This will display the Line Loads
dialog box.
6. In this dialog box:
• Accept the default load case name as DEAD.
• Enter 2 in the Load box in the Loads area.
• Click on the Add to existing loads in the Options area.
• Click on the OK button.
This will show the line load on the beam.
84
Modifying the Structure
Chapter V Quick Tutorial
Similarly, add a 1 kip/ft line load to the LIVE load case.
7. Change the units from “Kip-ft” to “Kip-in” from the drop-down list at the
bottom-right corner of the window.
Modifying the X-Strip Definition
The slab has been extended. The strips definitions are still the default ones. The default definitions can still be used for designing the old parts of the slab. However, to
include the cantilever extension of the slab in the already defined strips, the strip
definitions have to be modified. In this tutorial, we will modify the X-strip definitions and add one extra strip for the Y direction.
• Click on the Set X-Strip in the View menu.
• Create a gridline D parallel to the gridline C
– Double click on the gridline C. This will pop up a dialog box. In this dialog
box,
– Add a new Grid with name D and with location 400.
– Click OK to create the new gridline.
• Reshape the existing definitions of the X-Strip rectangular areas. To do this:
– Click on the Reshaper button on the Side Toolbar.
– Click on the top Strip defined by the rectangle to select it. This will highlight the rectangle and will show four nodes which can be moved.
Modifying the Structure
85
SAFE User's Manual
– Click on the node at the right side of the rectangle
– Hold down the mouse button and move the edge to the gridline D
– The point will snap to the gridline and the strip is redefined
Similarly, resize the other X-strips accordingly. The final strip definitions are
shown as follows:
• Click on the Set Y-Strip in the View menu.
• Create one more Y-Strip for the cantilever part of the slab. To do this:
– Click on the Draw Rectangular Area Object Button
– Place the cursor on the top-left corner of the cantilever slab
– Click once
– Move the cursor to the bottom-right corner of the cantilever part of the slab
– Double click. The rectangular strip object is created
– Click on the Pointer button to return to the SELECTION mode
Re-analyzing the Model
Now, the model is complete. At this point you may want to consider re-analyzing
and re-designing the slab system again. Also, the model should be saved preferably
with a different name for future use.
86
Modifying the Structure
Chapter V Quick Tutorial
• Save the filename as Tutor1.FDB by clicking on the Save File As... button in
the File menu.
• Select Run Analysis from the Analyze menu.
• Click OK when finished.
• Click on the 3D View button on the Main Toolbar.
Starting Design
Since we have modified and re-analyzed the model, we need to re-design the
slab system. This time, there are beams which are also designed.
Before we design, the design code must be selected. We already selected the
“ACI 318-95” design code earlier in this tutorial.
Click on the Start Design button on the Design menu. After processing, the
slab reinforcement for the default design strips (X-strips in this case) is displayed.
Modifying the Structure
87
SAFE User's Manual
After re-designing, we can display the design output as before. We will only display
the beam design results, because it was not displayed earlier.
Displaying Beam Forces
As an example, we will plot the moment diagram for load case DEAD.
1. Click on the Show Beam Forces... button on the Display menu. This will display the Beam Forces dialog box.
88
Modifying the Structure
Chapter V Quick Tutorial
You can also do the same thing by clicking on the Show Beam Forces button
on the Main Toolbar.
2. In this dialog box:
• Select DEAD Load Case in the Load area.
• Select Moment in the Component area.
• Click on the OK button.
The moment diagrams for all the beams are displayed.
Modifying the Structure
89
SAFE User's Manual
Note 1: Beam shear forces or torsion can be selected for display in a similar manner.
Note 2: Results can also be displayed or printed in a tabulated form by choosing
Show Output Tables... from the Display menu or Print Output Tables... from the
File menu.
Displaying Beam Reinforcement
The beam reinforcement can be displayed once the beams are designed.
• Click on the Display Beam Design Info... button on the Design menu. This
will display the Beam Reinforcing dialog box. In this dialog box:
– Select Flexural Reinforcing
– Click OK
90
Modifying the Structure
Chapter V Quick Tutorial
The reinforcement is displayed as follows.
Saving the Model
The model can be saved and retrieved for future use. To save the model:
• Click on the Save button on the File menu.
Modifying the Structure
91
SAFE User's Manual
Concluding Remarks
This marks the end of the quick tour of SAFE. The intent has been to highlight and
demonstrate a few of the basic features. Feel free to experiment and explore other
options. Additional information is available within the Help menu.
92
Concluding Remarks
C h a p t e r VI
Program Output
Overview
SAFE creates output in two different formats  graphical and tabular. The graphical output can be either a screen display or in printed form. The tabular output can
similarly be displayed on screen as a spreadsheet, saved to a text file or printed.
The graphical output can be in either 2D or 3D views. In 2D (plan) views the program will report the value of the plotted result at a particular location as the mouse
cursor is moved over the display. In 3D views most plots can be shown on the deformed shape or can be shown extruded. Plots on deformed shapes can also be animated. Analysis output is available from the Display menu and the design output is
available from the Design menu.
The tabular output for display is available through the Show Output Tables and
Show Design Tables commands under the Display and Design menus, respectively. For printing and saving to text files the tabular output is available through
the Print Output Tables and Print Design Tables commands under the File menu.
Another type of tabular result is also available. This allows the user to export all
available input and output quantities to a database. This option is available through
the Access Database File command under the Export sub menu of the File Menu.
Tabulated output can produce huge amounts of data. The amount of tabular output
can be reduced by selecting the objects for which results are to be printed. If no objects are selected then the results for all objects are tabulated.
Overview
93
SAFE User's Manual
The analysis results are available for each load case or loading combination. The
graphical display commands ask you to pick a particular load case or combination
for which results are to be displayed. The tabular result commands allow you to select several load cases or combinations for which the tables are to be output. Optionally, you can request enveloping results to be printed. It should be noted that if a
nonlinear uplift analysis is requested it is only performed on loading combinations.
The load case results are from a linear analysis and may be meaningless.
All design is always developed for the loading combinations specified for design
but only the enveloping results are reported or displayed.
The following types of output are available:
• Displacements
• Reactions
• Integrated strip moments and shears
• Beam moments and shears
• Slab moments and shears
• Slab reinforcing
• Beam reinforcing
• Punching shear results
The following sections briefly describe the different outputs. Where a station location is given as a length along a line object it should be noted that the positive direction of a line is along the positive X axis, except if the line is parallel to the Y axis it
is along the positive Y axis.
Displacements
Displacement results can be viewed as displacement contours and/or as deformed
shapes. If a cracked section analysis was requested then the results for that analysis
can also be displayed. When deformed shapes are plotted a wire frame plot of the
undeformed shape can be superimposed. Exaggeration scale for the deformations
can be specified. The plots can also be animated.
The tabular results for displacements include a point label, a point location identified with mesh numbers (I in the X-direction and J in the Y-direction), the load case
or combination label, the displacement (UZ) and rotations (RX and RY) and if a
cracked analysis was requested then the cracked displacement (UZ). Positive displacements are along the positive direction of the axes using the right hand rule.
94
Displacements
Chapter VI Program Output
Reactions
Column reactions (forces and moments) are displayed as vectorial lines with numerical values at the column locations. Total wall reactions are shown in a similar
manner at the center of the length of the wall. Soil reactions are displayed as bearing
pressure contours and can be plotted on the deformed shape or, alternatively, the
bearing pressures can be extruded.
The tabular results for column reactions include a column (point) label, a column
location identified with mesh numbers (I and J), the load case or combination label,
vertical reaction (F ) and moments (M and M ). Positive reactions are along the
positive direction of the axes using the right hand rule.
z
x
y
The tabular results for wall reactions include a wall (line) label, a wall location
identified with the mesh numbers (I and J of the start and end of the wall), the load
case or combination label, total vertical reaction (F ), and total moments (M and
M ) about the center of the wall. Positive reactions are along the positive direction
of the axes using the right hand rule.
z
x
y
The tabular results for soil reactions include a soil (area) label, a location identified
with the mesh numbers (I and J), the load case or combination label, and vertical
bearing pressure. Positive bearing pressures are compressive.
Integrated Strip Moments and Shears
Integrated moments and shears for each design strip are displayed as bending moment and shear force diagrams along the center of the strip. X-strip results and Ystrip results are shown separately. Numerical values can be shown on the diagrams.
The tabular results for integrated strip moments and shears include the strip label,
the strip width, the load case or combination label, the station location ordinate, the
moment to the left of the station, the shear to the left of the station, the moment to
the right of the station and the shear to the right of the station. Positive moments
produce compression on the top of the slab.
Beam Moments and Shears
Beam moments, shears and torque for each beam are displayed as bending moment
and shear force and torque diagrams along the beam. Results for all beams are
shown together. Numerical values can be shown on the diagrams.
Reactions
95
SAFE User's Manual
The tabular results for beam forces include the beam label, the load case or combination label, and for each end of the beam analysis element, the station location
along the full beam, the shear force, torque and bending moment. Positive moments
produce compression on the top of the beam.
Slab Moments and Shears
Slab resultant moments and shears in per unit length units are displayed as slab
contours. Displays are available for moments producing x-stresses (M ), moments
producing y-stresses (M ), twisting moments (M ), principal moments (M
and M ), shear forces on the x-face (V ), shear forces on the y-face (V ) and the
maximum shear force (V ). For contour plots, the values are interpolated within
the element between their corresponding nodal values. The nodal values can be
from the individual element or can be the average over the elements meeting at that
joint. In general the average values should be used. However, where the averaging
happens over a discontinuity, like a support point, the average values may be meaningless. The user is allowed control over how the averaging is done and selective
averaging is possible.
xx
yy
xy
min
max
xx
yy
max
The tabular results for slab resultant moments and shear include the slab label, the
location of the slab analysis element given as mesh numbers (I and J), the load case
or combination label, the element node number (1 to 4), moments producing xstresses (M ), moments producing y-stresses (M ), twisting moments (M ),
shear forces on the x-face (V ) and shear forces on the y-face (V ). Positive moments produce compression on the top of the slab.
xx
yy
xx
xy
yy
Slab Reinforcing
Required slab reinforcement for each design strip is displayed in reinforcement diagrams along the center of the strip. X-strip results and Y-strip results are shown
separately. Required top and bottom reinforcement in either total area required or
as number of bars of a user chosen size are displayed. Optionally, only the amount
of reinforcement required over a user specified value can be displayed. Numerical
values of required reinforcement can be displayed at every design station or at controlling points along the strip length. The extent of required reinforcement can be
shown. This does not currently include any allowance for development lengths, etc.
Whether the required slab reinforcing satisfies the code minimums is dependent on
the user-controlled setting of this option.
The tabular results for slab reinforcing include the strip label, the strip width, the
station location ordinate, the top rebar required to the left of the station, the top re-
96
Slab Moments and Shears
Chapter VI Program Output
bar required to the right of the station, the bottom rebar required to the left of the station and the bottom rebar required to the right of the station. All results are total rebar areas for the strip width. A blank indicates no required rebar. Again, development length, etc., are not considered. The satisfaction of the minimum code required reinforcement is dependent on the user-controlled setting.
One other type of tabulated output is available for slab flexural design. Instead of
printing the required reinforcement the user can request the printing of the controlling design bending moments in the strip.
Beam Reinforcing
Required beam flexural and shear reinforcement for each beam is displayed in reinforcement diagrams along the beam. Flexural and shear reinforcement are shown
separately. Required top and bottom flexural reinforcement is displayed as total
area required. The required shear reinforcement is shown as area required per unit
length of beam (sq-in/ft, sq-cm/m or sq-mm/m units). Numerical values of required
reinforcement can be displayed at every design station or at controlling points along
the beam length. The extent of required reinforcement can be shown. This does not
currently include any allowance for development lengths, etc. Whether the required
beam reinforcing satisfies the code minimums is dependent on the user-controlled
setting of this option.
The tabular results for beam reinforcing include the beam label, the station location
along the length of the beam, the top rebar required to the left of the station, the top
rebar required to the right of the station, the bottom rebar required to the left of the
station, the bottom rebar required to the right of the station, the shear rebar required
to the left of the station, and the shear rebar required to the right of the station. Flexural results are total rebar areas for the beam, shear results are area required per unit
length of beam. A blank indicates no required rebar. Again, development length,
etc., are not considered. The satisfaction of the minimum code required reinforcement is dependent on the user controlled setting. It is noted again that currently no
design is done for the torque in the beam.
One other type of tabulated output is available for beam flexural and shear design.
Instead of printing the required reinforcement the user can request the printing of
the controlling design bending moments and shears in the beam.
Beam Reinforcing
97
SAFE User's Manual
Punching Shear Results
Punching shear results are displayed as a ratio of maximum calculated shear with
respect to capacity. A ratio above 1.0 would indicate capacity was exceeded somewhere along the critical section. The ratio is displayed for each column and each
point load. A notation of N/C means the value was not calculated by the program.
The tabular results for punching shear include the identification of the location by a
column or point load label, the calculated capacity ratio, the governing load combination, the maximum calculated shear stress, the shear stress capacity, the transferred shear and moments about the x- and y-axes, the slab effective depth, the perimeter of the critical section, and the program-assumed location of the column or
load.
98
Punching Shear Results
Appendix A
Design for ACI 318-95
This Appendix describes in detail the various aspects of the concrete design procedure that is used by SAFE when the user selects the American code ACI 318-95
(ACI 1995). Various notations used in this Appendix are listed in Table A-1. For
referencing to the pertinent sections of the ACI code in this Appendix, a prefix
“ACI” followed by the section number is used here.
The design is based on user-specified loading combinations. But the program provides a set of default load combinations that should satisfy requirements for the design of most building type structures.
English as well as SI and MKS metric units can be used for input. But the code is
based on Inch-Pound-Second units. For simplicity, all equations and descriptions
presented in this Appendix correspond to Inch-Pound-Second units unless otherwise noted.
Design Load Combinations
The design load combinations are the various combinations of the prescribed load
cases for which the structure needs to be checked. For this code, if a structure is subjected to dead load (DL), live load (LL), pattern live load (PLL), wind (WL), and
earthquake (EL) loads, and considering that wind and earthquake forces are reversible, then the following load combinations have to be considered (ACI 9.2).
Design Load Combinations
99
SAFE User's Manual
A
A
A′
Gross area of concrete, sq-in
Area of tension reinforcement, sq-in
Area of compression reinforcement, sq-in
g
s
s
A
A
A s
a
a
a
b
b
b
b
b
b
s ( required
v
v
b
max
f
w
0
1
2
c
c
d
d′
d
E
E
b
s
c
s
f
′
c
f
f
h
M
P
s
y
ys
u
u
)
Area of steel required for tension reinforcement, sq-in
Area of shear reinforcement, sq-in
Area of shear reinforcement per unit length of the member, sq-in/in
Depth of compression block, in
Depth of compression block at balanced condition, in
Maximum allowed depth of compression block, in
Width of member, in
Effective width of flange (T-Beam section), in
Width of web (T-Beam section), in
Perimeter of the punching critical section, in
Width of the punching critical section in the direction of bending, in
Width of the punching critical section perpendicular to the direction of
bending, in
Depth to neutral axis, in
Depth to neutral axis at balanced conditions, in
Distance from compression face to tension reinforcement, in
Concrete cover to center of reinforcing, in
Thickness of slab (T-Beam section), in
Modulus of elasticity of concrete, psi
Modulus of elasticity of reinforcement, assumed as 29,000,000 psi
(ACI 8.5.2)
Specified compressive strength of concrete, psi
Specified yield strength of flexural reinforcement, psi
Specified yield strength of shear reinforcement, psi
Overall depth of a section, in
Factored moment at section, lb-in
Factored axial load at section, lb
Spacing of the shear reinforcement along the length of the beam, in
Table A-1
List of Symbols Used in the ACI code
100
Design Load Combinations
Appendix A Design for ACI 318-95
V
V
V
V
β
β
c
max
u
s
ε
ε
ϕ
γ
γ
1
c
c
s
f
v
Shear force resisted by concrete, lb
Maximum permitted total factored shear force at a section, lb
Factored shear force at a section, lb
Shear force resisted by steel, lb
Factor for obtaining depth of compression block in concrete
Ratio of the maximum to the minimum dimensions of the punching
critical section
Strain in concrete
Strain in reinforcing steel
Strength reduction factor
Fraction of unbalanced moment transferred by flexure
Fraction of unbalanced moment transferred by eccentricity of shear
Table A-1
List of Symbols Used in the ACI code
Design Load Combinations
101
SAFE User's Manual
1.4 DL
1.4 DL + 1.7 LL
1.4 DL + 1.7 * 0.75 PLL
(ACI 9.2.1)
(ACI 13.7.6.3)
0.9 DL ± 1.3 WL
0.75 (1.4 DL + 1.7 LL ± 1.7 WL)
(ACI 9.2.2)
0.9 DL ± 1.3 * 1.1 EL
0.75 (1.4 DL + 1.7 LL ± 1.7 * 1.1 EL)
(ACI 9.2.3)
These are also the default design load combinations in SAFE whenever the ACI
318-95 code is used. The user should use other appropriate loading combinations if
roof live load is separately treated, or other types of loads are present.
Strength Reduction Factors
The strength reduction factors, ϕ, are applied on the specified strength to obtain the
design strength provided by a member. The ϕ factors for flexure and shear are as
follows:
ϕ = 0.90 for flexure and
(ACI 9.3.2.1)
ϕ = 0.85 for shear.
(ACI 9.3.2.3)
The user is allowed to overwrite these values. However, caution is advised.
Beam Design
In the design of concrete beams, SAFE calculates and reports the required areas of
steel for flexure and shear based upon the beam moments, shear forces, load combination factors, and other criteria described below. The reinforcement requirements
are calculated at the ends of the beam elements.
All beams are only designed for major direction flexure and shear. Effects due to
any axial forces, minor direction bending, and torsion that may exist in the beams
must be investigated independently by the user.
The beam design procedure involves the following steps:
• Design flexural reinforcement
• Design shear reinforcement
102
Strength Reduction Factors
Appendix A Design for ACI 318-95
Design Flexural Reinforcement
The beam top and bottom flexural steel is designed at the two stations at the ends of
the beam elements. In designing the flexural reinforcement for the major moment
of a particular beam for a particular station, the following steps are involved:
• Determine factored moments
• Determine required flexural reinforcement
Determine Factored Moments
In the design of flexural reinforcement of concrete beams, the factored moments for
each load combination at a particular beam section are obtained by factoring the
corresponding moments for different load cases with the corresponding load factors.
The beam section is then designed for the maximum positive and maximum negative factored moments obtained from all of the load combinations. Positive beam
moments produce bottom steel. In such cases the beam may be designed as a Rectangular- or a T-beam. Negative beam moments produce top steel. In such cases the
beam is always designed as a rectangular section.
Determine Required Flexural Reinforcement
In the flexural reinforcement design process, the program calculates both the tension and compression reinforcement. Compression reinforcement is added when
the applied design moment exceeds the maximum moment capacity of a singly reinforced section. The user has the option of avoiding the compression reinforcement by increasing the effective depth, the width, or the grade of concrete.
The design procedure is based on the simplified rectangular stress block as shown
in Figure A-1 (ACI 10.2). Furthermore it is assumed that the compression carried
by concrete is less than 0.75 times that which can be carried at the balanced condition (ACI 10.3.3). When the applied moment exceeds the moment capacity at this
design balanced condition, the area of compression reinforcement is calculated on
the assumption that the additional moment will be carried by compression and additional tension reinforcement.
The design procedure used by SAFE, for both rectangular and flanged sections (Land T-beams) is summarized below. It is assumed that the design ultimate axial
force does not exceed ϕ(0.1 f ′ A ) (ACI 10.3.3), hence all the beams are designed
c
g
for major direction flexure and shear only.
Beam Design
103
SAFE User's Manual
Design for Rectangular Beam
In designing for a factored negative or positive moment, M , (i.e. designing top or
bottom steel) the depth of the compression block is given by a (see Figure A-1),
where,
u
a= d−
d −
2 M
2
u
′
0.85 f ϕ b
,
(ACI 10.2)
c
where, the value of ϕ is 0.90 (ACI 9.3.2.1) in the above and the following equations.
Also β and c are calculated as follows:
1
b
 f ′ − 4000 
,
β = 0.85 − 0.05 
1000 

c
1
c =
b
87 000
87 000 + f
0.65 ≤ β ≤ 0.85,
1
d.
(ACI 10.2.7.3)
(ACI 10.2.2)
y
The maximum allowed depth of compression block is given by
a
max
• If a ≤ a
A =
s
= 0.75β c .
1
max
(ACI 10.3.3)
b
(ACI 10.3.3), the area of tensile steel reinforcement is then given by
M
.
a

ϕ f d − 
2

u
y
This steel is to be placed at the bottom if M is positive, or at the top if M is
negative.
u
u
• If a > a , compression reinforcement is required (ACI 10.3.3) and is calculated as follows:
max
– The compressive force developed in concrete alone is given by
C = 0.85 f ′ ba
c
max
, and
(ACI 10.2.7.1)
the moment resisted by concrete compression and tensile steel is
M
104
a 

 ϕ.
= C d −
2 

max
uc
Beam Design
Appendix A Design for ACI 318-95
– Therefore the moment resisted by compression steel and tensile steel is
M =M −M
us
u
.
uc
ε = 0.003
0.85f'c
b
Cs
d'
A's
1c
a=
c
d
εs
As
Beam Section
Ts
Strain Diagram
Tc
Stress Diagram
Figure A-1
Rectangular Beam Design
– So the required compression steel is given by
A′ =
s
M
us
′
( f − 0.85 f ′ )( d − d′ ) ϕ
s
, where
c
 c − d′ 
f ′ = 0.003 E 
≤f .
 c 
s
s
y
(ACI 10.2.2 and ACI 10.2.4)
– The required tensile steel for balancing the compression in concrete is
A =
s1
M
f (d −
y
uc
a
max
2
, and
)ϕ
Beam Design
105
SAFE User's Manual
the tensile steel for balancing the compression in steel is given by
M
.
f ( d − d′ )ϕ
A =
us
s2
y
– Therefore, the total tensile reinforcement, A = A + A , and total compression reinforcement is A ′ . A is to be placed at the bottom and A ′ is to be
placed at the top if M is positive, and vice versa if M is negative.
s
s
s1
s2
s
s
u
u
Design for T-Beam
(i) Flanged Beam Under Negative Moment
In designing for a factored negative moment, M , (i.e. designing top steel), the calculation of the steel area is exactly the same as above, i.e., no T-Beam data is to be
used.
u
(ii) Flanged Beam Under Positive Moment
If M > 0 , the depth of the compression block is given by
u
a= d−
2M
d −
2
u
,
′
0.85 f ϕ b
c
(ACI 10.2)
f
where, the value of ϕ is 0.90 (ACI 9.3.2.1) in the above and the following equations.
Also β and c are calculated as follows:
1
b
 f ′ − 4000 
,
β = 0.85 − 0.05 
1000 

c
1
c =
b
87 000
87 000 + f
d.
0.65 ≤ β ≤ 0.85 ,
1
(ACI 10.2.7.3)
(ACI 10.2.2)
y
The maximum depth of compression block under design balanced condition is
given by
a
106
max
= 0.75β c .
Beam Design
1
b
(ACI 10.3.3)
Appendix A Design for ACI 318-95
ε = 0.003
ds
bf
d'
fs'
0.85f'c
0.85f'c
Cs
As'
a=
Cf
1c
c
d
Cw
εs
As
Ts
Tf
Tw
bw
Beam Section
Strain Diagram
Stress Diagram
Figure A-2
T-Beam Design
• If a ≤ d , the subsequent calculations for A are exactly the same as previously
defined for the rectangular section design. However, in this case the width of
the beam is taken as b . Whether compression reinforcement is required depends on whether a > a .
s
s
f
max
• If a > d , calculation for A is done in two parts. The first part is for balancing
the compressive force from the flange, C , and the second part is for balancing
the compressive force from the web,C , as shown in Figure A-2.C is given by
s
s
f
w
C = 0.85 f ( b − b ) min(d a
′
f
c
Therefore, A =
s1
f
s,
w
C
f
f
y
max
f
).
and the portion of M that is resisted by the flange is
u
given by
M

min(d a
= C  d −
2

s,
uf
f
max
) 
ϕ.

Beam Design
107
SAFE User's Manual
Again, the value for ϕ is 0.90. Therefore, the balance of the moment, M to be
carried by the web is given by
u
M
uw
= M − M
u
.
uf
The web is a rectangular section of dimensions b and d, for which the design
depth of the compression block is recalculated as
w
a = d− d −
2M
2
1
uw
′
0.85 f ϕ b
c
• If a ≤ a
given by
1
.
(ACI 10.2)
w
(ACI 10.3.3), the area of tensile steel reinforcement is then
max
M
, and
a 


ϕ f d −
2 

A =
uw
s2
1
y
A =A +A .
s1
s
s2
This steel is to be placed at the bottom of the T-beam.
• If a > a , compression reinforcement is required (ACI 10.3.3) and is calculated as follows:
1
max
– The compressive force in the web concrete alone is given by
C = 0.85 f ′ b a
c
w
.
max
(ACI 10.2.7.1)
– Therefore the moment resisted by the concrete web and tensile steel is
M
a 

 ϕ , and
= C d −
2 

max
uc
the moment resisted by compression steel and tensile steel is
M =M
us
uw
−M
uc
.
– Therefore, the compression steel is computed as
A′ =
s
M
us
′
( f − 0.85 f ′ )( d − d′ ) ϕ
s
 c − d′ 
f ′ = 0.003 E 
≤f .
 c 
s
108
Beam Design
, where
c
s
y
(ACI 10.2.2 and ACI 10.2.4)
Appendix A Design for ACI 318-95
– The tensile steel for balancing compression in web concrete is
A =
s2
M
f (d −
uc
a
y
max
2
, and
)ϕ
the tensile steel for balancing compression in steel is
A =
s3
M
.
f ( d − d′ )ϕ
us
y
– The total tensile reinforcement, A = A + A + A , and total compression reinforcement is A ′ . A is to be placed at the bottom and A ′ is to be
placed at the top.
s
s
s1
s
s2
s3
s
Minimum and Maximum Tensile Reinforcement
The minimum flexural tensile steel required in a beam section is given by the minimum of the two following limits:
 3 f ′
A ≥ max
b d and
 f
c
s
w
y
A ≥
s
4
A
3
s ( required

200
b d  or
f

w
(ACI 10.5.1)
y
).
(ACI 10.5.3)
An upper limit of 0.04 times the gross web area on both the tension reinforcement
and the compression reinforcement is imposed upon request as follows:
 0.04 b d Rectangular beam
A ≤
 0.04 b d T -beam
s
w
 0.04 b d Rectangular beam
A′ ≤ 
 0.04 b d T -beam
s
w
Design Beam Shear Reinforcement
The shear reinforcement is designed for each load combination at two stations at the
ends of each beam element. In designing the shear reinforcement for a particular
beam for a particular loading combination at a particular station due to the beam
major shear, the following steps are involved:
Beam Design
109
SAFE User's Manual
• Determine the factored shear force,V .
u
• Determine the shear force,V , that can be resisted by the concrete.
c
• Determine the reinforcement steel required to carry the balance.
The following three sections describe in detail the algorithms associated with the
above-mentioned steps.
Determine Shear Force
In the design of the beam shear reinforcement of a concrete beam, the shear forces
for a particular load combination at a particular beam section are obtained by factoring the associated shear forces and moments with the corresponding load combination factors.
Determine Concrete Shear Capacity
The shear force carried by the concrete,V , is calculated as follows:
c
V = 2 f ′ b d.
c
c
(ACI 11.3.1.1)
w
A limit is imposed on the value of
f ′ as
c
f ′ ≤ 100 .
c
(ACI 11.1.2)
Determine Required Shear Reinforcement
• The shear force is limited to a maximum limit of
V
max
(
=V + 8 f
c
′
c
)b d.
(ACI 11.5.6.8)
w
• Given V ,V andV , the required shear reinforcement is calculated as follows
where, ϕ, the strength reduction factor, is 0.85 (ACI 9.3.2.3).
u
c
max
If V ≤ (V 2) ϕ ,
u
c
A
=0,
s
v
(ACI 11.5.5.1)
else if (V 2) ϕ < V ≤ (V + 50 b d ) ϕ ,
c
u
A 50 b
,
=
s
f
v
w
ys
110
Beam Design
c
w
(ACI 11.5.5.3)
Appendix A Design for ACI 318-95
else if (V + 50 b d ) ϕ < V ≤ ϕV
c
w
u
max
A
(V − ϕV )
,
=
s
ϕf d
v
u
c
,
(ACI 11.5.6.2)
ys
else if V > ϕV
u
max
,
a failure condition is declared.
(ACI 11.5.6.8)
The maximum of all the calculated A s values, obtained from each load combination, is reported along with the controlling shear force and associated load combination number.
v
The beam shear reinforcement requirements displayed by the program are based
purely upon shear strength considerations. Any minimum stirrup requirements to
satisfy spacing and volumetric considerations must be investigated independently
of the program by the user.
Slab Design
As is done in conventional design, the SAFE slab design procedure involves defining sets of strips in two mutually perpendicular directions. The locations of the
strips are usually governed by the locations of the slab supports. The moments for a
particular strip are recovered from the analysis and a flexural design is carried out
based on the ultimate strength design method (ACI 318-95) for reinforced concrete
as described in the following sections. To learn more about the design strips, refer
to the section “Integrated Strip Moments and Shears” on page 25.
Design for Flexure
SAFE designs the slab on a strip-by-strip basis. The moments used for the design of
the slab elements are the nodal reactive moments, which are obtained by multiplying the slab element stiffness matrices by the element nodal displacement vectors.
These moments will always be in static equilibrium with the applied loads, irrespective of the refinement of the finite element mesh.
The design of the slab reinforcement for a particular strip is carried out at specific
locations along the length of the strip. These locations correspond to the element
boundaries. Controlling reinforcement is computed on either side of these element
boundaries. The slab flexural design procedure for each load combination involves
the following:
Slab Design
111
SAFE User's Manual
• Determine factored moments for each slab strip.
• Design flexural reinforcement for the strip.
These two steps described below are repeated for every load combination. The
maximum reinforcement calculated for the top and bottom of the slab within each
design strip, along with the corresponding controlling load combination numbers,
is obtained and reported.
Determine Factored Moments for the Strip
For each element within the design strip, for each load combination the program
calculates the nodal reactive moments. The nodal moments are then added to get
the strip moments.
Design Flexural reinforcement for the Strip
The reinforcement computation for each slab design strip given the bending moment is identical to the design of rectangular beam sections described earlier.
Where the slab properties (depth, etc.) vary over the width of the strip the program
automatically designs slab widths of each property separately for the bending moment they are subjected to before summing up the reinforcement for the full width.
Where openings occur the slab width is adjusted accordingly.
Minimum and Maximum Slab Reinforcement
The minimum flexural tensile reinforcement required for each direction of a slab is
given by the following limits (ACI 7.12.2):
A ≥ 0.0018 bh
s
60 000
f
(ACI 7.12.2.1)
y
0.0014 bh ≤ A ≤ 0.0020 bh
s
(ACI 7.12.2.1)
In addition, an upper limit on both the tension reinforcement and compression reinforcement has been imposed to be 0.04 times the gross cross-sectional area.
Check for Punching Shear
The algorithm for checking punching shear is detailed in section “Checking Punching Shear Capacity” on page 26. Only the code specific items are described in the
following.
112
Slab Design
Appendix A Design for ACI 318-95
Critical Section for Punching Shear
The punching shear is checked on a critical section at a distance of d 2 from the face
of the support (ACI 11.12.1.2). For rectangular columns and concentrated loads,
the critical area is taken as a rectangular area with the sides parallel to the sides of
the columns or the point loads (ACI 11.12.1.3).
Transfer of Unbalanced Moment
The fraction of unbalanced moment transferred by flexure is taken to be γ M and
the fraction of unbalanced moment transferred by eccentricity of shear is taken to
be γ M , where
f
v
u
u
γ =
f
1
1 + ( 2 3) b b
1
, and
(ACI 13.5.3.2)
2
γ = 1− γ ,
v
(ACI 13.5.3.1)
f
where b is the width of the critical section measured in the direction of the span and
b is the width of the critical section measured in the direction perpendicular to the
span.
1
2
Determination of Concrete Capacity
The concrete punching shear stress capacity is taken as the minimum of the following three limits:
 
4 ′
 ϕ  2 +  f
β 
 
 
α d
 f
v = min  ϕ  2 +
b 
 
 ϕ4 f ′


c
c
s
c
′
(ACI 11.12.2.1)
c
0
c
where, β is the ratio of the minimum to the maximum dimensions of the critical
section, b is the perimeter of the critical section, and α is a scale factor based on
the location of the critical section.
c
0
 40

α =  30
 20

s
s
for interior columns,
for edge columns, and
for corner columns.
(ACI 11.12.2.1)
Slab Design
113
SAFE User's Manual
A limit is imposed on the value of
f ′ ≤ 100 .
c
f ′ as
c
(ACI 11.1.2)
Determination of Capacity Ratio
Given the punching shear force and the fractions of moments transferred by eccentricity of shear about the two axes, the shear stress is computed assuming linear
variation along the perimeter of the critical section. The ratio of the maximum shear
stress and the concrete punching shear stress capacity is reported by SAFE.
114
Slab Design
Appendix B
Design for CSA A23.3-94
This Appendix describes in detail the various aspects of the concrete design procedure that is used by SAFE when the user selects the Canadian code, CSA A23.3-94
(CSA 1994). Various notations used in this Appendix are listed in Table B-1. For
referencing to the pertinent sections of the Canadian code in this Appendix, a prefix
“CSA” followed by the section number is used here.
The design is based on user-specified loading combinations. But the program provides a set of default load combinations that should satisfy requirements for the design of most building type structures.
English as well as SI and MKS metric units can be used for input. But the code is
based on Newton-Millimeter-Second units. For simplicity, all equations and descriptions presented in this Appendix correspond to Newton-Millimeter-Second
units unless otherwise noted.
Design Load Combinations
The design load combinations are the various combinations of the prescribed load
cases for which the structure needs to be checked. For this code, if a structure is subjected to dead load (DL), live load (LL), pattern live load (PLL), wind (WL), and
earthquake (EL) loads, and considering that wind and earthquake forces are reversible, then the following load combinations may have to be considered (CSA 8.3):
Design Load Combinations
115
SAFE User's Manual
A
A′
Area of tension reinforcement, sq-mm
Area of compression reinforcement, sq-mm
s
s
A
A
A s
a
a
b
b
b
b
b
b
c
c
d
d′
d
E
E
f′
Area of steel required for tension reinforcement, sq-mm
Area of shear reinforcement, sq-mm
Area of shear reinforcement per unit length of the member, sq-mm/mm
Depth of compression block, mm
Depth of compression block at balanced condition, mm
Width of member, mm
Effective width of flange (T-Beam section), mm
Width of web (T-Beam section), mm
Perimeter of the punching critical section, mm
Width of the punching critical section in the direction of bending, mm
Width of the punching critical section perpendicular to the direction of
bending, mm
Depth to neutral axis, mm
Depth to neutral axis at balanced conditions, mm
Distance from compression face to tension reinforcement, mm
Concrete cover to center of reinforcing, mm
Thickness of slab (T-Beam section), mm
Modulus of elasticity of concrete, MPa
Modulus of elasticity of reinforcement, assumed as 200,000 MPa
Specified compressive strength of concrete, MPa
f
f
h
M
s
V
V
V
Specified yield strength of flexural reinforcement, MPa
Specified yield strength of shear reinforcement, MPa
Overall depth of a section, mm
Factored moment at section, N-mm
Spacing of the shear reinforcement along the length of the beam, in
Shear resisted by concrete, N
Maximum permitted total factored shear force at a section, lb
Factored shear force at a section, N
s ( required
v
v
b
f
w
0
1
2
b
s
c
s
c
y
ys
f
c
max
f
)
Table B-1
List of Symbols Used in the Canadian Code
116
Design Load Combinations
Appendix B Design for CSA A23.3-94
V
α
s
1
β
β
ε
ε
ϕ
ϕ
ϕ
γ
γ
λ
1
c
c
s
c
s
m
f
v
Shear force at a section resisted by steel, N
Ratio of average stress in rectangular stress block to the specified concrete strength
Factor for obtaining depth of compression block in concrete
Ratio of the maximum to the minimum dimensions of the punching
critical section
Strain in concrete
Strain in reinforcing steel
Strength reduction factor for concrete
Strength reduction factor for steel
Strength reduction factor for member
Fraction of unbalanced moment transferred by flexure
Fraction of unbalanced moment transferred by eccentricity of shear
Shear strength factor
Table B-1
List of Symbols Used in the Canadian code (continued)
Design Load Combinations
117
SAFE User's Manual
1.25 DL
1.25 DL + 1.50 LL
1.25 DL + 1.50 *0.75 PLL
(CSA 8.3.2)
(CSA 13.9.4.3)
1.25 DL ± 1.50 WL
0.85 DL ± 1.50 WL
1.25 DL + 0.7 (1.50 LL ± 1.50 WL)
(CSA 8.3.2)
1.00 DL ± 1.00 EL
1.00 DL + (0.50 LL ± 1.00 EL)
(CSA 8.3.2)
These are also the default design load combinations in SAFE whenever the CSA
A23.3-94 code is used. The user should use other appropriate loading combinations
if roof live load is separately treated, or other types of loads are present.
Strength Reduction Factors
The strength reduction factor, ϕ, is material dependent and is defined as
ϕ = 0.60 for concrete and
(CSA 8.4.2)
ϕ = 0.85 for steel.
(CSA 8.4.3)
c
s
The user is allowed to overwrite these values. However, caution is advised.
Beam Design
In the design of concrete beams, SAFE calculates and reports the required areas of
steel for flexure and shear based upon the beam moments, shear forces, load combination factors, and other criteria described below. The reinforcement requirements
are calculated at the end of the beam elements.
All the beams are only designed for major direction flexure and shear. Effects due
to any axial forces, minor direction bending, and torsion that may exist in the beams
must be investigated independently by the user.
The beam design procedure involves the following steps:
• Design beam flexural reinforcement
• Design beam shear reinforcement
118
Strength Reduction Factors
Appendix B Design for CSA A23.3-94
Design Beam Flexural Reinforcement
The beam top and bottom flexural steel is designed at the two stations at the ends of
the beam elements. In designing the flexural reinforcement for the major moment
of a particular beam for a particular station, the following steps are involved:
• Determine the maximum factored moments
• Determine the reinforcing steel
Determine Factored Moments
In the design of flexural reinforcement of concrete beams, the factored moments for
each load combination at a particular beam section are obtained by factoring the
corresponding moments for different load cases with the corresponding load factors.
The beam section is then designed for the maximum positive and maximum negative factored moments obtained from all of the load combinations. Positive beam
moments produce bottom steel. In such cases the beam may be designed as a Rectangular- or a T-beam. Negative beam moments produce top steel. In such cases the
beam is always designed as a rectangular section.
Determine Required Flexural Reinforcement
In the flexural reinforcement design process, the program calculates both the tension and compression reinforcement. Compression reinforcement is added when
the applied design moment exceeds the maximum moment capacity of a singly reinforced section. The user has the option of avoiding the compression reinforcement by increasing the effective depth, the width, or the grade of concrete.
The design procedure is based on the simplified rectangular stress block as shown
in Figure B-1 (CSA 10.1.7). Furthermore it is assumed that the compression carried
by concrete is less than or equal to that which can be carried at the balanced condition (CSA 10.1.4). When the applied moment exceeds the moment capacity at the
balanced condition, the area of compression reinforcement is calculated on the assumption that the additional moment will be carried by compression and additional
tension reinforcement.
In designing the beam flexural reinforcement, the following limits are imposed on
the steel tensile strength and the concrete compressive strength:
Beam Design
119
SAFE User's Manual
f ≤ 500 MPa
(CSA 8.5.1)
f ′ ≤ 80 MPa
(CSA 8.6.1.1)
y
c
The design procedure used by SAFE for both rectangular and flanged sections (Land T-beams) is summarized below. It is assumed that the design ultimate axial
force in a beam is negligible, hence all the beams are designed for major direction
flexure and shear only.
Design for Flexure of a Rectangular Beam
In designing for a factored negative or positive moment, M , (i.e. designing top or
bottom steel) the depth of the compression block is given by a as shown in Figure
B-1, where,
f
a= d−
d −
2 M
2
f
′
α f ϕ b
1
c
,
(CSA 10.1)
c
where the value of ϕ is 0.60 (CSA 9.4.2) in the above and following equations. See
Figure B-1. Also α , β , and c are calculated as follows:
c
1
1
b
α = 0.85 − 0.0015 f ′ ≥ 0.67 ,
(CSA 10.1.7)
β = 0.97 − 0.0025 f ′ ≥ 0.67 , and
(CSA 10.1.7)
1
c
1
c =
b
c
700
700 + f
d.
(CSA 10.5.2)
y
The balanced depth of compression block is given by
a =β c .
b
1
(CSA 10.1.7)
b
• If a ≤ a (CSA 10.5.2), the area of tensile steel reinforcement is then given by
b
A =
s
M
f
a

ϕ f d − 
2

s
.
y
This steel is to be placed at the bottom if M is positive, or at the top if M is
negative.
f
f
• If a > a (CSA 10.5.2), compression reinforcement is required and is calculated
as follows:
b
120
Beam Design
Appendix B Design for CSA A23.3-94
– The factored compressive force developed in concrete alone is given by
C = ϕ α f ′ ba , and
c
1
c
(CSA 10.1.7)
b
the factored moment resisted by concrete and bottom steel is
a 

M = C d −  .
2

b
fc
– The moment resisted by compression steel and tensile steel is
M =M −M
fs
f
.
fc
ε= 0.0035
α1 fc' φc
b
Cs
A's
d'
a=
c
1c
d
εs
As
Beam Section
Stress Diagram
Ts
Tc
Strain Diagram
Figure B-1
Design of a Rectangular Beam Section
– So the required compression steel is given by
A′ =
s
M
fs
′
(ϕ f − ϕ α f ′ )( d − d′ )
s
s
c
1
 c − d′ 
f ′ = 0.0035 E 
≤f .
 c 
s
s
, where
c
y
(CSA 10.1.2 and CSA 10.1.3)
Beam Design
121
SAFE User's Manual
– The required tensile steel for the balancing the compression in concrete is
A =
s1
M
fc
a
f (d − ) ϕ
2
, and
b
y
s
the tensile steel for balancing the compression in steel is
M
A =
fs
f ( d − d′ ) ϕ
s2
y
.
s
– Therefore, the total tensile reinforcement, A = A + A , and total compression reinforcement is A ′ . A is to be placed at the bottom and A ′ is to be
placed at the top if M is positive, and vice versa.
s
s
s1
s2
s
s
f
Design for Flexure of a T-Beam
(i) Flanged Beam Under Negative Moment
In designing for a factored negative moment, M , (i.e. designing top steel), the calculation of the steel area is exactly the same as above, i.e., no T-Beam data is to be
used.
f
(ii) Flanged Beam Under Positive Moment
If M > 0, the depth of the compression block is given by (see Figure B-2).
f
a= d−
d −
2M
2
f
.
′
α f ϕ b
1
c
c
(CSA 10.1)
f
where the value of ϕ is 0.60 (CSA 9.4.2) in the above and following equations. See
Figure B-2. Also α , β , and c are calculated as follows:
c
1
1
b
′
α = 0.85 − 0.0015 f ≥ 0.67 ,
(CSA 10.1.7)
β = 0.97 − 0.0025 f ′ ≥ 0.67 , and
(CSA 10.1.7)
1
c
1
c =
b
c
700
700 + f
d.
(CSA 10.5.2)
y
The depth of compression block under balanced condition is given by
a = βc .
b
122
1
Beam Design
b
(CSA 10.1.4)
Appendix B Design for CSA A23.3-94
ε = 0.0035
ds
bf
d'
α1 fc' φc
fs'
α1 fc' φc
Cs
As'
Cf
c
d
Cw
εs
As
Ts
Tf
Tw
bw
Beam Section
Strain Diagram
Stress Diagram
Figure B-2
Design of a T-Beam Section
• If a ≤ d , the subsequent calculations for A are exactly the same as previously
done for the rectangular section design. However, in this case the width of the
beam is taken as b . Whether compression reinforcement is required depends
on whether a > a .
s
s
f
b
• If a > d , calculation for A is done in two parts. The first part is for balancing
the compressive force from the flange, C , and the second part is for balancing
the compressive force from the web, C . As shown in Figure B-2,
s
s
f
w
C = α f ′ ( b − b ) min( d , a
1
f
c
f
Therefore, A =
s1
w
s
C ϕ
c
f ϕ
s
f
y
max
).
(CSA 10.1.7)
and the portion of M that is resisted by the flange is
f
given by
M
min( d , a

= C d−
2

s
ff
f
max
)
ϕ .

c
Beam Design
123
SAFE User's Manual
Therefore, the balance of the moment, M to be carried by the web is given by
f
M
fw
= M − M .
f
ff
The web is a rectangular section of dimensions b and d, for which the depth of
the compression block is recalculated as
w
a = d−
2M
d −
2
1
α f ϕ b
1
• If a ≤ a
given by
1
c
fw
a 


ϕ f d −
2 

s2
c
.
(CSA 10.1)
w
(CSA 10.5.2), the area of tensile steel reinforcement is then
b
M
A =
fw
′
, and
1
s
y
A = A +A .
s1
s
s2
This steel is to be placed at the bottom of the T-beam.
• If a > a (CSA 10.5.2), compression reinforcement is required and is calculated as follows:
1
b
– The compressive force in the concrete web alone is given by
C = α f ′ b a , and
1
c
w
(CSA 10.1.7)
b
the moment resisted by the concrete web and tensile steel is
a 

M = C d −  ϕ .
2

b
fc
c
– The moment resisted by compression steel and tensile steel is
M = M
fs
fw
−M
fc
.
– Therefore, the compression steel is computed as
A′ =
s
M
fs
′
( ϕ f − ϕ α f ′ )( d − d′ )
s
s
c
1
 c − d′ 
f ′ = 0.0035 E 
≤f .
 c 
s
124
Beam Design
s
, where
c
y
(CSA 10.1.2 and CSA 10.1.3)
Appendix B Design for CSA A23.3-94
– The tensile steel for balancing compression in web concrete is
A =
s2
M
fc
a
f (d − ) ϕ
2
, and
b
y
s
the tensile steel for balancing compression in steel is
A =
s3
M
fs
f ( d − d′ ) ϕ
y
.
s
– Total tensile reinforcement, A = A + A + A , and total compression
reinforcement is A ′ . A is to be placed at the bottom and A ′ is to be
placed at the top.
s
s
s1
s
s2
s3
s
Minimum and Maximum Tensile Reinforcement
The minimum flexural tensile steel required for a beam section is given by the minimum of the two limits:
A ≥
0.2 f
f
s
A ≥
s
4
A
3
s
′
c
b h, or
w
(CSA 10.5.1.2)
.
(CSA 10.5.1.3)
y
( required )
In addition, the minimum flexural tensile steel provided in a T-section with flange
under tension in an ordinary moment resisting frame is given by the limit:
A ≥ 0.004 ( b − b ) d .
s
w
s
(CSA 10.5.3.1)
An upper limit of 0.04 times the gross web area on both the tension reinforcement
and the compression reinforcement is imposed upon request as follows:
 0.04 b d Rectangular beam
A ≤
 0.04 b d T -beam
s
w
 0.04 b d Rectangular beam
A′ ≤ 
 0.04 b d T -beam
s
w
Beam Design
125
SAFE User's Manual
Design Beam Shear Reinforcement
The shear reinforcement is designed for each load combination at the two stations at
the ends of the beam elements. In designing the shear reinforcement for a particular
beam for a particular loading combination at a particular station due to the beam
major shear, the following steps are involved:
• Determine the factored shear force,V .
f
• Determine the shear force,V , that can be resisted by the concrete.
c
• Determine the reinforcement steel required to carry the balance.
In designing the beam shear reinforcement, the following limits are imposed on the
steel tensile strength and the concrete compressive strength:
f
ys
≤ 500 MPa
(CSA 8.5.1)
f ′ ≤ 80 MPa
(CSA 8.6.1.1)
c
The following three sections describe in detail the algorithms associated with the
above-mentioned steps.
Determine Shear Force and Moment
In the design of the beam shear reinforcement of a concrete beam, the shear forces
and moments for a particular load combination at a particular beam section are obtained by factoring the associated shear forces and moments with the corresponding
load combination factors.
Determine Concrete Shear Capacity
The shear force carried by the concrete,V , is calculated as follows:
c
V = 0.2ϕ λ f ′ b d ,
if d ≤ 300
(CSA 11.3.5.1)
260
ϕ λ f ′ b d ≥ 0.1 ϕ λ f ′ b d , if d > 300
1000 + d
(CSA 11.3.5.2)
c
V =
c
c
c
c
w
c
w
c
c
w
where λ is taken as one for normal weight concrete.
Determine Required Shear Reinforcement
• The shear force is limited to a maximum limit of
126
Beam Design
Appendix B Design for CSA A23.3-94
V
max
=V + 0.8 ϕ λ f ′ b d .
c
c
c
(CSA 11.3.4)
w
• Given V ,V andV , the required shear reinforcement in area/unit length is
calculated as follows:
u
c
max
If V ≤ (V 2) ,
f
c
A
=0,
s
v
(CSA 11.2.8.1)
[
else if (V 2) < V ≤ V + ϕ
c
f
c
s
(0.06
f′ b d
c
w
)] ,
′
A 0.06 f b
,
=
s
f
c
v
w
(CSA 11.2.8.4)
ys
else if
[V + ϕ (0.06
c
s
f′ b d
c
w
)]<V
(V − V )
A
,
=
ϕ f d
s
f
v
s
else if V >V
f
max
c
f
≤V
max
,
(CSA 11.3.7)
ys
,
a failure condition is declared.
(CSA 11.3.4)
The maximum of all the calculated A s values, obtained from each load combination, is reported along with the controlling shear force and associated load combination number.
v
The beam shear reinforcement requirements displayed by the program are based
purely upon shear strength considerations. Any minimum stirrup requirements to
satisfy spacing and volumetric considerations must be investigated independently
of the program by the user.
Slab Design
As is done in conventional design, the SAFE slab design procedure involves defining sets of strips in two mutually perpendicular directions. The locations of the
strips are usually governed by the locations of the slab supports. The moments for a
particular strip are recovered from the analysis and a flexural design is carried out
based on the ultimate strength design method for reinforced concrete as described
Slab Design
127
SAFE User's Manual
in the following sections. To learn more about the design strips, refer to the section
“Integrated Strip Moments and Shears” on page 25.
Design for Flexure
SAFE designs the slab on a strip-by-strip basis. The moments used for the design of
the slab elements are the nodal reactive moments, which are obtained by multiplying the slab element stiffness matrices by the element nodal displacement vectors.
These moments will always be in static equilibrium with the applied loads, irrespective of the refinement of the finite element mesh.
The design of the slab reinforcement for a particular strip is carried out at specific
locations along the length of the strip. These locations correspond to the element
boundaries. Controlling reinforcement is computed on either side of these element
boundaries. The slab flexural design procedure for each load combination involves
the following:
• Determine factored moments for each slab strip.
• Design flexural reinforcement for the strip.
These two steps described below are repeated for every load combination. The
maximum reinforcement calculated for the top and bottom of the slab within each
design strip, along with the corresponding controlling load combination numbers,
is obtained and reported.
Determine Factored Moments for the Strip
For each element within the design strip, for each load combination the program
calculates the nodal reactive moments. The nodal moments are then added to get
the strip moments.
Design Flexural reinforcement for the Strip
The reinforcement computation for each slab design strip given the bending moment is identical to the design of rectangular beam sections described earlier.
Where the slab properties (depth, etc.) vary over the width of the strip the program
automatically designs slab widths of each property separately for the bending moment they are subjected to before summing up the reinforcement for the full width.
Where openings occur the slab width is adjusted accordingly.
128
Slab Design
Appendix B Design for CSA A23.3-94
Minimum and Maximum Slab Reinforcement
The minimum flexural tensile reinforcement provided in each direction of a slab is
given by the following limit (CSA 13.11.1):
A ≥ 0.0020 bh
(CSA 7.8.1)
s
In addition, an upper limit on both the tension reinforcement and compression reinforcement has been imposed to be 0.04 times the gross cross-sectional area.
Check for Punching Shear
The algorithm for checking punching shear is detailed in section “Checking Punching Shear Capacity” on page 26. Only the code specific items are described in the
following.
Critical Section for Punching Shear
The punching shear is checked on a critical section at a distance of d 2 from the face
of the support (CSA 13.4.3.1 and CSA 13.4.3.2). For rectangular columns and
concentrated loads, the critical area is taken as a rectangular area with the sides parallel to the sides of the columns or the point loads (CSA 13.4.3.3).
Transfer of Unbalanced Moment
The fraction of unbalanced moment transferred by flexure is taken to be γ M and
the fraction of unbalanced moment transferred by eccentricity of shear is taken to
be γ M , where
f
v
u
u
γ =
f
1
1 + ( 2 3) b b
1
γ = 1−
v
, and
(CSA 13.11.2)
,
(CSA 13.4.5.3)
2
1
1 + ( 2 3) b b
1
2
where b is the width of the critical section measured in the direction of the span and
b is the width of the critical section measured in the direction perpendicular to the
span.
1
2
Slab Design
129
SAFE User's Manual
Determination of Concrete Capacity
The concrete punching shear factored strength is taken as the minimum of the following three limits:

ϕ


v = min ϕ

ϕ


c
c
c
s
c
c

2
1 +  0.2 λ f ′
 β 

α d
 0.2 +
 λ f ′
b


(CSA 13.4.4)
c
0
c
0.4 λ f
′
c
where, β is the ratio of the minimum to the maximum dimensions of the critical
section, b is the perimeter of the critical section, and α is a scale factor based on
the location of the critical section.
c
0
4

α = 3
2

s
s
for interior columns,
for edge columns, and
for corner columns.
(CSA 13.4.4)
Also the following limits are imposed on the steel and concrete strengths:
f ≤ 500 MPa
(CSA 8.5.1)
f ′ ≤ 80 MPa
(CSA 8.6.1.1)
y
c
Determination of Capacity Ratio
Given the punching shear force and the fractions of moments transferred by eccentricity of shear about the two axes, the shear stress is computed assuming linear
variation along the perimeter of the critical section. The ratio of the maximum shear
stress and the concrete punching shear stress capacity is reported by SAFE.
130
Slab Design
Appendix C
Design for BS 8110-85
This Appendix describes in detail the various aspects of the concrete design procedure that is used by SAFE when the user selects the British limit state design code
BS 8110 (BSI 1989). Various notations used in this Appendix are listed in Table
C-1. For referencing to the pertinent sections of the British code in this Appendix, a
prefix “BS” followed by the section number is used here.
The design is based on user-specified loading combinations. But the program provides a set of default load combinations that should satisfy requirements for the design of most building type structures.
English as well as SI and MKS metric units can be used for input. But the code is
based on Newton-Millimeter-Second units. For simplicity, all equations and descriptions presented in this Appendix correspond to Newton-Millimeter-Second
units unless otherwise noted.
Design Load Combinations
The design load combinations are the various combinations of the prescribed load
cases for which the structure needs to be checked. For this code, if a structure is subjected to dead load (DL), live load (LL), pattern live load (PLL), wind (WL), and
earthquake (EL) loads, and considering that wind and earthquake forces are reversible, then the following load combinations have to be considered (BS 2.4.3):
Design Load Combinations
131
SAFE User's Manual
A
A
A
A′
Area of section for shear resistance, mm2
Gross area of cross-section, mm2
Area of tension reinforcement, mm2
Area of compression reinforcement, mm2
A
A s
a
b
b
b
d
d′
E
E
f
Total cross-sectional area of links at the neutral axis, mm2
Area of shear reinforcement per unit length of the member, mm2/mm
Depth of compression block, mm
Width or effective width of the section in the compression zone, mm
Width or effective width of flange, mm
Average web width of a flanged beam, mm
Effective depth of tension reinforcement, mm
Depth to center of compression reinforcement, mm
Modulus of elasticity of concrete, MPa
Modulus of elasticity of reinforcement, assumed as 200,000 MPa
Characteristic cube strength at 28 days, MPa
cv
g
s
s
sv
sv
v
f
w
c
s
cu
f
′
Compressive stress in a beam compression steel, MPa
s
f
f
h
h
K
K′
y
yv
f
k
1
k
2
M
M
s
T
V
v
Characteristic strength of reinforcement, MPa
Characteristic strength of link reinforcement, MPa (< 460 MPa)
Overall depth of a section in the plane of bending, mm
Flange thickness, mm
Normalized design moment, M bd f
Limiting normalized moment for a singly reinforced concrete section
taken as 0.156
Shear strength enhancement factor for support compression
2
cu
Concrete shear strength factor, [ f
single
25]
1/ 3
cu
Design moment at a section, MPa
Limiting moment capacity as a singly reinforced beam, MPa
Spacing of the links along the length of the beam, in
Tension force, N
Design shear force at ultimate design load, N
Table C-1
List of Symbols Used in the BS code
132
Design Load Combinations
Appendix C Design for BS 8110-85
u
v
v
v
c
max
x
x
z
β
γ
γ
ε
ε
ε′
bal
b
f
m
c
s
s
Perimeter of the punch critical section, mm
Design shear stress at a beam cross-section or at a punch critical
section, MPa
Design ultimate shear stress resistance of a concrete beam, MPa
Maximum permitted design factored shear stress at a beam section or at
the punch critical section, MPa
Neutral axis depth, mm
Depth of neutral axis in a balanced section, mm
Lever arm, mm
Moment redistribution factor in a member
Partial safety factor for load
Partial safety factor for material strength
Maximum concrete strain, 0.0035
Strain in tension steel
Strain in compression steel
Table C-1
List of Symbols Used in the BS code (continued)
Design Load Combinations
133
SAFE User's Manual
1.4 DL
1.4 DL + 1.6 LL
(BS 2.4.3.1.1)
1.4 DL + 1.6 PLL
1.0 DL ± 1.4 WL
1.4 DL ± 1.4 WL
1.2 DL + 1.2 LL ± 1.2 WL
(BS 2.4.3.1.1)
1.0 DL ± 1.4 EL
1.4 DL ± 1.4 EL
1.2 DL + 1.2 LL ± 1.2 EL
These are also the default design load combinations in SAFE whenever the BS
8110-85 code is used. The user should use other appropriate loading combinations
if roof live load is separately treated, or other types of loads are present.
Design Strength
The design strength for concrete and steel are obtained by dividing the characteristic strength of the material by a partial factor of safety, γ . The values of γ used in
the program are listed below which is taken from BS Table 2.2 (BS 2.4.4.1):
m
m
Values of γ m for the ultimate limit state
Reinforcement
1.15
Concrete in flexure and
axial load
1.50
Shear strength without
shear reinforcement
1.25
These factors are already incorporated in the design equations and tables in the
code. SAFE does not allow them to be overwritten.
Beam Design
In the design of concrete beams, SAFE calculates and reports the required areas of
steel for flexure and shear based upon the beam moments, shear forces, load combination factors, and other criteria described below. The reinforcement requirements
are calculated at two check stations at the ends of the beam elements.
134
Design Strength
Appendix C Design for BS 8110-85
All the beams are only designed for major direction flexure and shear. Effects due
to any axial forces, minor direction bending, and torsion that may exist in the beams
must be investigated independently by the user.
The beam design procedure involves the following steps:
• Design beam flexural reinforcement
• Design beam shear reinforcement
Design Beam Flexural Reinforcement
The beam top and bottom flexural steel is designed at the two stations at the ends of
the beam elements. In designing the flexural reinforcement for the major moment
of a particular beam for a particular station, the following steps are involved:
• Determine the maximum factored moments
• Determine the reinforcing steel
Determine Factored Moments
In the design of flexural reinforcement of concrete beams, the factored moments for
each load combination at a particular beam section are obtained by factoring the
corresponding moments for different load cases with the corresponding load factors.
The beam section is then designed for the maximum positive and maximum negative factored moments obtained from all of the load combinations at that section.
Positive beam moments produce bottom steel. In such cases the beam may be designed as a Rectangular- or a T-beam. Negative beam moments produce top steel.
In such cases the beam is always designed as a rectangular section.
Determine Required Flexural Reinforcement
In the flexural reinforcement design process, the program calculates both the tension and compression reinforcement. Compression reinforcement is added when
the applied design moment exceeds the maximum moment capacity of a singly reinforced section. The user has the option of avoiding the compression reinforcement by increasing the effective depth, the width, or the grade of concrete.
The design procedure is based on the simplified rectangular stress block as shown
in Figure C-1 (BS 3.4.4.1). Furthermore it is assumed that moment redistribution in
the member does not exceed 10% (i.e. β ≥ 0.9) (BS 3.4.4.4). The code also places a
b
Beam Design
135
SAFE User's Manual
limitation on the neutral axis depth, x d ≤ 0.5, to safeguard against non-ductile failures (BS 3.4.4.4). In addition, the area of compression reinforcement is calculated
on the assumption that the neutral axis depth remains at the maximum permitted
value.
The design procedure used by SAFE, for both rectangular and flanged sections (Land T-beams) is summarized below. It is assumed that the design ultimate axial
force does not exceed 0.1 f A (BS 3.4.4.1), hence all the beams are designed for
major direction flexure and shear only.
cu
g
Design of a Rectangular beam
For rectangular beams, the limiting moment capacity as a singly reinforced beam,
, is obtained first for a section. The reinforcing steel area is determined based
M
on whether M is greater than, less than, or equal to M
. See Figure C-1.
single
single
0.67fcu/γm
ε = 0.0035
b
fs'
A's
d'
Cs
a=0.9x
x
d
εs
As
Beam Section
Strain Diagram
Figure C-1
Design of Rectangular Beam Section
136
Beam Design
Ts
Tc
Stress Diagram
Appendix C Design for BS 8110-85
• Calculate the ultimate limiting moment of resistance of the section as singly reinforced.
M
= K ′ f bd , where
2
single
(BS 3.4.4.4)
cu
K ′ = 0.156 .
• If M ≤ M
A =
s
single
the area of tension reinforcement, A , is obtained from
s
M
, where
( 0.87 f ) z
(BS 3.4.4.4)
y

K 
z = d  0.5 + 0.25 −
 ≤ 0.95d , and
0.9 

(BS 3.4.4.4)
M
.
f bd
K=
(BS 3.4.4.4)
2
cu
This is the top steel if the section is under negative moment and the bottom
steel if the section is under positive moment.
• If M > M
A′ =
s
single
, the area of compression reinforcement, A ′ , is given by
s
M−M
single
′
f ( d − d′ )
,
(BS 3.4.4.4)
s
where d′ is the depth of the compression steel from the concrete compression
face, and

d′ 
f ′ = E ε 1 −
 ≤ 0.87 f .
x 

s
s
c
(BS 3.4.4.4, 2.5.3)
y
max
This is the bottom steel if the section is under negative moment. From equilibrium, the area of tension reinforcement is calculated as
A =
s
M
single
( 0.87 f ) z
y
+
M−M
single
( 0.87 f ) ( d − d′ )
, where

K′ 
z = d  0.5 + 0.25 −
 = 0.777 d ,
0.9 

x
max
= ( d − z ) 0.45 .
(BS 3.4.4.4)
y
(BS 3.4.4.4)
(BS 3.4.4.4)
Beam Design
137
SAFE User's Manual
Design as a T-Beam
(i) Flanged Beam Under Negative Moment
The contribution of the flange to the strength of the beam is ignored. The design
procedure is therefore identical to the one used for rectangular beams except that in
the corresponding equations b is replaced by b .
w
(ii) Flanged Beam Under Positive Moment
With the flange in compression, the program analyzes the section by considering
alternative locations of the neutral axis. Initially the neutral axis is assumed to be located in the flange. Based on this assumption, the program calculates the exact
depth of the neutral axis. If the stress block does not extend beyond the flange thickness the section is designed as a rectangular beam of width b . If the stress block extends beyond the flange width, then the contribution of the web to the flexural
strength of the beam is taken into account. See Figure C-2.
f
Assuming the neutral axis to lie in the flange, the normalized moment is given by
K=
M
.
f b d
2
cu
(BS 3.4.4.4)
f
Then the moment arm is computed as

K 
z = d  0.5 + 0.25 −
 ≤ 0.95d ,
0.9 

(BS 3.4.4.4)
the depth of neutral axis is computed as
x=
1
( d − z ) , and
0.45
(BS 3.4.4.4)
the depth of compression block is given by
a = 0.9 x .
138
Beam Design
(BS 3.4.4.4)
Appendix C Design for BS 8110-85
d'
fs'
0.67 fcu/γm
0.67 fcu/γm
ε = 0.0035
hf
bf
Cs
As'
Cf
x
d
Cw
εs
As
Tf
Tw
Ts
bw
Beam Section
Strain Diagram
Stress Diagram
Figure C-2
Design of a T-Beam Section
• If a ≤ h , the subsequent calculations for A are exactly the same as previously
defined for the rectangular section design. However, in this case the width of
the beam is taken as b . Whether compression reinforcement is required depends on whether K > K ′.
f
s
f
• If a > h , calculation for A is done in two parts. The first part is for balancing
the compressive force from the flange, C , and the second part is for balancing
the compressive force from the web, C , as shown in Figure C-2.
f
s
f
w
In this case, the ultimate resistance moment of the flange is given by
M = 0.45 f ( b − b ) min( h , a
f
cu
f
w
f
max
) [d − 0.5 min( h , a
f
max
)] , (BS 3.4.4.5)
the moment taken by the web is computed as
M = M − M , and
w
f
the normalized moment resisted by the web is given by
K =
w
M
.
f b d
w
2
cu
(BS 3.4.4.4)
w
Beam Design
139
SAFE User's Manual
– If K ≤ K ′ (BS 3.4.4.4), the beam is designed as a singly reinforced concrete
beam. The area of steel is calculated as the sum of two parts, one to balance
compression in the flange and one to balance compression in the web.
w
A =
s
M
0.87 f
y
f
[d − 0.5 min( h
f
,a
max
)]
+
M
, where
0.87 f z
w
y

K 
z = d  0.5 + 0.25 −
 ≤ 0.95d .
0.9 

w
– If K > K ′ (BS 3.4.4.4), compression reinforcement is required and is calculated as follows:
w
The ultimate moment of resistance of the web only is given by
M
= K′ f b d .
2
uw
cu
(BS 3.4.4.4)
w
The compression reinforcement is required to resist a moment of magnitude
M − M . The compression reinforcement is computed as
w
uw
A′ =
s
M − M
w
uw
′
f ( d − d′ )
,
s
where, d′ is the depth of the compression steel from the concrete compression
face, and

d′ 
f ′ = E ε 1 −
 ≤ 0.87 f .
x 

s
s
c
(BS 3.4.4.4, 2.5.3)
y
max
The area of tension reinforcement is obtained from equilibrium
A=
s
M
f
0.87 f ( d − 0.5 h )
y
f
+
M
uw
0.87 f ( 0.777 d )
y
+
M − M
.
0.87 f ( d − d′ )
w
uw
y
Minimum and Maximum Tensile Reinforcement
The minimum flexural tensile steel required for a beam section is given by the following table which is taken from BS Table 3.27 (BS 3.12.5.3) with interpolation
for reinforcement of intermediate strength:
140
Beam Design
Appendix C Design for BS 8110-85
Section
Rectangular
T-Beam with web
in tension
T-Beam with web
in compression
Situation
Definition of
percentage
Minimum percentage
f y = 250 MPa
f y = 460 MPa
As
bh
0.24
0.13

100
bw
< 0.4
bf
100
As
bw h
0.32
0.18
bw
≥ 0.4
bf
100
As
bw h
0.24
0.13

100
As
bw h
0.48
0.26
The minimum flexural compression steel, if it is required at all, provided in a rectangular or T-beam section is given by the following table which is taken from BS
Table 3.27 (BS 3.12.5.3) with interpolation for reinforcement of intermediate
strength:
Section
Rectangular
Situation

Definition of
percentage
Minimum
percentage
As′
bh
0.20
As′
bf hf
0.40
As′
bw h
0.20
100
Web in tension
100
Web in compression
100
T-Beam
In addition, an upper limit on both the tension reinforcement and compression reinforcement has been imposed to be 0.04 times the gross cross-sectional area (BS
3.12.6.1).
Beam Design
141
SAFE User's Manual
Design Beam Shear Reinforcement
The shear reinforcement is designed for each loading combination in the major direction of the beam. In designing the shear reinforcement for a particular beam for a
particular loading combination, the following steps are involved (BS 3.4.5):
• Calculate the design shear stress as
V
, A = b d , where
A
v=
cv
(BS 3.4.5.2)
w
cv
v≤ v
v
max
max
, and
(BS 3.4.5.2)
= min(0.8 f , 5 MPa) .
(BS 3.4.5.2)
cu
• Calculate the design concrete shear stress from
1
1
0.79 k k  100 A  3  400  4

 
v =
 ,
γ
 bd   d 
1
2
s
c
(BS 3.4.5.4)
m
where,
k is the enhancement factor for support compression, and is conservatively taken as 1,
(BS 3.4.5.8)
1
1
f 3
 ≥ 1 , and
k = 
 25 
(BS 3.4.5.4)
γ
(BS 3.4.5.2)
cu
2
m
= 1.25 .
However, the following limitations also apply:
0.15 ≤
100 A
≤ 3,
bd
s
400
≥ 1 , and
d
f
cu
(BS 3.4.5.4)
(BS 3.4.5.4)
≤ 40 MPa (for calculation purpose only).
(BS 3.4.5.4)
A is the area of tensile steel.
s
• Given v , v and v , the required shear reinforcement in area/unit length is
calculated as follows (BS Table 3.8, BS 3.4.5.3):
c
142
Beam Design
max
Appendix C Design for BS 8110-85
If v ≤ v + 0.4 ,
c
A
0.4 b
=
s
0.87 f
sv
w
v
,
(BS 3.4.5.3)
yv
else if ( v + 0.4) < v ≤ v
c
A
s
sv
v
=
max
,
(v − v ) b
.
0.87 f
else if v > v
c
w
(BS 3.4.5.3)
yv
max
,
a failure condition is declared.
(BS 3.4.5.2)
In the above expressions, a limit is imposed on the f
f
yv
≥ 460 MPa .
yv
as
(BS 3.4.5.1)
The maximum of all the calculated A s values, obtained from each load combination, is reported along with the controlling shear force and associated load combination number.
sv
v
The beam shear reinforcement requirements displayed by the program are based
purely upon shear strength considerations. Any minimum stirrup requirements to
satisfy spacing and volumetric considerations must be investigated independently
of the program by the user.
Slab Design
As is done in conventional design, the SAFE slab design procedure involves defining sets of strips in two mutually perpendicular directions. The locations of the
strips are usually governed by the locations of the slab supports. The moments for a
particular strip are recovered from the analysis and a flexural design is carried out
based on the ultimate strength design method for reinforced concrete (BS 8110-85)
as described in the following sections. To learn more about the design strips, refer
to the section “Integrated Strip Moments and Shears” on page 25.
Design for Flexure
SAFE designs the slab on a strip-by-strip basis. The moments used for the design of
the slab elements are the nodal reactive moments, which are obtained by multiplying the slab element stiffness matrices by the element nodal displacement vectors.
Slab Design
143
SAFE User's Manual
These moments will always be in static equilibrium with the applied loads, irrespective of the refinement of the finite element mesh.
The design of the slab reinforcement for a particular strip is carried out at specific
locations along the length of the strip. These locations correspond to the element
boundaries. Controlling reinforcement is computed on either side of these element
boundaries. The slab flexural design procedure for each load combination involves
the following:
• Determine factored moments for each slab strip.
• Design flexural reinforcement for the strip.
These two steps described below are repeated for every load combination. The
maximum reinforcement calculated for the top and bottom of the slab within each
design strip, along with the corresponding controlling load combination numbers,
is obtained and reported.
Determine Factored Moments for the Strip
For each element within the design strip, for each load combination the program
calculates the nodal reactive moments. The nodal moments are then added to get
the strip moments.
Design Flexural reinforcement for the Strip
The reinforcement computation for each slab design strip given the bending moment is identical to the design of rectangular beam sections described earlier.
Where the slab properties (depth, etc.) vary over the width of the strip the program
automatically designs slab widths of each property separately for the bending moment they are subjected to before summing up the reinforcement for the full width.
Where openings occur the slab width is adjusted accordingly.
Minimum and Maximum Slab Reinforcement
The minimum flexural tensile reinforcement required in each direction of a slab is
given by the following limit (BS 3.12.5.3, BS Table 3.27) with interpolation for reinforcement of intermediate strength:
 0.0024 bh if f ≤ 250 MPa
A ≥
 0.0013 bh if f ≥ 460 MPa
y
s
y
144
Slab Design
(BS 3.12.5.3)
Appendix C Design for BS 8110-85
In addition, an upper limit on both the tension reinforcement and compression reinforcement has been imposed to be 0.04 times the gross cross-sectional area (BS
3.12.6.1).
Check for Punching Shear
The algorithm for checking punching shear is detailed in section “Checking Punching Shear Capacity” on page 26. Only the code specific items are described in the
following.
Critical Section for Punching Shear
The punching shear is checked on a critical section at a distance of 1.5d from the
face of the support (BS 3.7.7.4). For rectangular columns and concentrated loads,
the critical area is taken as a rectangular area with the sides parallel to the sides of
the columns or the point loads (BS 3.7.7.1).
Determination of Concrete Capacity
The concrete punching shear factored strength is taken as follows (BS 3.7.7.4):
1
1
0.79 k k  100 A  3  400  4

 
v =
 , where,
γ
 bd   d 
1
2
s
c
(BS 3.4.5.4)
m
k is the enhancement factor for support compression, and is conservatively
taken as 1,
(BS 3.4.5.8)
1
1
f 3
 ≥ 1 , and
k = 
 25 
(BS 3.4.5.4)
γ
(BS 3.4.5.2)
cu
2
m
= 1.25 .
However, the following limitations also apply:
0.15 ≤
100 A
≤ 3,
bd
s
400
≥ 1,
d
(BS 3.4.5.4)
(BS 3.4.5.4)
v ≤ min(0.8 f , 5 MPa) , and
cu
(BS 3.4.5.2)
Slab Design
145
SAFE User's Manual
f
≤ 40 MPa (for calculation purpose only).
cu
(BS 3.4.5.4)
A = area of tensile steel which is taken as zero in current implementation.
s
Determination of Capacity Ratio
Given the punching shear force and the fractions of moments transferred by eccentricity of shear about the two axes, the nominal design shear stress, v, is calculated
from the following equation:
v=
V
V
eff
ud
, where
(BS 3.7.7.3)
M

M 
= V  f + 1.5
+ 1.5
,
Vx
V y

y
eff
x
(BS 3.7.6.2 and BS 3.7.6.3)
u is the perimeter of the critical section,
x and y are the length of the side of the critical section parallel to the axis of
bending,
M and M are the design moment transmitted from the slab to the column at
connection,
x
y
V is the total punching shear force, and
f is a factor to consider the eccentricity of punching shear force and is taken as
1.00

f =  1.25
 1.25

for interior columns,
for edge columns, and
for corner columns.
(BS 3.7.6.2 and BS 3.7.6.3)
The ratio of the maximum shear stress and the concrete punching shear stress capacity is reported by SAFE.
146
Slab Design
Appendix D
Design for Eurocode 2
This Appendix describes in detail the various aspects of the concrete design procedure that is used by SAFE when the user selects the European concrete design code,
1992 Eurocode 2 (CEN 1992). Various notations used in this Appendix are listed
in Table D-1. For referencing to the pertinent sections of the Eurocode in this Appendix, a prefix “EC2” followed by the section number is used here.
The design is based on user-specified loading combinations. However, the program
provides a set of default load combinations that should satisfy requirements for the
design of most building type structures.
English as well as SI and MKS metric units can be used for input. But the code is
based on Newton-Millimeter-Second units. For simplicity, all equations and descriptions presented in this Appendix correspond to Newton-Millimeter-Second
units unless otherwise noted.
Design Load Combinations
The design load combinations are the various combinations of the prescribed load
cases for which the structure needs to be checked. For this code, if a structure is subjected to dead load (DL), live load (LL), pattern live load (PLL), wind (WL), and
earthquake (EL) loads, and considering that wind and earthquake forces are reversible, then the following load combinations have to be considered (EC2 2.3.3):
Design Load Combinations
147
SAFE User's Manual
A
A
A′
Area of concrete section, mm2
Area of tension reinforcement, mm2
Area of compression reinforcement, mm2
A
A s
a
b
b
b
d
d′
E
E
f
f
f
f
f′
Total cross-sectional area of links at the neutral axis, mm2
Area of shear reinforcement per unit length of the member, mm2
Depth of compression block, mm
Width or effective width of the section in the compression zone, mm
Width or effective width of flange, mm
Average web width of a flanged beam, mm
Effective depth of tension reinforcement, mm
Effective depth of compression reinforcement, mm
Modulus of elasticity of concrete, MPa
Modulus of elasticity of reinforcement, assumed as 200,000 MPa
Design concrete strength = f γ , MPa
Characteristic compressive concrete cylinder strength at 28 days, MPa
Design yield strength of reinforcing steel = f γ , MPa
Characteristic yield strength of reinforcement, MPa
Compressive stress in a beam compression steel, MPa
c
s
s
sw
sw
f
w
c
s
cd
ck
yd
yk
s
f
f
h
h
M
m
m
s
u
V
V
V
ywd
ywk
f
c
yk
Rd 1
2
ywk
Table D-1
List of Symbols Used in the Eurocode 2
148
s
Design strength of shear reinforcement = f
γ , MPa
Characteristic strength of shear reinforcement, MPa
Overall thickness of slab, mm
Flange thickness, mm
Design moment at a section, N-mm
Normalized design moment, M bd αf
Limiting normalized moment capacity as a singly reinforced beam
Spacing of the shear reinforcement along the length of the beam, mm
Perimeter of the punch critical section, mm
Design shear resistance from concrete alone, N
Design limiting shear resistance of a cross-section, N
Shear force at ultimate design load, N
cd
lim
Sd
ck
2
v
Rd
v
Design Load Combinations
s
Appendix D Design for Eurocode 2
x
x
α
γ
γ
γ
γ
δ
ε
ε
ν
ρ
ω
ω′
Depth of neutral axis, mm
Limiting depth of neutral axis, mm
Concrete strength reduction factor for sustained loading and
stress-block
Enhancement factor of shear resistance for concentrated load,
Also the coefficient which takes account of the eccentricity of loading in determining punching shear stress,
Factor for the depth of compressive stress block
Partial safety factor for load
Partial safety factor for concrete strength
Partial safety factor for material strength
Partial safety factor for steel strength
Redistribution factor
Concrete strain
Strain in tension steel
Effectiveness factor for shear resistance without concrete crushing
Tension reinforcement ratio, A bd
Normalized tensile steel ratio, A f αf bd
Normalized compression steel ratio, A ′ f γ αf ′ bd
ω
Normalized limiting tensile steel ratio
lim
β
f
c
m
s
c
s
lim
s
s
yd
cd
s
yd
s
s
Table D-1
List of Symbols Used in the Eurocode 2 (continued)
Design Load Combinations
149
SAFE User's Manual
1.35 DL
1.35 DL + 1.50 LL
(EC2 2.3.3.1)
1.35 DL + 1.50 PLL
1.35 DL ± 1.50 WL
1.00 DL ± 1.50 WL
1.35 DL + 1.35 LL ± 1.35 WL
(EC2 2.3.3.1)
1.00 DL ± 1.00 EL
1.00 DL + 1.5*0.3 LL ± 1.0 EL
(EC2 2.3.3.1)
These are also the default design load combinations in SAFE whenever the
Eurocode is used. The user should use other appropriate loading combinations if
roof live load is separately treated, or other types of loads are present.
Design Strength
The design strength for concrete and steel are obtained by dividing the characteristic strength of the material by a partial factor of safety, γ . The values of γ used in
the program are listed below. These values are recommended by the code to give an
acceptable level of safety for normal structures under regular design situations
(EC2 2.3.3.2). For accidental and earthquake situations, the recommended values
are less than the tabulated value. The user should consider those separately.
m
m
The partial safety factors for the materials, the design strengths of concrete and
steel are given below:
Partial safety factor for steel, γ = 1.15 , and
(EC2 2.3.3.2)
Partial safety factor for concrete, γ = 1.5 .
(EC2 2.3.3.2)
s
c
The user is allowed to overwrite these values. However, caution is advised.
Beam Design
In the design of concrete beams, SAFE calculates and reports the required areas of
steel for flexure and shear based upon the beam moments, shears, load combination
factors, and other criteria described below. The reinforcement requirements are calculated at two check stations at the ends of the beam elements. All the beams are
only designed for major direction flexure and shear. Effects due to any axial forces,
minor direction bending, and torsion that may exist in the beams must be investigated independently by the user.
150
Design Strength
Appendix D Design for Eurocode 2
The beam design procedure involves the following steps:
• Design beam flexural reinforcement
• Design beam shear reinforcement
Design Beam Flexural Reinforcement
The beam top and bottom flexural steel is designed at the two stations at the ends of
the beam elements. In designing the flexural reinforcement for the major moment
of a particular beam for a particular station, the following steps are involved:
• Determine the maximum factored moments
• Determine the reinforcing steel
Determine Factored Moments
In the design of flexural reinforcement of concrete beams, the factored moments for
each load combination at a particular beam section are obtained by factoring the
corresponding moments for different load cases with the corresponding load factors.
The beam section is then designed for the maximum positive and maximum negative factored moments obtained from all the of the load combinations. Positive
beam moments produce bottom steel. In such cases the beam may be designed as a
Rectangular- or a T-beam. Negative beam moments produce top steel. In such cases
the beam is always designed as a rectangular section.
Determine Required Flexural Reinforcement
In the flexural reinforcement design process, the program calculates both the tension and compression reinforcement. Compression reinforcement is added when
the applied design moment exceeds the maximum moment capacity of a singly reinforced section. The user has the option of avoiding the compression reinforcement by increasing the effective depth, the width, or the grade of concrete.
The design procedure is based on the simplified rectangular stress block as shown
in Figure D-1 (EC2 4.3.1.2). The area of the stress block and the depth of the center
of the compressive force from the most compressed fiber are taken as
C =α f
cd
a b and
a = β x,
Beam Design
151
SAFE User's Manual
where x is the depth of the neutral axis, and α and β are taken respectively as
α = 0.8 ,
and
(EC2 4.2.1.3.3)
β = 0.8 .
(EC2 4.2.1.3.3)
α is the reduction factor to account for sustained compression and rectangular
stress block. α is generally assumed to be 0.80 for the assumed rectangular stress
block (EC2 4.2.1.3.3). β factor considers the depth of the stress block and it is assumed to be 0.8 (EC2 4.2.1.3.3).
Furthermore, it is assumed that moment redistribution in the member does not exceed the code specified limiting value. The code also places a limitation on the neutral axis depth, to safeguard against non-ductile failures (EC2 2.5.3.4.2). When the
applied moment exceeds the limiting moment capacity as a singly reinforced beam,
the area of compression reinforcement is calculated on the assumption that the neutral axis depth remains at the maximum permitted value.
The design procedure used by SAFE, for both rectangular and flanged sections (Land T-beams) is summarized below. It is assumed that the design ultimate axial
force does not exceed 0.08 f A (EC2 4.3.1.2), hence all the beams are designed
for major direction flexure and shear only.
ck
g
Design as a Rectangular Beam
For rectangular beams, the normalized moment, m, and the normalized section capacity as a singly reinforce beam, m , are obtained first. The reinforcing steel area
is determined based on whether m is greater than, less than, or equal to m .
lim
lim
• Calculate the normalized design moment, m.
m=
M
bd αf
, where
2
cd
α is the reduction factor to account for sustained compression and β factor considers the depth of the neutral axis. α is generally assumed to be 0.80 for assumed rectangular stress block, (EC2 4.2.1.3.3). α is also generally assumed to
be 0.80 for assumed rectangular stress block, (EC2 4.2.1.3.3). The concrete
compression stress block is assumed to be rectangular (See Figure D-1), with a
stress value of αf , where f is the design concrete strength and is equal to
f γ .
cd
ck
cd
c
• Calculate the normalized concrete moment capacity as a singly reinforced
beam, m .
lim
152
Beam Design
Appendix D Design for Eurocode 2
m
lim
 x
= β 
d
lim
 β  x
1 −  
 2 d
lim

,

where the limiting value of the ratio of the neutral axis depth at the ultimate
limit state to the effective depth, [ x d] , is expressed as a function of the ratio
of the redistributed moment to the moment before redistribution, δ, as follows:
lim
 x
 
d
 x
 
d
=
δ − 0.44
, if
1.25
f
ck
≤ 35 ,
(EC2 2.5.3.4.2)
=
δ − 0.56
, if
1.25
f
ck
> 35 , and
(EC2 2.5.3.4.2)
lim
lim
δ is assumed to be 1.
αfck/γc
ε = 0.0035
b
fs'
A's
h
Ts
εs
As
Beam Section
a=β x
x
d'
d
Cs
Strain Diagram
Tc
Stress Diagram
Figure D-1
Design of a Rectangular Beam Section
• If m ≤ m , a singly reinforced beam will suffice. Calculate the normalized
steel ratio,
lim
ω= 1 − 1 − 2m .
Calculate the area of tension reinforcement, A , from
s
Beam Design
153
SAFE User's Manual
 αf bd 
A = ω
.
 f

cd
s
yd
This is the top steel if the section is under negative moment and the bottom
steel if the section is under positive moment.
• If m > m , the beam will not suffice as a singly reinforced beam. Both top and
bottom steel are required.
lim
– Calculate the normalized steel ratios ω′, ω , and ω .
lim
ω
lim
ω′=
 x
= β 
d
= 1− 1− 2 m ,
lim
lim
m− m
, and
1 − d′/ d
lim
ω= ω
+ ω′
lim
where, d′ is the depth of the compression steel from the concrete
compression face.
– Calculate the area of compression and tension reinforcement, A ′ and A , as
follows:
s
s
 αf bd 
A ′ = ω′ 
 , and
′
 f

cd
s
s
 αf bd 
A = ω
,
 f

cd
s
yd
where, f ′ is the stress in the compression steel, and is given by
s

d′ 
f ′= E ε 1 −
≤ f
x 

s
s
c
yd
.
(EC2 4.2.2.3.2)
lim
Design as a T-Beam
(i) Flanged Beam Under Negative Moment
The contribution of the flange to the strength of the beam is ignored if the flange is
in the tension side. See Figure D-2. The design procedure is therefore identical to
154
Beam Design
Appendix D Design for Eurocode 2
the one used for rectangular beams. However, the width of the web, b , is taken as
the width of the beam.
w
(ii) Flanged Beam Under Positive Moment
With the flange in compression, the program analyzes the section by considering
alternative locations of the neutral axis. Initially the neutral axis is assumed to be located within the flange. Based on this assumption, the program calculates the depth
of the neutral axis. If the stress block does not extend beyond the flange thickness
the section is designed as a rectangular beam of width b . If the stress block extends
beyond the flange, additional calculation is required. See Figure D-2.
f
• Calculate the normalized design moment, m.
m=
M
b d αf
, where
2
f
cd
α is the reduction factor to account for sustained compression. α is generally assumed to be 0.80 for assumed rectangular stress block, (EC2 4.2.1.3). See also
page 152 for α . The concrete compression stress block is assumed to be rectangular, with a stress value of αf .
cd
• Calculate the limiting value of the ratio of the neutral axis depth at the ultimate
limit state to the effective depth, [ x d] ,which is expressed as a function of the
ratio of the redistributed moment to the moment before redistribution, δ, as follows:
lim
 x
 
d
 x
 
d
=
δ − 0.44
, if
1.25
f
ck
≤ 35 ,
(EC2 2.5.3.4.1)
=
δ − 0.56
, if
1.25
f
ck
> 35 ,
(EC2 2.5.3.4.1)
lim
lim
δ is assumed to be 1.
• Calculate the limiting values:
m
lim
ω
lim
 x
= β 
d
lim
 β  x
1 −  
 2 d
lim

,

 x
= β  ,
d
lim
a
max
= ω d,
lim
Beam Design
155
SAFE User's Manual
• Calculate ω, a, and
x
as follows:
d
ω= 1 − 1 − 2m , and
a = ωd ≤ a
.
max
x ω
= .
d β
• If a ≤ h , the neutral axis lies within the flange. Calculate the area of tension
reinforcement, A , as follows:
f
s
– If m ≤ m ,
lim
ω= 1 − 1 − 2m , and
 αf b d 
A = ω
.
 f

cd
w
s
yd
– If m > m
lim
,
ω′=
m− m
,
1 − d′/ d
ω
 x
= β  ,
d
lim
lim
lim
ω= ω
lim
+ ω′ ,
 αf b d 
A = ω
 , and
 f

cd
w
s
yd
 αf bd 
A ′ = ω′ 
 , where
′
 f

cd
s
s

d′ 
f ′= E ε 1 −
≤ f
x 

s
s
c
yd
.
(EC2 4.2.2.3.2)
lim
• If a > h , the neutral axis lies below the flange.
f
Calculate steel area required for equilibrating the flange compression, A .
s2
156
Beam Design
Appendix D Design for Eurocode 2
A =
( b − b ) h αf
f
w
f
s2
f
cd
,
yd
and the corresponding resistive moment is given by
h

M = A f  d −
2

f
2
s2
yd

 .

ε = 0.0035
hf
bf
d'
fs'
As'
α fck/γc
α fck/γc
Cs
Cf
a = βx
x
d
Cw
εs
As
Ts
Tf
Tw
bw
Beam Section
Strain Diagram
Stress Diagram
Figure D-2
Design of a T-Beam Section
Calculate steel area required for rectangular section of width b to resist
moment, M = M − M , as follows:
w
1
m =
1
2
M
b d αf
1
, and
2
w
cd
– If m ≤ m ,
1
lim
ω = 1 − 1 − 2m , and
1
1
 αf b d 
A =ω 
.
 f

cd
s1
w
1
yd
Beam Design
157
SAFE User's Manual
– If m > m
1
,
lim
ω′=
m −m
,
1 − d′/ d
ω
 x
= β  ,
d
lim
1
lim
lim
ω1 = ω
lim
+ ω′ ,
 αf bd 
A ′ = ω′ 
 , and
′
 f

cd
s
s
 αf b d 
A = ω 
,
 f

cd
s1
w
1
yd
where, f ′ is given by
s

d′ 
f ′= E ε 1 −
≤ f
x 

s
s
c
yd
.
(EC2 4.2.2.3.2)
lim
– Calculate total steel area required for the tension side.
A = A +A
s1
s
s2
Minimum and Maximum Tensile Reinforcement
The minimum flexural tensile steel required for a beam section is given by the following equation (EC2 5.4.2.1.1):
 0.6
 f bd

A ≥
 0.6
f b d

Rectangular beam
yk
(EC2 5.4.2.1.1)
s
w
T -beam
yk
In no case in the above equation, should the factor 0.6 f
0.0015.
0.6
≥ 0.0015
f
yk
158
Beam Design
yk
be taken as less than
(EC2 5.4.2.1.1)
Appendix D Design for Eurocode 2
The minimum flexural tension reinforcement required for control of cracking (EC2
4.4.2) should be investigated independently by the user.
An upper limit on the tension reinforcement and compression reinforcement has
been imposed to be 0.04 times the gross cross-sectional area (EC2 5.4.2.1.1).
Design Beam Shear Reinforcement
The shear reinforcement is designed for each loading combination at the two stations at the ends of the beam elements. The assumptions in designing the shear reinforcement are as follows:
• The beam sections are assumed to be prismatic. The effect of any variation of
width in the beam section on the concrete shear capacity is neglected.
• The effect on the concrete shear capacity of any concentrated or distributed
load in the span of the beam between two columns is ignored. Also, the effect of
the direct support on the beams provided by the columns is ignored.
• All shear reinforcement is assumed to be perpendicular to the longitudinal reinforcement.
• The effect of any torsion is neglected for the design of shear reinforcement.
In designing the shear reinforcement for a particular beam for a particular loading
combination, the following steps of the standard method are involved.
• Obtain the design value of the applied shear force V
results.
Sd
from the SAFE analysis
• Calculate the design shear resistance of the member without shear reinforcement.
V
Rd 1
= β [τ k (1.2 + 40 ρ )] ( b d ) , where
1
Rd
(EC2 4.3.2.3)
w
β = enhancement factor for shear resistance for members with concentrated loads located near the face of the support. β is taken as 1.
τ
= basic design shear strength of concrete = 0.25 f
Rd
f
ctk
f
ctm
0. 05
= 0.7 f
= 0.3 f
2
ck
ctm
3
,
,
ctk
0.05
γ ,
c
(EC2 3.1.2.3)
(EC2 3.1.2.3)
k = strength magnification factor for curtailment of longitudinal reinforcement and is considered to be 1,
Beam Design
159
SAFE User's Manual
ρ = tension reinforcement ratio =
1
A
≤ 0.02 , and
b d
s1
w
A = area of tension reinforcement.
s1
• Calculate the maximum design shear force that can be carried without crushing
of the notional concrete compressive struts,V .
Rd
V
Rd
2
2
1 f 
ν 
 ( 0.9 b d ) , where
2 γ 
=
ck
(EC2 4.3.2.3)
w
c
ν is the effectiveness factor = 0.7 −
f
≥ 0.5 .
200
ck
(EC2 4.3.2.3)
• Given V , V and V
, the required shear reinforcement in area/unit
length is calculated as follows:
Rd 1
Sd
If V
Sd
≤V
Rd2,red
,
Rd 1
A
=0,
s
sw
(EC2 4.3.2.3)
v
else if V
Rd 1
<V
Sd
≤V
Rd2
,
A
(V − V ) γ
,
=
s
0.9 d f
sw
Rd 1
Sd
v
s
(EC2 4.3.2.4.3)
ywk
else if V
Sd
>V
Rd2
,
a failure condition is declared.
(EC2 4.3.2.2)
An upper limit is imposed on the steel tensile strength:
f
ywk
γ ≤ 400 MPa
(EC2 4.3.2.2)
s
The maximum of all the calculated A s values, obtained from each load combination, is reported along with the controlling shear force and associated load combination number.
sw
A lower limit is imposed on A
sw
A
≥ρ
s
sw
w , min
v
s:
v
b
w
v
where ρ
160
w , min
Beam Design
is obtained from the following table (EC2 Table 5.5):
(EC2 5.4.2.2)
Appendix D Design for Eurocode 2
Minimum Values of Shear Stress Ratio, ρw min
(EC2 5.4.2.2, EC2 Table 5.5)
,
Concrete Strength
f y ≤ 220
220 < f y ≤ 400
f y > 400
f c′ ≤ 20
0.0016
0.0009
0.0007
20 < f c′ ≤ 35
0.0024
0.0013
0.0011
f c′ > 35
0.0030
0.0016
0.0013
The beam shear reinforcement requirements displayed by the program are based
purely upon shear strength considerations. Any minimum stirrup requirements to
satisfy spacing and volumetric considerations must be investigated independently
of the program by the user.
Slab Design
As is done in conventional design, the SAFE slab design procedure involves defining sets of strips in two mutually perpendicular directions. The locations of the
strips are usually governed by the locations of the slab supports. The moments for a
particular strip are recovered from the analysis and a flexural design is carried out
based on the ultimate strength design method (Eurocode 2) for reinforced concrete
as described in the following sections. To learn more about the design strips, refer
to the section “Integrated Strip Moments and Shears” on page 25.
Design for Flexure
SAFE designs the slab on a strip-by-strip basis. The moments used for the design of
the slab elements are the nodal reactive moments, which are obtained by multiplying the slab element stiffness matrices by the element nodal displacement vectors.
These moments will always be in static equilibrium with the applied loads, irrespective of the refinement of the finite element mesh.
The design of the slab reinforcement for a particular strip is carried out at specific
locations along the length of the strip. These locations correspond to the element
boundaries. Controlling reinforcement is computed on either side of these element
boundaries. The slab flexural design procedure for each load combination involves
the following:
Slab Design
161
SAFE User's Manual
• Determine factored moments for each slab strip.
• Design flexural reinforcement for the strip.
These two steps described below are repeated for every load combination. The
maximum reinforcement calculated for the top and bottom of the slab within each
design strip, along with the corresponding controlling load combination numbers,
is obtained and reported.
Determine Factored Moments for the Strip
For each element within the design strip, for each load combination the program
calculates the nodal reactive moments. The nodal moments are then added to get
the strip moments.
Design Flexural reinforcement for the Strip
The reinforcement computation for each slab design strip given the bending moment is identical to the design of rectangular beam sections described earlier.
Where the slab properties (depth, etc.) vary over the width of the strip the program
automatically designs slab widths of each property separately for the bending moment they are subjected to before summing up the reinforcement for the full width.
Where openings occur the slab width is adjusted accordingly.
Minimum and Maximum Slab Reinforcement
The minimum flexural tensile reinforcement required in each direction of a slab is
given by the following limits:
 0.6
bd

A ≥ f
 0.0015 bd
s
y
(EC2 5.4.2.1.1)
In addition, an upper limit on both the tension reinforcement and compression reinforcement has been imposed to be 0.04 times the gross cross-sectional area (EC2
5.4.2.1.1).
Check for Punching Shear
The algorithm for checking punching shear is detailed in section “Checking Punching Shear Capacity” on page 26. Only the code specific items are described in the
following.
162
Slab Design
Appendix D Design for Eurocode 2
Critical Section for Punching Shear
The punching shear is checked on a critical section at a distance of 1.5d from the
face of the support (EC2 4.3.4.2.2).
Determination of Concrete Capacity
The factored concrete punching shear strength is taken as the design shear resistance per unit length without shear reinforcement.
v
Rd 1
τ
Rd
= [τ k (1.2 + 40 ρ )] d , where
= basic design shear strength =
f
ctk
f
ctm
0. 05
= 0.7 f
= 0.3 f
2
ck
ρ = ρ ρ
d=
ctm
3
0.25 f
γ
ctk
0.05
1x
d +d
x
1y
y
2
,
(EC2 4.3.2.3)
c
,
,
d
≥ 1.0 , d in mm
1000
k = 1.6 −
1
(EC2 4.3.4.5.1)
1
Rd
(EC2 3.1.2.3)
(EC2 3.1.2.3)
(EC2 4.3.4.5.1)
≤ 0.015
,
ρ and ρ are the reinforcement ratios in the X and Y directions respectively,
conservatively taken as zeros, and
1x
1y
d and d are the effective depths of the slab at the points of intersection between the design failure surface and the longitudinal reinforcement, in the X
and Y directions respectively.
x
y
Determination of Capacity Ratio
Given the punching shear force and the fractions of moments transferred by eccentricity of shear about the two axes, the factored punching shear force per unit length
is taken as follows:
v =
Sd
V
Sd
V β
, where
u
Sd
(EC2 4.3.4.3)
is the total design shear force developed,
Slab Design
163
SAFE User's Manual
u is the perimeter of the critical section, and
β is the coefficient which takes account of the effects of eccentricity of
loading
 1.15

β = 1.40
1.50

for interior columns,
for edge columns, and
for corner columns.
(EC2 4.3.4.3)
The ratio of the maximum factored shear force and the concrete punching shear
resistance is reported by SAFE.
164
Slab Design
Appendix E
Design for NZS 3101-95
This Appendix describes in detail the various aspects of the concrete design procedure that is used by SAFE when the user selects the New Zealand code, NZS
3101-95 (NZS 1995). Various notations used in this Appendix are listed in Table
E-1. For referencing to the pertinent sections of the New Zealand code in this
Appendix, a prefix “NZS” followed by the section number is used here.
The design is based on user-specified loading combinations. But the program provides a set of default load combinations that should satisfy requirements for the design of most building type structures.
English as well as SI and MKS metric units can be used for input. But the code is
based on Newton-Millimeter-Second units. For simplicity, all equations and descriptions presented in this Appendix correspond to Newton-Millimeter-Second
units unless otherwise noted.
Design Load Combinations
The design load combinations are the various combinations of the prescribed load
cases for which the structure needs to be checked. For this code, if a structure is subjected to dead load (DL), live load (LL), pattern live load (PLL), wind (WL), and
earthquake (EL) loads, and considering that wind and earthquake forces are re-
Design Load Combinations
165
SAFE User's Manual
A
A
A
A′
Area of concrete used to determine shear stress, sq-mm
Gross area of concrete, sq-mm
Area of tension reinforcement, sq-mm
Area of compression reinforcement, sq-mm
cv
g
s
s
A
A
A s
s
a
a
a
b
b
b
b
b
b
c
c
d
d′
d
E
E
f′
Area of steel required for tension reinforcement, sq-mm
Area of shear reinforcement, sq-mm
Area of shear reinforcement per unit length of the member, sq-mm/mm
Spacing of the shear reinforcement along the length of the beam, mm
Depth of compression block, mm
Depth of compression block at balanced condition, mm
Maximum allowed depth of compression block, mm
Width of member, mm
Effective width of flange (T-Beam section), mm
Width of web (T-Beam section), mm
Perimeter of the punching critical section, mm
Width of the punching critical section in the direction of bending, mm
Width of the punching critical section perpendicular to the direction of
bending, mm
Depth to neutral axis, mm
Depth to neutral axis at balanced conditions, mm
Distance from compression face to tension reinforcement, mm
Concrete cover to center of reinforcing, mm
Thickness of slab (T-Beam section), mm
Modulus of elasticity of concrete, MPa
Modulus of elasticity of reinforcement, assumed as 200,000 MPa
Specified compressive strength of concrete, MPa (17.5 ≤ f ′ ≤ 100)
f
f
h
M
Specified yield strength of flexural reinforcement, MPa ( f ≤ 500)
Specified yield strength of shear reinforcement, MPa ( f ≤ 800)
Overall thickness of a slab or overall depth of a beam, mm
Factored moment at section, N-mm
s ( required
v
v
b
max
f
w
0
1
2
b
s
c
s
c
)
c
y
y
yt
t
*
Table E-1
List of Symbols Used in the New Zealand code
166
Design Load Combinations
Appendix E Design for NZS 3101-95
V
V
V
V
v
v
v
v
α
c
max
*
s
b
c
max
1
β
β
ε
ε
ϕ
ϕ
γ
γ
1
c
c
s
b
s
f
v
Shear resisted by concrete, N
Maximum permitted total factored shear force at a section, lb
Factored shear force at a section, N
Shear force at a section resisted by steel, N
Average design shear stress at a section, MPa
Basic design shear stress resisted by concrete, MPa
Design shear stress resisted by concrete, MPa
Maximum design shear stress permitted at a section, MPa
Concrete strength factor to account for sustained loading and equivalent
stress block
Factor for obtaining depth of compression block in concrete
Ratio of the maximum to the minimum dimensions of the punching
critical section
Strain in concrete
Strain in reinforcing steel
Strength reduction factor for bending
Strength reduction factor for shear
Fraction of unbalanced moment transferred by flexure
Fraction of unbalanced moment transferred by eccentricity of shear
Table E-1
List of Symbols Used in the New Zealand code (continued)
Design Load Combinations
167
SAFE User's Manual
versible, then the following load combinations have to be considered (NZS 420392 2.4.3):
1.4 DL
1.2 DL + 1.6 LL
1.2 DL + 1.6*0.75 PLL
(NZS 4203-92 2.4.3.3)
(NZS 3101-95 14.9.6.3)
1.2 DL ± 1.0 WL
0.9 DL ± 1.0 WL
1.2 DL + 0.4 LL ± 1.0 WL
(NZS 4203-92 2.4.3.3)
1.0 DL ± 1.0 EL
1.0 DL + 0.4 LL ± 1.0 EL
(NZS 4203-92 2.4.3.3)
These are also the default design load combinations in SAFE whenever the NZS
3101-95 code is used. The user should use other appropriate loading combinations
if roof live load is separately treated, or other types of loads are present.
Strength Reduction Factors
The default strength reduction factor, ϕ, is taken as
ϕ = 0.85 for bending,
(NZS 3.4.2.2)
ϕ = 0.75 for shear.
(NZS 3.4.2.2)
b
s
The user is allowed to overwrite these values. However, caution is advised.
Beam Design
In the design of concrete beams, SAFE calculates and reports the required areas of
steel for flexure and shear based upon the beam moments, shear forces, load combination factors and other criteria described below. The reinforcement requirements
are calculated at two check stations at the ends of the beam elements. All the beams
are only designed for major direction flexure and shear. Effects due to any axial
forces, minor direction bending, and torsion that may exist in the beams must be investigated independently by the user.
The beam design procedure involves the following steps:
• Design beam flexural reinforcement
• Design beam shear reinforcement
168
Strength Reduction Factors
Appendix E Design for NZS 3101-95
Design Beam Flexural Reinforcement
The beam top and bottom flexural steel is designed at the two stations at the ends of
the beam elements. In designing the flexural reinforcement for the major moment
of a particular beam for a particular station, the following steps are involved:
• Determine the maximum factored moments
• Determine the reinforcing steel
Determine Factored Moments
In the design of flexural reinforcement of concrete beams, the factored moments for
each load combination at a particular beam section are obtained by factoring the
corresponding moments for different load cases with the corresponding load factors.
The beam section is then designed for the maximum positive and maximum negative factored moments obtained from all the of the load combinations. Positive
beam moments produce bottom steel. In such cases the beam may be designed as a
Rectangular- or a T-beam. Negative beam moments produce top steel. In such cases
the beam is always designed as a rectangular section.
Determine Required Flexural Reinforcement
In the flexural reinforcement design process, the program calculates both the tension and compression reinforcement. Compression reinforcement is added when
the applied design moment exceeds the maximum moment capacity of a singly reinforced section. The user has the option of avoiding the compression reinforcement by increasing the effective depth, the width, or the grade of concrete.
The design procedure is based on the simplified rectangular stress block as shown
in Figure E-1 (NZS 8.3.1.6). Furthermore it is assumed that the compression carried
by concrete is 0.75 times that which can be carried at the balanced condition (NZS
8.4.2). When the applied moment exceeds the moment capacity at the balanced
condition, the area of compression reinforcement is calculated on the assumption
that the additional moment will be carried by compression and additional tension
reinforcement.
In designing the beam flexural reinforcement, the following limits are imposed on
the steel tensile strength and the concrete compressive strength:
Beam Design
169
SAFE User's Manual
f ≤ 500 MPa
(NZS 3.8.2.1)
f ′ ≤ 100 MPa
(NZS 3.8.1.1)
y
c
The design procedure used by SAFE, for both rectangular and flanged sections (Land T-beams) is summarized below. All the beams are designed only for major direction flexure and shear.
Design for Flexure of a Rectangular Beam
In designing for a factored negative or positive moment, M , (i.e. designing top or
bottom steel) the depth of the compression block, a (See Figure E-1), is computed
as,
*
a= d−
d −
2 M
2
*
α f′ϕ b
1
c
,
(NZS 8.3.1)
b
where the default value of ϕ is 0.85 (NZS 3.4.2.2) in the above and following
equations. Also α is calculated as follows:
b
1
α = 0.85 − 0.004( f ′ − 55) , 0.75 ≤ α ≤ 0.85 .
1
c
1
(NZS 8.3.1.7)
Also β and c are calculated as follows:
1
b
β = 0.85 − 0.008( f ′ − 30) , 0.65 ≤ β ≤ 0.85 , and
1
c
600
600 + f
c =
b
1
d.
(NZS 8.3.1.7)
(NZS 8.4.1.2)
y
The maximum allowed depth of the compression block is given by
a
max
= 0.75β c .
1
• If a ≤ a
A =
s
max
(NZS 8.4.2 and NZS 8.3.1.7)
b
(NZS 8.4.2), the area of tensile steel reinforcement is then given by
M
.
a

ϕ f d − 
2

*
b
y
This steel is to be placed at the bottom if M is positive, or at the top if M is
negative.
*
170
Beam Design
*
Appendix E Design for NZS 3101-95
• If a > a (NZS 8.4.2), compression reinforcement is required (NZS 8.4.1.3)
and is calculated as follows:
max
– The compressive force developed in concrete alone is given by
C = α f ′ ba
1
c
max
, and
(NZS 8.3.1.7)
the moment resisted by concrete and bottom steel is
a 

ϕ .
M = C d −
2 

*
max
c
b
– The moment resisted by compression steel and tensile steel is
M =M −M .
*
*
*
s
c
α1 f'c
ε = 0.003
b
Cs
d'
A's
a=
c
1c
d
εs
As
Beam Section
Strain Diagram
Ts
Tc
Stress Diagram
Figure E-1
Design of a Rectangular Beam Section
– So the required compression steel is given by
M
′
A =
s
*
s
( f ′ − α f ′ )( d − d′ ) ϕ
s
1
c
, where
b
Beam Design
171
SAFE User's Manual
 c − d′ 
f ′ = 0.003 E 
≤f .
 c 
s
s
(NZS 8.3.1.2 and NZS 8.3.1.3)
y
– The required tensile steel for the balancing the compression in concrete is
A =
s1
M
a
f (d −
*
c
, and
max
y
2
)ϕ
b
the tensile steel for balancing the compression in steel is
A =
s2
M
.
f ( d − d′ ) ϕ
*
s
y
b
– Therefore, the total tensile reinforcement, A = A + A , and total compression reinforcement is A ′ . A is to be placed at the bottom and A ′ is to be
placed at the top if M is positive, and vice versa.
s
s
s1
s2
s
s
*
Design for Flexure of a T-Beam
(i) Flanged Beam Under Negative Moment
In designing for a factored negative moment, M , (i.e. designing top steel), the calculation of the steel area is exactly the same as above, i.e., no T-Beam data is to be
used.
*
(ii) Flanged Beam Under Positive Moment
If M > 0, the depth of the compression block is given by (see Figure E-2).
*
a= d−
2 M
d −
2
*
α f′ϕ b
1
c
b
,
(NZS 8.3.1)
f
The maximum allowed depth of the compression block is given by
a
max
= 0.75 β c .
1
(NZS 8.4.2 and NZS 8.3.1.7)
b
• If a ≤ d (NZS 8.4.2), the subsequent calculations for A are exactly the same as
previously done for the rectangular section design. However, in this case the
width of the beam is taken as b . Whether compression reinforcement is required depends on whether a > a .
s
s
f
max
172
Beam Design
Appendix E Design for NZS 3101-95
• If a > d (NZS 8.4.2), calculation for A is done in two parts. The first part is for
balancing the compressive force from the flange, C , and the second part is for
balancing the compressive force from the web, C . As shown in Figure E-2,
s
s
f
w
′
C = α f ( b − b ) min( d , a
1
f
c
f
w
s
max
).
d'
α1 f'c
α1 f'c
ε = 0.003
ds
bf
(NZS 8.3.1.7)
fs'
Cs
As'
a=
Cf
1c
c
d
Cw
εs
As
Ts
Tw
Tf
bw
Beam Section
Strain Diagram
Stress Diagram
Figure E-2
Design of a T-Beam Section
Therefore, A =
C
f
f
y
s1
and the portion of M that is resisted by the flange is
*
given by
min( d , a

M = C d−
2

*
f
s
f
max
)
ϕ .

b
Therefore, the balance of the moment, M to be carried by the web is given by
*
M = M −M .
*
w
*
*
f
The web is a rectangular section of dimensions b and d, for which the depth of
the compression block is recalculated as
w
Beam Design
173
SAFE User's Manual
a = d−
d −
2M
2
1
1
.
α f′ϕ b
1
• If a ≤ a
given by
*
w
c
b
(NZS 8.3.1)
w
(NZS 8.4.2), the area of tensile steel reinforcement is then
max
M
, and
a 


ϕ f d −
2 

*
A =
w
s2
1
b
y
A = A +A .
s1
s
s2
This steel is to be placed at the bottom of the T-beam.
• If a > a (NZS 8.4.2), compression reinforcement is required and is calculated as follows:
1
max
– The compressive force in the concrete web alone is given by
C = α f ′b a
1
w
c
w
, and
max
(NZS 8.3.1.7)
the moment resisted by the concrete web and tensile steel is
a 

ϕ .
M = C d −
2 

*
max
c
w
b
– The moment resisted by compression steel and tensile steel is
M =M −M .
*
*
*
s
w
c
– Therefore, the compression steel is computed as
A′ =
s
M
*
s
( f ′ − α f ′ )( d − d′ ) ϕ
1
s
c
, where
b
 c − d′ 
f ′ = 0.003 E 
≤ f .
 c 
s
s
y
(NZS 8.3.1.2 and NZS 8.3.1.3)
– The tensile steel for balancing compression in web concrete is
A =
s2
M
, and
a 

ϕ
f d −
2 

*
c
max
y
174
Beam Design
b
Appendix E Design for NZS 3101-95
the tensile steel for balancing compression in steel is
A =
s3
M
.
f ( d − d′) ϕ
*
s
y
b
– Total tensile reinforcement, A = A + A + A , and total compression
reinforcement is A ′ . A is to be placed at the bottom and A ′ is to be
placed at the top.
s1
s
s
s2
s3
s
s
Minimum and Maximum Tensile Reinforcement
The minimum flexural tensile steel required for a beam section is given by the minimum of the two limits:
A ≥
s
A ≥
s
f
′
c
4f
4
A
3
s
b d, or
(NZS 8.4.3.1)
w
y
( required )
.
(NZS 8.4.3.3)
An upper limit of 0.04 times the gross web area on both the tension reinforcement
and the compression reinforcement is imposed upon request as follows:
 0.04 b d Rectangular beam
A ≤
 0.04 b d T -beam
s
w
 0.04 b d Rectangular beam
A′ ≤ 
 0.04 b d T -beam
s
w
Design Beam Shear Reinforcement
The shear reinforcement is designed for each load combination at two stations at the
ends of each beam elements. In designing the shear reinforcement of a particular
beam for a particular loading combination at a particular station due to the beam
major shear, the following steps are involved:
*
• Determine the factored shear force,V .
• Determine the shear force,V , that can be resisted by the concrete.
c
• Determine the reinforcement steel required to carry the balance.
Beam Design
175
SAFE User's Manual
In designing the beam shear reinforcement, the following limits are imposed on the
steel tensile strength and the concrete compressive strength:
≤ 500 MPa
(NZS 3.8.2.1 and NZS 9.3.6.1)
f ′ ≤ 100 MPa
(NZS 3.8.1.1)
f
yt
c
The following three sections describe in detail the algorithms associated with the
above-mentioned steps.
Determine Shear Force and Moment
In the design of the beam shear reinforcement of concrete frame, the shear forces
and moments for a particular load combination at a particular beam section are obtained by factoring the associated shear forces and moments with the corresponding
load combination factors.
Determine Concrete Shear Capacity
The shear force carried by the concrete,V , is calculated as follows:
c
• The basic shear strength for rectangular section is computed as,

A 
v =  0.07 + 10
 f
b d

s
b
′
c
, where
(NZS 9.3.2.1)
w
f ′ ≤ 70 , and
(NZS 9.3.2.1)
c
′
0.08 f
c
≤ v ≤ 0.2 f ′ .
b
c
(NZS 9.3.2.1)
• The allowable shear capacity is given by,
v = v .
c
b
(NZS 9.3.2.1)
Determine Required Shear Reinforcement
• The average shear stress is computed for a rectangular section as,
V
.
b d
*
v =
*
w
• The average shear stress is limited to a maximum limit of,
176
Beam Design
(NZS 9.3.1.1)
Appendix E Design for NZS 3101-95
v
max
{
}
= min 1.1 f ′ , 0.2 f ′ , 9 Mpa .
c
c
(NZS 9.3.1.8)
• The shear reinforcement is computed as follows:
If v ≤ ϕ ( v 2) ,
*
s
c
A
=0,
s
v
(NZS 9.3.4.1)
else if ϕ ( v 2) < v ≤ ϕ ( v + 0.35) ,
*
s
c
s
c
A 0.35b
,
=
s
f
v
w
(NZS 9.3.4.3)
yt
else if ϕ ( v + 0.35) < v ≤ ϕ v
*
s
c
s
max
A (v − ϕ v ) b
,
=
s
ϕ f
,
*
v
s
s
else if v > v
*
max
c
w
(NZS 9.3.6.3)
yt
,
a failure condition is declared.
(NZS 9.3.1.8)
The maximum of all the calculated A s values, obtained from each load combination, is reported along with the controlling shear force and associated load combination number.
v
The beam shear reinforcement requirements displayed by the program are based
purely upon shear strength considerations. Any minimum stirrup requirements to
satisfy spacing and volumetric considerations must be investigated independently
of the program by the user.
Slab Design
As is done in conventional design, the SAFE slab design procedure involves defining sets of strips in two mutually perpendicular directions. The locations of the
strips are usually governed by the locations of the slab supports. The moments for a
particular strip are recovered from the analysis and a flexural design is carried out
based on the ultimate strength design method for reinforced concrete (NZS
3101-95) as described in the following sections. To learn more about the design
strips, refer to the section “Integrated Strip Moments and Shears” on page 25.
Slab Design
177
SAFE User's Manual
Design for Flexure
SAFE designs the slab on a strip-by-strip basis. The moments used for the design of
the slab elements are the nodal reactive moments, which are obtained by multiplying the slab element stiffness matrices by the element nodal displacement vectors.
These moments will always be in static equilibrium with the applied loads, irrespective of the refinement of the finite element mesh.
The design of the slab reinforcement for a particular strip is carried out at specific
locations along the length of the strip. These locations correspond to the element
boundaries. Controlling reinforcement is computed on either side of these element
boundaries. The slab flexural design procedure for each load combination involves
the following:
• Determine factored moments for each slab strip.
• Design flexural reinforcement for the strip.
These two steps described below are repeated for every load combination. The
maximum reinforcement calculated for the top and bottom of the slab within each
design strip, along with the corresponding controlling load combination numbers,
is obtained and reported.
Determine Factored Moments for the Strip
For each element within the design strip, for each load combination the program
calculates the nodal reactive moments. The nodal moments are then added to get
the strip moments.
Design Flexural reinforcement for the Strip
The reinforcement computation for each slab design strip given the bending moment is identical to the design of rectangular beam sections described earlier.
Where the slab properties (depth, etc.) vary over the width of the strip the program
automatically designs slab widths of each property separately for the bending moment they are subjected to before summing up the reinforcement for the full width.
Where openings occur the slab width is adjusted accordingly.
Minimum Slab Reinforcement
The minimum flexural tensile reinforcement required for each direction of a slab is
given by the following limit (NZS 8.4.3.4):
178
Slab Design
Appendix E Design for NZS 3101-95
 0.7
bh
if f < 500 MPa

A ≥ f
 0.0014 bh if f ≥ 500 MPa
y
s
y
(NZS 7.3.30.1)
y
In addition, an upper limit on both the tension reinforcement and compression reinforcement has been imposed to be 0.04 times the gross cross-sectional area.
Check for Punching Shear
The algorithm for checking punching shear is detailed in section “Checking Punching Shear Capacity” on page 26. Only the code specific items are described in the
following.
Critical Section for Punching Shear
The punching shear is checked on a critical section at a distance of d 2 from the face
of the support (NZS 9.3.15.1). For rectangular columns and concentrated loads, the
critical area is taken as a rectangular area with the sides parallel to the sides of the
columns or the point loads (NZS 9.3.15.1).
Transfer of Unbalanced Moment
The fraction of unbalanced moment transferred by flexure is taken to be γ M and
the fraction of unbalanced moment transferred by eccentricity of shear is taken to
be γ M , where
*
f
*
v
γ =
f
1
1 + ( 2 3) b b
1
γ = 1−
v
, and
(NZS 14.3.5)
2
1
1 + ( 2 3) b b
1
,
(NZS 9.3.16.2)
2
where b is the width of the critical section measured in the direction of the span and
b is the width of the critical section measured in the direction perpendicular to the
span.
1
2
Determination of Capacity Ratio
The concrete punching shear factored strength is taken as the minimum of the following three limits:
Slab Design
179
SAFE User's Manual
ϕ


v = min  ϕ

ϕ

c
s
(1 + 2β ) 0.17 f
c
 α d
1 +
 0.17 f
 2b 
0.33 f ′
s
s
′
c
′
(NZS 9.3.15.2)
c
0
s
c
where, β is the ratio of the minimum to the maximum dimensions of the critical
section, b is the perimeter of the critical section, and α is a scale factor based on
the location of the critical section.
c
0
 40

α =  30
 20

s
A limit on
s
for interior columns,
for edge columns, and
for corner columns.
(NZS 9.3.15.2)
f ′ is imposed as follows:
c
f ′ ≤ 70
c
(NZS 9.3.2.1)
Determination of Capacity Ratio
Given the punching shear force and the fractions of moments transferred by
eccentricity of shear about the two axes, the shear stress is computed assuming linear variation along the perimeter of the critical section. The ratio of the
maximum shear stress and the concrete punching shear stress capacity is reported by SAFE.
180
Slab Design
Appendix F
Design for IS 456-78 (R1996)
This Appendix describes in detail the various aspects of the concrete design procedure that is used by SAFE when the user selects the Indian Code IS 345-78 Revision 1996 (IS 1996). Various notations used in this Appendix are listed in Table
F-1. For referencing to the pertinent sections of the Indian code in this Appendix, a
prefix “IS” followed by the section number is used here.
The design is based on user-specified loading combinations. However, the program
provides a set of default load combinations that should satisfy requirements for the
design of most building type structures.
English as well as SI and MKS metric units can be used for input. But the code is
based on Newton-Millimeter-Second units. For simplicity, all equations and descriptions presented in this Appendix correspond to Newton-Millimeter-Second
units unless otherwise noted.
Design Load Combinations
The design load combinations are the various combinations of the prescribed load
cases for which the structure needs to be checked. For this code, if a structure is subjected to dead load (DL), live load (LL), pattern live load (PLL), wind (WL), and
earthquake (EL) loads, and considering that wind and earthquake forces are
reversible, then the following load combinations have to be considered (IS 35.4):
Design Load Combinations
181
SAFE User's Manual
A
A
A
A
A′
Area of concrete, mm2
Area of section for shear resistance, mm2
Gross cross-sectional area of a frame member, mm2
Area of tension reinforcement, mm2
Area of compression reinforcement, mm2
A
A
a
a
Total cross-sectional area of links at the neutral axis, mm2
Area of shear reinforcement per unit length of the member, mm2/mm
Width of the punching critical section in the direction of bending, mm
Width of the punching critical section perpendicular to the direction of
bending, mm
Width or effective width of the section in the compression zone, mm
Width or effective width of flange, mm
Average web width of a flanged beam, mm
Effective depth of tension reinforcement, mm
Effective depth of compression reinforcement, mm
Depth of center of compression block from most compressed face, mm
Overall depth of a beam or slab, mm
Flange thickness in a T-beam, mm
Modulus of elasticity of concrete, MPa
Modulus of elasticity of reinforcement, assumed as 200,000 MPa
Design concrete strength = f γ , MPa
Characteristic compressive strength of concrete, Mpa
Compressive stress in a beam compression steel, MPa
c
cv
g
s
s
sv
sv
s
v
1
2
b
b
b
d
d′
d
D
D
E
E
f
f
f′
f
w
compression
f
c
s
cd
ck
s
f
f
f
h
k
M
single
M
u
yd
y
ys
ck
c
Design yield strength of reinforcing steel = f γ , MPa
Characteristic strength of reinforcement, MPa
Characteristic strength of shear reinforcement, MPa
Overall thickness of a slab, mm
Enhancement factor of shear strength for depth of the beam
Design moment resistance of a section as a singly reinforced section,
N-mm
Ultimate factored design moment at a section obtained, N-mm
y
Table F-1
List of Symbols Used in the Indian Code
182
Design Load Combinations
s
Appendix F Design for IS 456-78 (R1996)
m
s
V
v
x
x
Z
α
2
ck
v
u
c
u
u,max
β
β
γ
γ
Normalized design moment, M bd αf
Spacing of the shear reinforcement along the length of the beam, mm
Shear force at ultimate design load, N
Allowable shear stress in punching shear mode, N
Depth of neutral axis, mm
Maximum permitted depth of neutral axis, mm
Lever arm, mm
Concrete strength reduction factor for sustained loading,
Also fraction of moment to be transferred by flexure in a slabcolumn joint
Factor for the depth of compressive force resultant of the concrete
stress block
Ratio of the maximum to the minimum dimensions of the punching
critical section
Partial safety factor for concrete strength
Partial safety factor for load, and
Fraction of unbalanced moment transferred by flexure
Partial safety factor for material strength
Partial safety factor for steel strength
Fraction of unbalanced moment transferred by eccentricity of shear
Enhancement factor of shear strength for compression
Maximum concrete strain in the beam and slab (= 0.0035)
Strain in tension steel
Strain in compression steel
Tension reinforcement ratio, A bd
Average design shear stress at a section, MPa
Basic design shear stress resisted by concrete, MPa
Maximum possible design shear stress permitted at a section, MPa
Design shear stress resisted by concrete, Mpa
c
c
f
γ
γ
γ
δ
ε
ε
ε ′
ρ
τ
τ
τ
τ
m
s
v
c,max
s
s
v
c
c , max
cd
s
Table F-1
List of Symbols Used in the Indian Code (continued)
Design Load Combinations
183
SAFE User's Manual
1.5 DL
1.5 DL + 1.5 LL
(IS 35.4.1)
1.5 DL + 1.5*0.75 PLL
(IS 30.5.2.3)
1.5 DL ± 1.5 WL
0.9 DL ± 1.5 WL
1.2 DL + 1.2 LL ± 1.2 WL
(IS 35.4.1)
1.5 DL ± 1.5 EL
0.9 DL ± 1.5 EL
1.2 DL + 1.2 LL ± 1.2 EL
(IS 35.4.1)
These are also the default design load combinations in SAFE whenever the Indian
Code is used. The user should use other appropriate loading combinations if roof
live load is separately treated, or other types of loads are present.
Design Strength
The design strength for concrete and steel are obtained by dividing the characteristic strength of the material by a partial factor of safety, γ . The values of γ used in
the program are listed below:
m
m
Partial safety factor for steel, γ = 1.15 , and
(IS 35.4.2.1)
Partial safety factor for concrete, γ = 1.5 .
(IS 35.4.2.1)
s
c
These factors are already incorporated in the design equations and tables in the
code. SAFE does not allow them to be overwritten.
Beam Design
In the design of concrete beams, SAFE calculates and reports the required areas of
steel for flexure and shear based upon the beam moments, shears, load combination
factors, and other criteria described below. The reinforcement requirements are calculated at two check stations at the ends of the beam elements.
All the beams are only designed for major direction flexure and shear. Effects due
to any axial forces, minor direction bending, and torsion that may exist in the beams
must be investigated independently by the user.
184
Design Strength
Appendix F Design for IS 456-78 (R1996)
The beam design procedure involves the following steps:
• Design beam flexural reinforcement
• Design beam shear reinforcement
Design Beam Flexural Reinforcement
The beam top and bottom flexural steel is designed at the two stations at the ends of
the beam elements. In designing the flexural reinforcement for the major moment
of a particular beam for a particular station, the following steps are involved:
• Determine the maximum factored moments
• Determine the reinforcing steel
Determine Factored Moments
In the design of flexural reinforcement of concrete beams, the factored moments for
each load combination at a particular beam section are obtained by factoring the
corresponding moments for different load cases with the corresponding load factors.
The beam section is then designed for the maximum positive and maximum negative factored moments obtained from all the of the load combinations. Positive
beam moments produce bottom steel. In such cases the beam may be designed as a
Rectangular- or a T-beam. Negative beam moments produce top steel. In such cases
the beam is always designed as a rectangular section.
Determine Required Flexural Reinforcement
In the flexural reinforcement design process, the program calculates both the tension and compression reinforcement. Compression reinforcement is added when
the applied design moment exceeds the maximum moment capacity of a singly reinforced section. The user has the option of avoiding the compression reinforcement by increasing the effective depth, the width, or the grade of concrete.
The design procedure is based on the simplified parabolic stress block as shown in
Figure F-1 (IS 37.1). The area of the stress block, C, and the depth of the center of
the compressive force from the most compressed fiber, d, are taken as
C = α f x and
(IS 37.1)
=βx ,
(IS 37.1)
ck
d
compression
u
u
Beam Design
185
SAFE User's Manual
where x is the depth of the compression block, and α and β are taken respectively
as
u
α = 0.36 ,
and
(IS 37.1)
β = 0.42 .
(IS 37.1)
α is the reduction factor to account for sustained compression and the partial safety
factor for concrete. α is generally assumed to be 0.36 for the assumed parabolic
stress block (IS 37.1). β factor considers the depth of the neutral axis.
0.67fck/γm
ε = 0.0035
b
fs'
A's
d'
Cs
0.42 xu
xu
C
d
εs
As
Beam Section
Strain Diagram
Ts
Tc
Stress Diagram
Figure F-1
Design of a Rectangular Beam Section
Furthermore, it is assumed that moment redistribution in the member does not exceed the code specified limiting value. The code also places a limitation on the neutral axis depth as shown below, to safeguard against non-ductile failures (IS 37.1).
186
Beam Design
fy
x u max d
250
0.53
415
0.48
500
0.46
,
Appendix F Design for IS 456-78 (R1996)
SAFE uses interpolation between the three discrete points given in the code.
x
 0.53

f − 250
 0.53− 0.05

165
=
f − 415
 0.48 − 0.02

85
 0.46
y
u , max
d
y
if
f ≤ 250
if
250 < f ≤ 415
y
y
(IS 37.1)
if
415 < f ≤ 500
if
f ≥ 500
y
y
When the applied moment exceeds the capacity of the beam as a singly reinforced
beam, the area of compression reinforcement is calculated on the assumption that
the neutral axis depth remains at the maximum permitted value. The maximum fiber compression is taken as
ε
c , max
= 0.0035 ,
(IS 37.1)
and the modulus of elasticity of steel is taken to be
E = 200, 000 MPa .
(IS 37.1)
s
The design procedure used by SAFE, for both rectangular and flanged sections (Land T-beams) is summarized below. It is assumed that the design ultimate axial
force can be neglected, hence all the beams are designed for major direction flexure
and shear only.
Design as a Rectangular Beam
, and the moment
For rectangular beams, the limiting depth of neutral axis, x
capacity as a singly reinforced beam, M
, are obtained first for the section. The
reinforcing steel area is determined based on whether M is greater than, less than,
or equal to M
. See Figure F-1.
u , max
single
u
single
• Calculate the limiting depth of the neutral axis.
x
 0.53

f − 250
 0.53− 0.05

165
=
f − 415
 0.48 − 0.02

85
 0.46
y
u , max
d
y
if
f ≤ 250
if
250 < f ≤ 415
y
y
(IS 37.1)
if
415 < f ≤ 500
if
f ≥ 500
y
y
• Calculate the limiting ultimate moment of resistance as a singly reinforced
beam.
Beam Design
187
SAFE User's Manual
M
= αf bd
single
2
x
u , max
ck
α = 0.36 ,
d
x


1 − β
 , where
d 

u , max
(IS E-1.1)
and
(IS E-1.1)
β = 0.42 .
(IS E-1.1)
• Calculate the depth of neutral axis, x as
u
1− 1− 4 β m
x
,
=
d
2β
u
where the normalized design moment, m , is given by
M
bd αf
m=
• If M
u
≤ M
u
.
2
A =
s
ck
the area of tension reinforcement, A , is obtained from
single
s
M
, where
(f γ )z
u
y
(IS E-1.1)
s
x 

z = d 1− β
.
d 

u
(IS 37.1)
This is the top steel if the section is under negative moment and the bottom steel
if the section is under positive moment.
• If M
> M
u
A′ =
single
, the area of compression reinforcement, A ′ , is given by
s
M −M
s
u
single
f ′ ( d - d′ )
,
(IS E-1.2)
s
where d′ is the depth of the compression steel from the concrete compression
face, and
f′= ε
s

f
d′ 
.
E 1 −
 ≤
γ
x


y
c , max
s
u , max
(IS E-1.2)
s
This is the bottom steel if the section is under negative moment. From equilibrium, the area of tension reinforcement is calculated as
188
Beam Design
Appendix F Design for IS 456-78 (R1996)
M
A =
(f
s
single
γ )z
y
+
s
x

z = d 1− β
d

u , max
M −M
u
(f
y
single
γ )( d − d ′ )
, where
(IS E-1.2)
s

.

(IS 37.1)
Design as a T-Beam
(i) Flanged Beam Under Negative Moment
The contribution of the flange to the strength of the beam is ignored if the flange is
in the tension side. See Figure F-2. The design procedure is therefore identical to
the one used for rectangular beams. However, the width of the web, b , is taken as
the width of the beam.
w
(ii) Flanged Beam Under Positive Moment
With the flange in compression, the program analyzes the section by considering
alternative locations of the neutral axis. Initially the neutral axis is assumed to be located within the flange. Based on this assumption, the program calculates the depth
of the neutral axis. If the stress block does not extend beyond the flange thickness
the section is designed as a rectangular beam of width b . If the stress block extends
beyond the flange, additional calculation is required. See Figure F-2.
f
• Assuming the neutral axis to lie in the flange, calculate the depth of neutral
axis, x , as
u
1− 1− 4 β m
x
,
=
d
2β
u
where the normalized design moment, m , is given by
m=
M
b d αf
u
.
2
f
ck
 x  D 
 , the neutral axis lies within the flange. The subsequent calcula• If   ≤ 
d  d 
tions for A are exactly the same as previously defined for the rectangular section design (IS E-2.1). However, in this case the width of the compression
flange, b , is taken as the width of the beam, b, for analysis. Whether compression reinforcement is required depends on whether M > M
.
f
u
s
f
u
single
Beam Design
189
SAFE User's Manual
d'
fs'
0.42 xu
Cs
As'
0.67 fck/γm
0.67 fck/γm
ε = 0.0035
Df
bf
Cf
C
xu
d
Cw
εs
As
Ts
Tf
Tw
bw
Beam Section
Strain Diagram
Stress Diagram
Figure F-2
Design of a T-Beam Section
 x  D 
 , the neutral axis lies below the flange. Then calculation for
• If   > 
d  d 
A is done in two parts. The first part is for balancing the compressive force
from the flange, C , and the second part is for balancing the compressive force
from the web, C , as shown in Figure F-2.
f
u
s
f
w
– Calculate the ultimate resistance moment of the flange as
M = 0.45 f ( b − b ) y ( d − 0.5 y ) ,
f
ck
f
w
f
f
(IS E-2.2)
where y is taken as follows:
f
D
y =
 0.15x + 0.65D
f
f
u
f
if
if
D ≤ 0.2d
D > 0.2d
f
(IS E-2.2)
f
– Calculate the moment taken by the web as
M = M − M .
w
u
f
– Calculate the limiting ultimate moment of resistance of the web for only tension reinforcement.
190
Beam Design
Appendix F Design for IS 456-78 (R1996)
M
x
= αf b d
w , single
ck
2
x
u , max
d
w
x


1− β
 , where
d 

u , max
 0.53

f − 250
 0.53− 0.05

165
=
f − 415
 0.48 − 0.02

85
 0.46
y
u , max
d
if
f ≤ 250
if
250 < f ≤ 415
if
415 < f ≤ 500
if
f ≥ 500
y
y
(IS 37.1)
y
α = 0.36 ,
(IS E-1.1)
y
y
and
(IS 37.1)
β = 0.42 .
(IS 37.1)
, the beam is designed as a singly reinforced concrete
– If M ≤ M
beam. The area of steel is calculated as the sum of two parts, one to balance
compression in the flange and one to balance compression in the web.
w , single
w
M
A =
(f
s
f
γ )( d − 0.5 y )
y
s
f
+
M
, where
(f γ )z
w
y
s
x 

z = d 1− β
,
d 

u
1 − 1 − 4β m
x
, and
=
d
2β
u
m=
M
b d αf
w
w
– If M
> M
w
.
2
A′ =
ck
w , single
, the area of compression reinforcement, A ′ , is given by
M −M
s
w
′
s
w , single
f ( d − d′ )
,
s
where d′ is the depth of the compression steel from the concrete compression face, and
f′= ε
s

f
d′ 
.
E 1 −
 ≤
γ
x


y
c , max
s
u , max
(IS E-1.2)
s
Beam Design
191
SAFE User's Manual
This is the bottom steel if the section is under negative moment. From equilibrium, the area of tension reinforcement is calculated as
A =
s
M
(f
y
f
γ )( d − 0.5y )
s
+
f
M
(f
y
w,single
γ )z
s
+
M −M
w
(f
y
w , single
γ )( d − d ′ )
,
s
where
x

z = d 1− β
d

u , max

.

Minimum Tensile Reinforcement
The minimum flexural tensile steel required for a beam section is given by the following equation (IS 25.5.1.1):
 0.85
 f bd

A ≥
 0.85
 f b d

Rectangular beam
y
(IS 25.5.1.1)
s
w
T -beam
y
An upper limit on the tension reinforcement (IS 25.5.1.1) and compression reinforcement (IS 25.5.1.2) has been imposed to be 0.04 times the gross web area.
 0.04 b d Rectangular beam
A ≤
 0.04 b d T -beam
(IS 25.5.1.1)
 0.04 b d Rectangular beam
A′ ≤ 
 0.04 b d T -beam
(IS 25.5.1.2)
s
w
s
w
Design Beam Shear Reinforcement
The shear reinforcement is designed for each loading combination at two stations at
the ends of each beam element. The assumptions in designing the shear reinforcement are as follows:
• The beam sections are assumed to be prismatic. The effect of any variation of
width in the beam section on the concrete shear capacity is neglected.
192
Beam Design
Appendix F Design for IS 456-78 (R1996)
• The effect on the concrete shear capacity of any concentrated or distributed
load in the span of the beam between two columns is ignored. Also, the effect of
the direct support on the beams provided by the columns is ignored.
• All shear reinforcement is assumed to be perpendicular to the longitudinal reinforcement.
• The effect of any torsion is neglected for the design of shear reinforcement.
The shear reinforcement is designed for each loading combination in the major direction of the beam. In designing the shear reinforcement for a particular beam for a
particular loading combination, the following steps are involved (IS 39.2):
• Calculate the design nominal shear stress as
τ =
v
V
, A = b d , where
A
u
cv
(IS 39.1)
w
cv
τ ≤ τ
v
c , max
, and
(IS 39.2.3)
the maximum nominal shear stress, τ
c , max
, is given in the IS Table 14 as follows:
Maximum Shear Stress, τ c max ( MPa )
(IS 39.2.3, IS Table 14)
,
Concrete Grade
τc
,
max
(MPa )
M15
M20
M25
M30
M35
M40
2.5
2.8
3.1
3.5
3.7
4.0
The maximum nominal shear stress, τ
, is computed by the following equation which matches the IS Table 14 exactly.
c , max
Beam Design
193
SAFE User's Manual
τ
c , max
 2.5

f
 2.5 + 0.3

 2.8 + 0.3 f


f
=  3.1 + 0.4

 3.5 + 0.2 f


f
 3.7 + 0.3
 4.0

ck
ck
ck
ck
ck
− 15
5
− 20
5
− 25
5
− 30
5
− 35
5
if
f
ck
< 15
if
15 ≤ f
ck
< 20
if
20 ≤ f
ck
< 25
if
25 ≤ f
ck
< 30
if
30 ≤ f
ck
< 35
if
35 ≤ f
ck
< 40
if
f
ck
≥ 40
(IS 39.2.3)
• Calculate the design shear strength of concrete from
τ
cd
= k δτ ,
(IS 39.2)
c
where k is the enhancement factor for the depth of the beam section and
is computed by
k = 1.6 − 0.002 d ,
1.0 ≤ k ≤ 1.3 .
(IS 39.2.1.1)
The above expression represents the table given in IS 39.2.1.1, which is shown
below:
The Value of the Enhancement Factor, k
(IS 39.2.1.1)
Overall depth of slab, d (mm)
≥300
275
250
225
200
175
≤150
Factor, k
1.00
1.05
1.10
1.15
1.20
1.25
1.30
δ is the enhancement factor for compression and is given by
P

1 + 3
δ= 
A f
1
≤ 1.5 if
u
g
ck
if
P > 0, Under Compression
u
(IS 39.2.2)
P ≤ 0, Under Tension
u
δ is always taken as 1, and
τ is the basic design shear strength for concrete which is given by
c
194
Beam Design
Appendix F Design for IS 456-78 (R1996)
1
1
 100 A  3  f  4
 .
 
τ = 0.64 
 bd   25 
s
ck
(IS 39.2.1)
c
The above expression tries to represent the IS Table 13 approximately. It
should be mentioned that the value of γ has already been incorporated in the
IS Table 13 (See Note in IS 35.4.2.1). The following limitations are enforced in
the determination of the design shear strength as is done in the Table.
c
0.25 ≤
f
ck
100 A
≤ 3,
bd
s
(IS 39.2.1)
≤ 40 MPa (for calculation purpose only).
(IS 39.2.1)
• The shear reinforcement is computed as follows:
If τ ≤ τ + 0.4 , provide minimum links defined by
v
cd
A
s
sv
≥
v
0.4 b
0.87 f
w
,
(IS 39.3 and IS 25.5.1.6)
ys
else if τ + 0.4 < τ ≤ τ
cd
A
s
sv
≥
v
v
c , max
, provide links given by
(τ − τ ) b
,
0.87 f
v
cd
w
(IS 39.4)
ys
else if τ > τ
v
c , max
,
a failure condition is declared.
(IS 39.2.3)
In calculating the shear reinforcement, a limit was imposed on the f
f
ys
≤ 415 MPa .
yv
as
(IS 39.4)
The maximum of all the calculated A s values, obtained from each load
combination, is reported along with the controlling shear force and associated
load combination number.
sv
v
The beam shear reinforcement requirements displayed by the program are
based purely upon shear strength considerations. Any minimum stirrup requirements to satisfy spacing and volumetric considerations must be investigated independently of the program by the user.
Beam Design
195
SAFE User's Manual
Slab Design
As is done in conventional design, the SAFE slab design procedure involves defining sets of strips in two mutually perpendicular directions. The locations of the
strips are usually governed by the locations of the slab supports. The moments for a
particular strip are recovered from the analysis and a flexural design is carried out
based on the limit state of collapse for reinforced concrete (IS 37) as described in
the following sections. To learn more about the design strips, refer to the section
“Integrated Strip Moments and Shears” on page 25.
Design for Flexure
SAFE designs the slab on a strip-by-strip basis. The moments used for the design of
the slab elements are the nodal reactive moments, which are obtained by multiplying the slab element stiffness matrices by the element nodal displacement vectors.
These moments will always be in static equilibrium with the applied loads, irrespective of the refinement of the finite element mesh.
The design of the slab reinforcement for a particular strip is carried out at specific
locations along the length of the strip. These locations correspond to the element
boundaries. Controlling reinforcement is computed on either side of these element
boundaries. The slab flexural design procedure for each load combination involves
the following:
• Determine factored moments for each slab strip.
• Design flexural reinforcement for the strip.
These two steps described below are repeated for every load combination. The
maximum reinforcement calculated for the top and bottom of the slab within each
design strip, along with the corresponding controlling load combination numbers,
is obtained and reported.
Determine Factored Moments for the Strip
For each element within the design strip, for each load combination the program
calculates the nodal reactive moments. The nodal moments are then added to get
the strip moments.
Design Flexural reinforcement for the Strip
The reinforcement computation for each slab design strip given the bending moment is identical to the design of rectangular beam sections described earlier.
196
Slab Design
Appendix F Design for IS 456-78 (R1996)
Where the slab properties (depth, etc.) vary over the width of the strip the program
automatically designs slab widths of each property separately for the bending moment they are subjected to before summing up the reinforcement for the full width.
Where openings occur the slab width is adjusted accordingly.
Minimum Slab Reinforcement
The minimum flexural tensile reinforcement required for each direction of a slab is
given by the following limits (IS 25.5.2):
 0.0015 bh if f < 500 MPa
A ≥
 0.0012 bh if f ≥ 500 MPa
y
s
(IS 25.5.2.1)
y
In addition, an upper limit on both the tension reinforcement and compression reinforcement has been imposed to be 0.04 times the gross cross-sectional area (IS
25.5.1.1).
Check for Punching Shear
The algorithm for checking punching shear is detailed in section “Checking Punching Shear Capacity” on page 26. Only the code specific items are described in the
following.
Critical Section for Punching Shear
The punching shear is checked on a critical section at a distance of d 2 from the face
of the support (IS 30.6.1). For rectangular columns and concentrated loads, the
critical area is taken as a rectangular area with the sides parallel to the sides of the
columns or the point loads (IS 30.6.1).
Transfer of Unbalanced Moment
The fraction of unbalanced moment transferred by flexure is taken to be αM and
the fraction of unbalanced moment transferred by eccentricity of shear is taken to
be (1− α) M (IS 30.6.2.2), where
u
u
α=
1
1 + ( 2 3) a a
1
, and
(IS 30.3.3)
2
where a is the width of the critical section measured in the direction of the span and
a is the width of the critical section measured in the direction perpendicular to the
span.
1
2
Slab Design
197
SAFE User's Manual
Determination of Concrete Capacity
The concrete punching shear factored strength is taken as the following.
v = k τ , where
(IS 30.6.3.1)
k = 0.5 + β ≤ 1.0 ,
(IS 30.6.3.1)
τ = 0.25 f , and
(IS 30.6.3.1)
c
s
c
s
c
c
ck
β = ratio of the minimum to the maximum dimensions of the support section.
c
Determination of Capacity Ratio
Given the punching shear force and the fractions of moments transferred by eccentricity of shear about the two axes, the shear stress is computed assuming
linear variation along the perimeter of the critical section. The ratio of the maximum shear stress and the concrete punching shear stress capacity is reported by
SAFE.
198
Slab Design
References
ACI, 1995
Building Code Requirements for Reinforced Concrete (ACI 318-95) and Commentary (ACI 318R-95), American Concrete Institute, Detroit, Michigan,
1995.
BSI, 1989
BS 8110 : Part 1, Structural Use of Concrete, Part 1, Code of Practice for Design and Construction, British Standards Institution, London, UK, Issue 2,
1989.
CEN, 1992
ENV 1992-1-1, Eurocode 2: Design of Concrete Structures, Part 1, General
Rules and Rules for Buildings, European Committee for Standardization, Brussels, Belgium, 1992.
CEN, 1994
ENV 1991-1, Eurocode 1: Basis of Design and Action on Structures ¾ Part 1,
Basis of Design, European Committee for Standardization, Brussels, Belgium,
1994.
CSA, 1994
A23.3-94, Design of Concrete Structures, Structures Design, Canadian Standards Association, Rexdale, Ontario, Canada, 1994.
CSI, 1998
SAP2000 Analysis Reference, Vols. I and II, Computers and Structures, Inc.,
Berkeley, California, 1998.
199
SAFE User's Manual
ICBO, 1997
Uniform Building Code, International Conference of Building Officials, Whittier, California, 1997.
IS, 1996
Code of Practice for Plain and Reinforced Concrete, Third Edition, Twentieth
Reprint March 1996, Bureau of Indian Standards, Nanak Bhavan, 9 Bahadur
Shah Zafar Marg, New Delhi 110002, India, 1996.
NZS, 1995
Concrete Structures Standard, Part 1 C Design of Concrete Structures, Standards New Zealand, Private Bag 2439, Wellington, New Zealand, 1995.
PCA, 1996
Notes on ACI 318-95, Building Code Requirements for Reinforced Concrete,
with Design Applications, Portland Cement Association, Skokie, Illinois,
1996.
A. Ibrahimbegovic, 1993
“Quadrilateral Finite Elements for Analysis of Thick and Thin Plates”, Computer Methods in Applied Mechanics and Engineering, Volume 110, p 195209, 1993.
G. R. Morris, 1984
“The ‘Integrated Bending Field’ Plate Element,” Proceedings 5th Engineering
Mechanics Division Specialty Conference, ASCE, Laramie, WY, p. 252-255,
1984.
S. Timoshenko and Woinowsky-Krieger, 1959
Theory of Plates and Shells, McGraw-Hill, 1959.
O. C. Zienkiewicz and Y. K. Cheung, 1964
The Finite Element Method for Analysis of Elastic, Isotropic and Orthotropic
Slabs, Proceedings of the Institute of Civil Engineering, 1964.
200
Index
Analysis
Cracked deflection, 28
Elastic analysis, 28
Finite element mesh, 17
No-tension support, 28
Analyzing model, 41
Assigning objects, 40
Balanced condition
ACI, 104, 108
British, 136, 140
Canadian, 120, 123
Eurocode, 152, 155
Indian, 187, 190
New Zealand, 170, 172
Beam flexural design
ACI, 102
British, 134
Canadian, 118
Eurocode, 150
Indian, 184
New Zealand, 168
Beam shear design, 28
ACI, 109
British, 142
Canadian, 126
Eurocode, 158
Indian, 192 - 193
New Zealand, 175
Checking punching shear, 26
ACI, 113
British, 145
Canadian, 129
Eurocode, 162
Indian, 197
New Zealand, 179
Compression block
ACI, 103
British, 135
Canadian, 119
Eurocode, 151
Indian, 185
New Zealand, 169
Compression reinforcement, 28
ACI, 104, 108
British, 137, 140
Canadian, 120, 123
Eurocode, 153, 155
Indian, 188, 191
New Zealand, 171, 173
Concrete shear capacity
ACI, 110
201
SAFE User's Manual
British, 142
Canadian, 126
Eurocode, 158
Indian, 194
New Zealand, 176
Defining objects, 41
Deleting objects, 40
Demonstration, 45
Adding opening in slab, 80
Adding slab, 72
Adjusting coordinate, 73
Analyzing, 56
Assigning beam property, 77
Assigning surface load, 81
Checking punching shear, 66
Creating from template, 46
Defining beam property, 76
Defining design strip, 55
Defining slab property, 49, 51
Deleting slab, 79
Designing slab, 63, 87
Display beam forces, 88
Display beam reinforcement, 90
Display deformed shape, 59
Display slab reinforcement, 64
Display slab stresses, 60
Modifying a model, 72
Re-analysis, 85 - 86
Saving model, 91
Selecting design code, 61
Setting analysis options, 56
Design
Beam design assumptions, 27
Beam flexural design, 27
Beam shear design, 28
Slab design assumption, 26
Slabs segments, 24
Design load combinations, 23
ACI, 99
202
British, 131
Canadian, 115
Eurocode, 147
Indian, 181
New Zealand, 165
Design of T-beams
See also "T-Beam design"
ACI, 106
British, 138
Canadian, 122
Eurocode, 154
Indian, 189
New Zealand, 172
Design rectangular beam
See "Rectangular beam design"
Design strips, 24
ACI, 112
British, 144
Canadian, 128
Eurocode, 161
Indian, 196
New Zealand, 178
Designing beam for shear
See "Shear reinforcement"
Designing concrete structures, 43
Designing slabs
See "Strip design"
Discontinuities in slabs, 2
Displaying output, 42
Graphical display, 42
Tabular display, 42
Editing objects, 40
Factored forces and moments, 23
Factored moments, 26
ACI, 112
British, 144
Canadian, 128
Index
Eurocode, 161
Indian, 196
New Zealand, 178
Factored moments and forces
ACI, 103
British, 135
Canadian, 119
Eurocode, 151
Indian, 185
New Zealand, 169
Flexural reinforcement
ACI, 103
British, 135
Canadian, 119
Eurocode, 151
Indian, 185
New Zealand, 169
Gridline, 36
Integrated strip moments
for design, 25
for reporting, 95
Internal forces
Beam, 19
Slab, 25
L-Beam
See "T-Beam design"
Load combinations
See "Design load combinations"
Loading, 22
Line load, 22
Point load, 22
Positive direction, 22
Surface load, 22
Tributary areas, 22
Tributary lengths, 22
Locking model, 43
Meshing, 36
Minimum slab reinforcement
ACI, 112
British, 144
Canadian, 129
Eurocode, 161
Indian, 197
New Zealand, 178
Minimum tensile reinforcement
ACI, 109
British, 140
Canadian, 125
Eurocode, 157
Indian, 192
New Zealand, 175
Mode
Draw mode, 37
Selection mode, 39
No-tension iterations, 2, 28
Openings in slab, 2
Output, 93
Beam forces, 95 - 96
Beam reinforcement, 97
Deflected shape, 94
Integrated strip forces, 95
Joint displacement, 94
Joint reactions, 95
Punching shear results, 98
Reactive forces, 95
Slab forces, 96
Slab reinforcement, 96
Soil pressure, 95
Stress on slab, 96
Plate element
Thick, 2, 18
Thin, 2, 18
203
SAFE User's Manual
Punching shear capacity, 26
See also "Checking punching shear"
Slab design
See "Strip design"
Rectangular beam design
ACI, 104
British, 136
Canadian, 120
Eurocode, 152
Indian, 187
New Zealand, 170
Slab design strips, 26
Reinforcement
Beam flexural reinforcement, 27
Beam minimum reinforcement, 27
Beam shear reinforcement, 28
Slab flexural reinforcement, 24
Slab minimum reinforcement, 26
SAFE GUI
Active display window, 34
Main window, 33
Menu bar, 33
Screen, 32
Status line, 34
Tool bars, 33
Selecting
Selection mode, 39
Selection, 39
Reselect, 40
Unselect, 40
Self-weight
Beam, 19
Slab, 18
Setting preferences, 44
Shear reinforcement
ACI, 110
British, 142
Canadian, 127
Eurocode, 159
Indian, 195
New Zealand, 177
204
Slab property
Material, 18
Segments, 24
Thickness, 18
Strength reduction factors
ACI, 102
British, 134
Canadian, 118
Eurocode, 150
Indian, 184
New Zealand, 168
Strip design
ACI, 111
British, 144
Canadian, 128
Eurocode, 161
Indian, 196
New Zealand, 178
Supported design codes, 2, 23
ACI, 23, 99
British, 23, 131
Canadian, 23, 115
Eurocode, 23, 147
Indian, 23, 181
New Zealand, 23, 165
Supports, 2
Column supports, 2
Line supports, 19
Point supports, 19
Soil supports, 2
Support reactions, 19
Surface supports, 19
Wall supports, 2
T-Beam design, 19
See also "Design of T-Beams"
ACI, 106
Index
British, 138
Canadian, 122
Eurocode, 154
Indian, 189
New Zealand, 172
Undo and Redo, 43
Units, 29
ACI, 99
British, 131
Canadian, 115
Eurocode, 147
Indian, 181
New Zealand, 165
Viewing options, 34
2D, 3D, 34
Aerial, 34
Elements view options, 35
Panning, 35
Strip layer, 35
Structural layer, 35
Zooming, 35
205