Design Guide for
Economical Reinforced
Concrete Structures
A guide to assist design professionals
in achieving overall economy in the
design and detailing of reinforced
concrete structures.
First Edition
Concrete Reinforcing
Steel Institute
2016
Founded in 1924, the Concrete Reinforcing Steel Institute (CRSI) is a technical institute and an ANSI-accredited Standards Developing
Organization (SDO) that stands as the authoritative resource for information related to steel reinforced concrete construction. Serving
the needs of engineers, architects and construction professionals, CRSI offers many industry-trusted technical publications, standards
documents, design aids, reference materials and educational opportunities. CRSI Industry members include manufacturers, fabricators,
material suppliers and placers of steel reinforcing bars and related products. Our Professional members are involved in the research,
design, and construction of steel reinforced concrete. CRSI also has a broad Region Manager network that supports both members
and industry professionals and creates awareness among the design/construction community through outreach activities. Together,
they form a complete network of industry information and support.
Design Guide for Economical Reinforced Concrete Structures
Publicaton No:
10-DG-STRUCTURES
ISBN: 978-1-943961-20-7
Copyright © 2016
By Concrete Reinforcing Steel Institute
First Edition Printed 2016
All rights reserved. This guide or any part thereof may not be reproduced in any form without
the written permission of the Concrete Reinforcing Steel Institue.
Printed in the U.S.A
This publication is intended for the use of professionals competent to evaluate the significance and limitations of its contents and
who will accept responsibility for the application of the material it contains. The Concrete Reinforcing Steel Institute reports
the foregoing material as a matter of information and, therefore, disclaims any and all responsibility for application of the stated
principles or for the accuracy of the sources other than material developed by the Institute.
Concrete Reinforcing Steel Institute
i
Design Guide for Economical Reinforced Concrete Structures
Author
David A. Fanella, Ph.D., S.E., P.E., F.ASCE, F.ACI is the Senior Director of Engineering at the Concrete Reinforcing
Steel Institute. He has over 25 years of experience in the design of a wide variety of low-, mid-, and high-rise
buildings and other structures. Fanella has authored numerous technical publications and recently authored a
textbook on reinforced concrete design for McGraw Hill. He is a member of ACI Committees 314, Simplified
Design of Concrete Buildings; 374, Performance-Based Seismic Design of Concrete Buildings; 375, PerformanceBased Design of Concrete Buildings for Wind Loads; and SA04, Design Award. Fanella is a Fellow of the American Concrete Institute (ACI) and the American Society of Civil Engineers (ASCE). He also serves as an Associate
Member of ASCE Committee 7, Minimum Design Loads for Buildings and Other Structures. He received his BS,
MS, and PhD in structural engineering from the University of Illinois at Chicago, Chicago, IL. He is a licensed
structural and professional engineer in Illinois and is a licensed professional engineer in many other states.
The following figures and tables courtesy of Reinforced Concrete Structures: Analysis and Design, Second Edition by David Fanella.
©2015, McGraw-Hill Education:
Figures 3.2, 4.1, 4.2, 4.3, 4.4, 4.5, 4.8, 4.9, 4.11, 4.12, 5.6, 5.24, 5.25, 5.26, 5.27, 5.28, 5.29, 5.30, 5.31, 5.32, 6.1, 6.2, 6.3, 6.11, 6.12,
6.13, 6.14, 6.15, 6.16, 7.22, 7.23, 7.24, 8.1, 8.2, 9.1, 9.2, 9.15, 9.16, 9.17, and 9.18
Tables 6.1 and 6.2
ii
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Contents
Author
ii
Chapter 1
Introduction
1-1
1.1 Overview
1-1
2.2 Scope
1-1
Chapter 2
Economical Reinforced Concrete
Floor Systems
2-1
Chapter 4
Two-way Slabs
4.1 Overview
4-1
4.3 Detailing Requirements and Guidelines
for Flexural Reinforcement
4-2
4.3.1 Overview
4-2
4.3.2 Concrete Cover
4-2
4.3.3 Minimum and Maximum Bar Spacing
4-2
4.3.4 Corner Reinforcement
4-2
4-3
4-3
2.1 Overview
2-1
2.2 General Guidelines for Economical Reinforced
Concrete Floor Systems
2-1
2.2.1 Overview
2-1
4.3.6 Guidelines for Detailing the Flexural
Reinforcement
2.2.2 Formwork
2-1
2.2.4 Concrete
2.3 Selecting an Economical Reinforced
Concrete Floor System
2-2
2-4
2-5
2.3.1 Overview
2-5
2.3.2 One-way Joist System
2-5
2.3.3 Flat Plate System
2-8
2.3.4 Flat Slab System
2.3.5 Two-way Joist System
Chapter 3
One-way Slabs
2-9
2-11
3-1
3.1 Overview
3-1
3.2 Determining the Slab Thickness
3-1
3.3 Detailing Requirements and Guidelines
for Flexural Reinforcement
3-1
4-1
4.2 Determining the Slab Thickness
4.3.5 Development of Longitudinal
Reinforcement, Flexural Cutoff Points,
and Splices
2.2.3 Reinforcement
4-1
4.3.7 Openings in Slab Systems
4.4 Detailing Requirements and Guidelines
for Shear Reinforcement
4.4.1 Overview
4-4
4-4
4-4
4.4.2 Single- or Multiple-leg Stirrups
4-5
4.4.3 Headed Shear Studs
4-5
4.5 Detailing Requirements and Guidelines
for SDC C
Chapter 5
Beams
4-6
5-1
5.1 Overview
5-1
5.2 Sizing the Cross-section
5-1
5.2.1 Beam Depth
5-1
5.2.2 Beam Width
5-1
5.3 Detailing Requirements and Guidelines
for Flexural Reinforcement
5-2
5.3.1 Overview
5-2
5.3.2 Concrete Cover
5-2
3-2
5.3.3 Distribution of Flexural Reinforcement
for Crack Control
5-2
3.3.4 Minimum Spacing of Flexural
Reinforcement
3-2
5.3.4 Minimum Spacing of Flexural
Reinforcement
5-3
3.3.5 Development of Longitudinal
Reinforcement, Flexural Cutoff Points,
and Splices
3-2
5.3.5 Development of Longitudinal
Reinforcement, Flexural Cutoff Points,
and Splices
5-4
3.3.1 Overview
3-1
3.3.2 Concrete Cover
3-1
3.3.3 Distribution of Flexural Reinforcement
for Crack Control
Concrete Reinforcing Steel Institute
5.4 Detailing Requirements and Guidelines
for Shear Reinforcement
5-5
5.4.1 Overview
5-5
5.4.2 Stirrup Configurations
5-5
5.4.3 Development of Shear Reinforcement
5-7
iii
Design Guide for Economical Reinforced Concrete Structures
Contents
5.5 Detailing Requirements and Guidelines
for Torsional Reinforcement
5-8
5.5.2 Detailing Requirements and Guidelines
for the Transverse Reinforcement
5-9
5.5.3 Detailing Requirements and Guidelines
for the Longitudinal Reinforcement
5-9
5.5.4 Detailing Requirements and Guidelines
for Combined Effects
5-9
5.6 Steps in Beams
5-10
5.6.1 Overview
5-10
5.6.2 Top Steps
5-10
5.6.3 Bottom Steps
5-11
5.6.4 Deep Steps
5-11
5-11
5.7.1 Overview
5-11
5.7.2 Design for Flexure
5-11
5.7.3 Design for Shear
5.8 Detailing Requirements and Guidelines
for SDC D, E, or F
5.8.1 Overview
5-12
5-13
5-13
5.8.2 Dimensional Limits
5-13
5.8.3 Design for Flexure
5-13
5.8.4 Design for Shear
5-13
5.9 Beams Not Designated as Part of the SFRS
Chapter 6
Columns
6.6.1 Overview
6-8
6.6.2 Longitudinal Reinforcement Requirements 6-8
5.5.1 Overview
5.7 Detailing Requirements and Guidelines
for SDC C
5-14
6.6.3 Transverse Reinforcement Requirements
6.7 Detailing Requirements and Guidelines
for SDC D, E, or F
6-1
6-1
6.2 Preliminary Column Sizing
6-1
6.3 Detailing Requirements and Guidelines
for Longitudinal Reinforcement
6-2
6.3.1 Overview
6-2
6.3.2 Minimum Number of Longitudinal Bars
6-2
6.3.3 Spacing of Longitudinal Bars
6-2
6.3.4 Splices
6-3
6-8
6-9
6.7.1 Overview
6-9
6.7.2 Dimensional Limits
6-9
6.7.3 Longitudinal Reinforcement Requirements 6-9
6.7.4 Transverse Reinforcement Requirements
6.8 Columns Not Designated as Part of the SFRS
Chapter 7
Walls
6-9
6-11
7-1
7.1 Overview
7-1
7.2 Determination of Wall Thickness
7-1
7.3 Minimum Reinforcement
7-1
7.4 Detailing Requirements and Guidelines
for Reinforcement
7-2
7.4.1 Overview
7-2
7.4.2 Concrete Cover
7-2
7.4.3 Spacing Requirements
7-2
7.4.4 Lateral Support of Longitudinal
Reinforcement
7-2
7.4.5 Wall Openings
7-3
7.4.6 Wall Corners and Intersections
7-4
7.5 Detailing Requirements and Guidelines
for SDC D, E, or F
6.1 Overview
7-7
7.5.1 Overview
7-7
7.5.2 Web Reinforcement Requirements
7-7
7.5.3 Boundary Elements
7-8
Chapter 8
Diaphragms
8-1
8.1 Overview
8-1
8.2 Determing the Diaphragm Thickness
8-1
8-1
6-3
8.3 Detailing Requirements and Guidelines
for Reinforcement
6-3
8.4 Detailing Requirements and Guidelines
for SDC D, E, or F
8-2
6.4.1 Overview
6.4.2 Spiral Reinforcement
6-3
8.4.1 Overview
8-2
6.4 Detailing Requirements and Guidelines
for Transverse Reinforcement
6.4.3 Tie Reinforcement
iv
5-8
6-4
8.4.2 Minimum Thickness
8-2
6.5 Detailing Requirements and Guidelines
for Dowels
6-7
8.4.3 Minimum Reinforcement
8-2
6.6 Detailing Requirements and Guidelines
for SDC C
6-8
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Chapter 9
Foundations
9-1
9.1 Overview
9-1
9.2 Spread Footings
9-1
9.2.1 Material Selection
9-1
9.2.2 Determining the Base Dimensions and
Thickness
9-1
9.2.3 Detailing Requirements and Guidelines
for Reinforcement
9-1
9.3 Mat Foundations
9-3
9.3.1 Overview
9-3
9.3.2 Determining the Mat Thickness
9-3
9.3.3 Detailing Requirements and Guidelines
for Reinforcement
9-3
9.4 Drilled Piers
9-4
9.4.1 Overview
9-4
9.4.2 Determining the Shaft Diameter
9-5
9.4.3 Determining the Bell Diameter
9-5
9.4.4 Detailing Requirements and Guidelines
for Reinforcement
9-5
9.5 Grade Beams
9-7
9.6 Detailing Requirements and Guidelines
for SDC D, E, or F
9-9
9.6.1 Overview
9-9
9.6.2 Footings and Foundation Mats
9-9
9.6.3 Grade Beams
9-10
9.6.4 Piles, Piers, and Caissons
9-10
Chapter 10
References
10-1
Notations
N-1
Concrete Reinforcing Steel Institute
v
Design Guide for Economical Reinforced Concrete Structures
CHA PTER 1
Introduction
1.1 Overview
One of the main advantages of reinforced concrete is the
ability to mold it into essentially any shape or form. There
are no inherent restrictions that limit imagination and creativity when it comes to the aesthetic design of a reinforced
concrete structure. Along with the freedom of shape and form
comes the reality of cost. A finite budget is the norm on the
vast majority of projects that are undertaken and the cost of a
structure can be needlessly larger than it has to be if there is
not a basic understanding of what it takes to achieve overall
economy in a reinforced concrete structure.
Chapters 3 through 9 present requirements and guidelines
for sizing, designing, and detailing the following structural
members:
• One-way slabs
• Two-way slabs
• Beams
• Columns
• Walls
• Diaphragms
• Foundations
The purpose of this Guide is twofold:
• To present information on how to select an economical
reinforced concrete floor system.
• To present requirements and guidelines on how to size,
design, and detail reinforced concrete structural members
that, where implemented, will result in an economical
reinforced concrete structure.
The emphasis here is on building structures, but some of the
information that is presented can be used in the design of
bridges and other nonbuilding structures.
It is assumed that the reader has a basic understanding of
the design and detailing of reinforced concrete structural
members for combinations of gravity and lateral loads in
accordance with the requirements of ACI 318, Building Code
Requirements for Structural Concrete. This Guide is not a comprehensive design guide on the fundamentals of reinforced
concrete design. Rather, the information that is presented
here is to be used by a design professional that will help in
achieving overall economy in a reinforced concrete structure.
Included in the discussion for each member type are the
specific design and detailing requirements that are applicable
to structures in areas of high seismic risk, that is, structures
assigned to seismic design category (SDC) D, E, or F. Emphasis is placed on constructability, which has a direct link to
economy.
The references that are cited in this Guide can be found in
Chapter 10.
Throughout the chapters, reference is made to the provisions
of the 2014 edition of ACI 318, Building Code Requirements for
Structural Concrete (Reference 1). For example, reference to
Section 8.3 in ACI 318-14 is denoted here as ACI 8.3. A similar
designation is provided for tables and figures from that
document.
1.2 Scope
Chapter 2 of this Guide contains general guidelines and
information on how to select an economical reinforced concrete floor system. In particular, wide-module joist, flat plate,
flat slab, and two-way joist systems are covered. Tables are
provided that give relative cost indices of floor systems for
various span and load conditions. This information can help in
determining the most economical system for a given set of
constraints.
Concrete Reinforcing Steel Institute
1-1
Design Guide for Economical Reinforced Concrete Structures
CHA PTER 2
Economical Reinforced Concrete
Floor Systems
2.1 Overview
for the crew when erecting the forms, resulting in
reduced labor costs. In cases where multiple framing
systems are specified, a separate forming system is
needed for each system, which translates to additional
costs associated with material and its mobilization.
There are obvious exceptions to this guideline, particularly in areas of a building that have different usages.
For example, it would be practical to have one framing
system for the parking levels in a building and another
for the typical residential or office floors.
General information is provided in this chapter on how to
choose an economical reinforced concrete floor system and
once chosen, how to achieve cost-savings when designing
and detailing the structural members in the system. Tables
are presented that can be utilized in selecting an economical
system for a given set of constraints.
2.2 General Guidelines for Economical
Reinforced Concrete Floor Systems
2.2.1 Overview
2.
Through careful planning and detailing, the overall cost of the
structure of a building utilizing reinforced concrete can be
reduced considering the overall costs related to the main components of any reinforced concrete building, which are formwork, reinforcement, and concrete. The costs associated with
formwork are generally 40 to 60 percent of the completed
structure. Material costs for the concrete and reinforcement
range from 10 to 30 percent of the overall cost. The labor cost
for placing the concrete and reinforcement is the remainder.
This section covers general guidelines that will result in more
economical reinforced concrete structures. Specific cost-saving guidelines and techniques are given in the next section and
the following chapters of this Guide for particular reinforced
concrete floor systems and reinforced concrete members.
Column capitals and drop panels are usually expensive
to form. Consider using shear reinforcement to augment two-way shear capacity of a slab.
3.
Use modular formwork whenever practical. Traditionally, modular forms have been used for floors and
walls where the forms can be moved in large sections
and reused often (usually between 10 and 20 times).
Such proprietary forming systems have become more
common and are being used to form smaller members.
This type of formwork can also be used in customized
applications such as slip-formed shafts for elevators and
stairways and curved exterior walls. The cost of using
such specialized forms can usually be justified if they
can be reused multiple times in a project.
4.
Use floor framing systems of minimum depth with
a constant elevation for the bottom surface of the
system. For most residential and office applications,
the depth of the floor system is governed by serviceability (deflection) considerations. Providing the minimum depth based on these requirements will result
in minimum floor-to-floor heights and, thus, an overall
reduction in the building height. Overall height reduction
translates to a reduction in the costs associated with
essentially all of the vertical runs in the building (façade;
elevators; stairs; interior partition walls; and plumbing,
electrical, and mechanical conduit and ductwork).
2.2.2 Formwork
By definition, formwork is the total system of support for
freshly placed concrete, which includes the mold or sheathing
that is in contact with the concrete and all of the supporting
members, hardware, and bracing.
Project specifications can have a major impact on formwork
design and speed of construction. Examples include stripping
time, tolerances, concrete finish requirements, strength of
concrete at time of form removal, and reinforcing steel and accessory requirements. It is important that these items, as well
as any other pertinent ones, be discussed with the concrete
contractor as early as possible.
Because formwork and the labor associated with it are typically the largest cost in a reinforced concrete structure, it
is important to follow some basic guidelines, which when
implemented, can result in overall cost savings. The following
guidelines, which are not meant to be comprehensive, should
be considered at the onset of any project.
1.
Select one framing system and use it throughout
the structure wherever possible. Using the same
framing system as often as practical throughout the
structure has been shown to result in significant cost
savings. Forms are reused many times and it is easier
Concrete Reinforcing Steel Institute
Use standard shaped forms. Rectilinear members are
the most cost effective to form. Whenever possible,
avoid shapes that have to be either fabricated by the
form supplier or customized by carpenters in the field.
Large field fabrication costs can be incurred, for example, when the forms have to be modified for tapered
members or for haunches.
The underside of a reinforced concrete floor or roof
should be kept level for maximum economy. Sloping of
floor or roof surfaces should be accomplished by varying the structural slab thickness or by using concrete
fill. Depressions for floor coverings should be made by
varying the top surface of the slab rather than by adjusting formwork beneath the slab.
2-1
Design Guide for Economical Reinforced Concrete Structures
5.
Orient one-way structural members to span in the
same direction throughout the entire structure. Experience has shown that structures that have one-way members oriented in the same direction throughout the entire
structure tend to be constructed more efficiently than
those where multiple framing directions are used. This is
attributed to less confusion and fewer mistakes made in
the field because of the overall regularity of the structure.
6.
Arrange columns in a regular pattern. If possible, the
columns should be arranged in a regular pattern throughout each floor of the structure. This helps in achieving
consistency in the formwork and reinforcement layout
of all the structural members. Installing the formwork in
such cases is repetitive and efficient and the formwork
can be reused easily. This repetitiveness and efficiency
carries over to all aspects related to the reinforcing bars.
7.
Use a consistent column size. Experience has shown
that it is more efficient to limit the number of changes in
the column sizes throughout the height of a structure. In
low-rise buildings, the same column size should be used
throughout the entire height as should the same compressive strength of the concrete; the number of reinforcing
bars can change over the height as needed. In taller buildings, the same column size should be used over a number
of floors and then changed accordingly over the height
depending on the total number of stories in the building.
The concrete compression strength and the number of
reinforcing bars vary over the height as well.
8.
Specify the time when forms may be stripped for selfsupporting members and the strength when forms may
be stripped for other members. Forms for columns and
walls can be stripped based on time after the concrete has
been placed (e.g., 12 hours). For beams and slabs, forms can
be stripped after a specific percentage of concrete compressive strength has been attained (e.g., 75% of the specified
28-day compressive strength). It is important to note that
beams and slabs must be reshored until the compressive
strength has been attained to minimize deflections. Appropriate stripping specifications will minimize the required
amount of formwork and will result in lower formwork costs.
9.
Use high early strength concrete. The use of high
early strength concrete enables the formwork to be
stripped sooner than conventional concrete. Faster
cycle times may allow for a faster overall construction
time, which translates to significant overall cost savings.
10. Use predetermined construction joints. The location for
construction joints should be the contractor’s prerogative
with input from the engineer of record where required.
Properly located construction joints will allow the contractor to sequence concrete placement efficiently. The use of
dowel bar mechanical splices at construction joints should be
considered (see Fig. 2.1). This splice type contains a flange
that is nailed to the forms. After the forms are stripped, the
adjoining reinforcement can be screwed into the coupler. This
eliminates bar or dowel penetration through the forms.
2-2
Fig. 2.1 Dowel Bar Mechanical Splice.
2.2.3 Reinforcement
1.
Use Grade 60 reinforcing bars. ASTM A615 Grade 60
bars are the most widely used and inventoried reinforcing
bars. Specifying Grade 40 bars may require 50% more
steel than using Grade 60 bars. ASTM A615 Grade 75 or 80
bars are readily available, but are not normally inventoried
by fabricators. It is important to note that these bars are
usually available on mill orders ranging from 25 to 75 tons
per bar size. However, smaller quantities may be obtained
from warehouses, if available. In taller structures, the use
of Grade 75 or 80 longitudinal bars in columns may decrease congestion at the joints and may reduce the number of crossties because a smaller number of longitudinal
bars would generally be required.
2.
Use the largest bar size possible. Placing and fabrication costs are minimized by using the largest practical
bar sizes that satisfy both strength and serviceability
requirements. It is important to keep in mind that a
greater quantity of smaller bars may be required for
crack control or for other serviceability issues.
3.
Use straight bars wherever possible. Fabricating and
placing straight bars is faster and easier than bent bars.
4.
Use ACI standard bar bend types. Specify standard bar
shapes and bends provided in Reference 2. Nonstandard
bends disrupt shop routine and are more costly to fabricate.
5.
Use bars in one plane. Wherever possible, reinforcing
bars should have bends located in one geometric plane.
Bars with bends in two or three planes are difficult
and expensive to fabricate. Additionally, it is difficult to
maintain proper field tolerances because adjustment of
the bar in one direction impacts the tolerance in one or
more of the other directions.
6.
Use repetitive bar sizes and lengths. The standard
length for reinforcing bars is 60 ft, although some
fabricators stock shorter lengths. In general, the longest
available (and possible) bar lengths should be used to
reduce fabrication and placing costs. Also, the number
of bar sizes specified in a particular project should be
minimized. This reduces the number of sizes that must
be handled in the shop and placed in the field.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
tains a list of overall bar diameters. Hook dimensions
and bend radii for standard hooks and stirrup/tie hooks
are given in Chapter 6 of Reference 3.
Lap Varies,
•0LQLPXP
Table 2.1 Overall Reinforcing Bar Diameter
SECT. A
7RS%DUV/HQJWK³$´
%RWWRP%DUV/HQJWK³&´
Nominal
Diameter
7RS%DUV/HQJWK³%´
%RWWRP%DUV/HQJWK³&´
Fig. 2.2 Using Stock Length Bars Cut and Spliced in the Field.
8.
9.
Use stock length bars. In the case of irregularlyshaped walls and slabs, it is usually more cost effective to use stock length bars that are cut and spliced in
the field in lieu of using individual bars that have been
sheared to a required length (see Fig. 2.2). The added
cost associated with the extra material used due to variable lap lengths is usually minor and is more than offset
by the savings due to reduced labor that would otherwise be required to cut and sort the individual bars.
Use the appropriate splice in the appropriate situation. Wherever possible, bars should be lap spliced.
A consistent lap splice length should be specified for a
given bar size. For columns utilizing #14 and #18 bars,
and for #11 and smaller bars where congestion is an
issue, use mechanical splices. A compression mechanical splice should be specified for bars that will always
be in compression because these types of splices are
considered to be the fastest to install in the field.
Provide a 4- to 6-in. gap to place concrete where
bars are closely spaced. In heavily reinforced members, such as transfer girders, where the spacing
between bars is relatively close, provide a gap of 4 to
6 in. between bars, if possible. Based on experience, a
4-in. slump concrete with 3/4-in. aggregate will not flow
easily though a 2-in. space between bars. Also, vibrator
heads, which are usually 2 to 3 in. in width, may not fit
between the bars or can become entangled in the bars
if the space between bars is too small.
10. Draw details to scale to ensure that the reinforcing
bars will fit within the section. Scaled drawings that
show all of the reinforcement are essential, especially
in the following cases:
• Narrow beams
A
A
Overall
Diameter
Approximate Diameter Outside
Deformations, in.
Bar Size
#3
7/
16
#4
9/
16
#5
11/
#6
7/
#7
1
#8
11/8
#9
11/4
#10
17/16
#11
15/8
#14
17/8
#18
21/2
16
8
Figure 2.3 illustrates how a scaled detail drawing can help
identify problems. The conceptual beam detail with the
reinforcement depicted as lines and dots is given in the figure
as is the detail where the reinforcement has been drawn to
scale. It can be seen in the scaled drawing that the stirrup
hooks will likely interfere with the top bars and the minimum
clearance between the bars may not be met.
#3 closed
stirrups
3-#6 T&B
• Slabs with multiple openings, especially near supports and edges
• Slab-column and beam-column joints
• Columns with more than 2% longitudinal reinforcement
It is important to include the overall dimensions of the
reinforcing bars, as well as hook dimensions and bend
radii when drawing the scaled details. Table 2.1 con-
Concrete Reinforcing Steel Institute
Interference
between
stirrups &
top bars
7 1/2"
7.
6"
Beam Detail (Conceptual)
Insufficent
clear distance
between bars
Beam Detail (Scaled)
Fig. 2.3 Beam Detail, Conceptual and Scaled.
2-3
Design Guide for Economical Reinforced Concrete Structures
forced sections and complex formwork while ensuring
good construction quality which may lead to increased
productivity, reduces the labor requirement and cost,
or both;
2.2.4 Concrete
1. Use moderate-strength concrete. 4,000 to 5,000
psi compressive strength concrete is usually sufficient.
Exceptions are for columns in high-rises and floor systems
in which there are shear capacity issues. Columns, shear
walls, and joints may require higher strength concrete to
enhance their axial and flexural capacity.
• Improved flexibility in spreading placing points during casting. This can reduce the need for frequent
movement of transit trucks and the need to move the
pump lines to place concrete (possible reduction in the
number of pumps, pump operators, and so on). This
greater flexibility in scheduling construction activities
and procuring the required resources results in both
time and resource savings.
2. Use high-performance concrete where placement
and consolidation is expected to be difficult. Highperformance concrete is defined within ACI 116 as concrete
meeting special combinations of performance and uniformity requirements that cannot always be achieved routinely
using conventional constituents and normal mixing, placing,
and curing practices. These requirements could potentially
include the following enhancements:
SCC may be evaluated in the field using a standard
slump test; however, the slump cone is often inverted.
Instead of measuring the distance between the top
of the cone and the top of the sample, the puddle of
concrete is measured in 2 orthogonal directions to
determine the spread diameter. Standard slump measurements of highly flowable concrete is practically
irrelevant, as it has no measureable slump (>> 12 in.).
Other mixture evaluation tests include the J-ring test,
used to evaluate the flow and segregation characteristics of high-performance concrete.
• Ease of placement and consolidation without affecting
strength;
• Long-term mechanical properties;
• Durability in severe environments;
• High early strength;
• Toughness;
• Volume stability.
These properties are usually achieved with special admixtures, which alter the plastic properties and workability of
the concrete during placement, making it less viscous (more
fluid) than conventional concrete. Long-term strength properties are usually unaffected.
Self-consolidating concrete (SCC) is a special type of highperformance concrete. It is defined by the National ReadyMix Concrete Association (NRMCA) as a highly flowable,
non-segregating concrete that can flow into place, fill the
formwork, and encapsulate the reinforcement without any
mechanical consolidation. In general, SCC is concrete made
with conventional concrete materials and, in most cases,
with a viscosity-modifying admixture (VMA). SCC is also
useful in applications where high quality surface finishes are
desired without bugholes or honeycombing. Increased form
pressures may be generated when SCC is used, necessitating possible changes in formwork design.
3.
Use high-strength concrete in columns. Highstrength concrete can be justified in columns if the
use of higher strength concrete reduces the amount of
longitudinal reinforcement. Similarly, column sizes can
be reduced or just use one column size on a project.
Specify the same strength concrete in all columns of a
story, to minimize mistakes.
4.
Specify few mix designs. On most projects only two
strengths of concrete are necessary, a normal mix
(4,000 to 5,000 psi) and a high-strength mix (8,000 psi
or greater). Some projects may necessitate three.
Consistent with the construction shown in Figure 2.4,
it is most economical to use the high-strength column
concrete in the slab puddling zone. In an effort to
optimize concrete mixes on a project, some engineers
have specified a separate puddling mix, because ACI
318 only allows a design concrete strength of 10,000
psi in shear. Some high-strength column concretes may
have compressive strengths ranging from 12,000 psi to
15,000 psi.
ACI Committee Report 237R (Reference 24) indicates that
SCC provides the following features, which are equally applicable to general high-performance concrete:
To make placement easier and avoid potential placement mistakes on the project, it is usually more
economical to use the column concrete in the puddling
zone, and design for a maximum concrete strength of
10,000 psi; a separate puddling mix is thus not recommended.
• It is good at replicating architectural form features;
• Free fall into the formwork can be greater than the
conventional limit of 5 ft.;
• Less screeding operations are required to ensure flat
surfaces (self-leveling characteristic);
• It facilitates accelerated construction, through higher
rate of casting or placing and shorter construction
duration;
• It facilitates and expedites the filling of highly rein-
2-4
5.
Limit coarse aggregate size to ¾ inch. As a matter of
practice limit the coarse aggregate to ¾ inch since the
minimum clear bar spacing is normally 1 inch and ACI
318 Code requires a clear distance of four-thirds the
aggregate size.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Column concrete
placed in the
nearby slab
section.
Fig. 2.4 Concrete “Puddling” around Columns. Photo courtesy of Skidmore,
Owings and Merrill LLP.
2.3 Selecting an Economical Reinforced
Concrete Floor System
2.3.1 Overview
Numerous types of cast-in-place, reinforced concrete floor
systems are available to satisfy virtually any span and loading
condition that is required. Because the cost of the floor system is often the major part of the structural cost of a building,
selecting the most effective system for a given set of constraints is vital in achieving overall economy. This is especially
important for low- and mid-rise buildings and for buildings
subjected to relatively low wind and seismic forces because
the cost of the lateral force-resisting systems in such cases is
minimal compared to the typical floor systems.
Provided in this chapter are preliminary estimates of material quantities for various cast-in-place reinforced concrete
floor systems with a variety of span and loading conditions.
In particular, the following conventionally reinforced concrete
systems are covered:
• One-way joist
• Flat plate
• Flat slab
• Two-way joist (waffle)
Voided slabs are reinforced concrete slabs similar to flat plates
that contain regularly-spaced voids. The voids are usually
created using hollow recycled plastic void formers and are
positioned in wire cages to create modules, which are placed
between the top and bottom layers of flexural reinforcement
in the slab. Both squat and spherical void formers are available
in different sizes. The main purpose of the voids is to eliminate
concrete in areas where it is not needed, thereby reducing
the overall weight of the floor system. Voided slabs are not
addressed in this Guide; more information can be found in
Reference 4 and in manufacturers’ literature.
The structural members of the floor systems that are covered
in this chapter were designed and detailed for the effects
of gravity load in accordance with ACI 318-14 (Reference 1).
CRSI’s Reinforced Concrete Concept, which is a preliminary
design tool that provides material and cost estimates for a
Concrete Reinforcing Steel Institute
variety of conventionally reinforced concrete floor systems,
was used to generate the information provided in the following tables (http://concept.crsi.org/index.cfm). It is assumed
that the members in the various floor systems are not part of
the lateral force-resisting system. Span and loading conditions
that are typical for residential and office buildings are included
in the analysis.
In all cases, normal-weight concrete with a density of 150 pcf
and a specified compressive strength of 4,000 psi is utilized.
Also, Grade 60 reinforcing bars are used. The live load varies
from 40 psf to 100 psf, and the superimposed dead load is
taken as 10 psf in all cases.
Concrete, reinforcing steel, and formwork quantities are given
in the tables for various span and loading conditions. In general, unlimited design solutions are possible for a given set of
constraints. The member sizes in the tables for a particular bay
size and superimposed loading satisfy all applicable ACI 318
requirements and were chosen based on the guidelines presented in this Guide, practicality, experience, and formwork
economy. This does not imply, however, the following: (1) the
provided sizes result in the most economical solution because
no mathematical attempt was made to optimize the overall
cost of the floor system for a given set of constraints and (2)
members sizes not contained in the tables are uneconomical
and/or impractical and that they should not be considered for
the case at hand.
Cost indices of the various floor systems are also provided in
the tables. Unit in-place costs for concrete, reinforcement, and
formwork used in this analysis were obtained from Reference
5. These unit costs, which include both materials and installation, represent national average costs for major cities in the
U.S. The cost index is the ratio of the total cost—in-place costs
of concrete, reinforcement, and formwork for that particular
case—to the average total cost of all cases in all systems
considered in this Guide. These cost indices can be used to
compare relative costs between different systems as a function
of span and loading. The size and geographic location of the
project, the availability of skilled labor, and local building code
requirements are a few of the many factors that significantly affect costs. Thus, it is important to use the data in the tables as
a preliminary guide in selecting an economical floor system.
2.3.2 One-way Joist System
Overview
A one-way joist floor system, which is commonly referred to
as a wide-module joist system or a “skip” joist system when
the clear spacing between the joist ribs exceeds 30 inches,
consists of regularly spaced concrete joists (ribs) spanning in
one direction, a reinforced concrete slab cast integrally with
the joists, and beams (or, girders) that span between the columns, perpendicular to the joists (see Fig. 2.5). The joists are
formed by using pan forms that are either 53 or 66 in. wide.
Systems formed by the 66-in.-wide pans that range in depth
between 14 and 24 in. are considered in this Guide.
2-5
Design Guide for Economical Reinforced Concrete Structures
Table 2.2 Maximum Span Lengths for One-way Joist Systems
with 66-in.-wide Pans
Fig. 2.5 One-way Joist System.
The main advantages of a one-way joist system are: (1) they
are economical for long spans with heavy loads, (2) the pan
voids reduce the dead load, and (3) electrical and mechanical
equipment can be placed between joists, which means the
overall floor depth need not be increased to accommodate
this equipment. The longer spans and inherent vibration resistance make this an attractive floor system for office buildings,
hospitals, and schools.
It is important to note that wide-module joist construction
does not satisfy the limitations of ACI 9.8.1 of standard joist
systems; therefore, the members of the floor system are to
be designed as one-way slabs and beams.
Member Sizes
The thickness of the slab spanning between the joists
(beams) can be controlled by either structural or fire resistance requirements. Specifying a lightweight aggregate may
be advantageous in certain situations because a 2-hour fireresistance rating can be achieved with a relatively thin slab.
This would also result in a reduction of dead load. A normalweight concrete slab with a 4.5-in. thickness is used in all
cases considered in this Guide.
One layer of reinforcement is usually provided in the slab at
mid-depth perpendicular to the joists. The minimum amount
of reinforcement required for temperature and shrinkage, as
prescribed in ACI 7.6, usually governs.
The dimensions of the joists depend on deflection and
strength requirements. The minimum thickness of nonprestressed beams that are not supporting or attached to partitions and other construction likely to be damaged by deflections is given in ACI Table 9.3.1.1. According to this table, the
slab thickness plus pan depth should be greater than or equal
to C18.5 (exterior span) or C21 (interior span) in the case of
normal-weight concrete and Grade 60 reinforcement, where C
is the span length defined in ACI Chapter 2. Table 2.2 contains
the maximum span lengths for one-way joist systems, assuming
a 4.5-in. thick slab.
2-6
Pan Depth
(in.)
Exterior Span,
Maximum Span
Length, C (ft)
Interior Span,
Maximum Span
Length, C(ft)
14
28.5
32.4
16
31.6
35.9
20
37.8
42.9
24
43.9
49.9
The overall depths of the systems contained in the tables in
the Summary section satisfy the requirements of ACI Table
9.3.1.1. A thickness less than that prescribed in this table is allowed if it can be demonstrated that computed deflections are
less than or equal to the limits prescribed in ACI Table 24.2.2.
Once a thickness has been established, a joist width is chosen.
The width of the joists can be tailored to satisfy virtually any
requirement. In most cases, the thinnest practical joist width, for
a given rib spacing, will be adequate for structural requirements.
Bay sizes and floor layouts may also have an influence on the
width of the joists. In certain cases, specific joist widths may be
necessary in order to provide economical and practical formwork.
The thickness of the supporting beams (or, girders) is dictated by
the thickness of the joists. To achieve overall formwork economy,
the depth of supporting members should be the same as the
overall depth of the joists. If additional capacity is required, beams
should be made wider, not deeper. Also, beams should be wider
than the columns into which they frame, if possible. In addition
to assuring formwork economy, this also alleviates some of the
reinforcement congestion that can occur at the joints.
In the tables in the Summary section below, the second to
last column contains the pan area percentage, which is the
percentage of the floor area that requires pan formwork.
Joist Orientation
Depending on span lengths and superimposed loads, it is usually
more cost effective to span the joists in the long direction. This
also helps in assuring that a level floor soffit is achieved because
the beams are spanning in the short direction. For bays with aspect ratios less than 1.5, the cost differential between joists framing in the short direction and long direction is typically very small.
Live Load Effects
Material quantities are, to a large extent, controlled by deflection
requirements. An increase in live loads does not have a proportional
impact on cost. A live load of 100 psf results in an increase of less
than 5% over the cost of a system designed for a live load of 40 psf.
Panel Aspect Ratio Effects
The aspect ratio of the slab panels has a minimal effect on
material quantities for ratios less than 1.5. As noted above,
spanning the joists in the long direction usually results in the
most economical solution.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Summary
One-way joist systems are economically viable for medium to
long spans with moderate to heavy loads. Systems formed
with 66-in. pans are feasible for span lengths ranging from
35 to 50 ft and beyond. Large, column-free spaces can be
achieved without vibration problems for typical residential and
office occupancies.
Tables 2.3, 2.4, and 2.5 contain material quantities and cost
indices for one-way joist systems with live loads of 40, 65,
and 100 psf, respectively.
Table 2.3 Material Quantities and Cost Indices for One-way Joist Floor Systems, LL = 40 psf
Bay Size (ft)
Pan Depth
(in.)
Beam Width
(in.)
Square
Column Size
(in.)
Concrete
(ft3/ft2)
Reinforcement (psf)
Pan Area
(%)
Cost Index
25 w 25
14
26
22
0.62
2.09
89
0.80
30 w 30
16
32
28
0.65
2.43
89
0.83
30 w 35
20
34
30
0.71
2.36
90
0.85
30 w 40
24
36
32
0.77
2.53
90
0.88
35 w 35
20
34
30
0.71
2.65
90
0.86
35 w 40
24
36
32
0.77
2.76
90
0.89
40 w 40
24
36
32
0.77
3.05
90
0.91
Table 2.4 Material Quantities and Cost Indices for One-way Joist Floor Systems, LL = 65 psf
Bay Size (ft)
Pan Depth
(in.)
Beam Width
(in.)
Square
Column Size
(in.)
Concrete
(ft3/ft2)
Reinforcement (psf)
Pan Area
(%)
Cost Index
25 w 25
14
28
24
0.62
2.49
88
0.82
30 w 30
16
34
30
0.65
2.73
88
0.84
30 w 35
20
36
32
0.71
2.75
89
0.87
30 w 40
24
38
34
0.77
2.70
90
0.89
35 w 35
20
36
32
0.71
3.16
89
0.89
35 w 40
24
38
34
0.77
3.00
90
0.90
40 w 40
24
38
34
0.77
3.36
90
0.92
Table 2.5 Material Quantities and Cost Indices for One-way Joist Floor Systems, LL = 100 psf
Bay Size (ft)
Pan Depth
(in.)
Beam Width
(in.)
Square
Column Size
(in.)
Concrete
(ft3/ft2)
Reinforcement (psf)
Pan Area
(%)
Cost Index
25 w 25
14
30
26
0.63
2.82
87
0.84
30 w 30
16
36
32
0.66
3.41
87
0.88
30 w 35
20
38
34
0.72
3.18
89
0.89
30 w 40
24
40
36
0.78
3.29
89
0.92
35 w 35
20
38
34
0.72
3.67
89
0.92
35 w 40
24
40
36
0.78
3.70
89
0.94
40 w 40
24
40
36
0.78
4.10
89
0.96
Concrete Reinforcing Steel Institute
2-7
Design Guide for Economical Reinforced Concrete Structures
compressive strength. Specifying a compressive strength
greater than 4,000 psi will increase the cost of the concrete
without any allowable reduction in slab thickness. Therefore,
for live loads of 40 psf or less, the most economical flat plate
floor system is one where a minimum thickness computed
by ACI Table 8.3.1.1 and a concrete compressive strength of
4,000 psi are specified.
Fig. 2.6 Flat Plate.
2.3.3 Flat Plate System
Overview
A flat plate floor system is a two-way concrete slab supported
directly on columns with reinforcement in two orthogonal
directions (see Fig. 2.6). Primarily used in hotels, multi-family
residential buildings, and office buildings, this system has
the advantages of simple construction and formwork and a
flat ceiling, the latter of which reduces ceiling finishing costs
because the architectural finish can be applied directly to
the underside of the slab. Even more significant are the cost
savings associated with the low story heights made possible
by the shallow floor system. Smaller vertical runs of cladding,
partition walls, mechanical systems, plumbing, and other
primarily vertical items of construction translate to large cost
savings, especially for medium- and high-rise buildings. Moreover, where the total height of a building is restricted, using a
flat plate can result in more stories accommodated within the
set height.
Minimum Slab Thickness
Minimum slab thickness requirements for flat plates are given
in ACI Table 8.3.1.1. The minimum thickness of exterior and
interior panels of flat plates without edge beams and containing reinforcement with a yield strength of 60,000 psi is equal
to Cn 30 and Cn 33, respectively, where Cn is the length of the
clear span in the long direction. The panel that yields the largest thickness is used throughout the entire floor plate. In no
case should the thickness be less than 5 in.
Live Load Effects
For live loads of 40 psf or less, the thickness of the slab will
usually be controlled by deflection requirements. Also, the
flexural reinforcement at the critical sections in the column
and middle strips will be about the minimum amount prescribed in ACI Table 8.6.1.1. Thus, using a slab thickness
greater than the minimum allowable thickness is not economical because a thicker slab will increase the concrete quantity
and not reduce the reinforcement quantity. Note that minimum thickness requirements are independent of the concrete
2-8
For live loads of 100 psf or more, the thickness of the slab will
more than likely be controlled by the two-way shear stresses
at the critical section around the columns and the bending moments in the slab, and not by the deflection criteria
described above. Thicker slabs are generally provided to resist
the larger shear stresses due to larger live loads. Although a
thicker slab may result in a decrease in the required amount of
flexural reinforcement, the reduction in the cost of reinforcement will not offset the increase in the cost of concrete. Also,
using a higher strength concrete is not the most effective
way of increasing the nominal moment strength and, more
importantly, the nominal two-way shear strength provided
by the concrete at the critical section around the columns.
Cost analyses show that the cost of a flat plate system with
a concrete strength greater than 4,000 psi is greater than the
cost of one with a compressive strength of 4,000 psi, even
when reductions in thickness and/or reinforcement are taken
into consideration for the systems with the higher strength
concrete. Therefore, for live loads of 100 psf and greater, the
most cost-effective solution is to use a slab thickness equal to
the minimum required for strength and a concrete compressive strength equal to 4,000 psi. The use of shear studs to
counteract the effects of two-way shear stresses is discussed
in Chapter 4 of this Guide.
Panel Aspect Ratio Effects
The aspect ratio of a slab panel is defined as the larger
dimension of the panel divided by the smaller dimension of
the panel, measured center-to-center of supports. Where the
aspect ratio exceeds 2, the slab acts primarily as a one-way
slab spanning in the short direction.
As discussed above, the minimum slab thickness is dependent on the clear span length. The slab thickness requirement is the same in both directions for square bays. For an
aspect ratio other than 1, the longer span will dictate the slab
thickness, resulting in a loss of economy. A floor system that
contains rectangular bays with an aspect ratio of 2 costs approximately 30% more than one with an aspect ratio of 1, for
the same overall floor area. Unless column layout is dictated
by architectural or other functional requirements, square bays
should be used because they provide the most economical
layout.
Summary
Flat plate systems are economically viable for short to
medium spans and for moderate live loads. The deflection
criteria usually govern up to live loads of about 40 psf, and the
economical span length range is 15 to 30 ft. For live loads of
100 psf or more, two-way shear stresses at the columns and
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Tables 2.6, 2.7, and 2.8 contain material quantities and cost
indices for flat plate systems with live loads of 40, 65, and 100
psf, respectively.
bending moments in the slab control the design. For these
cases, the flat plate is economical for spans between 15
and 25 ft.
Table 2.6 Material Quantities and Cost Indices for Flat Plate Floor Systems, LL = 40 psf
Bay Size (ft)
Slab Thickness
(in.)
Square Column
Size (in.)
Concrete
(ft3/ft2)
Reinforcement
(psf)
Formwork
(ft2/ft2)
Cost Index
15 w 15
6.0
12
0.50
1.62
1.00
0.78
15 w 20
7.5
14
0.63
1.89
1.00
0.83
20 w 20
7.5
16
0.63
1.92
1.00
0.83
20 w 25
9.5
18
0.79
2.35
1.00
0.91
25 w 25
9.5
22
0.79
2.45
1.00
0.91
Table 2.7 Material Quantities and Cost Indices for Flat Plate Floor Systems, LL = 65 psf
Bay Size (ft)
Slab Thickness
(in.)
Square Column
Size (in.)
Concrete
(ft3/ft2)
Reinforcement
(psf)
Formwork
(ft2/ft2)
Cost Index
15 w 15
6.0
14
0.50
1.71
1.00
0.78
15 w 20
7.5
16
0.63
1.99
1.00
0.84
20 w 20
7.5
20
0.63
2.07
1.00
0.84
20 w 25
9.5
22
0.79
2.50
1.00
0.92
25 w 25
9.5
26
0.79
2.61
1.00
0.92
Table 2.8 Material Quantities and Cost Indices for Flat Plate Floor Systems, LL = 100 psf
Bay Size (ft)
Slab Thickness
(in.)
Square Column
Size (in.)
Concrete
(ft3/ft2)
Reinforcement
(psf)
Formwork
(ft2/ft2)
Cost Index
15 w 15
6.0
16
0.50
1.88
1.00
0.79
15 w 20
7.5
18
0.63
2.17
1.00
0.85
20 w 20
7.5
24
0.63
2.31
1.00
0.85
20 w 25
9.5
26
0.79
2.75
1.00
0.93
25 w 25
9.5
30
0.79
2.94
1.00
0.94
2.3.4 Flat Slab System
Overview
A flat slab floor system is similar to a flat plate floor system,
with the exception that the flat slab has thickened portions
around the columns called drop panels (see Fig. 2.7). The
primary purpose of the drop panels is to increase the nominal
two-way shear strength of the concrete at the critical section
around the columns. The flat slab system has the advantages
of relatively simple construction and formwork, low floorto-floor heights, and a relatively flat ceiling, which allows an
architectural finish to be applied directly to the underside of
the slab. This system is primarily used in buildings with moderate to heavy loads, such as office buildings, hospitals, and
warehouses.
Fig. 2.7 Flat Slab.
Concrete Reinforcing Steel Institute
2-9
Design Guide for Economical Reinforced Concrete Structures
To achieve formwork economy, standard lumber dimensions
should be used to form the drop panels. Table 2.9 contains
drop panel heights based on actual lumber dimensions and
3/ -in.-thick formwork sheathing. Using other depths will un4
necessarily increase formwork costs.
Fig. 2.8 Minimum Drop Panel Dimensions.
Minimum Slab Thickness and Drop Panel Dimensions
Minimum slab thickness requirements for flat slabs are given
in ACI Table 8.3.1.1. The minimum thickness of exterior and
interior panels of slabs with drop panels defined in ACI 8.2.4,
without edge beams, and containing reinforcement with a
yield strength of 60,000 psi is equal to Cn 33 and Cn 36, respectively, where Cn is the length of the clear span in the long
direction. It is evident that the minimum thickness of flat slabs
is 10% less than that required for flat plates; this is primarily
due to the decrease in deflection from the addition of the drop
panels around the columns. In no case should the slab thickness be less than 4 in.
Minimum dimensions for drop panels are given in ACI 8.2.4.
The drop panel should extend in each direction from the
centerline of the support a distance not less than one-sixth of
the span length measured from center-to-center of supports
in that direction (see Fig. 2.8). Also, the projection of the drop
panel below the slab should be at least one-quarter of the slab
thickness. The minimum slab thickness must be increased
by 10% if drop panel dimensions are provided that do not
conform to these provisions.
Table 2.9 Drop Panel Height for Formwork Economy
In the preliminary design stage, a slab thickness is chosen
based on the minimum thickness requirements of ACI Table
8.3.1.1. The plan dimensions of the drop panel are then determined based on the minimum lengths specified in ACI 8.2.4.
Two-way shear stresses at the critical section around the
column should be checked for a minimum drop depth of 2.25
in. If this proves to be inadequate, the next larger drop depth
(4.25 in.) should be used until the shear strength requirements are satisfied. According to ACI 22.6.4, shear stresses
must be checked at the critical sections around the columns
and the drop panels.
Live Load Effects
The material quantities for a flat slab are typically controlled by
deflections. Therefore, an increase in live loads will not cause
a proportional increase in costs. Flat slab systems subjected
to live loads of 100 psf are usually 3 to 7% more expensive
than those with live loads of 40 psf.
Panel Aspect Ratio Effects
Square bay sizes with an aspect ratio equal to 1 represent the
most economical floor layout because the required minimum
slab thickness is the same in both directions. A rectangular
bay with an aspect ratio of 1.2 is about 17% more expensive
than a square bay with the same floor area.
Summary
Flat slab systems are economically viable for medium spans
and for moderate to heavy live loads. For a live load of 65 psf
or less, flat slabs are cost-effective for span lengths between
30 ft and 35 ft. The economical range is 25 ft to 35 ft for a live
load of 100 psf. Although the drop panels result in somewhat
higher formwork costs, a relatively shallow slab system is
achieved in situations where two-way shear stresses would
otherwise preclude the use of a flat plate.
Tables 2.10, 2.11, and 2.12 contain material quantities and
cost indices for flat slab systems with live loads of 40, 65, and
100 psf, respectively.
Standard Lumber Dimensions and Drop Panel Height
Lumber Size
Nominal
Actual
Drop Panel
Height, h1*
2x
11/2"
21/4"
4x
31/
2"
41/4"
6x
51/2"
61/4"
8x
71/4"
8"
* 3/4"-inch form sheathing
2-10
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Table 2.10 Material Quantities and Cost Indices for Flat Slab Floor Systems, LL = 40 psf
Drop Size
Bay
Size (ft)
Slab
Thickness
(in.)
L w W
(ft)
20 w 20
7.0
7w7
8.5
81/
20 w 25
25 w 25
8.5
7w
81/
2
81/
2
w
81/
2
Concrete
(ft3/ft2)
Reinforcement
(psf)
Formwork
(ft2/ft2)
Cost
Index
2.25
14
0.61
2.01
1.01
0.84
2.25
16
0.73
2.23
1.01
0.89
2.25
18
0.73
2.36
1.01
0.90
4.25
20
0.92
2.82
1.02
0.99
25 w 30
10.5
30 w 30
10.5
10 w 10
4.25
24
0.92
2.99
1.02
0.99
30 w 35
12.0
10 w 12
4.25
26
1.04
3.44
1.02
1.06
35 w 35
12.0
12 w 12
4.25
30
1.05
3.69
1.01
1.07
2
w 10
h1
(in.)
Square
Column
Size (in.)
Table 2.11 Material Quantities and Cost Indices for Flat Slab Floor Systems, LL = 65 psf
Bay
Size (ft)
Slab
Thickness
(in.)
20 w 20
20 w 25
25 w 25
25 w 30
Drop Size
L w W
(ft)
h1
(in.)
Square
Column
Size (in.)
Concrete
(ft3/ft2)
Reinforcement
(psf)
Formwork
(ft2/ft2)
Cost
Index
7.0
7w7
2.25
16
0.61
2.15
1.01
0.85
8.5
81/
2.25
18
0.73
2.47
1.01
0.91
2.25
22
0.73
2.66
1.01
0.91
4.25
24
0.92
3.09
1.02
1.00
8.5
10.5
7w
81/
2
81/
w
2
2
81/
2
w 10
30 w 30
10.5
10 w 10
4.25
26
0.92
3.37
1.02
1.02
30 w 35
12.0
10 w 12
4.25
30
1.05
3.76
1.02
1.08
35 w 35
12.0
12 w 12
4.25
34
1.05
4.09
1.01
1.09
Table 2.12 Material Quantities and Cost Indices for Flat Slab Floor Systems, LL = 100 psf
Drop Size
Slab
Thickness
(in.)
L w W
(ft)
h1
(in.)
Square
Column
Size (in.)
Concrete
(ft3/ft2)
Reinforcement
(psf)
Formwork
(ft2/ft2)
Cost
Index
20 w 20
7.0
7w7
2.25
20
0.61
2.44
1.01
0.87
20 w 25
8.5
81/
2.25
22
0.73
2.79
1.01
0.92
25 w 25
8.5
81/2 w 81/2
2.25
26
0.73
3.08
1.01
0.94
25 w 30
10.5
81/2 w 10
4.25
28
0.92
3.47
1.02
1.02
30 w 30
10.5
10 w 10
4.25
32
0.92
3.85
1.02
1.04
30 w 35
12.0
10 w 12
4.25
34
1.06
4.22
1.02
1.10
35 w 35
12.0
12 w 12
6.25
40
1.07
4.68
1.02
1.14
Bay
Size (ft)
7w
2
2.3.5 Two-way Joist System
Overview
A two-way joist system, which is also commonly referred to as
a waffle slab, consists of evenly spaced concrete joists spanning
in both directions and a reinforced concrete slab cast integrally
with the joists (see Fig. 2.9). The floor system is formed with
domes that are 30, 41, and 52 in. wide, resulting in 3-, 4-, and 5-ft
modules, respectively. Systems with a 3-ft module are considered
in this Guide. A solid slab section around the columns is usually
provided for two-way shear resistance.
Fig. 2.9 Two-way Joist (Waffle Slab).
Concrete Reinforcing Steel Institute
2-11
Design Guide for Economical Reinforced Concrete Structures
The main advantages of this type of system are that they are
economical for long spans with heavy loads, the dome voids
reduce the dead load, and electrical fixtures or other items
can be placed in the voids. It is common for these systems to
be exposed so architectural finishes are usually not required,
which results in cost savings. Two-way joist systems are commonly used in office buildings, warehouses, libraries, civic
buildings, and industrial plants.
Member Sizes
The thickness of the slab is controlled by either structural or
fire resistance requirements. In most cases, the thickness is
governed by the latter. Specifying a lightweight aggregate may
be advantageous in certain situations. A normal-weight slab
with a 4.5-in. thickness is used in all cases considered in this
Guide.
The standard joist width is 6 in. for a 3-ft module. Because
slab thickness is controlled by fire resistance requirements
and joist width is set by industry standards, the only geometric variable to be determined is joist depth. Standard dome
depths for the 3-ft module are 8, 10, 12, 14, 16, 20 and 24 in.
For design purposes, waffle slabs are considered as flat slabs
with the solid heads acting as drop panels. Thus, the minimum
thickness of exterior and interior panels of two-way slabs with
drop panels defined in ACI 8.2.4, without edge beams, and
containing reinforcement with a yield strength of 60,000 psi is
equal to Cn33 and Cn36, respectively, where Cn is the length
of the clear span in the long direction. In no case should the
slab thickness be less than 4 in. To determine the deflection
requirements, the cross-section of the actual floor system is
transformed into an equivalent section of uniform thickness.
This is accomplished by determining a slab thickness that
provides the same moment of inertia as the two-way joist
section. Table 2.13 contains the equivalent slab thickness for
the standard domes depths of a 3-ft module waffle slab.
In the tables in the Summary section below, the second to
last column contains the dome area percentage, which is the
percentage of the floor area that requires dome formwork.
Live Load Effects
Because material quantities are typically controlled by deflection constraints, an increase in live load does not have a
proportionate impact on costs. Waffle slabs with live loads of
100 psf are typically only 3 to 7% more expensive than those
with live loads of 40 psf.
Panel Aspect Ratio Effects
Square bay sizes are the most cost-effective because the
deflection requirements are the same in both directions. A
rectangular bay with an aspect ratio of 2 is about 15% more
expensive than a square bay with the same floor area.
Summary
Two-way joist systems are economically viable for long spans
and heavy loads. Systems with 3-ft modules are usually economical for spans ranging from 40 to 50 ft and beyond.
Tables 2.14, 2.15, and 2.16 contain material quantities and
cost indices for two-way joist systems with live loads of 40,
65, and 100 psf, respectively.
Table 2.13 Equivalent Slab Thickness for Two-way Joists
with a 3-ft Module
Dome Depth
(in.)
Rib Width
(in.)
Equivalent Slab
Thickness (in.)
8
6
8.8
2-12
10
6
10.3
12
6
11.7
14
6
13.1
16
6
14.6
20
6
17.4
24
6
20.2
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Table 2.14 Material Quantities and Cost Indices for Two-way Joist Floor Systems, LL = 40 psf
Bay
Dome
Size (ft) Depth (in.)
Solid Head
Square
Column
Size (in.)
Concrete
(ft3/ft2)
Reinforcement
(psf)
Dome Area
(%)
Cost
Index
30 w 30
10
12'-6" w 12'-6"
24
0.81
1.97
84
1.11
36 w 36
14
14'-6" w 14'-6"
28
0.98
2.37
86
1.19
36 w 42
16
14'-6" w 16'-6"
30
1.09
2.75
86
1.24
42 w 42
16
16'-6" w 16'-6"
30
1.10
2.91
86
1.26
48 w 48
20
18'-6" w 18'-6"
32
1.30
3.85
85
1.37
51 w 51
20
20'-6" w 20'-6"
38
1.27
4.07
86
1.37
Table 2.15 Material Quantities and Cost Indices for Two-way Joist Floor Systems, LL = 65 psf
Bay
Dome
Size (ft) Depth (in.)
Solid Head
Square
Column
Size (in.)
Concrete
(ft3/ft2)
Reinforcement
(psf)
Dome Area
(%)
Cost
Index
30 w 30
10
12'-6" w 12'-6"
24
0.81
2.12
84
1.12
36 w 36
14
14'-6" w 14'-6"
28
0.98
2.83
86
1.21
36 w 42
16
14'-6" w 16'-6"
30
1.09
2.94
86
1.25
42 w 42
16
16'-6" w 16'-6"
32
1.10
3.11
86
1.27
48 w 48
20
18'-6" w 18'-6"
38
1.31
4.04
85
1.38
51 w 51
20
20'-6" w 20'-6"
44
1.28
4.24
86
1.38
Table 2.16 Material Quantities and Cost Indices for Two-way Joist Floor Systems, LL = 100 psf
Bay
Dome
Size (ft) Depth (in.)
Solid Head
Square
Column
Size (in.)
Concrete
(ft3/ft2)
Reinforcement
(psf)
Dome Area
(%)
Cost
Index
30 w 30
10
12'-6" w 12'-6"
26
0.81
2.85
84
1.16
36 w 36
14
14'-6" w 14'-6"
30
0.98
3.05
86
1.22
36 w 42
16
14'-6" w 16'-6"
34
1.09
3.13
86
1.26
42 w 42
16
16'-6" w 16'-6"
38
1.10
3.96
86
1.31
48 w 48
20
18'-6" w 18'-6"
44
1.31
4.28
85
1.40
51 w 51
20
20'-6" w 20'-6"
50
1.28
5.30
86
1.44
Concrete Reinforcing Steel Institute
2-13
Design Guide for Economical Reinforced Concrete Structures
CHA PTER 3
One-way Slabs
3.1 Overview
Guidelines and recommendations on the economical design
and detailing of one-way slabs are contained in this chapter.
Information is provided on determining the thickness of the
slab and detailing the flexural reinforcement.
Shear reinforcement is typically not provided in one-way slabs.
The design shear strength can be increased by providing a
thicker slab and/or by increasing the compressive strength of
the concrete, with the former being the most efficient solution in cases where more than a relatively small amount of
additional shear strength needs to be provided.
Because one-way slab systems are usually not part of the
seismic force-resisting system (SFRS), the following requirements and guidelines are essentially applicable for one-way
slabs in buildings assigned to any SDC.
3.2 Determining the Slab Thickness
The thickness of a one-way slab is usually determined initially
based on the minimum thickness requirements in ACI 7.3.1.
ACI Table 7.3.1.1 contains the minimum thickness h that must
be provided as a function of the support conditions and the
span length of the slab for normal-weight concrete and Grade
60 reinforcement in situations where the slab is not supporting or attached to partitions or other construction likely to be
damaged by large deflections.
For the usual case of continuous construction, the depth
of the slab must be the same for all spans and it should be
determined on the basis of the span that yields the largest
minimum depth. Specifying more than one slab depth results
in formwork that is not economical.
It is also important to consider fire resistance requirements
when specifying a slab thickness, especially for one-way slabs
that are supported by joists, which are spaced relatively closely together. It is possible in certain cases that the required
slab thickness based on fire resistance requirements needs
to be greater than the minimum slab thickness determined by
ACI Table 7.3.1.1 for serviceability.
to limit the size the flexural crack widths. Finally, a minimum
amount of concrete cover is needed to protect the bars from the
effects of fire, weather, and corrosive environments, to name a few.
The flexural reinforcement must be properly developed or anchored on both sides of a critical section. This ensures that the
one-way slab system will perform as intended in accordance
with the strength design method.
Temperature and shrinkage reinforcement in accordance with ACI
24.4.3 must be provided perpendicular to the main flexural reinforcement. ACI Table 24.4.3.2 contains minimum reinforcement
ratios to counteract temperature and shrinkage stresses and ACI
24.4.3.3 stipulates the maximum spacing of such reinforcement.
3.3.2 Concrete Cover
Reinforcing bars are placed in a concrete member with a
minimum concrete cover to protect it from weather, fire,
and other effects. Minimum cover requirements for nonprestressed, cast-in-place concrete members are given in ACI
Table 20.6.1.3.1. For one-way slabs, concrete cover is measured from the surface of the concrete to the outer edge of
the longitudinal reinforcement.
Drip grooves or drip edges along the edge of a slab soffit can
cause issues related to the required cover to the longitudinal
reinforcement. These grooves are usually formed using a form
chamfer strip or a one-inch piece of dimension lumber nailed to
the formwork deck near the slab edge. There are essentially two
ways to maintain the required concrete cover in such cases (Reference 6): (1) offset the bars crossing the groove (see Fig. 3.1a)
and (2) relocate the transverse and longitudinal layers of reinforcing bars so that the affected reinforced bar (shown as an open
circle in Fig. 3.1b) can be moved away from the groove, thereby
maintaining the required minimum cover.
3.3 Detailing Requirements and Guidelines
for Flexural Reinforcement
3.3.1 Overview
Once the required area of flexural reinforcement has been
determined for the factored bending moments along the span
length using the strength design method, the size of reinforcing bars must be chosen to provide an area of steel that is
greater than or equal to the amount that is required.
Additionally, minimum spacing between the flexural bars must be
provided so that concrete can adequately flow in the voids between
the bars. A maximum spacing between the flexural bars is required
Concrete Reinforcing Steel Institute
Fig. 3.1 Slab with Drip Groove at Edge of Soffit (a) Cover is Maintained
at Drip Groove by Offsetting the Bottom Longitudinal Bars (b) Cover is
Maintained at Drip Groove by Relocating Longitudinal Bars.
3-1
Design Guide for Economical Reinforced Concrete Structures
Layering of the top steel in the slab over intersecting beams
that are supporting the slab can create constructability issues
for the detailer and placer. More information on this topic can
be found in Section 5.3.2 of this Guide.
3.3.3 Distribution of Flexural Reinforcement for
Crack Control
Requirements for the distribution of flexural reinforcement in
one-way slabs (which are also applicable to beams) are given
in ACI 24.3. The intent of these requirements is to control
flexural cracking: a larger number of fine cracks are preferable
to a few wide cracks mainly for reasons of durability and appearance.
A simple approach to address crack control in flexural members is given in ACI 24.3.2. The maximum center-to-center bar
spacing s determined by the equations in ACI Table 24.3.2 for
deformed bars is specifically meant to control cracking:
40,000 40,000 s = 15 2.5cc 12 fs fs In this equation, fs is the calculated stress in the flexural reinforcement closest to the tension face of the section caused by
the service loads. Note that it is permitted to take fs equal to
2fy /3. The term cc is related to the clear cover of the reinforcement and is defined as the least distance from the surface
of the reinforcement to the tension face of the member. For
Grade 60 bars with cc " 0.75 in. (minimum specified cover in
ACI Table 20.6.1.3.1 for concrete that is not exposed to weather
or in contact with the ground), the longitudinal reinforcing bars
must be spaced no greater than 12 in. on center in order to
satisfy crack control requirements. This value is generally less
than the maximum spacing prescribed in ACI 7.7.2.3. Note that s
is independent of the size of the flexural bars.
are contained in ACI 7.7.3. Provided in these sections are required
development lengths and termination locations for the flexural bars.
Development of flexural reinforcement must occur at the
following critical sections in a one-way slab: (1) points of maximum stress, that is, sections of maximum bending moment
and (2) locations where adjacent reinforcement is terminated.
Development length or anchorage of reinforcement is required
on both sides of a critical section.
In continuous one-way slabs subjected to uniform loads, the
maximum positive and negative bending moments typically
occur near the midspan and at the faces of the supports,
respectively. Positive and negative flexural reinforcing bars
must be developed or anchored on both sides of these critical sections. For cost savings, it is common for some of the
reinforcing bars to be terminated (or cut off) at locations away
from the critical sections. For example, reinforcing bars are no
longer required past a point of inflection on the bending moment diagram. Also, a portion of the bars can be theoretically
cut off prior to the point of inflection at a location where the
continuing bars are adequate to supply the required design
strength. Because a critical section occurs at a cutoff point,
the bars must be properly developed at that location as well.
Recommended flexural reinforcement details for one-way
slabs are given in Fig. 3.2, which is adapted from Reference
7. The bar lengths in the figures are based on one-way slabs
subjected to uniformly distributed gravity loads. Adequate
bar lengths must be determined by calculation for members
subjected to the effects from other types of gravity loads.
The bar lengths in these figures can also be used for one-way
slabs that have been designed using the approximate bending
moment coefficients given in ACI Table 6.5.2.
3.3.4 Minimum Spacing of Flexural Reinforcement
Spacing limits for nonprestressed reinforcing bars in a horizontal layer are given in ACI 25.2.1. In particular, the clear spacing
between the bars must be at least the greatest of the following: 1 in., the diameter of the reinforcing bar, and (4/3) times the
diameter of the largest aggregate in the concrete mix. These
limits have been established primarily so that concrete can flow
readily into the spaces between adjoining reinforcing bars and
between reinforcing bars and formwork. Concrete must fully
surround the reinforcing bars without honeycombing so that a
good bond is established between the concrete and the steel.
3.3.5 Development of Longitudinal Reinforcement,
Flexural Cutoff Points, and Splices
Development of Flexural Reinforcement and
Cutoff Points
Flexural reinforcement must be properly developed or anchored
in a one-way slab in order for it to perform as intended in accordance with the strength design method. General requirements for
development of reinforcement are given in ACI 25.4 and provisions
for positive and negative flexural reinforcement in one-way slabs
3-2
Fig. 3.2 Recommended Flexural Reinforcement Details for One-way Slabs.
Splices
ACI 25.5 contains the requirements for lap splices, which, as
noted in Section 1.3.3, are typically the most economical type
of splice. Tension lap splices must be provided for flexural reinforcement, and a consistent lap splice length should be specified for a given bar size. Lap splice length is determined based
on the concrete strength, the grade of the reinforcement, and
the reinforcing bar size, location, and spacing.
Lap splice requirements for one-way slabs are essentially the
same as those for beams (see Section 5.3.5 of this Guide for
more information).
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Fig. 4.1 Minimum Slab Thickness for Two-way Slabs without Interior Beams with Grade 60 Reinforcement.
CHA PTER 4
Two-way Slabs
4.1 Overview
Guidelines and recommendations on the economical design
and detailing of two-way slabs are contained in this chapter.
Information is provided on determining the thickness of the
slab and detailing the reinforcement for the effects of flexure
and shear. Specific requirements for two-way slab systems
without beams that are part of the SFRS in structures assigned to SDC C are given in Section 4.5.
4.2 Determining the Slab Thickness
The first step in the design of a two-way slab system is to
determine a preliminary slab thickness. A minimum slab thickness must be provided to control deflections and to provide
adequate shear strength, where applicable.
Serviceability requirements for two-way slab systems with nonprestressed reinforcement are given in ACI 8.3.1. ACI Table 8.3.1.1
contains minimum thicknesses for two-way slabs without interior
beams in systems without drop panels (flat plates) and with drop
panels (two-way slabs). Also given in this table are minimum thicknesses for these systems where exterior panels have an edge
beam present and where they do not. Where beams are present
on all sides of a panel, the minimum thickness is given in ACI Table
8.3.1.2. Figure 4.1 provides a summary of the minimum slab thickness requirements for two-way slabs without interior beams.
For two-way slab systems without beams, the minimum slab
thickness that is required is often controlled by the two-way
shear stresses that occur in the slab around the perimeter of the
columns. Edge columns can be subjected to the largest shear
stresses in the entire two-way system. Because two-way shear
requirements are related to flexural requirements (the assumed
distribution of shear stress around the critical section of a column
includes the effects of unbalanced moments at a support), a
slab thickness that satisfies both sets of requirements cannot be
Concrete Reinforcing Steel Institute
Fig. 4.2 Preliminary Slab Thickness for Flat Plates.
obtained unless some simplifying assumptions are made. Figure
4.2, which is adapted from Reference 7, can be used to obtain a
preliminary slab thickness for flat plates. The information in the
figure is based on the following assumptions:
• Square edge column of size bending perpendicular to the
slab edge with a three-sided critical section
• Column supporting a tributary area A
• Square bays
• Gravity load moment transferred between the slab and
the edge column in accordance with the Direct Design
Method requirement of ACI 8.10
• 4,000 psi normal-weight concrete
4-1
Design Guide for Economical Reinforced Concrete Structures
The term qu is the total factored load, which must include an
estimate of the slab weight; this weight can be estimated
based on a slab thickness determined from the serviceability
requirements. The ratio d/c1 is determined from Fig. 4.2 as a
function of qu and the area ratio A/c12. A preliminary slab
thickness h can be obtained by adding 1.25 in. to d acquired
from the figure. The purpose of this design aid is to help decrease the number of iterations that are needed to establish a
viable slab thickness based on shear strength requirements; it
is not meant to replace shear strength calculations.
It is common that the slab thickness determined based on
strength and serviceability requirements will satisfy fire resistance requirements for typical residential and office occupancies. There is usually no need to increase the slab thickness to
achieve a required fire rating in such cases.
how to provide the required cover is given in Section 3.3.2 for
one-way slabs, which is also applicable to two-way slabs.
4.3.3 Minimum and Maximum Bar Spacing
The minimum and maximum spacing of the flexural reinforcement in two-way slabs is given in ACI 8.7. As in the case of
one-way slabs and beams, the minimum clear spacing is the
greatest of 1 in., the diameter of the flexural bar, and (4/3)
times the maximum aggregate size (ACI 25.2.1).
For nonprestressed solid slabs, the maximum center-to-center
spacing of the flexural reinforcement is the lesser of 2 times
the overall slab thickness and 18 in. This limitation helps control cracking and provides for the possibility of loads concentrated on small areas of the slab.
The depth of the slab must be the same for all spans and it
should be determined on the basis of the span that yields
the largest minimum depth based on serviceability and shear
strength requirements. Specifying more than one slab depth
results in formwork that is not economical.
When selecting the size of the reinforcing bars, the largest bar
size that will satisfy strength and serviceability requirements
will usually provide overall economy. The spacing of the top
bars should be limited to account for construction traffic. It is
recommended that not less than #4 bars spaced at 12 in. on
center be used to avoid displacement of the top bars.
4.3 Detailing Requirements and Guidelines
for Flexural Reinforcement
4.3.4 Corner Reinforcement
4.3.1 Overview
Once the required area of flexural reinforcement has been
determined in the column strips and middle strips for the
factored bending moments along the span length using the
strength design method, the size of reinforcing bars must be
chosen to provide an area of steel that is greater than or equal
to the amount that is required.
Additionally, minimum spacing between the flexural bars must
be provided so that concrete can adequately flow in the voids
between the bars. A maximum spacing between the flexural
bars is required to limit the size the flexural crack widths.
Finally, a minimum amount of concrete cover is needed to
protect the bars from the effects of fire, weather, and corrosive environments, to name a few.
ACI 8.7.3 addresses exterior corners of slabs that are supported by stiff elements such as walls and edge beams. The
presence of stiff elements restrains the lifting and causes
additional bending moments at the exterior corners.
Corner reinforcement must be provided at both the top and
the bottom of the slab, and the reinforcement in each layer
in each direction must be designed for a bending moment
equal to the largest positive bending moment per unit width
in the slab panel. The top and bottom reinforcement must be
placed parallel and perpendicular to the diagonal, respectively,
as shown in Fig. 4.3 for a distance of at least one-fifth of the
longer of the two span lengths in the corner panel. Reinforcement parallel to the edges is permitted to be used instead of
the diagonal bars (see Fig. 4.4). This layout is preferred because of ease in constructability compared to the other layout.
The flexural reinforcement must be properly developed or
anchored on both sides of a critical section. This ensures that
the two-way slab will perform as intended in accordance with
the strength design method.
4.3.2 Concrete Cover
Reinforcing bars are placed in a concrete member with a minimum concrete cover to protect it from weather, fire, and other
effects. Minimum cover requirements for nonprestressed, castin-place concrete members are given in ACI Table 20.6.1.3.1. Like
in the case of one-way slabs, concrete cover is measured from
the surface of the concrete to the outer edge of the longitudinal
reinforcement for two-way slabs without stirrups.
Drip grooves or drip edges along the edge of a slab soffit can
cause issues related to providing the required cover to the
longitudinal reinforcement in two-way slabs. A discussion on
4-2
Fig. 4.3 Reinforcement Required
at Corners of Slabs Supported by
Stiff Edge Members.
Fig. 4.4 Alternative Reinforcement
Layout at Corners of Slabs Supported
by Stiff Edge Members.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
4.3.5 Development of Longitudinal Reinforcement,
Flexural Cutoff Points, and Splices
Development of Flexural Reinforcement and
Cutoff Points
Flexural reinforcement must be properly developed or anchored in a two-way slab in order for it to perform as intended
in accordance with the strength design method. General
requirements for development of reinforcement are given
in ACI 25.4 and provisions for positive and negative flexural
reinforcement in column and middle strips of two-way slabs
are contained in ACI 8.7.4. Provisions for required development lengths and termination locations for the flexural bars
are given in that section.
Development of flexural reinforcement must occur at the following critical sections in a two-way slab in both the column
and middle strips: (1) points of maximum stress, that is, sections of maximum bending moment and (2) locations where
adjacent reinforcement is terminated. Development length
or anchorage of reinforcement is required on both sides of a
critical section.
In continuous two-way slabs subjected to uniform loads, the
maximum positive and negative bending moments in the
column and middle strips typically occur near the midspan and
at the faces of the supports, respectively. Positive and negative flexural reinforcing bars must be developed or anchored on
both sides of these critical sections. For cost savings, it is common for some of the reinforcing bars to be terminated (or cut
off) at locations away from the critical sections. For example,
reinforcing bars are no longer required past a point of inflection
on the bending moment diagram. Also, a portion of the bars
can be theoretically cut off prior to the point of inflection at a
location where the continuing bars are adequate to supply the
required design strength. Because a critical section occurs at a
cutoff point, the bars must be properly developed at that location as well.
ACI Fig. 8.7.4.1.3a contains the minimum bar extensions in the
column and middle strips in two-way slab systems without
beams. These minimum lengths and extensions were developed for uniformly distributed gravity loads only; adequate
bar lengths must be determined by calculation for members
subjected to the effects from other types of gravity loads and/
or lateral loads from wind or earthquakes.
The purpose of the structural integrity requirements of ACI
8.7.4.2 is to enable a two-way slab to span to adjacent supports should a single intermediate support be damaged or
destroyed. Two continuous column strip bottom bars through
a support are provided to give the slab some residual strength
after two-way shear failure at a single support.
Recommended flexural reinforcement details for two-way
slabs subjected to uniform gravity loads are given in Fig. 4.5,
which is adapted from Reference 7. Details for two-way slab
systems without beams that are part of the SFRS are given in
Section 4.5 of this Guide.
Concrete Reinforcing Steel Institute
Fig. 4.5 Recommended Flexural Reinforcement Details for Two-way Slabs.
Lap Splices
ACI 25.5 contains the requirements for lap splices, which, as
noted in Section 1.3.3, are typically the most economical type
of splice. Tension lap splices must be provided for flexural reinforcement, and a consistent lap splice length should be specified for a given bar size. Lap splice length is determined based
on the concrete strength, the grade of the reinforcement, and
the reinforcing bar size, location, and spacing.
Lap splices requirements for two-way slabs are essentially the
same as those for beams (see Section 5.3.5 of this Guide for
more information).
4.3.6 Guidelines for Detailing the Flexural Reinforcement
The following guidelines are recommended when detailing
the flexural reinforcement (Reference 8):
1.
Layering. It is important to identify which reinforcing
bars are to be placed in the outer layers and which are
to be placed in the inner layers. It is common for the
reinforcement in the direction of the larger design moments be placed in the outer layers. A note or a section
on the structural drawings can be provided to identify
the inner and outer layers of flexural reinforcement.
2.
Spacing. Reinforcing bars that are required in addition
to the main, uniformly-spaced reinforcing bars in the
column and middle strips should have a spacing that is
a multiple of that provided for the main bars. These bars
need to be clearly identified on the structural drawings.
4-3
Design Guide for Economical Reinforced Concrete Structures
Fig. 4.7 Placement of Slab Reinforcement at Column-line Beams.
Fig. 4.6 Placement of Reinforcement at Offset Columns.
3.
Offset columns. Where columns are offset in plan,
the top and bottom reinforcing bars should be placed
orthogonally, if possible (see Fig. 4.6). This minimizes
constructability issues compared to skewed bars. If
skewed bars are required, they should be provided
only in a separate, bottom layer; the top bars should be
placed orthogonally. Top bars in the middle strip should
be centered on a line connecting the column center
lines.
4.
Negative reinforcement at columns. In two-way slab
systems without beams, the amount of negative reinforcement at the columns may need to be increased
above that required for pure flexure to satisfy the requirements in ACI 8.4.2 pertaining to the portion of the
unbalanced moment transferred by flexure at the slabcolumn joint. This additional reinforcement needs to be
clearly documented on the structural drawings. Where
required, the additional bars are usually provided in the
columns strip directly over the column while maintaining the typical bar spacing for the columns strip bars.
5.
Beams. The location of the slab top reinforcement must
be clearly indicated on the structural drawings where
column-line beams are present. Because the minimum
cover to the slab bars is smaller than that of the beam
bars, the slab bars are typically placed above the top
bars in the beam in the same plane as the beam stirrups (see Fig. 4.7).
The total area of reinforcement in a panel without an opening
must be preserved in both directions of a panel with an opening. In other words, any reinforcement that is interrupted by
an opening must be replaced on each side of the opening.
4.4 Detailing Requirements and Guidelines for Shear Reinforcement
4.4.1 Overview
According to ACI 8.4.3 and 8.4.4, both one-way and two-way
shear strength requirements must be satisfied for any two-way
slab system supported directly on columns. One-way shear
rarely governs; in most cases, two-way shear is more critical.
4.3.7 Openings in Slab Systems
ACI 8.5.4.1 permits openings of any size in two-way slab
systems provided that an analysis of the system with the
openings is performed that shows that all applicable strength
and serviceability requirements of the Code are satisfied. For
slabs without beams, such an analysis is waived when the
provisions of ACI 8.5.4.2 are met. These provisions are illustrated in Fig. 4.8, which is adapted from Reference 7.
4-4
Fig. 4.8 Openings in Slab Systems Without Beams (ACI 8.5.4).
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
In cases where the two-way shear strength of the slab is not
adequate and where other means to increase shear strength
are not practical or feasible (for example, specifying a thicker
slab or a larger column, introducing column-line beams, or
providing drop panels or shear caps), it is permitted to supplement shear strength by providing one of the following types
of reinforcement (see ACI Fig. R8.7.6(a)-(c)):
1.
Single- or multiple-leg stirrups
2.
Shearheads
3.
Headed shear studs
Requirements for stirrups and headed shear studs are given
in the following sections. Although once popular, shearheads
and column capitals are rarely used anymore because they are
not cost effective.
4.4.2 Single- or Multiple-leg Stirrups
Research has shown that the two-way shear strength of slabs
can be increased by shear reinforcement consisting of properly anchored single- or multiple-leg stirrups fabricated from
bars or wires. The use of such reinforcement is permitted
provided that the effective depth of the slab d is greater than
6 in. but not less than 16 times the bar diameter of the shear
reinforcement (ACI 22.6.7.1).
Fig. 4.10 Shear Studs at an Exterior Column used to Increase Punching
Shear Capacity.
Anchorage provisions for stirrups are given in ACI 25.7.1.3
for deformed reinforcing bars. For Grade 60 #5 stirrups and
smaller and for Grade 40 #6 through #8 stirrups, anchorage
is to be provided using a standard hook around the longitudinal reinforcement. For Grade 60 #6 through #8 stirrups the
additional embedment length noted in that section must be
provided in addition to the standard hooks. Table 5.4 in Section
5.4.3 of this Guide gives the minimum depth that is needed
to develop Grade 60 #6 through #8 stirrups according to the
provisions of ACI 25.7.1.3; it is evident from the table that
these stirrups cannot be used in slabs of typical thickness that
are found in buildings with typical occupancies.
Illustrated in Fig. 4.9, which is adapted from Reference 7, are
required details for closed stirrup shear reinforcement in twoway slabs.
4.4.3 Headed Shear Studs
Tests have shown that shear reinforcement consisting of
large headed studs welded to flat steel rails are effective in
resisting two-way shear in slabs (see Fig. 4.10). Headed shear
stud reinforcement can take the place of or can be used in
conjunction with other means (drop panels, shear caps, etc.)
to increase design shear strength. The base rail, which is set
on chairs, is nailed to the formwork around the column. The
size and spacing of the studs and the length of the base rail
depends on the shear requirements.
Sufficient concrete cover must be provided to protect the
base rail and head from weather, fire, and other effects. ACI
20.6.1.3.5 contains the minimum cover requirements for
headed shear stud reinforcement. In particular, the concrete
cover for the base rail and heads must not be less than that
required for the reinforcement in the slab. ACI Fig. R20.6.1.3.5
illustrates these concrete cover requirements for headed
shear stud reinforcement in slabs with both top and bottom
bars
Fig. 4.9 Details for Closed Stirrup Shear Reinforcement in Two-way Slabs.
Concrete Reinforcing Steel Institute
Illustrated in Fig. 4.11, which is adapted from Reference 7, are
required details for headed shear stud reinforcement in twoway slabs.
4-5
Design Guide for Economical Reinforced Concrete Structures
Fig. 4.11 Details for Headed Shear Stud Reinforcement in Two-way Slabs.
Fig. 4.12 Flexural Reinforcement Details for Two-way Slabs Without
Beams in Structures Assigned to SDC C.
4.5 Detailing Requirements and Guidelines for SDC C
Two-way slabs without beams are permitted to part of an
intermediate moment frame, which is the required SFRS for
structures assigned to SDC C; they are not permitted to be
part of the SFRS in SDC D, E, or F.
All of the requirements and guidelines presented above are
also applicable when such systems are part of the SFRS. In
addition, the requirements in ACI 18.4.5 must be satisfied.
Flexural reinforcement details based on these requirements
are given in Fig. 4.12, which is adapted from Reference 7.
4-6
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
CHA PTER 5
Beams
5.1 Overview
Guidelines and recommendations on the economical design
and detailing of beams are contained in this chapter. Information is provided on sizing the cross-section and detailing the
reinforcement for the effects due to flexure, shear, and torsion
and combinations thereof. Specific requirements for beams
in intermediate moment frames (SDC C) and special moment
frames (SDC D, E, and F) are given in Sects. 5.7 and 5.8 of
this Guide, respectively.
5.2 Sizing the Cross-section
5.2.1 Beam Depth
Assuming f c’ " 4,000 psi, fy " 60,000 psi, and a reinforcement
ratio W of approximately 50% of that corresponding to the
reinforcement strain limit in ACI 9.3.3, the above equation for
bw reduces to the following:
bw "
20M u
d2
where Mu is in foot-kips and bw and d are in inches.
Providing a beam width that is equal to or greater than the
value from this equation will result in cross-sectional dimensions that satisfy both strength and serviceability requirements of ACI 318.
Establishing the dimensions of the cross-section is typically
the initial step in the design of a reinforced concrete beam.
The depth is usually determined first on the basis of deflection requirements (see ACI Table 9.3.1.1 and Section 2.2.2 of
this Guide). This depth sometimes needs to be modified for
constructability, economy, or architectural reasons, to name a
few.
Because beams are part of a continuous floor and/or roof
system, the largest factored bending moment Mu along the
spans should be used in this equation. The beam width determined from the maximum Mu must be used for all spans;
this will help in achieving economical formwork. Varying the
amount of flexural reinforcement along the span lengths for
different factored bending moments is by far more economical than varying the beam width (or depth).
It is important to consider economical formwork when choosing the depth of a beam. It is evident from ACI Table 9.3.1.1
that the minimum depth depends on the support conditions.
For the usual case of continuous construction, the depth of
the beam must be the same for all spans and it should be
determined on the basis of the span that yields the largest
minimum depth. More than one beam depth along the same
line of beams results in formwork that is not economical.
The same beam depth should be used not only throughout
an entire floor/roof level but the entire structure as often as
possible. In wide-module joist systems, the depth of the joists
(beams) and the supporting beams (girders) must be the
same for overall economy.
When selecting a beam width, it is also important to consider
the width of the columns at the ends of the beam. Consider
Cases A and B in Fig. 5.1. Greatest economy is achieved when
the beam is as wide as or wider than the column: the formwork is much simpler compared to Case C where the beam is
narrower than the column. Even though the formwork is simple where the width of the beam is the same as the column,
it is good practice to have a wider beam to avoid interference
between the longitudinal corner bars of the beam and the
column corner bars. It is recommended to have a beam width
that is at least 4 in. wider than the column it frames into.
Beamside Form
5.2.2 Beam Width
Once the overall depth of the beam has been established
based on serviceability requirements and economy, the width
of a beam can be determined by setting the design flexural
strength KMn equal to the required flexural strength Mu for
an assumed reinforcement ratio W. Using the basic principles
of the strength design method, the required width bw can be
calculated by the following equation:
Mu
bw "
Rn d 2
Beam
Bottom
Plyform
A
B
C
Plan View
In this equation, K"0.9 for tension-controlled sections, d "
distance from the extreme compression fiber to the centroid of
the reinforcing steel, and Rn " nominal strength coefficient of
resistance, which can be determined by the following equation:
0.59 f y Rn " f y 1
f c'
Concrete Reinforcing Steel Institute
Isometric
Fig. 5.1 Selecting a Beam Width for Formwork Economy.
5-1
Design Guide for Economical Reinforced Concrete Structures
5.3 Detailing Requirements and Guidelines
for Flexural Reinforcement
sures the beam will perform as intended in accordance with
the strength design method.
5.3.1 Overview
5.3.2 Concrete Cover
Once the required area of flexural reinforcement has been
determined for the factored bending moments along the
span length using the strength design method, the number
of reinforcing bars must be chosen to provide an area of steel
that is equal to or greater than the amount that is required. It
is important to ensure that the reinforcing bars will adequately
fit within the cross-section of the beam.
Concrete protection for reinforcement plays an important role
in the formulation of the requirements of bar spacing and
bar development. Reinforcing bars are placed in a concrete
member with a minimum concrete cover to protect it from
weather, fire, and other effects. Minimum cover requirements
for nonprestressed, cast-in-place concrete construction are
given in ACI Table 20.6.1.3.1. For beams that have transverse
reinforcement in the form of stirrups that enclose the main
flexural reinforcing bars, concrete cover is measured from the
surface of the concrete to the outer edge of the stirrups.
In general, the minimum and maximum number of reinforcing bars in a single layer is a function of the cover and spacing
requirements given in ACI 318-14. Minimum spacing between
the longitudinal bars needs to be provided so that concrete
can adequately flow in the voids between the bars. A maximum spacing between the longitudinal bars is required to limit
the size the flexural crack widths. Also, a minimum amount of
concrete cover is needed to protect the bars from the effects
of fire, weather, and corrosive environments, to name a few.
The longitudinal reinforcement must also be properly developed or anchored on both sides of a critical section. This en-
A drip groove or edge in a beam soffit often times presents
a problem in maintaining the required cover to the bars (see
Reference 6 and Fig. 5.2a). It is not feasible to increase the
concrete cover after the reinforcing bars in the beam have
been detailed. Raising the stirrups from the bottom to achieve
the required cover decreases the cover at the top (see Fig.
5.2b). The only practical solution is to measure the concrete
cover from the drip groove and detail the stirrups accordingly,
as shown in Fig. 5.2c. This will usually impact the overall
depth of the beam and should be accounted for in design.
Maintaining the proper concrete cover can also be challenging
at beam intersections. In particular, layering of the top steel in
the slab at such intersections can create constructability issues.
The sequencing and layering of beam and slab top reinforcement can also create serious congestions issues (see Fig. 5.3).
The following bar placing sequence is one way of avoiding the
problems associated with this situation (see Reference 9):
Fig. 5.2 Beam Sections Showing Drip Groove at Bottom Soffit: (a) Inadequate Cover at Drip; (b) Shifting Reinforcing Cage to Maintain Adequate
Cover at Drip Will Cause top Cover Problems; and (c) to Maintain
Adequate Cover at all Locations, Stirrup Sizes may Need to be Changed.
The Designer Must Consider the Effects of Shifting or Changing the Stirrups
on Beam Capacity.
1.
Erect the reinforcement for the primary beams (bottom
bars, stirrups, and top bars) as stand-alone cages and
set in place.
2.
Place the stirrups (bottom pieces of two-piece stirrups)
and the bottom bars for the secondary beams.
3.
Place the bottom bars for the slab (not depicted in
Fig. 5.3 for clarity).
4.
Place the top bars and the top pieces of the two-piece
stirrups for the secondary beams.
5.
Place the top bars for the slab.
5.3.3 Distribution of Flexural Reinforcement for
Crack Control
Requirements for the distribution of flexural reinforcement in
beams (which are also applicable to one-way slabs; see Section 3.3.3 of this Guide) are given in ACI 24.3.
As discussed in Section 3.3.3, the maximum center-to-center
bar spacing s determined by the equations in ACI Table 24.3.2
for deformed bars is as follows (see Fig. 5.4):
Fig. 5.3 Layering of Beam and Slab Reinforcing Bars can Create
Sequencing Issues. Structural Drawings Should Designate Layer
Locations and Concrete Covers.
5-2
40,000 40,000 s = 15 2.5cc 12 fs fs Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Table 5.1 Minimum Number of Reinforcing Bars Required
in a Single Layer
Bar
Size
Beam Width (in.)
12 14 16 18 20 22 24 26 28 30 36 42 48
Fig. 5.4 – Maximum Spacing Requirements of Flexural Reinforcement.
In this equation, fs is the calculated stress in the flexural
reinforcement closest to the tension face of the section
caused by the service loads. Note that it is permitted to take
fs equal to 2fy /3. The term cc is related to the clear cover of
the reinforcement and is defined as the least distance from
the surface of the reinforcement to the tension face of the
member. For Grade 60 bars with cc " 2 in. (1.5 in. cover to a #4
stirrup), the longitudinal reinforcing bars must be spaced no
greater than 10 in. on center in order to satisfy crack control
requirements. Note that s is independent of the size of the
flexural bars.
On the basis of the information given in Fig. 5.4 and the discussion
above, the following equation provides the minimum number of
bars nmin required in a single layer to control cracking:
nmin =
#4
2
2
3
3
3
3
3
4
4
4
5
5
6
#5
2
2
3
3
3
3
3
4
4
4
5
5
6
#6
2
2
3
3
3
3
3
4
4
4
5
5
6
#7
2
2
3
3
3
3
3
4
4
4
5
5
6
#8
2
2
3
3
3
3
3
4
4
4
5
5
6
#9
2
2
3
3
3
3
3
4
4
4
5
5
6
#10
2
2
3
3
3
3
3
4
4
4
5
5
6
#11
2
2
3
3
3
3
3
4
4
4
5
5
6
5.3.4 Minimum Spacing of Flexural Reinforcement
As noted in Section 3.3.4, spacing limits for reinforcing bars in
a horizontal layer are given in ACI 25.2.1. The spacing requirements are summarized in Fig. 5.5 for beams where dagg is the
nominal maximum aggregate size in the concrete mixture.
The following equation provides the maximum number of bars
nmax that can fit in a single layer on the basis of the spacing
requirements of ACI 25.2.1:
nmax =
bw 2 (c s + d s + r )
+1
(clear space )+db
bw 2 (cc + 0.5db )
+1
s
The values of nmin determined by this equation should be
rounded up to the next whole number. Note that a minimum
of two bars are required to anchor the stirrups in beams.
The minimum number of bars can be tabulated for various
beam widths, as shown in Table 5.1. The information in this
table is based on the following:
• Grade 60 reinforcement
• Overall reinforcing bar diameter given in Table 2.1
• Least distance from the surface of the reinforcement to
the tension face of the member cc " 2 in.
• Calculated stress in the flexural reinforcement closest
to the tension face of the section, caused by the service
loads fs " 40 ksi
Providing at least the number of flexural reinforcing bars in
Table 5.1 for a given beam width automatically satisfies the
crack control requirements of ACI 24.3.2.
Concrete Reinforcing Steel Institute
Fig. 5.5 Spacing Limits of Flexural Reinforcement.
Values of nmax determined by this equation should be rounded
down to the next whole number.
5-3
Design Guide for Economical Reinforced Concrete Structures
Table 5.2 contains the maximum number of bars that can fit in
a single layer for various beam widths. The information in this
table is based on the following:
• Grade 60 reinforcement.
• Clear cover to the stirrups cs " 1.5 in.
• Maximum aggregate size dagg " 3/4 in.
• #3 stirrups are used for #4 to #6 longitudinal bars, and #4
stirrups are used for #7 and larger longitudinal bars
Table 5.2 Maximum Number of Reinforcing Bars Permitted
in a Single Layer
Bar
Size
Beam Width (in.)
12 14 16 18 20 22 24 26 28 30 36 42 48
#4
5
6
7
8
10 11 12 14 15 16 20 24 28
#5
4
5
7
8
9
10 11 13 14 15 19 22 26
#6
4
5
6
7
8
9
10 11 12 14 17 20 23
#7
3
4
5
6
7
8
9
10 11 12 15 18 21
#8
3
4
5
6
7
7
8
9
10 11 14 16 19
#9
3
4
4
5
6
7
8
8
9
10 12 15 17
#10
2
3
4
5
5
6
7
7
8
9
11 13 15
#11
2
3
3
4
5
5
6
7
7
8
10 11 13
Selecting the number of bars within the limits of Tables 5.1
and 5.2 provides automatic conformity with the ACI 318
requirements for cover and spacing given the assumptions
noted above. As discussed in Section 1.3.3, using the largest
practical bar sizes that satisfy both strength and serviceability
requirements results in overall cost savings.
5.3.5 Development of Longitudinal Reinforcement,
Flexural Cutoff Points, and Splices
Development of Flexural Reinforcement and
Cutoff Points
Flexural reinforcement must be properly developed or anchored in a concrete beam in order for the member to perform
as intended in accordance with the strength design method.
General requirements for development of reinforcement are
given in ACI 25.4 and provisions for positive and negative
flexural reinforcement in nonprestressed beams are contained
in ACI 9.7.3. Provided in these sections are required development lengths and termination locations for the flexural bars.
Development of flexural reinforcement must occur at the
following critical sections in a reinforced concrete beam: (1)
points of maximum stress, that is, sections of maximum
bending moment and (2) locations where adjacent reinforcement is terminated. Development length or anchorage of
reinforcement is required on both sides of a critical section.
In continuous beams subjected to uniform loads, the maximum positive and negative bending moments typically occur
near the midspan and at the faces of the supports, respectively. Positive and negative flexural reinforcing bars must be
5-4
Fig. 5.6 Recommended Flexural Reinforcement Details for Beams.
developed or anchored on both sides of these critical sections.
For cost savings, it is common for some of the reinforcing
bars to be terminated (or cut off) at locations away from the
critical sections. For example, reinforcing bars are no longer
required past a point of inflection on the bending moment
diagram. Also, a portion of the bars can be theoretically cut off
prior to the point of inflection at a location where the continuing bars are adequate to supply the required design strength.
Because a critical section occurs at a cutoff point, the bars
must be properly developed at that location as well.
Recommended flexural reinforcement details for reinforced
concrete beams are given in Fig. 5.6, which is adapted from
Reference 7. Included are the structural integrity requirements
of ACI 9.7. The bar lengths in the figures are based on members subjected to uniformly distributed gravity loads. Adequate
bar lengths must be determined by calculation for members
subjected to the effects from other types of gravity loads and
lateral loads. The bar lengths in these figures can also be used
for members that have been designed using the approximate
bending moment coefficients given in ACI Table 6.5.2.
Lap Splices
Splices of reinforcing bars are unavoidable in any reinforced
concrete structure mostly because of transportation limitations.
As noted in Section 2.2.3, lap splices are typically the most economical type of splice. ACI 25.5 contains the requirements for lap
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
splices. Tension lap splices must be provided for flexural reinforcement, and a consistent lap splice length should be specified for a
given bar size. In a tension lap splice, the force in the reinforcing
bars is transferred to the concrete by bond, which, in turn, transfers the force back to the adjacent reinforcing bars resulting in an
essentially continuous line of reinforcement. As a result of this
interaction, lap splice length is determined based on the concrete
strength, the grade of the reinforcement, and the reinforcing bar
size, location, and spacing.
There are two types of tension lap splices: contact lap splices and
noncontact lap splices. The reinforcing bars in a contact lap splice
touch and are wired together (see Fig. 5.7a). This type of splice is
preferred because the bars are secured together and less likely to
displace during construction compared to a noncontact lap splice
where the bars do not touch (see Fig. 5.7b). There is a limit on
how far the bars can be separated in a noncontact lap splice: the
transverse center-to-center spacing of noncontact spliced bars
must not exceed the lesser of one-fifth the required lap splice
length and 6 in. (ACI 25.5.1.3).
Lap splice lengths of deformed bars in tension are given in ACI
Table 25.5.2.1, and are a function of the tension development
length of the bar Cd that is calculated in accordance with ACI
25.4.2.1(a). Class B tension splices are usually provided for beams.
Tension splices should be confined with transverse reinforcement, and if possible, located in zones of low tensile stresses (for
example, near inflection points). This is intended to help prevent
splice failure at the end of the splice due to splitting tensile
stresses in the concrete. The location of a lap splice is different
for top and bottom bars. For continuous top bars, lap splices
generally occur away from the supports, which are typically the
sections of maximum negative moment. Such splices are usually
located within the middle third of the span length. Similarly, for
bottom bars, the splices should occur near the supports.
Lapping of continuous bottom bars at supports often presents congestion and installation problems. Table 5.3, which is adapted from
Reference 10, contains four splice arrangements for the bottom
flexural bars along with their advantages and disadvantages based
on constructability. In Arrangement No. 1, all of the bottom bars
are spliced over the columns away from the section of maximum
Fig. 5.7 Contact and Noncontact Tension Lap Splices.
Concrete Reinforcing Steel Institute
positive moment, which is common. This arrangement can result in
the most congestion in the beam-column joint. Arrangement No. 2
consists of half of the bottom bars spliced on one side of the joint
and the other half on the other side of the joint, while Arrangement
No. 3 has all of the splices located on one side of the joint. Finally,
Arrangement No. 4 shows splice bars that pass through the joint,
which are spliced to the bottom bars on both sides of the joint.
Even though this arrangement increases the amount of steel that
is required, the cost of the additional steel may be more than offset
by the savings in labor and other costs, so it may be the most costeffective arrangement in certain situations. In addition to constructability, the appropriate splice arrangement must be chosen based on
structural requirements for a particular situation.
5.4 Detailing Requirements and Guidelines
for Shear Reinforcement
5.4.1 Overview
Shear reinforcement is provided in reinforced concrete beams
to supplement the shear strength provided by the concrete. ACI
22.5.10 permits the following types of shear reinforcement:
1.
Stirrups, ties, or hoops perpendicular to the longitudinal
axis of the member
2.
Welded wire reinforcement with wires located perpendicular to the longitudinal axis of the member
3.
Spiral reinforcement
4.
Inclined stirrups making an angle of at least 45 degrees
with the longitudinal axis of the member and crossing
the plane of the potential shear crack
5.
Longitudinal reinforcement that is bent an angle of 30
degrees or more with respect to the longitudinal axis of
the member
The most commonly used type of shear reinforcement in beams is
stirrups that are oriented perpendicular to the axis of the member
and are anchored to the longitudinal flexural reinforcement. The following discussion focuses on this type of shear reinforcement.
5.4.2 Stirrup Configurations
Illustrated in Fig. 5.8 is a two-legged U-stirrup, which is commonly utilized in reinforced concrete beams. Minimum inside
bend diameters and standard hook geometry for stirrups are
given in ACI Table 25.3.2.
Fig. 5.8 Two-legged U-stirrup.
5-5
Design Guide for Economical Reinforced Concrete Structures
Table 5.3 Splice Arrangement for Bottom Bars in a Reinforced Concrete Beam
Arrangement
Advantages
• Simplest to detail
1
LAP
• Suitable arrangement where
beams are wider than columns
LAP
BEAM
• No additional reinforcing steel is
required
Only continuous bottom bars are shown
COLUMN
Disadvantages
• Can cause significant congestion, especially where the beam
and column have the same
width and/or where a large
amount of continuous reinforcement is required
• Installation of single-bay preassembled beam cages is difficult
• Installation of multiple-bay
preassembled cages is virtually
impossible
• Detailing and preassembled
cages are slightly more complex
• Congestion is eased with no
splices over the columns
2
LAP
LAP
BEAM
LAP
LAP
• No additional reinforcing steel is
required
Only continuous bottom bars are shown
COLUMN
• Preassembled beam cages
are longer and more difficult to
install
• Installation of multiple-bay
preassembled cages is very
difficult
• Detailing and preassembled
cages are relatively simple
3
LAP
BEAM
• Preassembled cages pass
through only one joint, which
make them easier to install than
Arrangement No. 1 even though
both arrangements have the
same length
LAP
Only continuous bottom bars are shown
COLUMN
• It is important to ensure that
the cages are oriented correctly
if installation begins at the center of the beam and progresses
both ways
• No additional steel is required
• No congestion at columns because the splice bars that pass
through the column are added
later
• Preassembled cages are the
shortest of all the arrangements
4
LAP
LAP
BEAM
LAP
Only continuous bottom bars are shown
COLUMN
LAP
• The preassembled cages are
very easy to install because no
bottom bars pass through the
column during installation
• Additional steel is required
• Best arrangement for installation
of multiple-bay preassembled
cages
5-6
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
In general, the size and spacing of the stirrups depends on the
magnitude of the factored shear force at the section under
consideration. It is common for the maximum shear force to
occur at the supports and to decrease in magnitude to zero
near midspan. An intricate stirrup layout closely following the
variation in the shear diagram is not a cost-effective solution.
Small stirrup sizes at a close spacing require disproportionately high costs in labor for fabrication and placement. To achieve
overall economy, larger stirrups at wider spacing (preferably
the maximum spacing prescribed in ACI 318) should be
provided, and the number of changes in the stirrup spacing
along the span length should be kept to a minimum wherever
practical.
Fig. 5.9 Beam Stirrup Configuration with Three Closed Stirrups Distributed
Across the Beam Width.
As discussed in Section 5.2.2, beams should be wider than
the columns that they frame in to. As floor systems become
shallower, beams generally need to become wider. Proper
stirrup detailing in wide beams is essential to ensure that the
longitudinal flexural reinforcement and the stirrups are fully
effective.
Research has shown that locating stirrups solely around the
perimeter of a wide beam is not efficient where the beams
are subjected to a relatively high shear demand (Reference 11).
Stirrup legs are required in the interior of a wide beam. Illustrated in Fig. 5.9 is a common stirrup configuration for a wide
beam where three closed stirrups are provided. This configuration presents the following problems:
1.
2.
None of the stirrups traverse the full net width of the
beam (the net width is defined as the gross width of
the beam minus the required concrete cover on each
side). Because of this, the overall width of the stirrup
arrangement needs to be measured and verified in
the field prior to installation. During installation, it is
possible for the net width to change when the preassembled cage is hoisted into position by crane, which
increases the risk that the provided cover will be less
than that which is required.
If the stirrups are built in place instead of preassembled, the closed, one-piece stirrups make it difficult to
place all of the required longitudinal reinforcement in
the beam. It is especially difficult to place large, long
longitudinal bars through the stirrups when stirrup top
bars are present.
Two alternate stirrup configurations are illustrated in Figs.
5.10 and 5.11. In both configurations, a single, open stirrup is
provided that extends the full net width of the beam. A stirrup
cap consisting of a horizontal bar with a 135-degree hook at
one end and a 90-degree hook at the other end is provided at
the top of the configuration, which also extends the full net
width of the beam. Providing a full-width stirrup helps in maintaining the correct concrete cover and facilitates installation
of the beam reinforcement: the longitudinal bars can easily be
placed within the beam from the top prior to installation of the
stirrup cap.
Concrete Reinforcing Steel Institute
Fig. 5.10 Alternate #1 Beam Stirrup Configuration.
Fig. 5.11 Alternate #2 Beam Stirrup Configuration.
The difference between the configurations in Figs. 5.10 and
5.11 occurs within the interior portion of the beam. In Fig.
5.10, two sets of identical U-stirrups with 135-degree hooks
are shown symmetrically placed within the interior of the
beam. Figure 5.11 shows one narrower U-stirrup nested inside
a wider U-stirrup in the interior of the beam. Both of these
configurations provide a cost-effective way of providing shear
reinforcement for wide beams.
5.4.3 Development of Shear Reinforcement
Like in the case of flexural reinforcement, it is essential to
properly develop and anchor shear reinforcement in order
for it to be fully effective, that is, for it to develop its full yield
strength. Requirements for the development of stirrups
are given in ACI 25.7.1 and are illustrated in Fig. 5.12. Note
that stirrups are to be provided as close to the tension and
compression faces of the member as cover requirements and
other reinforcement in the section permits.
5-7
Design Guide for Economical Reinforced Concrete Structures
Table 5.5 Minimum Beam Widths for Stirrup Development
Standard hook per ACI 25.3.2
Stirrup Size
h/2
h/2
• #5 stirrup bars and smaller
• #6, #7 and #8 stirrup bars
with fyt f 40,000 psi
• #6, #7 and #8 stirrup bars
with fyt f 40,000 psi
Fig. 5.12 Anchorage Details for U-stirrups.
Each bend in the continuous portion of the U-stirrup must
enclose a longitudinal bar and the ends of the stirrups must
be anchored around the longitudinal bars using a standard
hook defined in ACI 25.3.2 for #5 bar and smaller bars and #6
through #8 bars with fyt less than or equal to 40,000 psi. In
addition to a standard hook, a minimum embedment length
(
equal to 0.014dbfyt / f c'
)
must be provided between the
outside edge of the hook and the mid-height of the member
where #6, #7, or #8 stirrups with fyt greater than 40,000 psi
are utilized. This additional anchorage requirement takes into
consideration that (1) it is not possible to bend a #6, #7, or #8
stirrup tightly around a longitudinal bar, and (2) a large force
can exist in the larger stirrup bars with fyt # 40,000 psi.
The beam height that must be provided to satisfy the development requirements of ACI 25.7.2.3 is controlled by the size of
the stirrup bar that is used. Minimum beam heights that satisfy these requirements are given in Table 5.4 for #6, #7, and
#8 stirrup bars. The information that is provided in the table is
based on the following:
• Normal-weight concrete
• Grade 60 reinforcement
• 1.5-in. cover to the stirrup hook
In short, #6, #7, and #8 stirrups are not permitted to be used in
beams with heights less than those listed in the table.
Beam Width bw (in.)
#3
10
#4
12
#5
14
#6
18
#7
20
#8
22
Provisions for closed stirrups formed from two U-stirrups
are given in ACI 25.7.1.7. The legs of the stirrups must be lap
spliced with a splice length of at least 1.3Cd but not less than
12 in. where the tension development length Cd is determined
in accordance with ACI 25.4.2 (see Fig. 5.13). In cases where
the required lap length cannot fit within a member that has a
height of at least 18 in., these stirrups can still be used, provided that the force in each leg is equal to or less than 9,000
lb. Thus, for Grade 60 reinforcement, only a #3 stirrup satisfies
this requirement (force in stirrup leg " 0.11 w 60,000 " 6,600 lb).
5.5 Detailing Requirements and Guidelines
for Torsional Reinforcement
5.5.1 Overview
Once a beam has cracked due to effects from a torsional moment, its torsional resistance is provided primarily by closed
stirrups and longitudinal bars. In beams subjected to torsion,
shear, and bending moments, the amounts of transverse reinforcement and longitudinal reinforcement required to resist
all actions are determined using superposition (ACI 9.5.4.3). In
other words, the required amounts of shear and torsion transverse reinforcement are added together as are the required
amounts of flexural and torsional longitudinal reinforcement.
It is important to note that only the two legs of the stirrups
that are adjacent to the sides of the beam are effective for torsion; stirrup legs within the interior of the beam can resist the
effects from shear but not from torsion. This is consistent with
the thin-walled tube methodology that forms the basis of the
torsional provisions in ACI 318.
Table 5.4 Minimum Beam Height to Accommodate #6, #7,
and #8 Stirrups of Grade 60 Reinforcement
Stirrup Size
Beam Height h (in.)
Concrete Compressive Strength f 'c (psi)
3,000
4,000
5,000
6,000
#6
26
23
21
20
#7
30
27
24
22
#8
34
30
27
25
Similarly, to allow for bend radii at corners of U stirrups, the
minimum beam widths given in Table 5.5 must be provided.
5-8
Fig. 5.13 Pair of U-Stirrups Forming a Closed Stirrup.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
permitted in beams subjected to torsion because tests have
shown that they are inadequate for resisting torsion due to a
loss of bond when the concrete cover spalls.
The spacing of the transverse reinforcement is limited to the
smaller of ph /8 and 12 in. where ph is equal to the perimeter
of the centerline of the closed stirrups (ACI 9.7.6.3.3).
5.5.3 Detailing Requirements and Guidelines for the
Longitudinal Reinforcement
Longitudinal torsional reinforcement must be developed at
both ends for tension. Proper bar anchorage is especially important at the ends of a beam where high torsional moments
commonly occur.
Fig. 5.14 Transverse Reinforcement Detail for Torsion Where Spalling is
Restrained.
5.5.2 Detailing Requirements and Guidelines for the
Transverse Reinforcement
Diagonal cracks can form around all faces of a beam when it
is subjected to a torsional moment in excess of that which
causes cracking. Consequently, closed stirrups conforming
to ACI 25.7.1.6 perpendicular to the axis of the beam must be
provided.
It has been observed that the corners of beams subjected
to torsion can spall off because of the inclined compressive
stresses that occur at these locations. Thus, the transverse reinforcement must be properly anchored so that it performs as
intended. Because spalling is essentially prevented in beams
with a slab on one or both sides of the web, ACI 25.7.1.6(b)
permits the transverse reinforcement to be anchored by
standard 90-degree hooks like in the case for shear anchorage
(see Fig. 5.14). The 90-degree hook for the beam shown in
this figure is located on the side that is adjacent to the slab,
which restrains spalling.
ACI 25.7.1.6(a) requires that the transverse reinforcement
be anchored by 135-degree hooks where spalling cannot be
restrained (see Fig. 5.15). It has been observed that closed
stirrups with 90-degree hooks fail when there is no restraint.
Lapped U-stirrups, which are depicted in Fig. 5.13, are not
The following detailing requirements must be satisfied for longitudinal reinforcement for torsion (see Fig. 5.16 and ACI 9.7.5):
1.
Longitudinal reinforcement must be distributed around
the perimeter of the closed stirrups at a maximum
spacing of 12 in.
2.
At least one longitudinal bar is required in each corner
of the stirrups.
3.
The diameter of the longitudinal bars must be greater
than or equal to 0.042 times the transverse reinforcement spacing, but not less than 3/8 in.
Fig. 5.16 Detailing Requirements for Longitudinal Torsional Reinforcement.
Torsional reinforcement must be provided for a distance that
is greater than or equal to bt d beyond the point that it is
theoretically required, where bt is the width of that part of
the cross-section that contains the closed stirrups resisting
torsion (ACI 9.7.5.3). This distance is larger than that used for
shear reinforcement and flexural reinforcement because, as
noted previously, torsional diagonal tension cracks develop in
a helical form around a member.
5.5.4 Detailing Requirements and Guidelines for
Combined Effects
Fig. 5.15 Transverse Reinforcement Detail for Torsion Where Spalling is
Not Restrained.
Concrete Reinforcing Steel Institute
As was discussed in Section 5.5.1, for beams subjected to
torsion, shear, and bending moments, the amounts of transverse reinforcement and longitudinal reinforcement required
to resist all actions are determined using superposition. The
5-9
Design Guide for Economical Reinforced Concrete Structures
more restrictive of the provisions associated with these combined effects must be satisfied.
Top Step
In Beam
Raised Floor System
The following must be considered when detailing the reinforcement for combined effects:
1.
The most restrictive requirements for reinforcement
spacing, cutoff points, and placement for torsion, shear,
and flexure must be satisfied.
2.
Negative and positive flexural reinforcement may be
cutoff using the provisions of ACI 9.7.3 (see Section
5.3.5). When determining the theoretical cutoff points,
the area of longitudinal torsional reinforcement must be
subtracted from the total area of longitudinal reinforcement provided at that face.
3.
Concrete Beam
Bottom Step
In Beam
Fig. 5.17 Top and Bottom Steps in a Reinforced Concrete Beam.
The structural integrity requirements of ACI 9.7.7 must
also be satisfied when detailing the reinforcement.
Provide Min.
Cover Per
Aci 318
5.6 Steps in Beams
≤ 3 in.
Additional Bars
For Crack Control
Increased Cover
To Main Bars
Optional
Per Analysis
D1
Fig. 5.18 Reinforcement Details for a Reinforced Concrete Beam with a
Top step Less Than or Equal to 3 in.
Ideal locations for steps would be at a column line or where
support is provided by another beam. Obviously, it is not always
possible to have the steps occur at these locations. The following
sections provide detailing guidelines for steps of various depths.
Where the top step in a beam is 3 in. or less, the recommended
detailing depends on when in the design and construction
phases of the project the top step is introduced. In cases where
the top step is known during the design phase, the beam can be
designed for the smaller overall depth D1, which is illustrated in
Fig. 5.18. The appropriate amounts of flexural and shear reinforcement are provided for this reduced depth. Additional longitudinal bars are provided in the deeper section for crack control.
In cases where the step occurs after the design is complete,
additional flexural and shear reinforcement may be required
compared to the original design because of the reduced beam
depth. Both flexural and shear strength need to be checked
and the corresponding longitudinal bars and stirrups may have
to be adjusted accordingly.
A top step introduced late in the design phase or early in the
construction phase can be accommodated using bent top
reinforcement as illustrated in Fig. 5.19. ACI 10.7.4.1 limits the
slope of the inclined portion of the offset bent longitudinal
bars to 1 in 6 relative to the longitudinal axis of the beam.
Additional stirrups need to be provided in the beam at this
location to resist the upward component of the tensile force
in the longitudinal bars. Two #4 bars are commonly provided at
bent bar locations.
5-10
Provide Min.
Cover Per
Aci 318
Max. 1 To 6 Slope
Bend Top Bars
*
D1
5.6.2 Top Steps
≤ 3 in.
D2
Steps in a reinforced concrete beam can occur for many
reasons (Reference 12). For example, as shown in Fig. 5.17,
the top of a beam would be needed to accommodate a raised
flooring system. A bottom step in a beam would be required
because of conflicts with mechanical equipment.
D2
5.6.1 Overview
* Alternately, Drape
Top Bars
2 in.
Provide Additional Stirrups
At Each Bent Bar To Resist
Upward Component Of Bar
Tension (2 # 4 Min.)
Fig. 5.19 Alternative Reinforcement Details for a Reinforced Concrete
Beam with a Top Step Less Than or Equal to 3 in.
In lieu of using the bent bar configuration illustrated in Fig.
5.19, either the top bars can be draped or the top reinforcement on either side of the step can be spliced using a noncontact lap splice provided the spacing limitations of ACI 25.5.1.3
can be satisfied.
In cases where top steps exceed 3 in., the recommended detail depends on where along the length of the beam the step
occurs. If the step occurs near midspan or at other sections
where the force in the top reinforcement is relatively low, the
top bars of the shallower beam can extend into the deeper
beam a distance equal to the development length of these
bars (see Fig. 5.20). The top bars of the deeper section can be
hooked at the location of the step as illustrated in the figure.
If the step occurs near a support or at other sections where
the force in the top bars are relatively high, structural design
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
> 3 in.
Splice *
D1
D2
D1
D2
Top Bars Hooked
Or Developed Into
Beam
Cover Per
ACI 318
Standard 90° Hook
90° Hook
Provide Additional Stirrups
As Required Per Design
* Development Length When Top Steel Is Not In Tension
Class 'B' Splice When Top Steel Is In Tension
Fig. 5.20 Reinforcement Details for a Reinforced Concrete Beam with a
Top Step Greater than 3 in.
Column
Fig. 5.21 Reinforcement Details for a Reinforced Concrete Beam with a
Top Step at a Column.
Greater Of
D1, D2, Or
Ldh + Cover
Additional Stirrups
As Required (Typ.)
Greater Of
D1 Or D2
If Possible Extend The Beam
And Bottom Reinforcement
To Support
D1
D1
D2
Beam Step
D2
Class 'B'
Splice (Min.)
Ldh Min.
Diagonal Bars As Required
Rigid Bent
Shear Stirrups
As Required
Standard 90° Hook
Fig. 5.22 Reinforcement Details for a Reinforced Concrete Beam with a
Bottom Step at a Column.
Fig. 5.23 Reinforcement Details for a Reinforced Concrete Beam with a Deep
Step.
of the reinforcement is required using conventional or strutand-tie methods. It is good practice to extend the top bars
of the shallower beam at least a Class B splice length into
the deeper beam (Note: technically this is not a lap splice
because the spacing requirements of ACI 25.5.1.3 are
not satisfied).
5.6.4 Deep Steps
Additional stirrups may be required at the location of the step
to resist the reaction of the shallower beam into the deeper
beam. The amount and spacing depends on the shear demand
at this section.
As noted previously, the ideal location for a top step occurs
where a beam frames into another beam or into a column.
Illustrated in Fig. 5.21 are recommended details where the
step occurs at a column. The top bars of the shallower beam
can be either hooked or extended a development length into
the deeper beam.
5.6.3 Bottom Steps
The reinforcement details illustrated in Fig. 5.22 can be used
where a bottom step in a beam is located near a column. The
length of the intersecting beam segment should be at least
equal to the depth of the deeper member to ensure that a
45-degree strut can form within this region.
Concrete Reinforcing Steel Institute
Illustrated in Fig. 5.23 are recommended details for beams
with deep steps, that is, steps that exceed the depth of the
beam. It is good practice to have the width of the bent greater
than or equal to the depths of the adjacent beams.
5.7 Detailing Requirements and Guidelines
for SDC C
5.7.1 Overview
The requirements in ACI 18.4.2 must be satisfied for beams
that are part of an intermediate moment frame, which is the
required SFRS for structures assigned to SDC C. All of the requirements and guidelines presented above are also applicable.
5.7.2 Design for Flexure
ACI 18.4.2.2 requires that the minimum positive moment strength
at the faces of the supports be equal to at least 33% of the negative moment strength at that joint. This allows for the possibility
that the positive moment caused by earthquake-induced lateral
displacements exceeds the negative moment due to gravity loads.
Similarly, the minimum negative and positive moment strength at
any section along the span of the beam must be equal to at least
20% of the maximum moment strength at either joint.
5-11
Design Guide for Economical Reinforced Concrete Structures
Fig. 5.24 Flexural requirements for beams in intermediate moment frames.
A summary of the flexural requirements for beams in intermediate moment frames is given in Fig. 5.24, which is adapted
from Reference 7.
ACI 18.4.2.2 does not contain any restrictions on where lap
splices of the flexural reinforcement can be located along the
span. As noted in Section 5.3.5, top reinforcement is spliced
near midspan and bottom reinforcement is spliced near the
ends. However, because the potential exists for plastic hinges
to form at the ends of the beam, it would be appropriate to
locate the splices of the bottom bars somewhere between
the ends of the beam and midspan.
Fig. 5.25 Examples of Hoops and Overlapping Hoops.
5.7.3 Design for Shear
ACI 18.4.2.3 contains two methods on how to determine the
maximum shear force on a beam in an intermediate moment
frame. In the first method, the maximum factored shear force
is obtained from the factored gravity loads acting on the beam
plus the shear force associated with the application of the
nominal moment strength Mn at each end of the beam. Both
sidesway to the right and to left must be considered. In the
second method, the maximum shear force is obtained from
the design load combinations that include earthquake effects
E, where E is assumed to be twice that prescribed by the
building code. It is permitted to design for not less than the
smaller of the two shear forces obtained from these methods.
The required shear reinforcement is obtained from the
maximum shear force described above. Because the shear
reinforcement depends on Mn, it is important not to needlessly provide more flexural reinforcement than required
because that can have a direct impact on the amount of shear
reinforcement that has to be provided.
Within a distance of at least 2h from the face of each support,
hoops must be provided to resist the required shear force.
A hoop is defined as a closed tie or continuously wound tie
that is made up of one or several reinforcement elements,
each having seismic hooks that conform to ACI 25.3.4 at both
5-12
Fig. 5.26 Transverse Reinforcement Requirements for Beams in Intermediate
Moment Frames.
ends (ACI 2.3 and 25.7.4.1). The ends of the reinforcement
elements in hoops must engage a longitudinal bar in the beam
(ACI 25.7.4.2). Examples of hoops and overlapping hoops are
illustrated in Fig. 5.25, which is adapted from Reference 7. As
discussed in Section 5.4.2, hoops made from Details B and
C make placement of the longitudinal bars in the beam much
easier than those using Detail A.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Fig. 5.28 Flexural Requirements for Beams in Special Moment Frames.
Fig. 5.27 Dimensional Limits of Beams in Special Moment Frames.
Once the required size and spacing of the hoops are determined,
the spacing must be checked against the minimum spacing
requirements of ACI 18.4.2.4. Outside of the regions where
hoops are required, stirrups may be used; these stirrups must be
provided over that entire region. Figure 5.26, which is adapted
from Reference 7, illustrates the transverse reinforcement requirements for beams in intermediate moment frames.
5.8 Detailing Requirements and Guidelines
for SDC D, E, or F
5.8.1 Overview
The requirements in ACI 18.6 must be satisfied for beams that
are part of a special moment frame, which is the required SFRS
for buildings assigned to SDC D, E, or F. All of the requirements
and guidelines presented above are also applicable.
loads. Similarly, the minimum negative and positive moment
strength at any section along the span of the beam must be equal
to at least 25% of the maximum moment strength at either joint.
A summary of the flexural requirements for beams in special
moment frames is given in Fig. 5.28, which is adapted from
Reference 7. It is usually best to specify a smaller number
of larger longitudinal bars to help reduce congestion at the
beam-column joints.
ACI 18.6.3.3 contains specific requirements for lap splice
locations in beams of special moment frames. Lap splices are
permitted as long as they are properly confined with hoop or
spiral reinforcement over the entire lap length and that they
are located away from potential hinge areas at the ends of
the beam. Provisions for lap splices are illustrated in Fig. 5.29,
which is adapted from Reference 7.
5.8.4 Design for Shear
5.8.2 Dimensional Limits
Dimensional limits for beams in special moment frames are
given in ACI 18.6.2.1. These limits have been guided by experimental evidence and observations of reinforced concrete
frames that have performed well in the past during an earthquake. A summary of these limits is given in Fig. 5.27, which
is adapted from Reference 7. It is important that these limits
are satisfied once the beam dimensions have been initially
established using the information in Section 5.2 of this Guide.
Shear design for beams in a special moment frame is related
to the maximum flexural strength that can be developed in the
5.8.3 Design for Flexure
ACI 18.6.3 requires that the minimum positive moment strength
at the faces of the supports be equal to at least 50% of the negative moment strength at that joint. This allows for the possibility
that the positive moment caused by earthquake-induced lateral
displacements exceeds the negative moment due to gravity
Concrete Reinforcing Steel Institute
Fig. 5.29 Lap Splice Requirements for Beams in Special Moment Frames.
5-13
Design Guide for Economical Reinforced Concrete Structures
beam, which is defined in ACI 18.6.5.1 as the probable flexural
strength Mpr. The maximum factored shear force is obtained
from the factored gravity loads acting on the beam plus the
shear force associated with the application of the probable
flexural strength Mpr at each end of the beam. Both sidesway
to the right and to the left must be considered.
The required shear reinforcement is obtained from the maximum shear force described above. Because the shear reinforcement depends on Mpr , which is a function of the amount
of flexural reinforcement in the section, it is important not to
needlessly provide more flexural reinforcement than required
because that can have a direct impact on the amount of shear
reinforcement that has to be provided.
According to ACI 18.6.4.2, the spacing between longitudinal
bars that are restrained by legs of crossties or hoops is limited
to 14 in. This provision helps to ensure that proper lateral
support is provided for such bars in case they are subjected to
compressive forces under moment reversals.
Within a distance of at least 2h from the face of each support,
hoops must be provided to resist the required shear force.
A hoop is defined as a closed tie or continuously wound tie
that is made up of one or several reinforcement elements,
each having seismic hooks that conform to ACI 25.3.4 at both
ends (ACI 2.3 and 25.7.4.1). The ends of the reinforcement
elements in hoops must engage a longitudinal bar in the beam
(ACI 25.7.4.2). Examples of hoops and overlapping hoops are
illustrated in Fig. 5.25, which is adapted from Reference 7. As
discussed in Section 5.4.2, hoops made from Details B and
C make placement of the longitudinal bars in the beam much
easier than those from Detail A.
Fig. 5.30 Transverse Reinforcement Requirements for Beams in Special
Moment Frames.
Once the required size and spacing of the hoops are determined,
the spacing must be checked against the maximum spacing requirements of ACI 18.6.4.4. Outside of the regions where hoops
are required, stirrups with seismic hooks may be used; these stirrups must be provided over that entire region. Figure 5.30, which
is adapted from Reference 7, illustrates the transverse reinforcement requirements for beams in special moment frames.
5.9 Beams Not Designated as Part
of the SFRS
Fig. 5.31 Requirements of ACI 18.14.3.2(a) for Beams.
Detailing requirements for beams that have not been assigned
to the SFRS are given in ACI 18.14.3.
In cases where the bending moments and shear forces in a
beam due to the lateral displacements from a seismic event
do not exceed the design moment and shear strength of the
beam, the detailing requirements of ACI 18.14.3.2(a) must
be satisfied. These requirements are illustrated in Fig. 5.31,
which is adapted from Reference 7.
Where the induced bending and shear exceed the design moment and shear strength of the beam, or where the induced
moments and shear are not calculated, the detailing requirements of ACI 18.14.3.3 must be satisfied (see Fig. 5.32, which
is adapted from Reference 7).
5-14
Fig. 5.32 Requirements of ACI 18.14.3.3 for Beams.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
CHA PTER 6
Columns
6.1 Overview
Guidelines and recommendations on the economical design
and detailing of columns are contained in this chapter. Information is provided on sizing the cross-section and detailing
the longitudinal and transverse reinforcement. Specific requirements for columns in intermediate moment frames (SDC
C) and special moment frames (SDC D, E, and F) are given in
Sects. 6.6 and 6.7 of this Guide, respectively.
6.2 Preliminary Column Sizing
The preliminary size of a typical column in a reinforced
concrete building is needed for a variety of reasons, including frame analysis and initial cost estimation. It is common
practice to obtain preliminary column sizes in the early stages
of design utilizing axial gravity loads only. It is assumed that
the effects from bending moments are relatively small and
that slenderness (secondary) effects are negligible. The first
of these assumptions is usually valid for columns that are not
part of the lateral force-resisting system. For many columns,
slenderness effects are not an issue.
A preliminary column size can be obtained by setting the total factored axial load Pu equal to the design axial load strength KPn,max
given in ACI Table 22.4.2.1 for columns with ties conforming to
ACI 22.4.2.4 and with spirals conforming to ACI 22.4.2.5. The
appropriate equation is solved for the gross area of the column
Ag, assuming practical values for the total area of longitudinal
reinforcement Ast , the compressive strength of the concrete f 'c ,
and the yield strength of the longitudinal reinforcement :
Tied Column:
Ag " Pu /0.80[(0.85)f 'c W) fy W]
Spiral Column: Ag " Pu
/0.85[(0.85)f '
c W) fy W]
where W " Ast /Ag.
The minimum and maximum areas of longitudinal reinforcement are prescribed in ACI 10.6.1.1. The following limits are
applicable regardless of the type of transverse reinforcement
that is used in the column:
• Minimum Ast " 0.01Ag
• Maximum Ast " 0.08Ag
The 1% lower limit is meant to provide resistance to any
bending moments that are not accounted for in the analysis
because of, for example, construction tolerances or misalignments. This lower limit is also meant to help reduce creep
and shrinkage in the concrete under sustained compressive
stresses. In order for the concrete to be properly placed and
consolidated, the size and number of longitudinal reinforcing
bars must be chosen to minimize reinforcement congestion
(see Section 6.3 of this Guide). The upper limit on the longitudinal reinforcement is meant to help achieve these goals. The
maximum area of reinforcement must not exceed 4% of the
gross column area at sections where lap splices are utilized.
Concrete Reinforcing Steel Institute
Fig. 6.1 Preliminary Sizing Chart for Nonslender Columns with Tie
Reinforcement.
A preliminary column size should be determined using a low
percentage of longitudinal reinforcement. Columns that have
longitudinal reinforcement ratios Ast /Ag in the range of 1 to
2% are usually the most economical because concrete carries
axial compressive loads more cost-effectively than reinforcing
steel. Generally, it is usually more economical to use larger
column sizes with less longitudinal reinforcement.
The information contained in Fig. 6.1, which is adapted from
Reference 7, can be used to obtain a preliminary size of a nonslender, tied column with Grade 60 longitudinal reinforcement.
The chart can be entered with a longitudinal reinforcement
ratio and concrete compressive strength; the ratio of factored
axial force Pu to gross area of the column Ag can be read from
the vertical axis, which can be solved for Ag. Similar design
charts can be generated for other column sizes and shapes
and other material strengths.
As noted in Section 2.2.2 of this Guide, the same column size
should be used as often as possible throughout the entire
building to achieve overall economy. The dimensions of a column can be influenced by architectural and functional requirements. One or both dimensions of a rectangular column may
be limited, which could result in a column that is slender.
A number of design aids are available that can be utilized in
the design of columns subjected to axial load and bending
moment. Reference 13 contains nondimensionalized nominal
strength interaction diagrams for rectangular and circular sections with a variety of bar arrangements. Numerous tables for
rectangular and circular columns are contained in Reference
14, which cover a wide range of cross-sectional dimensions,
6-1
Design Guide for Economical Reinforced Concrete Structures
concrete compressive strength, longitudinal reinforcement
ratios, and bar arrangements. These tables contain values corresponding to key points on the interaction diagram.
Table 6.1 Minimum Face Dimension (inches) of
Rectangular Tied Columns with Normal Lap Splices.
6.3 Detailing Requirements and Guidelines for Longitudinal Reinforcement
6.3.1 Overview
Longitudinal reinforcement for columns must satisfy the
requirements in ACI 10.7. Limitations are provided on the size
and spacing of the longitudinal bars.
Number of Bar Per Face
The longitudinal bars must be spaced far enough apart so
that concrete can flow easily between the bars. Minimum bar
spacing is especially critical at splice locations. Generally, it is
more economical to have a fewer number of larger longitudinal bars than a greater number of smaller bars.
Bar
Size
2
3
#5
8
10 12 14 17 19 21 23 25 27 29 31 34
#6
9
11 13 15 18 20 22 24 27 29 31 33 36
#7
9
11 14 16 18 21 23 26 28 30 33 35 37
Splice requirements for longitudinal reinforcement in columns are
given in ACI 10.7.5. The type of lap splice that must be provided is
based on the stress in the reinforcing bars under factored loads.
#8
9
12 14 17 19 22 24 27 29 32 34 37 39
6.3.2 Minimum Number of Longitudinal Bars
According to ACI 10.7.3.1, a minimum of four longitudinal bars
are required in columns where rectangular or circular ties are
used as transverse reinforcement. For columns where the
longitudinal reinforcement is enclosed by spirals, a minimum
of six longitudinal bars are required.
4
5
6
7
8
9
10 11 12 13 14
#9
10 13 16 18 21 24 26 30 33 35 38 41 44
#10
11 14 17 20 23 27 30 33 36 39 42 46 49
#11
11 15 18 22 25 29 32 36 40 43 47 50 54
Table 6.2 Maximum Number of Bars in Columns
Having Longitudinal Bars Arranged in a Circle and
Normal Lap Splices.
For other tie shapes, one bar should be provided at each apex
or corner and proper transverse reinforcement provided. For
example, a tied triangular column needs three longitudinal
bars, with one at each apex of the triangular ties.
6.3.3 Spacing of Longitudinal Bars
The longitudinal bars in reinforced concrete columns must be
spaced at a sufficient distance so that concrete can flow easily between the bars and between the bars and the formwork.
According to ACI 25.2.3 the minimum clear distance that is to
be provided between longitudinal bars is equal to the largest
of the following:
• 1.5 times the diameter of the longitudinal bar
Bar Size
h
(in.)
12
#5
8
#6
7
#7
6
#8
#9
#10
#11
6
4*
—
—
4*
• 1.5 in.
14
11
10
9
8
7
5*
• (4/3) times the diameter of the largest aggregate in the
concrete mix
16
14
13
12
11
9
7
6
18
17
16
14
13
11
9
8
These minimum clear distance requirements are also applicable to the clear distance between a contact lap splice and
any adjacent bars or splices.
20
20
19
17
16
13
11
10
22
23
21
20
18
16
13
12
24
26
24
22
21
18
15
13
Table 6.1, which is adapted from Reference 7, contains the
minimum face dimension of rectangular tied columns with
normal lap splices based on the requirements presented
above. The column face dimensions have been rounded to the
nearest inch and a 1.5-in. clear cover to #4 ties has been used.
26
29
27
25
23
20
17
15
28
32
30
28
26
22
19
17
30
35
33
30
28
25
21
19
32
38
35
33
31
27
23
21
34
41
38
36
33
29
25
22
36
44
41
38
36
31
27
24
The maximum number of bars in a circular or square column
that has longitudinal bars arranged in a circle with normal lap
* Applicable to circular tied columns only
6-2
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
splices is contained in Table 6.2, which is also adapted from
Reference 7. The information given in this figure satisfies the
minimum clear distance requirements of ACI 25.2 and the
reinforcement limits of ACI 10.6.1.1. The number of bars have
been rounded to the nearest whole number and were determined using a 1.5-in clear cover to #4 spirals or ties.
6.3.4 Splices
Provisions for lap splices, mechanical splices, butt-welded
splices, and end-bearing splices are given in ACI 10.7.5. In
general, column splices must satisfy the requirements for all
load combinations. Where the longitudinal bar stress due to
factored loads is compressive, all of the splice types listed
above may be used. Lap splices and mechanical or butt-welded splices are permitted when the longitudinal bar stress is
tensile; end-bearing splices are not permitted in such cases.
Lap splices are the most popular and usually the most
economical type of splices used in columns. The type of lap
splice—compressive or tensile—that must be used depends
on the stress in the longitudinal bars due to the factored load
combinations. Lap splices in columns that are not part of special moment frames are permitted to occur immediately above
the top of the slab, as shown in Fig. 6.2. This location facili-
tates the overall construction of the structure. The longitudinal
bars from the column below extend above the slab a distance
equal to or greater than the required lap splice length.
It is common to have construction documents that show lap
splices occurring at each floor level. Depending on a number
of factors, the tension lap splice lengths may be relatively
long, in some cases close to the entire story height. This
results in doubling of the longitudinal bars, which may cause
congestion in the column and make concrete placement more
difficult. As a general rule, if the lap splice length is more than
about one-third to one-half the story height, it may be more
economical to splice the bars every other floor, if possible.
Additional information on lap splice location and guidelines on
constructability can be found in Reference 15.
At lap splice locations or at locations where the column size
changes, offset bends conforming to ACI 10.7.4 are required
(see Fig. 6.4). It is standard construction practice for the longitudinal bars in the column below to be offset bent into the
column above. From a construction perspective, it is easier to
lower the larger column cage over the smaller offset cage that
protrudes from the floor slab.
6.4 Detailing Requirements and Guidelines for Transverse Reinforcement
6.4.1 Overview
Transverse reinforcement for columns must satisfy the requirements given in ACI 10.7. Limitations are provided on the size
and spacing of both tie and spiral transverse reinforcement.
The transverse bars must be spaced far enough apart so that
concrete can flow easily between the bars without honeycombing. Additionally, these bars must be spaced close enough to
provide adequate lateral support to the longitudinal reinforcement and to provide sufficient shear strength where needed.
6.4.2 Spiral Reinforcement
Requirements for columns with spiral reinforcement are given
in ACI 10.7.6 and 25.7.3. Standard spiral sizes are #3 to #5, and
the clear spacing between spirals should not exceed 3 in. or
be less than the greater of 1 in. or (4/3) times the diameter of
the largest aggregate in the concrete mix.
ACI Eq. (25.7.3.3) is to be used to determine the minimum
amount of spiral reinforcement that must be provided:
Ag
f'
s = 0.45 1 c
Ach
f yt
Fig. 6.2 Tie and Splice Details in a Reinforced Concrete Column.
Concrete Reinforcing Steel Institute
The volumetric spiral reinforcement ratio is equal to the
volume of the spiral reinforcement divided by the volume of
the concrete core measured to the outside edges of the spiral
reinforcement. The term Ach is the area of the column core
enclosed by the spiral, which is equal to U Dch )2/4 where Dch
is the diameter of the column core measured to the outside
edges of the spiral reinforcement (see Fig. 6.3, which is
adapted from Reference 7).
6-3
Design Guide for Economical Reinforced Concrete Structures
Thus, for a given spiral bar with an area of Abs , the center-tocenter spacing of the spirals s (i.e., the pitch) must be less
than or equal to the value obtained by the following equation:
s=
8.9Abs
Dch Ag /Ach 1 f c' /fyt
(
)
(
)
Spiral reinforcement provides a higher degree of lateral confinement than that provided by ties; this has a direct impact
on the design strength of a column. This is reflected in the
larger strength reduction factor K that is permitted to be used
in the design of a spiral column compared to that in a tied
column. One drawback of spiral reinforcement occurs at beam-column joints: it
may be difficult to thread the longitudinal
bars of the beam through the joint, especially where the pitch is relatively small.
Fig. 6.3 Spiral Reinforcement.
6.4.3 Tie Reinforcement
Requirements for columns with tie
reinforcement are given in ACI 10.7.6 and
25.7.2. Standard hook dimensions for ties,
which are the same as those for stirrups,
are given in ACI 25.3.2. Maximum tie
spacing and other requirements are illustrated in Fig. 6.4 (Reference 16).
Illustrated in ACI Fig. R25.7.2.3(a) are the
requirements of ACI 25.7.2.3 pertaining
to tie arrangement and maximum clear
spacing between laterally supported bars.
The corner bars and every other longitudinal bar must have lateral support in
cases where the center-to-center spacing
of the longitudinal bars on a side is equal
to or less than 6 in. plus the diameter
of the longitudinal bar. Additional lateral
support for the intermediate bars must
also be provided if the spacing is greater
than that. This is usually in the form of
a crosstie (sometimes referred to as a
candy cane because of its shape), which
is a reinforcing bar that has a seismic
hook on one end and a hook not less than
90 degrees with at least a six-diameter
extension on the other. A seismic hook
is defined as a hook with a bend that is
not less than 135 degrees and an extension that is not less than 6 bar diameters
or 3 in., whichever is greater. For circular
hoops, the bend should not be less than
90 degrees.
Standard arrangements of column ties
are depicted in Figs. 6.4 and 6.5. The
Notes: 1) Alternate position of hooks in placing successive sets of ties; 2) minimum lap shall be 12 in.; 3) “B” indicates bundled bars.
one-piece tie arrangements in Fig. 6.4 are Bundles shall not exceed four bars; and 4) elimination of tie for center bar in groups of three limits clear spacing to be 6 in. maximum.
sufficiently rigid to be lifted into place after Unless otherwise specified, bars should be so grouped.
being preassembled on site. If possible,
Fig. 6.4 Standard Column Ties Applicable for Either Preassembled Cages or Field Erection.
6-4
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
it is preferred to preassemble one-story column
cages where all of the lap splices occur at or near
the same elevation above the floor line.
There are numerous ways to arrange ties in a column and some arrangements are preferred more
than others. For example, consider the arrangements in Fig. 6.6a and 6.6b, which consist of an
outer confinement tie with an inner tie and crossties, respectively. These arrangements are generally preferred over the arrangement in Fig. 6.6c,
which consists of paired overlapping ties, because
of the following (Reference 16):
• The outer confinement tie acts as a template
for the ironworker to place the longitudinal
bars in the column.
• It is easier to maintain the required concrete
cover using side-form spacers.
• It is more efficient at preventing displacement
of the longitudinal bars while the column cage
is being moved into place by crane.
• The tasks that are needed to be completed by
the ironworker are simplified, which translates
to increased productivity.
Notes: 1) Alternate position of hooks in placing successive sets of ties; 2) minimum lap shall be 12 in.; 3) elimination of
tie for center bar in groups of three limits clear spacing to be 6 in. maximum. Unless otherwise specified, bars should
be so grouped; and 7) bars shown as open circles may be accommodated provided clear spaces between bars do not
exceed 6 in. (Figure does not include Notes 3-6.)
Fig. 6.5 Standard Column Ties Applicable for Either Preassembled Cages or Field Erection,
Special-shaped Columns, and Columns with Bars in Two Faces Only.
One exception to using outer confinement ties
is where a column is dimensionally large. In such
cases, the arrangement in Fig. 6.6c is preferred so
as to avoid difficulties associated with fabricating,
shipping, and placing the ties.
Generally, crossties (Fig. 6.6b) are preferred over
closed ties (Fig. 6.6a) because the latter are difficult
to place and align around the longitudinal bars.
Crossties can easily be placed after the column
cage has been constructed with the outer confinement ties.
(a)
(a)
(b)
The diamond ties depicted in Fig. 6.7 are difficult to
fabricate and difficult to place and align around the
longitudinal bars in the column. Crossties should be
used instead, which facilitates bar placement and
allows more accurate column cage fabrication.
(b)
Fig. 6.7 Column Tie Configurations
Using Multiple Bars: (a) Diamond
Tie (avoid use); and (b) Single
Closed Tie with Candy Cane Ties.
Illustrated in Fig. 6.8 are examples of tie arrangements where precise fabricating dimensions are
difficult to maintain and where the fabricated
pieces are costly to place (Reference 16). The alternate details are more efficient and economical for
the reasons stated in the figure.
(c)
Fig. 6.6 Column Tie Sets Comprising
Multiple Ties: (a) With Outer Confinement
Tie and Inner Closed Tie; (b) With Outer
Confinement Tie and Candy Cane Ties;
and (c) With Paired Overlapping Ties.
Concrete Reinforcing Steel Institute
6-5
Design Guide for Economical Reinforced Concrete Structures
TIES FOR 12 BAR COLUMN
Initial Detail
Problem: Any out of location
placement of the 12 bars
will affect the others
ALTERNATE
HOOKS (TYP.)
Suggested Alternate Detail
Advantage: Bars are less dependent
on location of others
TIES FOR 10 BAR COLUMN
ALTERNATE
HOOKS (TYP.)
Initial Detail
Problem: Any out of location
placement of the 10 bars
will affect the others
Suggested Alternate Detail
Advantage: Bars are less dependent
on location of others
TIES FOR 8 BAR COLUMN
ALTERNATE
HOOKS (TYP.)
Initial Detail
Problem: Out of location
placement of any bars
will affect the others
Suggested Alternate Detail
Advantage: Bars are less dependent
on location of others
SMALL DIAMETER (12” OR LESS) CIRCULAR COLUMNS
USING #3 OR #4 TIES
Initial Detail
Problem: Small circle (Bend Type T3) is difficult
to bend and keep in the same plane
Suggested Alternate Detail
Advantage: More accurate and
better alignment of bars
Fig. 6.8 Costly and Economical Column Tie Configurations.
6-6
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
The location of the dowels protruding from a footing can have
an impact on the installation of the preassembled reinforcing cages of the columns (Reference 17). Dowels should be
positioned so as not to interfere with the longitudinal bars or
the tie hooks from the column.
Fig. 6.9 Column and Footing Detail: (a) as shown in construction documents;
and (b) as detailed for constructibility, with dowels supported on the footing
reinforcing bars and straight column bars (no offsets).
6.5 Detailing Requirements and Guidelines
for Dowels
The interface between a column and a concrete foundation
must be designed to adequately transfer vertical and horizontal forces between the members (ACI 13.2.2). ACI 16.3
contains design requirements for force transfer from a column
to a footing.
Vertical compressive loads are transferred by bearing on the
concrete or by a combination of bearing and reinforcement
at the interface. Tensile loads must be resisted entirely by reinforcement, which may consist of extended longitudinal bars,
dowels, anchor bolts, or mechanical connectors. Lateral loads
are transferred using the shear friction provisions of ACI 22.9
or other appropriate methods.
Consider the arrangements of the column longitudinal bars
and the dowel bars depicted in Fig. 6.10a. Except for the bars
located adjacent to the center crosstie, the dowel bars are
offset by 45 degrees from the column longitudinal bars relative to the long side of the column. It is evident that there is
no interference between the dowel bars and the 135-degree
tie hooks in this arrangement. At the center crosstie, the
dowel bars are located 90 degrees inboard relative to the long
side of the column so that no interference occurs between
them and the hooks of the crosstie. Depicted in Fig. 6.10b
is the same column, but in this case, all of the dowel bars
occur adjacent to the tie on the long side of the column. This
arrangement is not as preferable as that shown in Fig. 6.10a,
however, it is manageable because the ends of the hooks are
relatively flexible and can be maneuvered around the dowels.
Finally, Fig. 6.10c shows some of the dowel bars located on
the long face of the column and some on the short face. This
is the least preferable arrangement because there is more potential for difficulties during installation; lowering the column
cage over the dowels will be challenging because the ties will
not allow the same degree of flexibility as will the hooks at
the ends of ties.
(a)
The amount of reinforcement that is required between a
reinforced concrete column and footing depends on the type
of stress in the bars of the supported member under all applicable load combinations. Minimum embedment lengths into
both members also depend on this stress.
Dowels are commonly used as interface reinforcement
between columns and footings. The dowel bars are set in the
footing prior to casting the footing concrete and are subsequently spliced to the longitudinal bars in the column. Dowel
bars should never be driven or pushed into position in wet
concrete. Where columns are supported on footings, the
minimum area of reinforcement across the interface is equal
to 0.5% of the gross area of the column (ACI 16.3.4.1).
To facilitate placement, a dowel should have a 90-degree hook
on its end that rests on the bottom mat of the footing bars, as
illustrated in Fig. 6.9b (Reference 16). If the dowel bars are detailed as shown in Fig. 6.9a, additional bars and bar supports
are required to position the dowel bars higher in the depth of
the footing, which is not cost effective.
Concrete Reinforcing Steel Institute
(b)
(c)
Fig. 6.10 (a) Ideal Arrangement of Dowels (b) Dowels Arranged on Long
Face of Column (c) Least Preferable Arrangement of Dowels.
6-7
Design Guide for Economical Reinforced Concrete Structures
6.6 Detailing Requirements and Guidelines
for SDC C
6.6.1 Overview
Requirements for columns that are part of an intermediate
moment frame, which is the required SFRS for structures
assigned to SDC C, are given in ACI 18.4.3. All of the
requirements and guidelines presented above are also
applicable.
6.6.2 Longitudinal Reinforcement Requirements
Limits for longitudinal reinforcement are given in ACI 10.6.1.1;
these are the same limits for columns in buildings assigned to
SDC A or B (see Section 6.2 of this Guide).
No restrictions are given on the location of splices of longitudinal reinforcement in columns in intermediate moment frames.
However, as discussed in Section 6.6.3 of this Guide, the
plastic hinge regions are anticipated to form at the ends of the
column. Thus, it is good practice to locate lap splices outside
of these regions.
6.6.3 Transverse Reinforcement Requirements
Transverse reinforcement requirements for columns in intermediate moment frame are given in ACI 18.4.3. Like beams,
plastic hinges are anticipated to form at the ends of the column where moments are usually maximum. As such, hoops
or spirals are required at each end over the distance Co. This
length is indicated in Fig. 6.11, which is adapted from Reference 7, for the case of transverse reinforcement consisting of
hoops. The hoops provide confinement to ensure column ductility in the event of hinge formation during a seismic event.
Outside of the anticipated hinge length Co, the spacing of
the transverse reinforcement must conform to the lateral
reinforcement provisions of ACI 25.7.2 for ties and ACI 25.7.3
for spirals, and to the provisions for spacing limits for shear
reinforcement of ACI 10.7.6.5.2. The smallest spacing obtained
from these requirements is to be used in the center region of
a column outside of the plastic hinge zones.
The transverse reinforcement requirements of ACI 18.4.3.6
must be satisfied for columns that support reactions from
discontinuous stiff members, such as walls.
Fig. 6.11 Transverse Reinforcement Requirements for Columns in Intermediate Moment Frames.
6-8
Fig. 6.12 Dimensional Limits of Columns
in Special Moment Frames.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
6.7 Detailing Requirements and Guidelines
for SDC D, E, or F
in all of the other SDCs. The main reason for this is to control
steel congestion and the development of high shear stresses.
6.7.1 Overview
Lap splices of the longitudinal reinforcement must occur
within the center half of the member length and must be
enclosed with transverse reinforcement that conforms to
ACI 18.7.5.2 and 18.7.5.3. The main reason for the location of
the lap splices is to keep them away from the regions where
plastic hinges are likely to form during a seismic event.
Requirements for columns that are part of a special moment
frame, which is the required SFRS for structures assigned to
SDC D, E, or F, are given in ACI 18.7. All of the requirements
and guidelines presented above are also applicable.
6.7.2 Dimensional Limits
Dimensional limits for columns in special moment frames are
given in ACI 18.7.2.1. These limits have been guided by previous
practice. A summary of these limits is given in Fig. 6.12, which
is adapted from Reference 7. It is important that these limits are
satisfied once the column dimensions have been initially established using the information in Section 6.2 of this Guide.
6.7.3 Longitudinal Reinforcement Requirements
Limits for longitudinal reinforcement are given in ACI 18.7.4.1.
The lower limit is 0.01Ag and the upper limit is 0.06Ag , which
is less than the upper limit for columns in buildings located
6.7.4 Transverse Reinforcement Requirements
Closely spaced transverse reinforcement, in the form of
hoops or spirals, is required over the length Co at each end of
a column to confine the concrete because the largest bending
moments are expected to occur at these locations, which
could lead to flexural yielding.
Transverse reinforcement requirements are illustrated in Fig.
6.13, which is adapted from Reference 7, for columns reinforced
with rectilinear hoops where Pu f 0.3Ag f c' and f c' f10,000 psi.
Figure 6.14 depicts the details where Pu > 0.3Ag f c' and/or
f c' #10,000 psi.
Fig. 6.13 Transverse Reinforcement Requirements for Rectilinear Hoops in Columns of Special Moment Frames where Pu f 0.3Ag f c' and f c' f10,000 psi.
Concrete Reinforcing Steel Institute
6-9
Design Guide for Economical Reinforced Concrete Structures
Fig. 6.14 Transverse Reinforcement Requirements for Rectilinear Hoops in Columns of Special Moment Frames where Pu # 0.3Ag f c' and/or f c' #10,000 psi.
Fig. 6.15 Transverse Reinforcement Requirements for Spiral or Circular Hoops in Columns of Special Moment Frames.
6-10
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
As mentioned previously, the use of crossties instead of
closed ties are preferred mostly for ease of construction.
Requirements for columns reinforced with spiral and circular
hoops are illustrated in Fig. 6.15, which is adapted from Reference 7. Spiral reinforcement is generally the most efficient
form of confinement reinforcement; however, the extension
of the spirals into the beam-column joint usually causes
construction difficulties, especially when placing longitudinal
reinforcement from the beam through the joint.
6.8 Columns Not Designated as Part
of the SFRS
In cases where the bending moments and shear forces in a
column due to the lateral displacements from a seismic event
do not exceed the design moment and shear strength of the
beam, the detailing are illustrated in Fig. 6.16, which is adapted
from Reference 7 where Pu f 0.3Ag f c' and f c' f10,000 psi.
Where the induced bending and shear exceed the design moment and shear strength of the beam, or where the induced
moments and shear are not calculated, the detailing requirements of ACI 18.14.3.3(c) are essentially the same as those
for columns in special moment frames (see Section 6.7 of this
Guide).
Detailing requirements for columns that have not been assigned to the SFRS are given in ACI 18.14.3.
Fig. 6.16 Requirements of ACI 18.14.3.2(b) and (c) for Columns.
Concrete Reinforcing Steel Institute
6-11
Design Guide for Economical Reinforced Concrete Structures
CHA PTER 7
Walls
7.1 Overview
Guidelines and recommendations on the economical design
and detailing of walls are contained in this chapter. The focus
is on walls found specifically in building structures; retaining
walls, for example, are not covered. Information is provided
on determining the wall thickness and detailing the longitudinal and transverse reinforcement. Specific requirements for
special structural walls in structures assigned to SDC D, E, or
F are given in Section 7.5 of this Guide.
7.2 Determination of Wall Thickness
In typical building structures, reinforced concrete walls are
usually located around stair and elevator openings. As such,
the lengths of the walls are often dictated by the architectural
requirements associated with these openings. In general, the
thickness of a wall is determined based on strength requirements for axial load, flexure, and shear and sometimes on serviceability requirements (overall building deflection), especially
for high-rise buildings.
The thickness of a wall in a low-rise building can be governed
by in-plane shear due to lateral forces, although a combination
of axial load and out-of-plane bending due to lateral forces
and/or eccentric gravity loads may control if the wall is relatively tall and slender. Where in-plane shear forces govern, the
following equation can be used to determine a conservative
estimate for the wall thickness h:
h=
0.8Vu
f c' w
This equation can be solved for h (where Ag " h Cw ) for a given
set of design criteria:
h=
2 k 2
P
n
c
+
' 32 1.1 f c l w Pn
+
1.1 f c' w
Relatively tall and/or slender walls are generally governed by a
combination of axial load and in-plane bending moments. The
strength design method must be used to design the wall in such
cases. A wall thickness and the size and spacing of the longitudinal reinforcement are assumed so that an interaction diagram
can be constructed. Applicable load combinations for combined
axial load and bending can then be checked. Because there is no
closed-form solution for multiple load cases, iterations must be
performed until all strength design criteria are satisfied.
In addition to satisfying all strength and serviceability requirements,
wall thicknesses are sometimes provided that make the columns
in the building part of a nonsway frame (that is, the frame is braced
against sidesway). This can be advantageous especially in situations where the columns are slender; secondary effects increase
dramatically with increasing sway. ACI 6.2.5 permits columns to be
considered braced against sidesway when the bracing elements in
the structure (typically, walls or a combination of walls and moment
frames) have a total lateral stiffness in the direction of analysis of at
least 12 times the gross lateral stiffness of all the columns within a
given story. This criterion can be used to determine the thicknesses
of the walls to produce a nonsway frame.
7.3 Minimum Reinforcement
In this equation, which is based on ACI Eq. (11.5.4.4), Vu is the
maximum factored shear force determined from the load combinations in ACI Table 5.3.1 and Cw is the length of the wall. This
equation will give a conservative value for h for walls of normalweight concrete because the contribution of the transverse reinforcement to the overall shear strength has not been included.
For relatively short walls subjected to only vertical loads, the
simplified method of ACI 11.5.3 can be used to determine a
preliminary wall thickness. The limitations of this method are
the following: (1) the wall has a solid, rectangular cross-section
and (2) the resultant of all applicable factored loads falls within
the middle third of the wall thickness. Where these limitations
are satisfied, ACI Eq. (11.5.3.1) is permitted to be used:
Minimum longitudinal and transverse reinforcement depend on the
magnitude of the in-plane factored shear force Vu. The minimum
longitudinal (vertical) distributed reinforcement ratio WC and the
minimum transverse (horizontal) distributed reinforcement ratio Wt
are given in Table 7.1 where Vu f 0.5KVc for deformed bars in castin-place concrete. Table 7.1 is based on Table 11.6.1 of ACI 318.
Table 7.1 Minimum Reinforcement Ratios where Vu f 0.5KVc
Bar Size
≤#5
f y(psi)
Minimum WC
Minimum Wt
v60,000
0.0012
0.0020
!60,000
0.0015
0.0025
Any
0.0015
0.0025
>#5
k 2 Pn = 0.55 f c' Ag 1 c 32h The limits in this table need not be satisfied if it can be demonstrated by structural analysis that the wall has adequate
strength and stability.
In this equation, Cc is the height of the wall and k is defined as
follows:
Where Vu # 0.5KVc , the following requirements must be satisfied:
• k " 0.8 when the wall is restrained against rotation at one
or both ends
• k " 1.0 when the wall is unrestrained against rotation at
both ends
Concrete Reinforcing Steel Institute
0.0025 + 0.5 2.5 h /
(
w w ) ( t 0.0025)
• WC v greater of • Wt v 0.0025
0.0025
Note that WC need not exceed Wt .
7-1
Design Guide for Economical Reinforced Concrete Structures
The maximum spacing is also the lesser of 3 times the wall
thickness and 18 in. for spacing of the transverse bars. The
spacing is limited to one-fifth of the length of the wall for
shear reinforcement that is required for in-plane shear.
Fig. 7.1 Rustication Over Entire Length or Height of a Wall.
7.4 Detailing Requirements and Guidelines
for Reinforcement
7.4.1 Overview
As noted in the previous section, the size and spacing of the
longitudinal and transverse reinforcement in a wall must be
chosen to satisfy all applicable requirements for strength and
serviceability. This section provides a summary of the requirements in ACI 318 and includes guidelines that can be used to
obtain more economical walls.
7.4.2 Concrete Cover
Concrete protection for reinforcement plays an important role
in the formulation of the requirements of bar spacing and bar
development. Reinforcing bars are placed in a concrete member with a minimum concrete cover to protect it from weather, fire, and other effects. Minimum cover requirements for
nonprestressed, cast-in-place concrete construction are given
in ACI Table 20.6.1.3.1. For walls, concrete cover is measured
from the surface of the concrete to the outer edge of the layer
of reinforcement closest to the wall surface.
Where reveals or rustications run the entire length or height of
a wall, the minimum required cover to the reinforcing bars is
indicated in Fig. 7.1 (Reference 6). A constant concrete cover
is maintained from the inside of the reveal to the surface of
the wall.
Potential problems with the minimum required concrete cover
can occur where rustications are located at specific areas of
a wall (see Fig. 7.2a). It is clear from the figure that the cover
to the transverse reinforcement is smaller than that which is
required. One solution is to offset the reinforcing bars in the
localized area to maintain the required cover (see Fig. 7.2b).
The detailing and placing of the reinforcement can become
quite challenging if more than one area of rustication is required and/or if the rustication is located near an opening in a
wall. A more viable solution is to treat the rustication area as
an opening and provide an inner layer of reinforcement with
the proper cover (see Fig. 7.2c). This reinforcement should be
developed beyond the rustication area in all directions.
Walls that are greater than 10 in. in thickness are required
to have two layers of reinforcement in both directions and
distributed in accordance with the provisions in ACI 11.7.2.3.
Flexural tension reinforcement is to be well distributed and
placed as close as practical to the tension face of the wall.
Like for beams and slabs, the longitudinal and transverse bars
in reinforced concrete walls must be spaced at a sufficient
distance so that concrete can flow easily between the bars
and between the bars and the formwork. According to ACI
25.2.3, the minimum clear distance that is to be provided
between bars is equal to the largest of the following:
• 1.5 times the diameter of the longitudinal bar
• 1.5 in.
• (4/3) times the diameter of the largest aggregate in the
concrete mix
To simplify placement of the reinforcement in the field, bars should
be placed at a consistent spacing or using multiples of a given
spacing. Similarly, to avoid installation errors, the same bar size
should be used in both the longitudinal and transverse directions.
7.4.4 Lateral Support of Longitudinal Reinforcement
In cases where the longitudinal reinforcement in a wall is required
for axial strength or where the area of the longitudinal reinforcement exceeds 1% of the gross area of the wall, transverse ties
are required around the longitudinal reinforcement (ACI 11.7.4).
(a)
(b)
7.4.3 Spacing Requirements
Spacing requirements for longitudinal and transverse reinforcement walls are given in ACI 11.7.2 and 11.7.3, respectively.
The spacing of longitudinal bars in cast-in-place walls should
not exceed the lesser of 3 times the wall thickness and 18 in.
For shear reinforcement that is required for in-plane shear, the
spacing is limited to one-third of the length of the wall.
7-2
(c)
Fig. 7.2 Rustication Over a Portion of a Wall (a) Minimum Concrete
Cover Not Provided (b) Offset Bars (c) Inner Layer of Bars.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
#
#
Fig. 7.3 Typical Reinforcement at Wall Openings.
While it may be feasible to provide such ties in thicker walls, it
is very difficult to do so in thinner walls, especially where the
bars are spaced relatively close together. Development of the
tie bars and interference of the adjoining hooks at the ends of
the ties can pose major problems.
7.4.5 Wall Openings
In a typical building, it is inevitable that openings of various
sizes and shapes for doors, windows, conduit, piping, and
ductwork will need to be made in the structural walls. Mechanical, plumbing, and electrical openings are usually located
just below the slab, but, in general, could occur anywhere.
Additional reinforcement must be provided around the perimeter
of wall openings and it is commonly referred to as trim bars,
opening bars, or corners bars (Reference 18). In essence, these
bars are to replace the reinforcement interrupted by the opening.
ACI 11.7.5 requires that for walls with one layer of reinforcement in both the longitudinal and transverse directions, at least
one #5 bar must be provided around an opening. Similarly, at
least two #5 bars are required around openings in walls that
have two layers of reinforcement in both directions. These are
the minimum amounts of reinforcement that is required; in
walls subjected to relatively large lateral loads, for example, an
analysis of the wall must be made and the required amounts
of reinforcement in the wall and around the perimeter of the
openings must be provided based on the analysis. Regardless
of the size and amount of the required reinforcement, the trim
bars must be fully anchored to develop the yield strength of the
bars in tension at the corners of an opening.
Unless required for structural purposes, longitudinal trim bars
around the sides of an opening that run the full height of a wall
and that get lap spliced with dowels protruding from the footing
Concrete Reinforcing Steel Institute
should be avoided (see Fig. 7.3). Detailing and placing full-height
trim bars can be a problem because the exact locations of the
wall openings may not be available at the time the concrete
for the footing is placed; thus, the dowels may not be at the
correct location. As noted above, longitudinal trim bars need to
be developed only past the edge of the opening. Providing fullheight bars when they are not required is not recommended.
In regards to the development length of the trim bars, the
preferred reference point to measure the development length
from is the corner of the opening, as shown in Fig. 7.4. This is
an advantageous location for the detailer and placer because it
is a fixed point. Measuring the
embedment length from a longitudinal or transverse trim bar is
frequently done, but the embedment length may wind up being
too short if the perpendicular
trim bars adjacent to the opening shift for whatever reason
Fig. 7.4 Preferred Reference Point
from their intended location
for Development Length of Trim
(see Fig. 7.5).
Bars.
Fig. 7.5 Development Length of Trim Bars Measured from Perpendicular
Trim Bars.
7-3
Design Guide for Economical Reinforced Concrete Structures
Fig. 7.6 Reinforcement Details for Column-like Wall Segments.
It is very important to indicate on the structural drawings the
limitations for typical reinforcement around an opening. When
openings become relatively wide or long, portions of the wall
may behave more like beams or columns and they need to be
detailed accordingly. For example, for relatively wide openings, the segment of the wall above and below the opening
may require beam-type reinforcement (longitudinal bars and
stirrups). Similarly, vertical wall segments adjacent to an opening may behave more like columns and should be detailed as
such. Recommended details are illustrated in Fig. 7.6.
The spacing of the trim bars need to be indicated on the structural drawings as well.
In cases where a large number of bars are cut either because
of the size of the opening or the amount of reinforcement
that is required in the wall, a large amount of trim bars will be
required on each side of the opening. Some of the bars may
be too far from the opening to be considered fully effective if
the same bar size is used for the trim bars as in the wall. This
is illustrated in Fig. 7.7 where the cut wall bars are replaced
one-for-one with trim bars.
Fig. 7.8 Cut Wall Bars Replaced with Larger Trim Bars.
The main purpose of the diagonal bars at the corners of
openings is to arrest cracks that can form at these reentrant
corners. For openings that occur close to the top of a wall or
where openings are stacked on top of each other, the typical
straight diagonal bar detail may not be possible. In order to
properly develop the diagonal bars, either a standard hook
needs to be provided at one end or the bar can be bent, as
illustrated in Fig. 7.9 for the case of stacked openings.
A possible solution to this is to use fewer bars that are larger.
This is illustrated in Fig. 7.8 for the case depicted in Fig. 7.7.
Fig. 7.9 Diagonal Bar Development.
7.4.6 Wall Corners and Intersections
Fig. 7.7 Cut Wall Bars Replaced One-for-one with Trim Bars.
7-4
The reinforcement at wall corners and intersections need to
be carefully detailed to avoid installation and other problems.
Long transverse bars with hooks at one or both ends should
be avoided because they are very difficult to install. Wall bars
are often assembled in curtains or mats that are lifted into
position. Hooks complicate preassembly, transportation, storage, and handling of the curtains. Constructability is enhanced
by providing straight horizontal bars that are lapped spliced
together by separate bars; by doing so, adjacent curtains can
be installed without interference (Reference 19). Furthermore,
the curtains can easily be adjusted to maintain proper con-
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Fig. 7.10 Wall Corner and Intersection Details that Should Be Avoided –
Single Layers of Transverse Reinforcement.
Fig. 7.14 Wall Intersection Detail That Should Be Avoided – Double Layers
of Transverse Reinforcement.
0 in. (typ.)
(a)
(b)
Fig. 7.11 Preferred Wall Corner and Intersection Details – Single Layers of
Transverse Reinforcement.
Fig. 7.15 Preferred Wall Intersection Details – Double Layers of Transverse
Reinforcement.
crete cover as the independent hooked bars used for the lap
splices are tied in place. The costs associated with the extra
reinforcing bars needed for the lap splices are far outweighed
by the costs associated with the labor needed for increased
handling and installation of the bars with hooks on the ends.
The detail illustrated in Fig. 7.14 should be avoided at wall
intersections for the reasons stated previously. The preferable
layouts are shown in Fig. 7.15. Once again, the layout in Fig.
7.15b is only possible in relatively thick walls.
Depicted in Fig. 7.10 are three examples of details at corners and
intersections that should be avoided in walls with one layer of transverse reinforcement because of the reasons noted above. Illustrated in Fig. 7.11 are the preferred details, which show the separate
hooked bars that are doweled to the straight bars in the wall.
The location of the longitudinal bars at wall corners and intersections must also be carefully investigated (Reference 20).
Depicted in Fig. 7.16 is a common detail for bar arrangement
at a corner of a wall. The location of the longitudinal bars at the
corner appears to be reasonable, but problems become readily
apparent once transverse bars are included (see Fig. 7.17).
The details shown in Fig. 7.12 at the corners of walls with
two layers of transverse reinforcement with hooks on their
ends should be avoided because they make it difficult to use
preassembled curtains of bars. Of the three arrangements
illustrated in Fig. 7.13, detail a is common, but detail b is preferred because the separate 90-degree hooked bars that are
lap spliced with the two preassembled double-bar curtains of
transverse reinforcement is easy to construct. Detail c is also
easy to construct for preassembled curtains but it can only be
used in walls that are thick enough to accommodate the width
of the U bars (hairpins) at the ends that are lap spliced to the
transverse reinforcement in the walls.
Fig. 7.16 Common Reinforcement Detail at Wall Corners (sp is the centerto-center distance between bars).
(a)
(b)
Fig. 7.12 Wall Corner Details That Should Be Avoided – Double Layers of
Transverse Reinforcement.
(a)
(b)
(c)
Fig. 7.17 Standard Details at Wall Corners (a) Longitudinal Bars Located
Outside of the Transverse Bars (b) Longitudinal Bars Located Inside of the
Transverse Bars.
Fig. 7.13 Preferred Wall Corner Details – Double Layers of Transverse
Reinforcement.
Concrete Reinforcing Steel Institute
7-5
Design Guide for Economical Reinforced Concrete Structures
(a)
(b)
Fig. 7.18 Preferred Details at Wall Corners (a) Longitudinal Bars Located Outside of the Transverse Bars (b) Longitudinal Bars Located outside of the Transverse
Bars.
Fabrication and placing tolerances for the transverse bars in
the wall can result in an irregular layout at the corner. Because
of this, placing a longitudinal bar at the intersection of the
transverse bars is not possible. Instead, the longitudinal bar
will need to be offset from this working point.
As noted above, the transverse bars in the wall at the corner
will be lap spliced together by a separate hooked bar. The
fabrication tolerance for the bend radius of this bar and the
angular deviation of the corner bars in the wall also make it difficult to locate and tie the longitudinal bar on the outside face.
Furthermore, if the two outside face curtains of reinforcing
steel were preassembled, it would be difficult to locate the
corner longitudinal bar once the curtains have been erected
and the transverse corner bars have been placed.
verse bars. It is evident that the longitudinal bar that is located
on the inside face of the core is not needed and only adds to
congestion at this location.
Illustrated in Fig. 7.21 is the preferred detail for the longitudinal
bars at a wall intersection.
(a)
The details illustrated in Fig. 7.18 are preferred because the
single longitudinal bar shown in Fig. 7.17 has been replaced
with two longitudinal bars (one on each wall located slightly
away from the corner). These longitudinal bars can be easily
placed, especially if the curtains are preassembled.
A similar situation occurs at wall intersections. Depicted in
Fig. 7.19 is a common detail for bar arrangement at a wall
intersection. Figure 7.20 shows the same detail with the trans-
Fig. 7.19 Common Reinforcement Detail at Wall Intersections.
7-6
(b)
Fig. 7.20 Standard Details at Wall Intersections (a) Longitudinal Bars Located Outside of the Transverse Bars (b) Longitudinal Bars Located Inside
of the transverse Bars.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
(b)
(a)
Fig. 7.21 Preferred Details at Wall Intersections (a) Longitudinal Bars Located Outside of the Transverse Bars (b) Longitudinal Bars Located Inside of the Transverse
Bars.
7.5 Detailing Requirements and Guidelines
for SDC D, E, or F
requirements for walls in structures assigned to SDC C; it is
assumed that the provisions in ACI Chapter 11 provide the
required level of ductility in such cases.
7.5.1 Overview
Special structural walls are required in structures assigned
to SDC D, E, or F that utilize bearing wall systems, building
frame systems, and dual systems. Detailing requirements for
such walls are given in ACI 18.10. All of the requirements and
guidelines presented above are also applicable.
The requirements in ACI Chapter 11 are applicable to walls in
structures assigned to SDC A, B, and C. Unlike two-way slabs
without beams, beams, and columns, there are no separate
7.5.2 Web Reinforcement Requirements
The provisions of ACI 18.10.2.1 for required web reinforcement in special structural walls are summarized in Fig. 7.22,
which is adapted from Reference 7. Reinforcement provided
for shear strength must be continuous and uniformly distributed across the shear plane. This uniform distribution helps
control the width of inclined cracks.
Fig. 7.22 Web Reinforcement Requirements for Grade 60 Bars in Special Structural Walls.
Concrete Reinforcing Steel Institute
7-7
Design Guide for Economical Reinforced Concrete Structures
Fig. 7.23 Design and Detailing Requirements for Special Boundary Elements.
7.5.3 Boundary Elements
During a seismic event, the ends of a wall and the edges
adjacent to openings can be subjected to large compressive
forces as the wall undergoes cyclic deformations. Special
transverse reinforcement may be required at these locations to confine the concrete and to restrain the longitudinal
reinforcement in the wall so that buckling of the bars does not
occur.
Regardless of the method, the detailing requirements of ACI
18.10.6.4 must be satisfied. A summary of these requirements is given in Fig. 7.23, which is adapted from Reference 7.
Even though special boundary elements may not be required,
additional transverse reinforcement at the ends of the wall
may be required where the provisions of ACI 18.10.6.5 are
met. The reinforcement details in this case are illustrated in
Fig. 7.24, which is adapted from Reference 7.
Two methods to determine whether special elements are
required or not are given in ACI 18.10.6.2 and 18.10.6.3.
Fig. 7.24 Reinforcement Details Where Special Boundary Elements are not Required and the Provisions of ACI 18.10.6.5 are Met.
7-8
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
CHA PTER 8
Diaphragms
8.1 Overview
Guidelines and recommendations on the economical design and
detailing of conventionally reinforced, cast-in-place diaphragms
and collector elements are contained in this chapter. Information is provided on determining the thickness and detailing the
longitudinal and transverse reinforcement. Specific requirements
for diaphragms and collectors in structures assigned to SDC D, E,
or F are given in Section 8.4 of this Guide.
8.2 Determining the Diaphragm Thickness
In general, the thickness of a diaphragm must be sufficient
to resist in-plane bending moments, shear forces, and axial
forces due to the combinations of gravity and lateral loads.
ACI Chapter 12 requires that floor and roof diaphragms in
buildings assigned to SDCs A through C have a thickness not
less than that required for floor and roof elements that are
contained in other chapters of ACI 318. Thus, diaphragms can
be initially checked for the applicable load combinations using
the thickness determined by the information provided in
Chapters 3 and 4 of this Guide. There are no minimum thickness requirements prescribed in ACI Chapter 12.
8.3 Detailing Requirements and Guidelines for Reinforcement
The reinforcement that is required in the diaphragm is determined using the applicable load combinations for axial force,
bending moment, and shear force.
According to ACI 12.5.2.3, nonprestressed chord reinforcement
must be located within h/4 of the tension edge of the diaphragm where h is the depth of the diaphragm in the direction
of analysis (see Fig. 8.1, which is adapted from Reference 7).
This helps ensure that the shear flow through the depth of the
diaphragm is uniform.
Chord reinforcement is usually positioned near the edge of
the diaphragm and is placed within the middle third of the slab
or beam depth to minimize interference with the slab or beam
longitudinal reinforcement. Furthermore, at this position,
the chord reinforcement has a minimal effect on the flexural
strength of the slab or beam.
Required transverse reinforcement for shear is commonly
incorporated into the bottom mat of the uniformly distributed
reinforcement in the slab. It is important to call out the required
lap splice lengths for these bars on the structural drawings
because they may exceed the lengths that are required for the
typical slab reinforcement.
Collector reinforcement is typically located within the
mid-depth of the slab, similar to chord reinforcement. The
amount of collector reinforcement is determined based on
the applicable load combinations for combined axial force
and bending moment. In cases where the slab is not sufficient to act as a collector, beams must be provided. The
requirements and guidelines given in Chapter 5 can be
used in such cases.
Fig. 8.1 Location of Reinforcement Resisting Tension Due to Moment and Axial Force (ACI 12.5.2.3).
Concrete Reinforcing Steel Institute
8-1
Design Guide for Economical Reinforced Concrete Structures
8.4 Detailing Requirements and Guidelines
for SDC D, E, or F
8.4.1 Overview
Earthquake design forces for diaphragms are to be obtained
from the general building code using the applicable provisions
and load combinations. In the case of the IBC and ASCE 7, the
load combinations amplify the code-prescribed earthquake
forces by the overstrength factor <o for collectors and their
connections in structures assigned to SDCs C through F. The
overstrength factor represents an upper bound lateral strength
and is appropriate to use when estimating the maximum
force that can be developed in nonyielding elements of the
SFRS during an earthquake. The intent of this requirement is
to ensure that collectors and their connections have adequate
strength and remain essentially elastic during a design event.
8.4.2 Minimum Thickness
A minimum thickness of 2 in. is prescribed in ACI 18.12.6 for
concrete slabs. This reflects the current practice in joist and
waffle slab systems in cast-in-place concrete. As always, it is
important to consider the fire-resistance requirements when
selecting an overall slab thickness.
8.4.3 Minimum Reinforcement
The minimum reinforcement ratios for the longitudinal and
transverse reinforcement in a diaphragm must conform to
those for temperature and shrinkage given in ACI 24.4. The
maximum spacing of 18 in. is intended to control the width of
inclined cracks that may form during a seismic event.
Bar development and lap splices in diaphragms and collectors are to be determined in accordance with ACI 25.4.2 and
25.5.2. Reductions in development or splice lengths are not
permitted in structures assigned to SDCs D, E, or F.
The requirements for chord reinforcement are the same as
those discussed in Section 8.3 of this Guide (see Fig. 8.1).
Collectors must be designed for the combined effects due
to flexure, shear, and axial compression or tension caused by
the gravity and seismic load effects. Transverse reinforcement
conforming to ACI 18.7.5.2(a) through (e) and ACI 18.7.5.3
must be provided in collectors where the compressive
stress in the collector is greater than 0.2f 'c (ACI 18.12.7.5). An
exception is that the spacing limit of ACI 18.7.5.3(a) should
be one-third the least dimension of the collector. Confining
reinforcement may be discontinued where the compressive
stress is less than 0.15f 'c. In cases where the forces have
been amplified by <o, the limits above are increased to 0.5f 'c
and 0.4f 'c, respectively.
Detailing requirements for the longitudinal reinforcement in
collectors at splice and anchorage zone locations are given
in ACI 18.12.7.6. A summary of these requirements and the
other noted previously are illustrated in Fig. 8.2, which is
adapted from Reference 7.
Like all elements that are part of the SFRS, it is good practice to ensure that the reinforcement in the diaphragms and
collectors can adequately fit within the sections and that the
connection and intersecting locations are not too congested.
Fig. 8.2 Detailing Requirements for Diaphragms and Collectors in Buildings Assigned to SDC D, E, or F.
8-2
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
CHA PTER 9
Foundations
9.1 Overview
Guidelines and recommendations on the economical design
and detailing of spread footings, mat foundations, drilled piers,
and grade beams are contained in this chapter. Information is
provided on sizing the members and detailing the reinforcement. Specific requirements for foundations in structures assigned to SDC D, E, or F are given in Section 9.6 of this Guide.
9.2 Spread Footings
9.2.1 Material Selection
Normal-weight concrete with a compressive strength of 3,000
psi is usually the most economical choice for footings. Higher
strength concrete may be used for various reasons, but usually the savings in concrete volume does not offset the higher
cost.
Grade 60 reinforcing bars are recommended for overall
economy.
9.2.2 Determining the Base Dimensions and Thickness
The base area of a symmetrically loaded, individual footing is
determined by dividing the unfactored loads acting on the supported member by the net permissible soil pressure, which is
the allowable bearing capacity of the soil minus the weight of
the surcharge above the footing. The allowable soil bearing capacity is typically obtained from a geotechnical report or from
local building authorities. Individual spread footings are usually
made square and are centered under the column it supports.
Rectangular footings may be required where there are space
limitations, such as adjacent to property lines.
For footings subjected to an axial load and bending moment
or, equivalently, to an axial load acting at an eccentricity, the
pressure beneath the footing is not uniform. Base dimensions
need to be provided such that the maximum pressure is less
than or equal to the net permissible soil pressure.
Once the required area of the footing Af has been established, the thickness of the footing must be determined
considering both flexure and shear. The location of the critical
section for flexure is given in ACI Table 13.2.7.1. For a concentrically loaded, square footing with a minimum amount
of Grade 60 reinforcement (reinforcement ratio of 0.0018)
and 3,000 psi, normal-weight concrete supporting a square
column, the following equation can be used to determine the
effective depth d of the footing:
d = 2.2c
Pu
Af
In this equation, c is the distance from the face of the column
to the edge of the footing (in feet), Pu is the factored axial force
on the column (in kips), and Af is the base area of the footing
(in square feet). The resulting effective depth d is in inches.
Concrete Reinforcing Steel Institute
The depth of the footing that is provided must also satisfy
one-way and two-way shear requirements. The critical section
for one-way shear in a footing is located a distance d from the
face of the column. The minimum effective depth d that satisfies one-way shear requirements can be obtained from the
following equation for normal-weight, 3,000 psi concrete:
d=
qu c
qu + 82
In this equation, qu is the factored pressure at the base of
the square footing (in psi). The distance c is in inches as is the
effective depth d.
The critical section for two-way shear is located a distance of d/2
from the face of the column. The minimum effective depth d that
satisfies two-way shear requirements can be obtained from the
following equation for normal-weight, 3,000 psi concrete:
qu
qu
2
q
A f
+164 +
+164 + qu u +164
1
2
2
2
4
c1
d = c1
q
2 u +164
4
In this equation, c1 is the dimension of the square column (in
inches), qu is the factored pressure at the base of the square
footing (in psi), and Af is the area of the square footing (in square
inches). The effective depth d is in inches. Two-way shear is usually more critical than one-way shear. Because shear reinforcement is not economical in footings, the depth of the footing must
be increased where shear capacity is not sufficient.
The largest d computed by these three equations is to be
used in determining the overall thickness of the footing.
Because the minimum cover to the reinforcement is equal to
3 in. for concrete cast against and permanently exposed to
earth (ACI Table 20.6.1.3.1), the overall depth of the footing
should be taken equal to at least 4 in. plus the effective depth
d. Note that the minimum d required by ACI 13.3.1.2 is 6 in.
9.2.3 Detailing Requirements and Guidelines for
Reinforcement
Flexural Reinforcement
Requirements for the distribution of flexural reinforcement
in two-way footings are given in ACI 13.3.2.2 and 13.3.3.3.
For square footings, the reinforcement is to be distributed
uniformly across the entire width of the footing in both directions. In the case of rectangular footings, the reinforcement
must be distributed in accordance with the requirements in
ACI 13.3.3.3, which are illustrated in Fig. 9.1. Reinforcement
in the long direction is uniformly distributed across the entire
width. A portion of the reinforcement in the short direction is
banded over the column with the remainder uniformly distributed outside of the band width.
9-1
Design Guide for Economical Reinforced Concrete Structures
psi concrete and Grade 60 reinforcement that is uncoated and is
placed at the bottom of the footing (i.e., not top bars).
Reinforcement Across the Interface
The amount of reinforcement that is required at the interface between the column and the footing depends on the type of stress
in the bars of the column under all applicable load combinations.
Dowels are commonly used as interface reinforcement between columns and footings. The dowels are set in the footing
prior to casting the footing concrete and are subsequently
spliced to the column bars.
In cases where the column bars are all in compression and
the factored bearing load Bu is less than or equal to the design
bearing strength KBn , which is determined in accordance with
ACI Table 22.8.3.2, a minimum area of reinforcement across the
interface is required; this minimum amount is 0.5% the area
of the column. Where Bu > KBn , the required area of interface
reinforcement As can be obtained from the following equation:
Bu Bn
0.005Ag
fy
Fig. 9.1 Distribution of Flexural Reinforcement in a Rectangular Footing.
As =
In order to minimize the potential for errors while placing the
bars in the short direction, a common practice is to increase
the amount of reinforcement in the short direction by 2G/(G 1)
(where G is the ratio of the long side to the short side of the
footing) and space it uniformly across the long dimension of
the footing instead of distributing the bars as shown in Fig. 9.1.
Illustrated in Fig. 9.2 are dowels across the interface between a
column and footing. For the case where all of the column bars
are in compression, the dowels must extend into the footing
a compression development length Cdc determined in accordance with ACI 25.4.9.2. The dowel bars are usually hooked and
extend to the level of the flexural reinforcement in the footing.
According to ACI 25.4.1.2, the hooked portion of the dowels
cannot be considered effective for developing the dowel bars
in compression. The following equation must be satisfied to
ensure adequate development of the dowels in the footing:
Flexural reinforcement in footings must be fully developed in
accordance with the applicable provisions of ACI Chapter 25.
For a concrete column supported by an isolated footing, the
required development length Cd must be less than or equal to
the available development length:
d L c1
3 in.
2
In this equation, L and c1 are the lengths of the footing and
column in the direction of analysis, respectively.
In typical cases, the clear spacing and cover requirements in the
first row of ACI Table 25.4.2.2 are satisfied for flexural reinforcement in footings. Table 9.1 contains the minimum development
lengths Cd based on those requirements for normal-weight, 3,000
Table 9.1 MinimumTension Development Length for
Flexural Reinforcement in Footings
9-2
Bar Size
Development length, Cd (in.)
#4
22
#5
28
#6
33
#7
48
#8
55
#9
62
#10
70
#11
78
h v Cdc r (db )dowel 2(db )f cover
In this equation, r is the radius of the dowel bar bend, and
(db )dowel and (db )f are the bar diameters for the dowel bars
and the flexural reinforcement, respectively.
Dowels must also be fully developed into the column; they
are typically lap spliced to the column bars.
Tensile forces (either direct or transferred by a moment) must
be resisted entirely by reinforcement across the interface. Tensile anchorage of the dowel bars into the footing is typically
accomplished by providing a 90-degree standard hook at the
ends of the dowel bars. A tension lap splice must be provided
between the dowel bars and the column reinforcement.
ACI 16.3.3.5 permits the shear-friction method of ACI 22.9 to
be used for transfer of lateral loads from a supported member
to a footing.
Additional design and detailing requirements for dowels can
be found in Section 6.5 of this Guide.
Reference 21 contains additional information on the design of
individual footings, including design tables that give material
quantities of concrete and reinforcement for a wide variety
of cases.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
The plan dimensions of a mat foundation are typically dictated
by the geometry of the building it supports, including the layout
of the vertical elements (columns and walls). Property lines and
other factors may also influence plan dimensions. It is important to provide dimensions so that the soil pressure beneath
the mat does not exceed the net permissible soil pressure.
The reinforcing system in a mat foundation can be substantial
depending on a number of factors. Improper detailing of the
reinforcement can result in constructability issues that can
impact schedule and cost (Reference 22). The following information describes ways to simplify the design, detailing, and
placement of the required reinforcement in a mat foundation.
9.3.2 Determining the Mat Thickness
The thickness of a mat foundation is typically controlled by shear
requirements. Both one-way and two-way shear must be investigated around the critical sections of the vertical members supported
by the mat. Like footings, it is common practice not to use shear
reinforcement in mats. The thickness of the mat is usually increased
where additional shear capacity is needed. For overall economy, the
thickness of the mat is constant over its entire extent.
9.3.3 Detailing Requirements and Guidelines for
Reinforcement
Fig. 9.2 Footing Dowels.
9.3 Mat Foundations
9.3.1 Overview
Mat foundations are used to support all or a portion of the
vertical elements in a building. They are commonly specified
where erratic or relatively weak soil strata are encountered
or where a large number of closely spaced spread footings
would be required.
Once the thickness of the mat has been established and the
required amounts of reinforcement are calculated at the critical sections, a suitable bar size and spacing must be selected.
The provided area of reinforcement must be greater than or
equal to the minimum reinforcement prescribed in ACI 8.6.1.1
for two-way slabs (ACI 13.3.4.4).
For deep mats, the reinforcing bars can be placed in two
layers (one mat) at both the top and bottom faces or in four
layers (two mats). Bars that are in the interior layers should be
aligned with those in the outer layer (see Fig. 9.3). This helps
reduce voids in the concrete because it provides clear passage for concrete placement.
Fig. 9.3 Typical Reinforcement Configuration in a Deep Mat Foundation.
Concrete Reinforcing Steel Institute
9-3
Design Guide for Economical Reinforced Concrete Structures
Fig. 9.5 Elevator Pit in a Mat Foundation.
in the mat require hooks at the ends or not. If the depth of the
mat cannot accommodate the pit, it can be locally thickened
as shown in Fig. 9.6 for the case of a trench drain.
9.4 Drilled Piers
Fig. 9.4 Dowels in a Mat Foundation.
9.4.1 Overview
The size of the bars in the interior layers should be the same size
as or smaller than the bars in the outer layers. It is recommended
that a 3-in. spacing be provided between the bars to facilitate
concrete placement.
In cases where additional bars are required in localized areas that
are heavily loaded, these bars should be spaced as a multiple or
sub-multiple of the spacing for the typical flexural reinforcement.
Where the column spacing is not on a regular, symmetric grid,
the layout of the reinforcing bars in the mat should be placed
on an orthogonal grid and should not be skewed to follow the
column layout. Additional bars can be placed at locations in the
regular grid wherever required. This greatly simplifies placing the
bars in the field.
A drilled pier, which is sometimes referred to as a pier or
caisson, transfers the loads from the superstructure to a soil
or rock stratum that is usually well below the ground surface.
The bottom of the shaft is often belled out to provide a larger
end-bearing area. Concrete is deposited into the shaft after
the reinforcement has been set in place.
The loads from the supported member are transferred to the
shaft by bearing. Skin friction, point bearing, and a combination
of the two are ways in which the load is transferred to the soil
surrounding and below the shaft or bell.
Staggering the splices for different layers of reinforcing bars leads
to confusion in the field with respect to placing and inspecting
the bars. Avoiding staggered splices is the preferred method
of placement for ease of constructability. Using the maximum
straight bar length as often as possible usually minimizes the
number of lap splices.
Like columns supported by spread footings, the dowels from
the columns and walls that are supported by the mat should
extend to the bottom layer of flexural reinforcement in the mat
(see Fig. 9.4). The dowels should have a 90-degree standard
hook at the bottom end; this allows the dowels to be tied to
both the top and bottom layers of reinforcement in the mat,
which secures the dowels from displacing before or during
concrete placement.
Mat foundations will usually have to incorporate pits for elevators or sumps. Where the depth of the mat can accommodate
the pit, additional layers of reinforcing steel can be added to
serve as the top steel in the mat (see Fig. 9.5). An analysis
should be performed to determine if the interrupted top bars
9-4
(a)
(b)
Fig. 9.6 Trench Drain in a Mat Foundation (a) Design Detail; and (b)
Reinforcing Bar Placing Detail.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
9.4.2 Determining the Shaft Diameter
Table 1810.3.2.6 in the 2015 IBC (Reference 25) contains
allowable stresses for deep foundation elements, including
drilled piers. The allowable stress in compression for cast-inplace concrete with a permanent casing is 0.4f 'c and is 0.3f 'c
where permanent casing is not provided.
The diameter of the shaft can be determined from the following
equation where permanent casing is not provided:
d shaft
9.4.4 Detailing Requirements and Guidelines for
Reinforcement
Recommended reinforcement details for drilled piers are
given in Fig. 9.7. A minimum longitudinal reinforcement ratio
of 0.005 is used, which corresponds to the ratio that is permitted in ACI 10.3.1.2 for columns with cross-sections that are
larger than required for the applied loads.
1/2
4P
=
0.3 f ' c
(
)
In this equation, P is the total service axial dead and live load
acting on the drilled pier. The diameter is typically specified in
multiples of 6 in.
Cover
Table 9.2 contains the maximum allowable axial load that can
supported by a drilled pier shaft for allowable stresses of 0.25f 'c
and is 0.30f 'c .
9.4.3 Determining the Bell Diameter
For end-bearing drilled piers, the diameter of the bell can be
determined from the following equation:
dbell
4P 1/2
=
qa In this equation, qa is the allowable bearing capacity of the soil
or rock.
Table 9.3 contains the safe bearing load for bells as a function
of bell diameter and allowable soil/rock bearing pressure.
Fig. 9.7 Reinforcement Details for Drilled Piers Subjected to Axial
Compression loads.
Table 9.2 Shaft Maximum Allowable Axial Loads (kips)
Shaft Maximum Allowable Axial Load—Kips*
Shaft
Diameter
(ft-in.)
Shaft
Area
in.2
1-6
2-0
*For
fc " 0.25f 'c
fc " 0.30f 'c
f 'c "
3,000 psi
f 'c "
4,000 psi
f 'c "
5,000 psi
f 'c "
6,000 psi
f 'c "
3,000 psi
f 'c "
4,000 psi
f 'c "
5,000 psi
f 'c "
6,000 psi
254
191
254
318
382
229
305
382
458
452
339
452
565
679
407
543
679
814
2-6
707
530
707
884
1060
636
848
1060
1272
3-0
1018
763
1018
1272
1527
916
1221
1527
1832
3-6
1385
1039
1385
1732
2078
1247
1663
2078
2494
4-0
1810
1357
1810
2262
2714
1629
2171
2714
3257
4-6
2290
1718
2290
2863
3435
2061
2748
3435
4122
5-0
2827
2121
2827
3534
4241
2545
3393
4241
5089
5-6
3421
2566
3421
4276
5132
3079
4105
5132
6158
6-0
4072
3054
4072
5089
6107
3664
4886
6107
7329
6-6
4778
3584
4778
5973
7168
4301
5734
7168
8601
7-0
5542
4156
5542
6927
8313
4988
6650
8313
9975
shafts designed as plain concrete piers, laterally braced by soil.
Concrete Reinforcing Steel Institute
9-5
Design Guide for Economical Reinforced Concrete Structures
Table 9.3 Bell Safe Bearing Load (kips)
Bell
Diameter
(ft-in.)
**As
9-6
Bearing
Area
(ft2)
Bell Safe Bearing Load Kips**
10,000 psf **
12,000 psf **
15,000 psf **
20,000 psf **
25,000 psf **
30,000 psf **
1-6
1.77
18
21
27
35
44
53
2-0
3.14
31
38
47
63
79
94
2-6
4.91
49
59
74
98
123
147
3-0
7.07
71
85
106
141
177
212
3-6
9.62
96
115
144
192
241
289
4-0
12.57
126
151
188
251
314
377
4-6
15.90
159
191
239
318
398
477
5-0
19.63
196
236
295
393
491
589
5-6
23.76
238
285
356
475
594
713
6-0
28.27
283
339
424
565
707
848
6-6
33.18
332
398
498
664
830
995
7-0
38.48
385
462
557
770
962
1155
7-6
44.18
442
530
663
884
1104
1325
8-0
50.27
503
603
754
1005
1257
1508
8-6
56.75
567
681
851
1135
1419
1702
9-0
63.62
636
763
954
1272
1590
1909
9-6
70.88
709
851
1063
1418
1772
2126
10-0
78.54
785
942
1178
1571
1963
2356
10-6
86.59
866
1039
1299
1732
2165
2598
11-0
95.03
950
1140
1425
1901
2376
2851
11-6
103.87
1039
1246
1558
2077
2597
3116
12-0
113.10
1131
1357
1696
2262
2827
3393
12-6
122.72
1227
1473
1841
2454
3068
3682
13-0
132.73
1327
1593
1991
2655
3318
3982
13-6
143.14
1431
1718
2147
2863
3578
4294
14-0
153.94
1539
1847
2309
3079
3848
4618
14-6
165.13
1651
1982
2477
3303
4128
4954
15-0
176.71
1767
2121
2651
3534
4418
5301
15-6
188.69
1887
2264
2830
3774
4717
5661
16-0
201.06
2011
2413
3016
4021
5027
6032
16-6
213.82
2138
2566
3207
4276
5346
6415
17-0
226.98
2270
2724
3405
4540
5675
6809
17-6
240.53
2405
2886
3608
4811
6013
7216
18-0
254.47
2545
3054
3817
5089
6362
7634
18-6
268.80
2688
3226
4032
5376
6720
8064
19-0
283.53
2835
3402
4253
5671
7088
8506
19-6
298.65
2986
3584
4480
5973
7466
8959
20-0
314.16
3142
3770
4712
6283
7854
9425
20-6
330.06
3301
3961
4951
6601
8252
9902
21-0
346.36
3464
4156
5195
6927
8659
10391
permitted by statutory building code or established by accepted tests.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Fig. 9.8 Reinforcement Details for a Grade Beam-drilled Pier Joint.
9.5 Grade Beams
Fig. 9.9 Option 1 – Extend Column Dowels Straight Into the Drilled Pier.
When designing grade beams, it is commonly assumed that
the soil beneath the grade beam is nonexistent and that
support occurs at its ends only. Therefore, the design and
detailing requirements and guidelines given in Chapter 5 of
this Guide are applicable.
A unique challenge with grade beams occurs at the grade
beam-drilled pier joint. If a grade beam is too shallow, congestion problems can occur at the joints (Reference 23). Consider
the detail depicted in Fig. 9.8. Because the depth of the
grade beam is relatively shallow, the longitudinal bars from
the column and the dowel bars from the drilled pier need to
be hooked to achieve proper development. Even with ideal
bar placement, it would be very difficult to properly fit all of
the bars. This congestion problem would be compounded if
the bars from the members were larger or if there were an
intersecting grade beam at the joint. Six options to alleviate
this problem are examined below.
Option 1 – Extend the column dowels straight into
the drilled pier
Extending the column dowel bars straight into the drilled pier
alleviates some of the congestion problems (see Fig. 9.9)
However, there are some issues associated with this detail:
• Special coordination would be required where the contractor
for the drilled pier is different than the contractor for the
remainder of the structure. The drilled pier contractor
may not be permitted to install the column dowels so this
would require coordination at a time when the building
contractor may not be on site yet.
Concrete Reinforcing Steel Institute
Fig. 9.10 Option 2 – Provide a Deeper Grade Beam.
9-7
Design Guide for Economical Reinforced Concrete Structures
Fig. 9.11 Option 3 – Provide a Deeper Grade Beam only at the Drilled
Pier.
Fig. 9.12 Option 4 – Provide a Pile Cap Under the Grade Beam at the
Drilled Pier.
Fig. 9.13 Option 5 – Hold Back the Concrete from the Pile Top.
9-8
Fig. 9.14 Option 6 – Place a Blockout at the Top of the Drilled Pier.
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Fig. 9.15 Transverse Reinforcement of Special Boundary Elements at Foundations.
• Column dowels that are cast into the drilled pier cannot
be moved or adjusted to accommodate grade beam reinforcement or column locations.
• For drilled piers with large diameters, the tolerance on
pier location is much larger than that for the column it is
supporting. Thus, if column dowels are installed in the
drilled pier in accordance with the drilled pier tolerances,
they may be positioned away from the intended locations.
In such cases, it is not clear which contractor would be
responsible to correct this problem.
Option 5 – Hold back the concrete from the pile top
Where a grade beam is supported by a concrete-filled steel pile
or casing, a viable option to alleviate congestion is to fill the steel
jacket with concrete to an elevation that is sufficiently below the
top of the jacket so that the column dowels can project into the pile
with the proper embedment length (see Fig. 9.13). This option is
similar to Option 1 except that in this option, the column dowels are
placed with the grade beam; this allows a certain amount of adjustment in placing the dowels. The top of the pile is subsequently filled
with concrete when the concrete for the grade beam is cast.
Option 2 – Provide a deeper grade beam
Option 6 – Place a blockout at the top of the drilled pier
Providing a deeper grade beam may eliminate the need to
provide hooks at the ends of the longitudinal reinforcement from
the drilled pier thereby reducing congestion in the joint (see Fig.
9.10). The volume of concrete is increased in this option, but the
amount of longitudinal reinforcement in the grade beam may be
reduced because of the larger effective depth for flexure.
This option is similar to Option 5 (see Fig. 9.14). The blockout
is filled when the concrete for the grade beam is cast.
Option 3 – Provide a deeper grade beam only at the
drilled pier
Design and detailing requirements for foundation elements
supporting structures assigned to SDC D, E, or F are given in
ACI 18.13. Specific requirements and guidelines for the foundation types covered in the previous sections of this chapter
are summarized below. All of the requirements and guidelines
presented above are also applicable.
Deepening the grade beam at the location of the drilled pier
only would be a viable option similar to Option 2 (see Fig.
9.11). The thickened section would be cast with the grade
beam. A smaller volume of concrete would be required compared to Option 2, and there would be a negligible difference
in the required amount of longitudinal reinforcement in the
grade beam.
Option 4 – Add a pile cap under the grade beam at
the drilled pier
Adding a pile cap beneath the grade beam at the location of the
drilled pier also alleviates congestion issues (see Fig. 9.12). This
pile cap would likely be cast separate of the grade beam.
Concrete Reinforcing Steel Institute
9.6 Detailing Requirements and Guidelines
for SDC D, E, or F
9.6.1 Overview
9.6.2 Footings and Foundation Mats
Longitudinal reinforcement of columns and structural walls
that are part of the SFRS of a structure must be fully developed for tension in a footing or mat foundation. Standard
hooks can be utilized at the ends of the bars where the foundation element is not deep enough to accommodate straight
bars, but providing straight bars is recommended.
9-9
Design Guide for Economical Reinforced Concrete Structures
Fig. 9.16 Requirements for Footings and Foundation Mats in Structures Assigned to SDC C, D, or F.
The transverse reinforcement of columns or boundary elements of special structural walls must extend at least 12 in.
into the supporting footing or mat provided the edge of the
column or wall is located greater than one-half the foundation
depth from the edge of the foundation (ACI 18.13.2.3). For
columns or boundary elements located closer than that, the
transverse reinforcement must extend a length equal to the
development length of the longitudinal reinforcement in the
column or boundary element (see Fig. 9.15 for the case of a
special boundary element, which is adapted from Reference
7). The intent is to prevent an edge failure of the foundation
element. Additional reinforcement details can be found in Fig.
9.16, which is adapted from Reference 7.
18.13.3 for grade beams are summarized in Fig. 9.17, which is
adapted from Reference 7. For grade beams that are part of
a mat foundation that resists flexural stresses from columns
that are part of the SFRS, the detailing requirements of ACI
18.6 for beams of special moment frames govern.
9.6.4 Piles, Piers, and Caissons
The design and detailing requirements for concrete piles,
piers, and caissons in ACI 18.13.4 are given in Fig. 9.18, which
is adapted from Reference 7. These provisions, as well as
those in ACI R1.4.6, helps to ensure that these foundation elements perform as intended during a design seismic event.
9.6.3 Grade Beams
Cross-section limitations and closed tie requirements of ACI
Fig. 9.17 Requirements for Grade Beams in Structures Assigned to SDC C, D, or F.
9-10
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Fig. 9.18 Requirements for Piles, Piers, and Caissons in Structures Assigned to SDC C, D, or F.
Concrete Reinforcing Steel Institute
9-11
Design Guide for Economical Reinforced Concrete Structures
CHA PTER 10
References
1. American Concrete Institute (ACI), Committee 318. 2014.
Building Code Requirements for Structural Concrete and
Commentary, ACI 318-14, Farmington Hills, MI.
2. Concrete Reinforcing Steel Institute (CRSI). 2015.
Reinforcing Bar Detailing, 5th Edition, Schaumburg, IL.
3. Concrete Reinforcing Steel Institute (CRSI). 2009. Manual
of Standard Practice, Schaumburg, IL.
4. Concrete Reinforcing Steel Institute (CRSI). 2014. Design
Guide for Voided Concrete Slabs, Schaumburg, IL.
5. R.S. Means Co., Inc. 2015. Concrete and Masonry Cost Data,
Rockland, MA.
6. American Concrete Institute (ACI). Concrete Cover at
Rustications, Drip Grooves, and Formliners, Concrete
International, June 2010, pp. 35-38.
7. Fanella, D. A. 2015. Reinforced Concrete Structures – Analysis
and Design, 2nd Ed., McGraw-Hill, New York, NY.
8. American Concrete Institute (ACI). Reinforcing Bar Layout
for Two-way Slabs, Concrete International, November 2012,
pp. 37-40.
9. American Concrete Institute (ACI). Layering Reinforcing
Bars, Concrete International, January 2010, pp. 53-56.
10. Birley, D. Beam-Column Joints, Concrete International,
December 2006, pp. 45-47.
11. American Concrete Institute (ACI). Wide Beam Stirrup
Configurations, Concrete International, March 2010, pp. 6264.
12. American Concrete Institute (ACI). Steps in Beams,
Concrete International, June 2012, pp. 41-44.
13. American Concrete Institute (ACI). 2009. ACI Design
Handbook, SP-17(09), Farmington Hills, MI.
Concrete Reinforcing Steel Institute
14. Concrete Reinforcing Steel Institute (CRSI). 2011. CRSI
Design Handbook, 11th Ed., Schaumburg, IL.
15. American Concrete Institute (ACI). Detailing Concrete
Columns, Concrete International, August 2011, pp. 47-53.
16. American Concrete Institute (ACI). Column Tie Configurations, Concrete International, March 2013, pp. 45-50.
17. American Concrete Institute (ACI). Column and Boundary
Element Dowels, Concrete International, December 2012,
pp. 44-48.
18. American Concrete Institute (ACI). Bar Detailing at
Wall Openings, Concrete International, December 2010,
pp. 52-56.
19. American Concrete Institute (ACI). Corner Details for
Wall Horizontal Bars, Concrete International, September
2009, pp. 43-45.
20. American Concrete Institute (ACI). Location of Vertical
Bars at Wall Intersections and RFI 12-02, Concrete
International, August 2012, pp. 47-51.
21. Concrete Reinforcing Steel Institute (CRSI). 2014.
Design Guide for Square Spread Footings for Individual
Columns, Schaumburg, IL.
22. American Concrete Institute (ACI). Reinforcing Bar
Details for Mat Foundations, Concrete International,
February 2012, pp. 48-52.
23. American Concrete Institute (ACI). Grade Beam Depth
and Dowel Embedment, Concrete International, May 2009,
pp. 53-56.
24. American Concrete Institute (ACI), Committee 237. SelfConsolidating Concrete, ACI 237R-07, Farmington Hills, MI.
25. International Code Council (ICC). 2015 International
Building Code, Washington, D.C.
10-1
Design Guide for Economical Reinforced Concrete Structures
Notations
A
= tributary column area, in.2
Abs
= cross-sectional area of spiral reinforcement, in.2
Ach
= cross-sectional area of a member measured to the outside edges of transverse reinforcement, in.2
Acp
= area enclosed by outside perimeter of concrete cross section, in.2
Acv
= gross area of concrete section bounded by web thickness and length of section in the direction of shear force
considered in the case of walls, and gross area of concrete section in the case of diaphragms, not to exceed
the thickness times the width of the diaphragm, in.2
Af
= required area of footing
Ag
= gross area of concrete section, in.2 For a hollow section, Ag is the area of the concrete only and does not include
the area of the void(s)
Ash
= total cross-sectional area of transverse reinforcement, including crossties, within spacing s and perpendicular to
dimension bc, in.2
As,min
= minimum area of flexural reinforcement, in.2
Ast
= total area of nonprestressed longitudinal reinforcement including bars or steel shapes, and excluding prestressing
reinforcement, in.2
b
= width of compression face of member, in.
bc
= cross-sectional dimension of member core measured to the outside edges of the transverse reinforcement
composing area Ash, in.
bt
= width of that part of cross section containing the closed stirrups resisting torsion, in.
bw
= web width or diameter of circular section, in.
Bn
= nominal bearing strength, lb
Bu
= factored bearing load, lb
c
= distance from extreme compression fiber to neutral axis, in.
= distance from face of column to edge of footing, ft
cc
= clear cover of reinforcement, in.
cs
= clear concrete cover to stirrups, in.
c1
= dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the
span for which moments are being determined, in.
c2
= dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction
perpendicular to c1, in.
d
= distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
dagg
= nominal maximum size of coarse aggregate, in.
db
= nominal diameter of bar, wire, or prestressing strand, in.
dbell
= bell diameter of a drilled pier
dshaft
= shaft diameter of a drilled pier
Concrete Reinforcing Steel Institute
N-1
Design Guide for Economical Reinforced Concrete Structures
ds
= diameter of stirrup reinforcement, in.
Dch
= diameter of the column core measured to the outside edges of the spiral reinforcement, in.
E
= effect of horizontal and vertical earthquake-induced forces
f c'
= specified compressive strength of concrete, psi
fs
= tensile stress in reinforcement at service loads, excluding prestressing reinforcement, psi
fy
= specified yield strength for nonprestressed reinforcement, psi
fyt
= specified yield strength of transverse reinforcement, psi
h
= overall thickness, height, or depth of member, in.
h1
= depth of drop panel, in.
hw
= height of entire wall from base to top, or clear height of wall segment or wall pier considered, in.
hx
= maximum center-to-center spacing of longitudinal bars laterally supported by corners of crossties or hoop legs
around the perimeter of the column, in.
k
= effective length factor for compression members
kf
= concrete strength factor
L
= length of footing or drop panel measured in the direction of analysis
ℓ
= span length of beam or one-way slab; clear projection of cantilever, in.
ℓc
= length of compression member, measured center-to-center of the joints, in.
ℓd
= development length in tension of deformed bar, deformed wire, plain and deformed welded wire reinforcement,
or pretensioned strand, in.
ℓdc
= development length in compression of deformed bars and deformed wire, in.
ℓn
= length of clear span measured face-to-face of supports, in.
ℓo
= length, measured from joint face along axis of member, over which special transverse reinforcement must be
provided, in.
ℓw
= length of entire wall, or length of wall segment or wall pier considered in direction of shear force, in.
Mn
= nominal flexural strength at section, in.-lb
Mpr
= probable flexural strength of members, with or without axial load, determined using the properties of the member
at joint faces assuming a tensile stress in the longitudinal bars of at least 1.25fy and a strength reduction factor K
of 1.0, in.-lb
Mu
= factored moment at section, in.-lb
n
= number of items, such as, bars, wires, monostrand anchorage devices, anchors, or shearhead arms
nmax
= maximum number of longitudinal reinforcing bars that can fit in a single layer
nmin
= minimum number of longitudinal reinforcing bars required in a single layer
P
= total service axial dead and live load on a drilled pier
ph
= perimeter of centerline of outermost closed transverse torsional reinforcement, in.
Pn
= nominal axial compressive strength of member, lb
N-2
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Pn,max
= maximum nominal axial compressive strength of a member, lb
Po
= nominal axial strength at zero eccentricity, lb
Pu
= factored axial force; to be taken as positive for compression and negative for tension, lb
qa
= allowable bearing capacity of the soil or rock, lb/ft2
qu
= factored load per unit area, lb/ft2
r
= bend radius of a reinforcing bar
Rn
= nominal strength coefficient of resistance
s
= center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or
anchors, in.
so
= center-to-center spacing of transverse reinforcement within the length ℓo, in.
Vc
= nominal shear strength provided by concrete, lb
Vu
= factored shear force at section, lb
W
= length of drop panel measured in the direction perpendicular to L
Ff
= ratio of flexural stiffness of beam section to flexural stiffness of a width of slab bounded laterally by centerlines
of adjacent panels, if any, on each side of the beam
G
= ratio of long to short dimensions: clear spans for two-way slabs, sides of column, concentrated load or reaction
area; or sides of a footing
Q
= modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normal weight
concrete of the same compressive strength
W
= ratio of As to bd
Wℓ
= ratio of area of distributed longitudinal reinforcement to gross concrete area perpendicular to that reinforcement
Ws
= ratio of volume of spiral reinforcement to total volume of core confined by the spiral, measured out-to-out of
spirals
Wt
= ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to that reinforcement
K
= strength reduction factor
Ωo
= amplification factor to account for overstrength of the seismic-force-resisting system determined in accordance
with the general building code
Concrete Reinforcing Steel Institute
N-3
Design Guide for Economical Reinforced Concrete Structures
Notes
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Notes
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Notes
Concrete Reinforcing Steel Institute
Design Guide for Economical Reinforced Concrete Structures
Notes
Concrete Reinforcing Steel Institute
Description of Manual
The purpose of this guide is to present information on how to
select economical reinforced concrete floor systems and to present
requirements and guidelines on how to size, design, and detail
reinforced concrete structural members that, where implemented,
will result in economical reinforced concrete structures.
ISBN 9781943961207
Concrete Reinforcing
Steel Institute
[
[
[
933 North Plum Grove Road Schaumburg, IL 60173 Tel. 847.517.1200 www.crsi.org
9 781943 961207
10-DG-STRUCTURES-2016-2m