Seismic Design of Cast-in-Place Concrete Special Structural Walls

NEHRP Seismic Design Technical Brief No. 6

Seismic Design of Cast-in-Place

Concrete Special Structural

Walls and Coupling Beams

A Guide for Practicing Engineers

NIST GCR 11-917-11REV-1

Jack P. Moehle

Tony Ghodsi

John D. Hooper

David C. Fields

Rajnikanth Gedhada

About The Authors

Jack P. Moehle, Ph.D., P.E., is T.Y. and Margaret Lin Professor of

Engineering at the University of California, Berkeley, where he teaches

and conducts research on earthquake-resistant concrete construction.

He is a Fellow of the American Concrete Institute, and has served on

the ACI Code Committee 318 since 1989 and as chair of the seismic

subcommittee since 1995. He is a Fellow of the Structural Engineers

Association of California and Honorary Member of the Structural

Engineers Association of Northern California.

Tony Ghodsi, P.E, S.E., is a Principal at Englekirk Structural Engineers, a

structural engineering rm headquartered in Los Angeles, California. He

is a member of the Los Angeles Tall Buildings Structural Design Council

and on the Board of Advisors at the University of Southern California

Department of Civil and Environmental Engineering.

About the Review Panel

The contributions of the three review panelists for this publication are

gratefully acknowledged.

D. E. Lehman. Ph.D., is the John R. Kiely Associate Professor of Civil

and Enviornmental Engineering at the University of Washinton. She

conducts research on seismic response of engineered structures with

an emphasis on the use of large-scale experimental methods. She is

also the Director of the Structural Research Laboratory at the University

of Washington.

John W. Wallace, Ph.D., P.E., is Professor of Structural/Earthquake

Engineering at the University of California, Los Angeles, where he

teaches and conducts research on earthquake-resistant concrete

construction. He is a Fellow of the American Concrete Institute and

has served on the ACI 318 seismic subcommittee since 1995. He also

has served as a member of the American Society of Civil Engineers

Seismic Subcommittee for ASCE 7-05 and the ASCE 41-06 Supplement

#1 concrete provisions update committee. He is a member of the Los

Angeles Tall Buildings Structural Design Council.

Loring A. Wyllie, Jr. is a Structural Engineer and Senior Principal of

Degenkolb Engineers in San Francisco, California. He is the 2007

recipient of the American Society of Civil Engineers Outstanding

Projects and Leaders (OPAL) design award. He is a past president of

the Structural Engineers Association of California and the Earthquake

Engineering Research Institute. He is a member of the Structural

Concrete Building Code Committee 318 of the American Concrete

Institute and an Honorary Member of ACI.

National Institute of

Standards and Technology

The National Institute of Standards and Technology (NIST) is a federal

technology agency within the U.S. Department of Commerce that

promotes U.S. innovation and industrial competitiveness by advancing

measurement science, standards, and technology in ways that enhance

economic security and improve our quality of life. It is the lead agency

of the National Earthquake Hazards Reduction Program (NEHRP).

Dr. John (Jack) R. Hayes, Jr. is the Director of NEHRP, within NIST’s

Engineering Laboratory (EL). Dr. Jeffery J. Dragovich managed the

project to produce this Technical Brief for EL.

NEHRP Consultants Joint Venture

This NIST-funded publication is one of the products of the work of

the NEHRP Consultants Joint Venture carried out under Contract

SB134107CQ0019, Task Order 10254. The partners in the NEHRP

Consultants Joint Venture are the Applied Technology Council (ATC) and

the Consortium of Universities for Research in Earthquake Engineering

(CUREE). The members of the Joint Venture Management Committee

are James R. Harris, Robert Reitherman, Christopher Rojahn, and

Andrew Whittaker, and the Program Manager is Jon A. Heintz.

Consortium of Universities for Research in

Earthquake Engineering (CUREE)

1301 South 46th Street - Building 420

Richmond, CA 94804

(510) 665-3529

www.curee.org email: [email protected]

Applied Technology Council (ATC)

201 Redwood Shores Parkway - Suite 240

Redwood City, California 94065

(650) 595-1542

www.atcouncil.org email: [email protected]

NEHRP Seismic Design

Technical Briefs

The National Earthquake Hazards Reduction Program (NEHRP)

Technical Briefs are published by the National Institute of Standards

and Technology (NIST), as aids to the efcient transfer of NEHRP and

other research into practice, thereby helping to reduce the nation’s

losses from earthquakes.

John D. Hooper, P.E., S.E., is Director of Earthquake Engineering at

Magnusson Klemencic Associates, a structural and civil engineering rm

headquartered in Seattle, Washington. He is a member of the Building

Seismic Safety Council’s 2014 Provisions Update Committee and chair

of the American Society of Civil Engineers Seismic Subcommittee for

ASCE 7-10.

David C. Fields, P.E., S.E., is a Senior Project Manager at Magnusson

Klemencic Associates, a structural and civil engineering firm

headquartered in Seattle, Washington. He is a member of American

Concrete Institute Committee 374: Performance Based Design of

Concrete Buildings and the Structural Engineers Association of

Washington Earthquake Engineering Committee.

Rajnikanth Gedhada, P.E., S.E., is a Project Structural Engineer

at Englekirk Structural Engineers, a structural engineering firm

headquartered in Los Angeles, California. He is a member of the

Structural Engineers Association of Southern California.

Jack P. Moehle, Ph.D., P.E.

University of California, Berkeley

Tony Ghodsi, P.E., S.E.

Englekirk Structural Engineers

John D. Hooper, P.E., S.E.

Magnusson Klemencic Associates

David C. Fields, P.E., S.E.

Magnusson Klemencic Associates

Rajnikanth Gedhada, P.E., S.E.

Englekirk Structural Engineers

August 2011

Revised March 2012

Prepared for

U.S. Department of Commerce

Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-8600

Seismic Design of Cast-in-Place Concrete

Special Structural Walls and

Coupling Beams

A Guide for Practicing Engineers

NIST GCR 11-917-11REV-1

U.S. Department of Commerce

John Bryson, Secretary

National Institute of Standards and Technology

Patrick D. Gallagher, Under Secretary of Commerce for

Standards and Technology and Director

Disclaimers

This Technical Brief was prepared for the Engineering Laboratory of the National Institute of Standards and Technology (NIST) under the

National Earthquake Hazards Reduction Program (NEHRP) Earthquake Structural and Engineering Research Contract SB134107CQ0019,

Task Order 10254. The statements and conclusions contained herein are those of the authors and do not necessarily reect the views

and policies of NIST or the U.S. Government.

This report was produced by the NEHRP Consultants Joint Venture, a partnership of the Applied Technology Council (ATC) and the

Consortium of Universities for Research in Earthquake Engineering (CUREE). While endeavoring to provide practical and accurate

information, the NEHRP Consultants Joint Venture, the authors, and the reviewers assume no liability for, nor express or imply any

warranty with regard to, the information contained herein. Users of the information contained in this report assume all liability arising

from such use.

The policy of NIST is to use the International System of Units (metric units) in all of its publications. However, in North America in the

construction and building materials industry, certain non-SI units are so widely used instead of SI units that it is more practical and less

confusing to include measurement values for customary units only in this publication.

Cover photo – Reinforcing of special reinforced concrete walls, Engineering 5 Building, UCLA.

How to Cite this Publication

Moehle, Jack P., Ghodsi, Tony, Hooper, John D., Fields, David C., and Gedhada, Rajnikanth (2011). “Seismic design of cast-in-place concrete

special structural walls and coupling beams: A guide for practicing engineers,”

NEHRP Seismic Design Technical Brief No. 6

, produced by

the NEHRP Consultants Joint Venture, a partnership of the Applied Technology Council and the Consortium of Universities for Research

in Earthquake Engineering, for the National Institute of Standards and Technology, Gaithersburg, MD, NIST GCR 11-917-11REV-1.

Introduction..............................................................................................1

The Use of Special Structural Walls................................................................2

Principles for Special Structural Wall Design...................................................7

Building Analysis Guidance.......................................................................11

Design Guidance......................................................................................13

Additional Requirements...........................................................................27

Detailing & Constructability Issues..............................................................30

References.............................................................................................33

Notation and Abbreviations........................................................................34

Credits....................................................................................................37

10.

Contents

Errata to GCR 11-917-11

Updated: March 2012

The following errors were contained in the August 2011 Edition of Technical Brief No. 6.

The error was in the last paragraph of Section 5.1, where it said: “For coupling beams,

= 0.85 for shear and 0.9

for exure.” The correction in this version says: “For diagonally reinforced coupling beams,

= 0.85 for shear. For

conventionally reinforced coupling beams,

= 0.75 for shear and 0.9 for exure.”

In the paragraph following Figure 5-1 on page 14, “c = 0.1l

” should be “c – 0.1l

”. Also the rst full paragraph in

the second column on page 20 includes the term (480 + 0.8f ’

cv. It should be

(480 + 0.08f ’

cv.

On page 22, the bold text following bullet b. should read “Coupling beams with l

/h < 2 and V

> 4

√f ’

”

The term A

was missing.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

The basic structural elements of an earthquake-resistant

building are diaphragms, vertical framing elements, and the

foundation. In reinforced concrete buildings, the vertical

elements are usually either moment-resisting frames or

structural walls (sometimes referred to as shear walls). Special

reinforced concrete structural walls are walls that have been

proportioned and detailed to meet special code requirements

for resisting combinations of shear, moment, and axial force

that result as a building sways through multiple displacement

cycles during strong earthquake ground shaking. Special

proportioning and detailing requirements result in a wall

capable of resisting strong earthquake shaking without

unacceptable loss of stiffness or strength.

Although special structural walls can be used in any building,

the International Building Code (IBC 2009) only requires

them wherever cast-in-place or precast walls are used to resist

seismic forces in new buildings assigned to Seismic Design

Category D, E, or F. The design force levels are specied in

Minimum Design Loads for Buildings and Other Structures

(ASCE/SEI 7-10) (ASCE 2010), and the design proportions

and details are dened in the Building Code Requirements

for Structural Concrete (ACI 318-11) and Commentary (ACI

2011). This Guide uses units of measure consistent with these

codes and standards, (e.g., inches, pounds, pounds per square

inch).

The design requirements for special structural walls are

governed by numerous interrelated requirements in these

three building codes or standards, making their application

challenging for even the most experienced designers. This

Guide rst describes the use of structural walls, then claries

intended behavior, and nally lays out the design steps and

details so that design and construction can be accomplished

efciently. The Guide is intended especially for the practicing

structural engineer, though it will also be useful for building

ofcials, educators, and students.

This Guide emphasizes the most common types of special

reinforced concrete structural walls, which use cast-in-

place, normalweight aggregate concrete and deformed, non-

prestressed reinforcement. Wall congurations vary depending

on the application, and may include coupling beams. Building

codes permit the use of special walls using precast concrete,

lightweight aggregate concrete, or prestressed reinforcement.

Building codes also permit the use of ordinary cast-in-place

structural walls in buildings assigned to Seismic Design

Category A, B, or C, and intermediate precast walls in some

buildings assigned to Seismic Design Category A, B, C, D, E,

or F. The interested reader is referred to ACI 318 for specic

requirements for these other systems, which are outside the

scope of this Guide.

1. Introduction

Sidebars in the Guide

Sidebars are used in this Guide to illustrate key points

and to provide additional guidance on good practices and

open issues in analysis, design, and construction.

Codes Referenced in this Guide

U.S. building codes are continually undergoing revisions

to introduce improvements in design and construction

practices. At the time of this writing, the building code

editions most commonly adopted by state and local

jurisdictions include the 2009 edition of the IBC, the

2005 edition of ASCE 7, and the 2008 edition of ACI

318. This Guide is written, however, according to the

latest editions of each of these documents, that is, IBC

(2009), ASCE 7 (2010), and ACI 318 (2011). In general,

the latest editions of these three documents are well

coordinated regarding terminology, system denition,

application limitations, and overall approach. The most

signicant changes relative to the previous editions

include:

ASCE 7 (2010) introduces Risk-targeted Maximum

Considered Earthquake (MCE

) ground motions

and replaces “occupancy categories” with “risk

categories.”

ACI 318 (2011) introduces provisions for wall piers

and modies requirements for anchorage of wall

horizontal reinforcement in wall boundaries.

Hereafter, this Guide uses IBC to refer to IBC 2009,

ASCE 7 to refer to ASCE 7 2010, and ACI 318 to refer

to ACI 318-2011.

•

This Guide emphasizes code requirements and accepted

approaches to their implementation. It also identies good

practices that go beyond the code minimum requirements.

Background information and illustrative sketches clarify the

requirements and recommendations.

Sections 2 and 3 describe the use of structural walls in

buildings and discuss intended behavior. Section 4 provides

analysis guidance. Section 5 presents the design and detailing

requirements of ACI 318 along with guidance on how to apply

them. Section 6 presents additional requirements for wall

buildings assigned to Seismic Design Category D, E, or F, and

Section 7 presents detailing and constructability challenges

for special structural walls with illustrative construction

examples.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

2.1 Structural Walls in Buildings

Walls proportioned to resist combinations of shears, moments,

and axial forces are referred to as structural walls. A special

structural wall is one satisfying the requirements of ACI

318, Chapter 21, intended to result in strength and toughness

required to resist earthquake effects in buildings assigned to

Seismic Design Categories D, E, or F. In buildings, they are

used in many different congurations; some are illustrated

in Figure 2-1. Solid walls are widely used to brace low-rise

buildings. Sometimes walls are perforated with openings. In

taller buildings, walls cantilever from a foundation to provide

bracing over the building height. Isolated walls can be

connected using coupling beams extending between window

and door openings, creating a coupled wall system that is stiffer

and stronger than the isolated pair of walls.

Structural Walls and Shear Walls

ACI 318 refers to structural walls and, with regard to

Seismic Design Categories D through F, special structural

walls. The equivalent terms used by ASCE 7 are shear

walls and special shear walls.

ASCE 7 imposes height limits for buildings in which special

structural walls compose the seismic force-resisting system,

specically 160 ft in Seismic Design Category D and E and

100 ft in Seismic Design Category F. These heights can be

increased to 240 ft and 160 ft, respectively, if the building

does not have an extreme torsional irregularity and the shear

in any line of walls does not exceed 60 % of the total story

shear (ASCE 7 § 12.2.5.4). There is no height limit for a dual

system combining walls with special moment frames capable

of resisting at least 25 % of prescribed seismic forces.

2.3 Wall Layout

Structural walls are generally stiff structural elements

whose placement in a building can strongly affect building

performance. Walls should be proportioned and located

considering the range of loads the building will experience

during its service life. The engineer and architect should work

together to arrive at a building conguration in which walls

are located to meet structural, architectural, and programmatic

requirements of the project.

2.3.1 Plan Layout

Walls should be well distributed within the building plan, with

multiple walls providing resistance to story shears in each

principal direction. Preferably, long diaphragm spans are

avoided. Furthermore, the walls should be positioned such

that their center of resistance is close to the center of mass,

thereby avoiding induced torsion (Figure 2-2). Walls located

near the perimeter may be preferred because they maximize

torsional resistance.

Tributary gravity loads help resist wall overturning moments,

reducing reinforcement and foundation uplift demands.

Therefore, it may be desirable to move walls inward from the

perimeter and away from adjacent columns so that they support

2. The Use of Special Structural Walls

Figure 2-1

– Some illustrative structural wall elevations.

2.2 When to Use Structural Walls

Selection of special structural walls as primary seismic force-

resisting elements is inuenced by considerations of seismic

performance, functionality, constructability, and cost. For low-

to mid-rise buildings, structural walls typically are more cost-

effective than other systems such as concrete special moment

frames. Structural walls are used in concrete buildings with

limited oor-to-oor heights or other architectural constraints

that cannot accommodate frame beam depths. Stairway

and elevator cores are natural locations for structural walls,

which serve a dual purpose of enclosing vertical shafts while

providing efcient axial and lateral resistance.

Building Torsion

ASCE 7 contains provisions that quantify torsional

irregularity, including penalties for large irregularities. The

code requirements refer only to linear-elastic response.

If a building is expected to respond inelastically, the

center of resistance ideally should coincide with center

of mass for both linear response and for response at

strength level. Where identical walls are symmetrically

placed (e.g., walls a and b in Figure 2-2a), this objective

is relatively easy to achieve. Additional design effort is

required where walls are asymmetrically arranged.

(b) Perforated wall (c) Slender wall (d) Coupled wall

(a) Low-rise wall

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

more gravity loads, as in Wall e in Figure 2-2a, even though

this reduces plan torsion resistance. Too much axial force can

result in undesirable compression-controlled exural response.

A good plan layout balances these competing objectives.

In buildings with post-tensioned slabs, stiff in-line walls can

act to resist slab elastic and creep shortening, sometimes with

deleterious effect. Walls c and d (Figure 2-2) would resist

slab shortening along line cd, such that post-tensioning force

would tend to transfer from the slab and into the walls. Walls

a, b, and e are well positioned to allow slab shortening.

Walls extending from the foundation and discontinued at some

intermediate level (Figure 2-3b) are permitted by ASCE 7, but

the design is penalized by increased seismic design forces. It is

preferred to have more gradual reduction in wall section (either

length, thickness, or both), as illustrated by Figure 2-3c.

Openings in walls disrupt the ow of forces and are best located

in regular patterns that produce predictable force transfers.

Figures 2-1b and d show examples of regularly located wall

openings. For such buildings, good design practice keeps

vertical wall segments (piers) stronger than beams so that story

failure mechanisms are avoided. Sometimes programmatic

demands require openings in a less regular pattern (Figure

2-3c). These should be avoided where feasible. Where

unavoidable, they require additional design and detailing effort

to develop force transfers around openings. See Section 5.9.

2.3.3 Diaphragm Connectivity

In a building braced by structural walls, inertial forces

generated by building vibration are transmitted through

diaphragms to the walls, which in turn transmit the forces to

the foundation. Good connections between diaphragms and

structural walls are essential to the seismic force path. This

subject is discussed in depth by Moehle et al. (2010).

Programmatic requirements often locate diaphragm openings

adjacent to structural walls, complicating the seismic force path.

This can be especially acute at podium slabs where large wall

forces may be transferred through the diaphragm to other stiff

elements (Figure 2-5a). Good diaphragm transfer capacity is

facilitated by solid diaphragms surrounding walls, rather than

signicantly perforated diaphragms (Figure 2-5b).

Figure 2-2

– Example plan layout. C.M. refers to center of mass.

2.3.2 Vertical Discontinuities

Considerations of function and cost sometimes lead to wall

openings and other wall discontinuities. Under lateral load-

ing, these irregularities can lead to stress concentrations and

localized lateral drift that may be difcult to quantify and

accommodate in design, and in some cases may result in

undesirable seismic response. Some irregularities should be

avoided without further consideration; other cases will require

additional analysis and design effort.

In the past, demand for open space in the rst story led to

many older buildings in which walls from upper stories

were discontinued in the rst story, creating a weak rst

story (Figure 2-3a). These have performed poorly in past

earthquakes (Figure 2-4). This conguration, classied by

ASCE 7 as an Extreme Weak Story Irregularity, is no longer

permitted in new buildings assigned to Seismic Design

Categories D, E, or F.

Figure 2-3

– Wall vertical irregularities.

Figure 2-4

– Weak story damage, 1971 San Fernando earthquake.

(a) Weak story (b) Discontinuous

wall

wall section

(a) Wall plan layout

(b) NS forces

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

2.4 Wall Foundations

In low-rise buildings with long walls supporting sufcient

gravity loads, spread footings may be adequate to resist design

overturning moments. For higher overturning demands, pile

foundations, possibly including tension tie-down capacity, can

be used. More commonly, foundation elements are extended to

pick up additional gravity loads. Figure 2-6a shows a grade

beam acting as a foundation outrigger. Basement walls also

can be proportioned to act as outrigger elements (Figure 2-6b) .

Alternatively, a wall extending into subterranean levels can

use a horizontal force couple formed between the grade-level

diaphragm and diaphragms below to transfer the overturning

moment to adjacent basement walls (Figure 2-6c).

If none of these solutions work, foundation rocking may need

to be accepted. U.S. building codes do not recognize uplifting

walls as an accepted seismic force-resisting system; either

special approval is required or the wall cannot be counted on

to provide seismic force resistance. Regardless, uplifting walls

can impose large deformation demands on adjacent framing

members that should be accommodated through design.

2.5 Wall Congurations

Special structural walls can be congured in numerous ways

(Figure 2-7). Rectangular cross sections are relatively easy to

design and construct; very thin sections can have performance

problems and should be avoided. “Bar bell” walls have

Figure 2-6

– Various ways to spread overturning resistance.

Figure 2-5

– Force transfers between walls and diaphragms.

Figure 2-7

– Various wall cross sections.

Figure 2-8

– Vertical and horizontal wall segments (hatched).

boundary columns that contain longitudinal reinforcement

for moment resistance, improve wall stability, and create an

element to anchor beams framing into the wall. The boundary

columns, however, might create an architectural impediment

and increase forming costs. Intersecting wall segments can

be combined to create anged walls, including T, L, C, and

I congurations. Core walls enclose elevators, stairways,

and other vertically extruded areas, with coupling beams

connecting wall components over doorways. In these walls,

any wall segment aligned parallel to the lateral shear force

acts as a web element resisting shear, axial force, and exure,

while orthogonal wall segments act as tension or compression

anges.

Walls with openings are considered to be composed of ver tical

and horizontal wall segments (Figure 2-8). A vertical wall

segment is bounded horizontally by two openings or by an

opening and an edge. Similarly, a horizontal wall segment is

bounded vertically by two openings or by an opening and an

edge. Some walls, including some tilt-up walls, have narrow

vertical wall segments that are essentially columns, but whose

dimensions do not satisfy requirements of special moment

frame columns. In consideration of these, ACI 318 denes

a wall pier as a vertical wall segment having l

≤ 6.0 and

≥ 2.0. The lower left vertical wall segment in Figure

2-8b might qualify as a wall pier. Special provisions apply

to wall piers (Section 5.7).

(a) Foundation

outrigger

(b) Coupled walls on

basement walls

by diaphragm couple

(a) Horizontal wall segments (b) Vertical wall segments

(a) Elevation (b) Section A

(a) Rectangular shape (b) “Bar bell” shape

(d) Possible conguration of a core-wall

coupling beam

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

The distributed web reinforcement ratios,

for vertical

reinforcement and

for horizontal reinforcement, must

be at least 0.0025, except that

and

are permitted to be

reduced if V

≤

λ√f ’

. Reinforcement spacing each way

is not to exceed 18 inches. At least two curtains (layers) of

reinforcement are required if V

λ√f ’

. Reinforcement

also is to be designed for wall shear forces, as described

in Section 5.4. Finally, if h

≤ 2.0,

is not to be less than

the provided

. ACI 318 has no requirements about whether

vertical or horizontal distributed reinforcement should be in the

outer layer, although lap splices of vertical reinforcement will

perform better if horizontal bars are placed outside the vertical

bars as shown in Figure 2-10.

The term coupled wall refers to a system in which cantilever

walls are connected by coupling beams aligned vertically

over wall height (Figure 2-9). The design goal is to develop

a ductile yielding mechanism in the coupling beams over the

height of the wall followed by exural yielding at the base

of the individual cantilever walls. Depending on geometry

and design forces, a coupling beam can be detailed as either

a conventionally reinforced beam or diagonally reinforced

beam. See Section 5.8.

In taller buildings, outriggers can be used to engage adjacent

columns, thereby increasing building stiffness and reducing

upper-story drifts. Outriggers can be incorporated conveniently

in oors housing mechanical equipment or at the roof level.

2.6 Wall Reinforcement

Figure 2-10 illustrates typical reinforcement for a special

structural wall of rectangular cross section. As a minimum, a

special structural wall must have distributed web reinforcement

in both horizontal and vertical directions. In many cases, a

special structural wall also will have vertical reinforcement

concentrated at the wall boundaries to provide additional

resistance to moment and axial force. Typically, longitudinal

reinforcement is enclosed in transverse reinforcement to

conne the concrete and restrain longitudinal bar buckling.

Figure 2-9

– Coupled wall geometry and target yield mechanism.

Figure 2-10

– Typical reinforcement for rectangular wall.

A boundary element is a portion along a structural wall edge

or opening that is strengthened by longitudinal and transverse

reinforcement. Where combined seismic and gravity loading

results in high compressive demands on the edge, ACI 318

requires a special boundary element. These have closely spaced

transverse reinforcement enclosing the vertical boundary bars

to increase compressive strain capacity of core concrete and to

restrain longitudinal bar buckling. See Section 5.3.3.

2.7 Wall Proportioning

Walls should be proportioned to satisfy strength and drift limit

requirements of ASCE 7, unless an alternative approach is

approved. According to ASCE 7, walls are designed for load

combinations in which seismic forces, E, are determined using

a force reduction factor, R. The value of R depends on whether

the wall is part of a Dual System (R = 7), a Building Frame

System (R = 6), or a Bearing Wall System (R = 5). To qualify as

a Dual System, the special structural walls must be combined

with special moment frames capable of resisting at least 25 %

of prescribed seismic forces. If it does not qualify as a Dual

System, then it can qualify as a Building Frame System if it

has an essentially complete space frame providing support for

vertical loads, with structural walls providing seismic force-

resistance. If there is not a complete space frame providing

support for vertical loads, the system must be designed as a

Bearing Wall System.

Building Frame System versus Bearing

Wall System

Different jurisdictions interpret the ASCE 7 provisions

differently. San Francisco (DBI, 2009) declares the

wall to be a bearing wall if it supports more than 5 %

of the entire building oor and roof loads in addition

to self-weight. SEAW (2009) recommends designing

a frame column into the wall boundary capable of

supporting tributary gravity loads, such that R = 6

can be used regardless of the tributary loads on the

wall. SEAOC (2008) recommends R = 6 without the

need to add a frame column where conned boundary

elements are provided. This Guide recommends

checking with the local jurisdiction. Note that ACI

318 and ASCE 7 dene a bearing wall as any wall that

supports more than 200 lb/linear ft of vertical load in

addition to self-weight. This denition of bearing wall

should not be confused with the Bearing Wall System

designation of ASCE 7.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

ASCE 7 species drift limits as a function of building height

and Occupancy Category (Table 2-1). Drift is calculated using

the design seismic forces E amplied by C

(ASCE 7 § 12.8.6).

is 5 for both Bearing Wall and Building Frame Systems and

is 5.5 for Dual Systems.

Table 2-1

– Allowable Interstory Drift Ratios per ASCE 7.

Although cost considerations might suggest designing

minimum-weight sections, such sections may be difcult to

construct and might not perform well. Once the decision has

been made to incorporate a wall in the building, formwork

and reinforcement detailing will dominate costs. Selecting a

thicker wall section is unlikely to have an appreciable effect on

construction cost or functionality, but will reduce reinforcement

congestion and improve earthquake performance. Although

ACI 318 has no prescriptive minimum thickness, 8 inches is a

practical lower limit for special structural walls. Construction

and performance are generally improved if the wall thickness

is at least 12 inches where special boundary elements are

used and at least 10 inches elsewhere. Walls that incorporate

coupling beams require a minimum thickness of approximately

14 inches to accommodate reinforcement, required cover, and

bar spacing, although 16 inches is a practical minimum where

diagonally reinforced coupling beams are used. Flanges and

enlarged boundary sections are helpful to stabilize boundaries

and anchor reinforcement from adjacent members.

See Section 5 for guidance on wall proportioning.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

In some cases, alternative mechanisms have to be accepted.

In very tall buildings, higher-mode response may cause some

wall exural yielding in intermediate stories in addition to

the primary yielding mechanism. Detail such locations so

they are capable of moderate ductility capacity. In highly

irregular walls, including walls with irregular openings, it

can be difcult to precisely identify and control the yielding

mechanism. Some conservatism in the design of these systems

can help achieve the desired performance.

3.1.2 Achieve Ductile Flexural Yielding

The intended critical section should be proportioned and

detailed to be capable of multiple inelastic cycles. Key factors

to improving cyclic ductility are (a) keep global compressive

and shear stresses low; (b) design a conned, stable exural

compression zone; and (c) avoid splice failures.

A good wall design keeps the axial force well below the

balanced point, such that exural tension reinforcement yields

before the exural compression zone reaches the compressive

strain capacity. Using ACI 318 terminology, compression-

controlled walls (concrete reaches strain of 0.003 before tension

reinforcement yields) should be avoided. It is noteworthy that

the 1997 Uniform Building Code § 1921.6.6.4(3) (UBC 1997)

limited wall axial force to P

≤

0.35P

, which corresponds

approximately to the balanced axial force in a symmetric wall.

ACI 318 does not have any limits on the wall axial force.

Although ACI 318 permits factored shear on individual wall

segments as high as V

√f ’

, the exural ductility

capacity for such walls is reduced compared with identical

walls having lower shear. This Guide recommends factored

shear, calculated considering exural overstrength (see Section

3.1.3), not exceed approximately 4

√f ’

to 6

√f ’

so that

exural ductility capacity is not overly compromised.

Buildings designed according to the provisions of ACI 318

Chapter 21 and ASCE 7 are intended to resist earthquake

motions through ductile inelastic response of selected

members. For structural walls, the nature and extent of

inelastic response will vary with wall layout and aspect

ratio. A good design anticipates the inelastic mechanism and

provides proportions and details in the wall that will enable

it to respond as intended. The following sections summarize

the key principles for the design of structural walls. Detailed

design guidance is presented later in the Guide.

3. Principles for Special Structural Wall Design

Slender versus squat walls

Expected behavior of walls depends partly on wall

aspect ratio. Slender walls (h

≥ 2.0) tend to behave

much like exural cantilevers. The preferred inelastic

behavior mode of slender walls is ductile flexural

yielding, without shear failure. In contrast, walls

with very low aspect ratios (h

≤

0.5) tend to resist

lateral forces through a diagonal strut mechanism in

which concrete and distributed horizontal and vertical

reinforcement resist shear. Wall behavior transitions

between these extremes for intermediate aspect ratios.

Shear yielding of slender walls generally is considered

unacceptable because it reduces inelastic deformation

capacity below expected values. Shear yielding of

very squat walls is often accepted because such walls

tend to have high inherent strength and low ductility

demands.

3.1 Slender Walls

3.1.1 Select Intended Yield Mechanism

For slender walls, the design should aim to achieve ductile

exural yielding at the base of the wall. For slender coupled

walls, the target mechanism should include ductile yielding of

coupling beams over the height of the wall plus ductile exural

yielding at the base of the walls. Wall shear failure and failure

of diaphragms and foundations generally should be avoided.

See Figures 2-9 and 3-1.

Where the design intent is to have a single critical section

for flexure and axial force, the designer should provide

a distribution of strength over wall height that inhibits

yielding at other critical sections. One approach is to design

the selected critical section to have strength in exure and

axial closely matching the required strength, with some

overstrength provided at other locations (Figure 3-1). Where

this approach is used, the special details for ductile response

can be concentrated around the selected critical section, with

relaxed detailing elsewhere.

Figure 3-1

– Provided versus required exural strength in a wall

with a single critical section.

(b) Moments(a) Wall elevation

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

Inelastic exural response may result in concrete compressive

strains exceeding the unconned crushing strain, typically

taken as 0.003. If the exural compression zone lacks properly

detailed transverse reinforcement, concrete crushing and

vertical reinforcement buckling at a section can result in a

locally weakened “notch” where deformations concentrate,

leading to relatively brittle behavior (Figure 3-2). Transverse

reinforcement is necessary to conne the boundary, thereby

enhancing concrete strain capacity and restraining longitudinal

bar buckling. The special boundary element transverse

reinforcement should comprise closely spaced hoops with

crossties engaging peripheral longitudinal bars (Figure 2-10).

In excessively thin walls, spalling of cover concrete can leave

a relatively narrow core of conned concrete that can be

unstable under compressive loading. This Guide recommends

a minimum wall thickness of 12 inches for sections requiring

special boundary elements unless tests on representative

sections demonstrate adequate performance for thinner

sections. Concrete cover over connement reinforcement

should be minimized such that cover spalling, if it occurs, will

not result in a large reduction in section area. Good detailing

practice also provides lateral support for every longitudinal bar

in special boundary elements located within the intended hinge

region. ACI 318 permits somewhat less stringent detailing

(see Section 5.3.3).

Figure 3-2

– Concrete crushing and reinforcement buckling of

inadequately conned wall, 2010 Chile earthquake.

to loading in the opposite direction, leaving a more exible pre-

cracked section. ACI 318 has no limits on slenderness of special

structural walls. This Guide recommends l

/b ≤ 10 within the

intended hinge region and l

/b ≤ 16 (the limit prescribed in the

1997 Uniform Building Code) elsewhere.

3.1.3 Avoid Shear Failure

Shear failure in a slender structural wall can lead to rapid

strength loss at drifts below those anticipated in design. Shear

failure also can compromise the wall axial strength. This is

especially so for walls resisting high shear forces (exceeding

around 10√f ’

), because shear failure in such walls can occur

by web cr ushing (Figure 3 - 4). For these reasons, the engineer

should design slender walls to avoid shear failure.

Lap splices of vertical reinforcement can result in a locally

strengthened section, such that yielding, if it occurs, may be

shifted above or below the lap splice. Consequences of this

shift should be considered. Lap splices subjected to multiple

yielding cycles can “unzip” unless they are conned by closely

spaced transverse reinforcement. For such splices, ACI 318

requires splice lengths at least 1.25 times lengths calculated for

in tension, with no requirement for connement. This Guide

recommends either that lap splices be moved out of the hinge

zone or else be conned by transverse reinforcement.

Slender boundary zones can be susceptible to overall buckling

under compressive loading (Figure 3-3). The problem can be

exacerbated if the section was yielded previously in tension due

Figure 3-3

– Wall buckling, 2011 Christchurch earthquake.

Figure 3-4

– Web crushing due to high shear force in laboratory test.

Design procedures in ACI 318 and ASCE 7 require consideration

of multiple load combinations, and this invariably leads to

exural strength M

n,CS

that, under some load combinations,

exceeds the required exural strength M

u,CS

(Figure 3-5).

Consequently, the lateral forces required to yield the wall in

exure, and the resulting wall shears, will be higher than the

design values. A good practice is to amplify the design shear

to account for this effect. One approach is to dene a exural

overstrength factor

= M

n,CS

u,CS

, which reects how much

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

exural overstrength is built into the wall, and to increase the

design shears by this same factor. ACI 318 encourages this

approach by permitting a higher strength reduction factor

for shear when this approach is used (See Section 5.1).

Anticipating that the wall will develop even higher exural

strength due to material overstrength and strain-hardening,

SEAOC (2008) recommends

= M

pr,CS

u,CS

. Note that M

n,CS

and M

pr,CS

depend on axial force, which varies for different load

combinations and, for coupled walls, with loading direction.

This Guide recommends using the load combination producing

the most conservative value of

wall area and concrete compressive strength. See Section

5.4. Sliding shear failure is evident in horizontal cracks and

sliding along construction joints and is controlled by proper

treatment of construction joints, including surface roughening

and possibly intermittent shear keys, as well as placement

of vertical reinforcement across the potential sliding plane

(Section 5.5).

3.2 Squat Walls

Walls tend to have high inherent exural strength and thus

are prone to inelastic response in shear rather than exural

yielding. Contrary to slender walls, such behavior can provide

sufcient post-yield stiffness and deformation capacity.

Squat walls are prone to two types of shear failure. “Shear

yielding” within the wall web involves development of inclined

cracks (Figure 3-6). Horizontal force equilibrium of segment

cde requires distributed horizontal reinforcement providing

force F

. Moment equilibrium of segment cde about e, or

segment ab about b, requires distributed vertical reinforcement

providing force F

. Thus, ACI 318 requires both vertical and

horizontal reinforcement to resist shear in squat walls. “Shear

sliding” tends to occur at construction joints, including the

wall-foundation interface. Axial force N

and distributed

vertical reinforcement A

(including added dowels) provide

a clamping force across the interface that resists sliding.

Reinforcement A

is most effective if distributed. Thus, it may

be preferred to distribute the exural reinforcement uniformly

without concentrated boundary elements. Reinforcement A

is more effective in resisting sliding if oriented at an angle

of ± 45°, although this creates a constructability challenge.

When concrete is placed against previously hardened concrete

at this interface, ACI 318 requires the surface be clean and

free of laitance. Intentional roughening increases sliding

resistance.

Figure 3-6

– Shear yielding and shear sliding in a squat wall.

Figure 3-5

– Wall lateral forces, shears, and moments; code-prescribed

forces and code-prescribed forces corresponding to development of

nominal exural strength.

(a) Lateral forces

(b) Wall elevation

(d) Moment

In multi-story buildings, dynamic response produces ever-

changing patterns of lateral inertial forces. Some prevalent

force patterns shift the centroid of lateral forces downward,

further increasing the shear forces corresponding to exural

strength at the critical section. To approximate this effect,

the design shear can be increased to V’

wϕ

, where

is a

dynamic amplication factor. For buildings designed by the

equivalent lateral force procedure (Section 4.1), SEAOC (2008)

recommends

= (0.9 + N/10) for buildings up to 6 stories and

(1.3 + N/30) for buildings over 6 stories. If shears are based on

modal response spectrum analysis,

need not exceed (1.2 +

N/50). N is the number of stories from base to roof, assuming

typical story heights. Equivalent story heights should be used

in buildings with unusually tall stories. Eurocode (2004) has

an alternative formulation. ACI 318 and ASCE 7 do not require

designing for this dynamic amplication factor.

Designing a wall to avoid shear failure requires consideration

of several failure modes. Diagonal tension failure is evident in

inclined cracks extending from the exural tension boundary

through the wall web, and it is controlled by provision of web

horizontal and vertical reinforcement (Section 5.4). Diagonal

compression failure is evident in crushing of the web near the

exural compression zone (Figure 3-4) and is controlled by

limiting the maximum value of wall shear as a function of

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

3.3 Diaphragms and Foundations

The intent of U.S. building codes is that signicant inelastic

response will be limited to vertical framing elements of the

seismic force-resisting system (for example, special moment

frames, and special structural walls) that are detailed for ductile

response. Diaphragms, foundations, and their connections,

are intended to remain essentially elastic. Sections 6.3.2

and 6.3.3 of this Guide summarize ACI 318 and ASCE 7

requirements.

Foundation design practices vary. Some engineers design

foundations for forces determined from load combinations

including E without consideration of the capacity of vertical

elements framing into the foundation. Others use capacity

design principles to determine foundation forces based on

the capacity of the vertical elements. Yet another practice

for squat walls is to acknowledge the difculty of tying down

the foundation, and to accept foundation rocking. Rocking

can impose large deformations on other components of the

structure of the building that must be considered in design.

Design requirements for rocking foundations are not included

in this Guide.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

4. Building Analysis Guidance

4.1 Analysis Procedures

ASCE 7 allows the seismic forces in a structural wall to be

determined by three types of analysis: Equivalent Lateral Force

Analysis, Modal Response Spectrum Analysis, and Seismic

Response History Analysis. The Equivalent Lateral Force

Analysis procedure is the simplest and can be used effectively

for basic low-rise structures. This analysis procedure is not

permitted for long-period structures (fundamental period T

greater than 3.5 seconds) or structures with certain horizontal

or vertical irregularities.

The seismic base shear V calculated according to Equivalent

Lateral Force Analysis is based on an approximate fundamental

period, T

, unless the period of the structure is determined by

analysis. Generally, analysis of moderate-to-tall structural

wall buildings will show that the building period is longer

than the approximate period, although the upper limit on

the period (C

) applies for the base shear calculation. The

longer analytical period will result in a reduced calculated

base shear when the period is greater than T

, often called the

transition period. Per ASCE 7 Equations 12.8-3 and 12.8-4,

the base shear in this range decreases as the considered period

increases, up to the point where the minimum base shear

equation governs.

Modal Response Spectrum Analysis is often preferred to

account for the elastic dynamic behavior of the structure

and to determine the calculated building periods. Another

advantage of Modal Response Spectrum Analysis is that the

combined modal base shear response can be less than the base

shear calculated using Equivalent Lateral Force procedure. In

such cases, however, the modal base shear must be scaled up

to a minimum of 85 % of the Equivalent Lateral Force base

shear.

For a Modal Response Spectrum or Seismic Response History

Analysis, a 3-D computational model is typically used as an

effective means of identifying the effects of inherent torsion

in the lateral system as well as the directional interaction of

anged walls. For such analyses, code-prescribed accidental

torsion forces typically are applied as static story torsions

combined linearly with the dynamic results.

ASCE 7 § 12.5 species the requirements for the directions

in which seismic forces are to be applied to the structure.

Although the design forces for structural walls often may

be based on the seismic forces applied in each orthogonal

direction independently, it is common to apply the seismic

forces using the orthogonal combination procedure of ASCE

7 § 12.5.3a. This combination considers 100 % of the seismic

force in one direction combined with 30 % of the seismic force

in the perpendicular direction. Multiple load combinations are

required to bound the orthogonal effects in both directions.

To avoid excessive conservatism, the resulting structural wall

demands typically are considered for each combination rather

than being enveloped. The orthogonal force combination

procedure is required for structural wall design only if that wall

forms part of two or more intersecting seismic force-resisting

systems and is subjected to axial load due to seismic forces

acting along either principal plan axis equaling or exceeding

20 % of the axial design strength of the wall.

ACI 318 § 21.1.2.1 requires that the interaction of all structural

and nonstructural members that affect the linear and nonlinear

response of the structure to earthquake motions be considered

in the analysis. Important examples include interactions with

masonry inlls (partial or full height), architectural concrete

walls, stairwells, cast-in-place stairways, and inclined parking

ramps. It is not always necessary to include these elements in

the global model. Instead, global analysis results can be used

to check whether interferences with nonstructural elements

occur, and construction details can be modied as needed.

4.2 Stiffness Recommendations

When analyzing a structural wall, it is important to model

appropriately the cracked section stiffness of the wall and

any coupling elements, as this stiffness determines the

building periods, base shear, story drifts, and internal force

distributions. According to ACI 318 § 8.8.2, wall stiffness

can be dened by (a) 50 % of gross-section stiffness; (b) I

0.70I

if uncracked or 0.35I

if cracked, and A

= 1.0A

; or (c)

more detailed analysis considering the reduced stiffness under

loading conditions. Act ual stiffness of structural walls depends

on reinforcement ratio, slip of reinforcement from foundations,

foundation rotation, axial force, and other parameters. The

exural and axial stiffness values prescribed by ACI 318

are reasonable for many cases; shear stiffness, however, is

typically as low as G

/10 to G

/20. ATC 72 (2010) provides

additional guidance.

ACI 318 provides frame beam effective stiffness values, but

these are not appropriate for typical coupling beams. Coupling

beams are expected to sustain damage before signicant

yielding occurs in walls, leading to faster stiffness reduction.

Coupling beam effective stiffness is further reduced because

of concentrated end rotations associated with reinforcement

slip from anchorage zones within the wall boundary. ATC

72 (ATC 2010) recommends taking E

= 0.15E

with shear

deformations calculated based on G

= 0.4E

for l

/h ≥ 2 and G

= 0.1E

for l

/h ≤ 1.4, with linear interpolation for intermediate

aspect ratios.

The preceding recommendations intend to approximate

secant stiffness to onset of yielding. Actual instantaneous

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

stiffness varies with time as a structure oscillates at varying

amplitude. A nonlinear analytical model can approximate

these instantaneous stiffness changes with time, but at

considerably greater expense in modeling and computation.

For additional guidance, see Deierlein et al. (2010).

Floor diaphragms can be modeled adequately as rigid elements

if the effects of in-plane oor deformations are expected to

be small. This is generally the case if the aspect ratio of the

diaphragm is small, if the structural walls are evenly distributed

across the diaphragm, and if there is not a signicant stiffness

discontinuity in the structural wall system. If these conditions

are not met, realistic stiffness properties, including effects

of any expected cracking, should be used to model in-plane

diaphragm exibility. This is especially important if the

diaphragm is used for large shear transfer, such as at setbacks

and podium levels (Figure 2-5). For additional guidance, see

Moehle et al. (2010).

4.3 Effective Flange Width

When a anged wall undergoes drift, the anges on both the

tension side and the compression side participate in resisting

axial force and moment (Figure 4-1). Actual normal stresses

in the ange decrease with increasing distance from the

web because of shear lag. The ange contribution varies

depending on deformation level and whether the ange is in

tension or compression. Conventional practice is to dene an

effective ange width and assume that concrete and anchored

longitudinal reinforcement within the effective width contribute

fully to strength (except concrete cracks on the tension side).

According to ACI 318 § 21.9.5.2, unless a more detailed analysis

is performed, effective ange widths of anged sections shall

extend from the face of the web a distance equal to the lesser

of one-half the distance to an adjacent wall web and 25 % of

the total wall height above the level in question.

Figure 4-1

– Effective ange activation.

4.4 Foundation Modeling

Base restraint can have a signicant effect on the behavior

of structural wall buildings. ASCE 7 § 12.7.1 (Foundation

Modeling) states “for purposes of determining seismic forces,

it is permitted to consider the structure to be xed at the base.

Alternatively, where foundation exibility is considered, it

shall be in accordance with Section 12.13.3 or Chapter 19.”

Unlike a moment frame lateral system, which may be detailed

to be xed or pinned at its base, a structural wall will always

be xed to the supporting foundation element. For this reason,

structural walls are typically modeled as having a xed base,

with no further foundation modeling. However, the foundation

elements supporting the structural wall need not be considered

xed with respect to the underlying soil. Foundation rocking

and other soil-structure interaction effects are available for

consideration and modeling, with guidance provided by

ASCE 7 – Chapter 19 (Soil-Structure Interaction for Seismic

Design). For buildings with multiple subterranean levels, a

wall extending into the basement is more likely to be nearly

xed because it is “locked in” by the diaphragms, such that

foundation rocking is less important.

The preceding discussion applies to f lexural strength

calculation. For determination of tributary gravity loads,

which resist uplift, use the full tributary ange width, not the

effective ange width.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

This section provides guidance for proportioning and detailing

special structural walls and coupling beams. Different

subsections of Section 5 apply, depending on wall geometry.

Table 5 -1 identies the subsections typically applicable to

different walls or parts of walls. For “slender walls” and for

“walls with h

≤ 2,” the subsections are listed in the order

in which they typically are applied for wall design.

5. Design Guidance

5.1 Load and Resistance Factors

ASCE 7 Section 12 denes the load combinations applicable to

special structural wall design. The load combinations require

horizontal seismic effects to be evaluated in conjunction with

vertical seismic effects, dead load, variable portions of the

live load, and other applied loads such as soil pressure, snow,

and uids. The horizontal seismic effect is dened as E

QE. The vertical seismic effect, dened as E

= 0.2S

D, can

increase or decrease the dead load effect.

The basic load combinations for strength design are:

Table 5-1

– Typical application of Section 5 to different walls

or parts of walls.

(a)

(b)

(1.2 + 0.2S

)D +

QE + (0.5 or 1.0)L + 0.2S

(0.9 – 0.2S

)D +

QE + 1.6H

(ASCE 7 § 12.4.2.3)

The load factor on L is permitted to equal 0.5 for all occupancies

in which L is less than or equal to 100 psf, with the exception

of garages or areas occupied as places of public assembly.

Otherwise, the load factor on L is 1.0.

To dene the redundancy factor

, consider only vertical wall

segments whose aspect ratio h

≥ 1, where h

= story height.

If removal of one of these segments results in either a 33 %

reduction in story strength or an extreme torsional irregularity,

= 1.3. Otherwise,

= 1.0. See ASCE 7 § 12.3.4.

For combined exure and axial force in a wall, the strength

reduction factor

is determined using the same procedure as

is used for columns. For this purpose,

is dened as the net

tensile strain in the extreme tension steel when the section

reaches nominal strength (

= 0.003). If

≥ 0.005,

= 0.9. If

≤

(taken as 0.002 for Grade 60),

= 0.65 for tied boundary

elements or 0.75 for spiral reinforced boundary elements. The

value of

is interpolated for intermediate values of

For wall shear including shear-friction, ACI 318 § 9.3 allows

= 0.75, except

= 0.6 if the nominal strength V

is less than

the shear corresponding to development of the wall nominal

flexural strength M

. This Guide recommends designing

slender walls so the design shear strength (

) is at least

the shear corresponding to development of the wall exural

strength. This typically is not practicable for squat walls; the

use of

= 0.6 usually is not a signicant penalty for squat walls

given their inherent strength.

For diagonally reinforced coupling beams,

= 0.85 for shear.

For conventionally reinforced coupling beams,

= 0.75 for

shear and 0.9 for exure.

5.2 Overall Proportioning

Initial structural wall sizing typically considers building

seismic base shear V versus wall design shear strength

Building seismic base shear V is determined from ASCE 7

procedures as discussed in Section 4.1. When considering

preliminary shear demands for individual walls, several

amplication factors should be considered.

Redundancy factor

may amplify shear. See Section 5.1.

Torsion, both inherent and accidental, increases wall shear.

Typical amplication factors, relative to the basic shear

without torsion, are in the range 1.2 – 1.5.

Where shear is resisted by multiple vertical wall segments

with different lengths, openings, and anges, the total shear

will be distributed nonuniformly among the segments.

The amplication factor for individual segments can vary

widely.

Designing for multiple load combinations invariably will

result in wall exural overstrength. For slender walls where

a exural yielding mode is desired, wall shears should be

amplied commensurately. A factor of approximately 1.4

is typical. See Section 3.1.3.

Dynamic effects can amplify wall shears in multi-story

buildings. For slender walls where a exural yielding

mode is desired, a dynamic amplication factor

, dened

in Section 3.1.3, can be applied.

The rst three factors apply to most buildings, whereas the last

two apply only to slender walls in multi-story buildings where

the engineer intends wall exural yielding to be the controlling

inelastic mechanism.

Condition

General

Slender walls

Walls with h

≤ 2.0

Wall piers l

≤ 6.0 and h

≤ 2.0

Coupled walls and coupling beams

Walls with discontinuities

Subsections

5.1, 5.2

5.3, 5.4, 5.5

5.6, 5.4, 5.5, 5.3

5.7

5.8 (and 5.3 - 5.7

as applicable)

5.9 and 5.10

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

ACI 318 § 21.9.4.4 denes the maximum design shear stress

as 8

√f ’

, although for any individual segment this can be as

high as 10

√f ’

. If the amplication factor of the fourth item

above is applied,

= 0.75; otherwise,

= 0.6 (ACI 318 § 9.3.4).

This Guide recommends targeting a lower design stress, in

the range 4

√f ’

to 6

√f ’

. A good rst approximation of total

required wall area in each direction is the amplied shear

demand divided by the design shear stress.

Design of midrise and taller buildings may be controlled by

drift limits (see Section 2.7 for ASCE 7 drift limits). For such

buildings, spectral displacement S

can be obtained, in inches,

from the design response spectrum as

Because most of these buildings will fall in the period range

where S

= S

/T, this expression can be recast as S

9.8TS

inches. For a xed-base, uniform, exural cantilever, the

fundamental period required to meet the Interstory Drift

Ratio limit is approximately , where h

and S

are in consistent units. The required total exural stiffness

of all walls is approximately . The basic

assumptions of the expression are (a) xed-base building,

uniform over height, (b) exural response in the rst mode

without torsion, and (c) inelastic drift can be estimated based

on response of a linear oscillator having exural stiffness EI

This expression can be used as a rst approximation of the

required wall properties for drift control. Values for Interstory

Drift Ratio limits are in Table 2-1.

5.3 Flexure and Axial Force

Design for flexure and axial force involves preliminary

proportioning, boundary element transverse reinforcement

layout, analysis for P-M strength, and iterations to optimize the

layout considering coordination of boundary element vertical

and horizontal reinforcement and section strength.

5.3.1 Preliminary Proportioning

For uncoupled rectangular wall sections, preliminary sizing of

the wall vertical reinforcement can be accomplished using the

model of Figure 5-1, which assumes there is both distributed

vertical reinforcement T

and boundary vertical reinforcement

. Summing moments about C results in

n,CS

= P

+ T

Magnitude and location of P

are determined from tributary

dead loads including self-weight for the load combination

shown; knowing location of P

, moment arm x

can be

approximated. The internal moment arms for distributed and

concentrated reinforcement can be approximated as j

0.4l

and j

= 0.8l

. One approach is to select the minimum

required distributed vertical reinforcement based on

0.0025, thereby approximately dening T

, and then use the

equation above to nd boundary element tension force T

required to achieve target moment strength M

n,CS

. (Note that

squat walls sometimes require

> 0.0025; see Section 5.6.)

Alternatively, if only distributed reinforcement is to be used,

set T

= 0 and use the equation to solve for T

. Required

distributed reinforcement is then A

= T

, but not less than

the minimum required distributed reinforcement. For anged

sections, reinforcement within the effective ange width in

tension contributes to T

The preceding discussion assumes the wall moment strength

is controlled by tensile yielding of vertical reinforcement, as

recommended by this Guide. If moment strength is controlled

by strength of the compression zone, a modied approach

is required, and axial force P

must be based on the load

combination of ASCE 7 § 12.4.2.3 (see Section 5.1).

Figure 5-1

– Model for initial selection of exural tension reinforcement.

Note: This is a model

showing forces to be

considered for estimation

of design tension forces

and T

for wall

without coupling.

n,CS

= M

u,CS

Wall base shear not shown.

It is good design practice to provide hoop reinforcement

to conne the most heavily strained portion of the exural

compression zone and to provide lateral support of vertical

reinforcement (Figure 2-10). If boundary elements are

required (Section 5.3.3), ACI 318 § 21.9.6.4 and 21.9.6.5 require

them to extend horizontally from the extreme compression ber

a distance at least the greater of c – 0.1l

and c/2, where c is

the largest neutral axis depth calculated under combinations

of P

and M

. Generally, P

for this calculation is based on the

load combination (a) from Section 5.1. Figure 5-2 presents a

chart for preliminary estimation of the neutral axis depth. If

concentrated exural tension reinforcement is provided in the

boundary, it can be spread out within t he conned region. If

it is too congested, either the proportions of the wall can be

reconsidered, or the conned region can be extended further

into the exural compression zone.

Having established preliminary proportions, the next step is

to conrm P-M strength and neutral axis depth using section

analysis.

5.3.2 P-M Strength Calculations

The strength calculations for structural walls resisting

combined exure and axial force directly match the calculations

T ≤

IDR

≥ 3.7 h

(

)

IDR

(

)

g = 9.8T

2π

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

Figure 5-2

– Approximate exural compression depth. For anged

sections, adjust A

, A ’

, and b considering effective ange width.

for concrete columns. Specically, the calculations assume

linear strain distribution, idealized stress-strain relations for

concrete and reinforcement, and material strain limits per

ACI 318 § 10.2 and 10.3. All developed vertical reinforcement

within effective ange widths, boundary elements, and the wall

web must be included. P-M interaction software can facilitate

the calculations. Also, the axial force P

must be correctly

located. Where axial force is based on tributary loads, with

loads followed through the structure using hand calculations,

usually the correct location of axial force is at the centroid

of loads tributary to the wall, including self-weight. Where

a computer model is used to establish axial force demand,

the correct location usually is the location reported from the

analytical model. Be aware that some computer programs

automatically place P

at the geometric centroid of the

section. If this location is incorrect, resulting moments must

be corrected by M

= P

e, where e is the eccentricity between

the correct and assigned location of P

Because wall geometry and concrete strength typically

are defined before detailed analysis, the design for P-M

resistance is generally a trial and error process using vertical

reinforcement size and placement as the variables. Boundary

element transverse reinforcement provides lateral support for

the vertical reinforcement, so the design of both needs to be

done in parallel. Boundary element detailing is considered

next.

5.3.3 Boundary Elements

A boundary element is a portion along a structural wall edge

or opening that is strengthened by longitudinal and transverse

reinforcement. Where combined seismic and gravity loading

results in high compressive demands on the edge, ACI 318

requires a special boundary element. Where compressive

demands are lower, special boundary elements are not required,

but boundary element transverse reinforcement still is required

if the longitudinal reinforcement ratio at the wall boundary, A

s,be

g,be

is greater than 400/f

. For clarity, this Guide refers to these

latter elements as ordinary boundary elements (a term not

used in ACI 318). Figure 5-3 shows examples of special and

ordinary boundary elements.

ACI 318 provides two methods for determining whether special

boundary elements are required. The preferred method (ACI

318 § 21.9.6.2), which this Guide refers to as Method I, applies

to walls or wall segments that are effectively continuous from

base of structure to top of wall or segment and designed to

have a single critical section for exure and axial force, as in

Figure 3-1. Some discontinuity over wall height is acceptable

provided the wall is proportioned so that the critical section

occurs where intended. To use the method, the seismic force-

resisting system is rst sized and then analyzed to determine the

top-level design displacement

and corresponding maximum

value of wall axial force P

. The exural compression depth c

corresponding to nominal moment strength M

n,CS

under axial

force P

is then calculated (Figure 5-4). If

where h

refers to total wall height from critical section to top

of wall, then special boundary elements are required.

Figure 5-3

– Special and ordinary boundary elements.

(a) Special boundary element

(b) Ordinary boundary element where

> 400/fy

(ACI 318 Eq. 21-8)

c ≥

600 (

)

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

Where special boundary elements are required by Method I,

they must extend vertically above and below the critical section

a distance not less than the greater of l

and M

u,CS

/4V

u,CS

. The

limit l

is based on the expectation that cover spalling in a

well-conned section typically will spread along a height

approaching the section depth. The limit M

u,CS

/4V

u,CS

denes

the height above the critical section at which the moment

will decrease to 0.75M

u,CS

, a value likely to be less than the

spalling moment, assuming a straight-line moment diagram.

Where the critical section occurs at or near the connection

with a footing, foundation mat, pile cap, or other support,

different requirements apply to the vertical extension of the

special boundary element. See Figure 5-5 and subsequent

discussion.

Figure 5-4

– Calculation of neutral axis depth c.

Figure 5-5

– Boundary element extensions for walls designed by

Method I, for critical section at foundation interface. For ordinary and

special boundary element details, see Figure 5-3.

Figure 5-6

– Boundary element requirements for walls designed by

Method II

For extensions into foundations, see Figure 5-5. For ordinary

and special boundary element details, see Figure 5-3.

The second method for determining if special boundary

elements are required, which this Guide refers to as Method

II, is based on nominal compressive stress (ACI 318 §

21.9.6.3). First, the seismic force-resisting system is sized

and analyzed to determine axial forces and moments under

d esig n loa d c o mb i n a t io n s. Usi ng a g r oss -s e c t ion m o del of t he

wall cross section, nominal stress at wall edges is calculated

from s = P

+ M

. Special boundary elements

are required at an edge if nominal stress exceeds 0.2f ’

. If a

special boundary element is required, it must be continued

vertically (upward and downward) until compressive stress

drops below 0.15f ’

. See Figure 5-6. Although Method II

can be used for any wall, the preferred use is for irregular or

discontinuous walls for which Method I does not apply.

At the interface with a footing, foundation mat, pile cap,

or other support, longitudinal reinforcement of structural

walls must be fully developed in tension. Where yielding

of longitudinal reinforcement is likely due to lateral drifts,

the development length is calculated for 1.25f

(ACI 318 §

21.9.2.3c); otherwise it is calculated for f

(ACI 318 § 21.12.2).

Where depth of foundation element precludes development of

straight bars, standard hooks having l

calculated for 1.25f

, as appropriate, are acceptable. The standard hook should

extend full-depth in most cases. See Figure 5-5.

Where a special boundary element terminates at a footing,

foundation mat, or pile cap, the special boundary element

transverse reinforcement must extend at least 12 inches into

the foundation element (ACI 318 § 21.9.6.4d). For any other

support, or where a boundary element has an edge within

one-half the footing depth from an edge of the footing (or

mat or pile cap), the transverse reinforcement must extend

into the support at least l

, calculated for f

in tension, of the

largest longitudinal reinforcement (ACI 318 § 21.9.6.4d and

21.12.2.3). See Figure 5-5.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

Confinement trigger for walls with single

critical section

Method I was derived from the simplied model shown

below. It assumes that displacement

is due entirely

to curvature

centered on the wall critical section

with plastic hinge length = l

/2. Dening

/c,

and setting

= 0.003, results in

= (0.0015l

)/c.

Rearranging and rounding leads to the following familiar

expression:

Figure 5-7

– Model to determine connement trigger.

(a) Wall elevation (b) Curvature (c) Strain

Where a special boundary element is required, ACI 318

§ 21.9.6.4 requires it to extend horizontally from the wall

edge a distance not less than the greater of c – 0.1l

and c/2

(Figure 5-3a). Flexural compression depth c is calculated at

nominal moment strength M

n,CS

under maximum axial force

(Figure 5-4). In anged sections, the special boundary

element, if required, must include the effective ange width in

compression and must extend at least 12 inches into the web.

Special boundary elements must have transverse connement

reinforcement satisfying

(ACI 318 Eq. 21-5)

Because f ’

and f

typically are selected independently of

boundary element requirements, the remaining variables are

connement bar size and horizontal and vertical spacing of

connement hoop legs and crossties. The parameters for

these variables are discussed in detail in Sections 5.3.4 and

7.1.

At wall boundaries where special boundary elements are

not required, ACI 318 § 21.9.6.5 requires ordinary boundary

elements if the boundary element longitudinal reinforcement

ratio A

s,be

g,be

> 400/f

, where A

s,be

g,be

is the local ratio at

the wall boundary only. Figure 5-3b shows requirements for

ordinary boundary elements. Where A

s,be

g,be

≤ 400/f

, ACI

318 § 14.3.6 permits the section to be detailed without ties

enclosing the vertical reinforcement. See Figure 5-5.

As discussed in Section 3.1.1, very tall wall buildings

sometimes develop secondary exural yielding near mid-

height due to apparent higher-mode response. A challenge

is that linear structural analysis, which is widely used, does

not indicate directly whether such yielding is occurring.

Nonlinear dynamic analysis can provide insight into this

issue. Some designers dene an intermediate boundary

element that satises all requirements for special boundary

elements except the volume ratio required by ACI 318 Eq.

21-5 is reduced by half; these intermediate boundary elements

are extended into the potential secondary yielding zone. As

a minimum, this Guide recommends that at least ordinary

boundary elements extend through elevations that show high

moment demands due to higher-mode response.

The illustration of Figure 5-5 is for the case where special

boundary elements are required at the foundation interface. If

special boundary elements are not required, ordinary boundary

elements still are required if A

s,be

g,be

400/f

. Requirements

over height are as shown in Figure 5-5, except there would be

no special boundary elements, and transverse reinforcement

is required to extend into the support only where it is near an

edge of the support. In some walls, notably squat walls, even

ordinary boundary elements are not required. This Guide

recommends providing at least ordinary boundary elements at

the wall boundary near the critical section for exure.

5.3.4 Vertical Reinforcement Layout

The process for laying out wall vertical reinforcement is

iterative, considering requirements for P-M strength and

boundary element transverse reinforcement. One approach

is as follows:

Determine the type of boundary element required (Section

5.3.3). If none required, go to step 4.

For special or ordinary boundary elements, determine the

required boundary element length l

(Figure 5-3), with c

estimated from Figure 5-2 or from P-M analysis.

Select trial boundary element transverse reinforcement

size (No. 3, 4, or 5) and vertical spacing. For special

boundary elements, use ACI 318 Eq. 21-5 to determine A

from which the number of hoop and crosstie legs in each

direction is determined. Check all vertical and horizontal

spacing requirements of Figure 5-3, as applicable.

= 0.09sb

f ’

c ≥

600 (

)

If c exceeds this value, connement is required.

from

the Building Code is an expected value for the Design

Basis Earthquake for 5% damping. Displacements

may exceed

because of dispersion around the

expected value, stronger shaking (for example, at the

Risk-targeted Maximum Considered Earthquake), or

lower damping. The combination of these factors

suggest that the coefcient 600 should be closer to

1000 if the objective is to avoid section failure. This

subject is being evaluated by ACI 318 at the time of

this writing.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

Select trial size and spacing of vertical reinforcement for

entire structural wall section. If a boundary element is

required, spacing of verticals in the boundary element is

dictated by hoop and crosstie arrangement from step 3,

with corner and at least alternate verticals restrained by a

hoop or crosstie. Verticals outside the boundary element

provide required

with spacing s ≤ 18 inches.

Determine P-M strength. If provided strength is inadequate

or over-conservative, rene bar sizes and repeat step 3 or

4. If acceptable, continue.

Use P-M analysis to check assumed boundary element

extent in step 2. If inadequate or over-conservative, return

to step 3 with new c. If acceptable, vertical reinforcement

layout is complete.

Alternative iteration schemes also can lead to efcient

designs. For example, some designers select boundary

vertical reinforcement and spread it within required boundary

length l

, then layout transverse reinforcement to support the

verticals and conne the core, and iterate until all requirements

are met.

In step 5 above, the basic design requirement of ACI 318 is

the same as for columns, that is, all combinations of (M

) must be less than corresponding design values (

). The value of

is dened in Section 5.1. In addition,

the maximum axial force cannot exceed the similar limit for

columns (ACI 318 § 10.3.6). The usual approach is to use

computer software to generate

interaction diagrams

and then check that M

, P

pairs for all load combinations fall

within the design limits. Section 5.3.5 discusses the relevant

load combinations.

5.3.5 Force Combinations from Modal Response

Spectrum Analysis

As noted in Section 4.1, Modal Response Spectrum Analysis

is a common method of determining wall design forces. This

technique considers multiple vibration modes and combines

the values of interest using either the square root of the sum

of the squares or the complete quadratic combination method.

Although the results from each mode correctly indicate the

sign of calculated quantities, the square root of the sum of the

squares and the complete quadratic combination results do not.

For an uncoupled wall resisting lateral force in two orthogonal

directions, there are four seismic load cases to be combined

with the non-seismic loads for the P-M check:

–M

In contrast, the interactions in coupled walls result in signicant

induced axial forces. Consideration of all possible sign

combinations results in eight possible seismic load cases:

–M

–P

–M

–P

–M

–P

–M

Again, these seismic forces are combined with dead, live, soil

and snow loads per ASCE 7 load combinations (Section 5.1)

for nal structural wall design.

Sometimes, inspection of the eight possible sign combinations

can identify combinations that are kinematically impossible

and therefore require no further consideration. For example,

consider the coupled planar structural wall shown in Figure

5-8. Lateral sway occurs with a single possible set of combined

moments and axial forces. For the left-hand wall, axial tension

occurs simultaneously with exure oriented so that maximum

tension is induced on the left edge of that wall. The reverse

combination is shown in the right-hand wall, where maximum

compression is induced on the right edge of that wall. These

axial and exural force sign pairings are determinant for these

wall segments. Subtracting T

from the left-hand wall or

from the right-hand wall would result in conditions that

cannot occur; including these combinations would result in

unnecessary wall exural overstrength, which can cascade to

increased design requirements elsewhere.

The sign-force combination of anged and coupled structural

walls is signicantly more complex because of bi-directional

interaction. Often the sign-force relationships revealed by an

Equivalent Lateral Force Analysis can help understand the

range of sign-force possibilities from the Modal Response

Spectrum Analysis results.

Figure 5-8

– Elevation of laterally displaced coupled wall system.

(a) Wall demands

(b) Kinematically

correct combinations

5.3.6 Termination of Vertical Reinforcement Over

Wall Height

Vertical reinforcement can be terminated where it is no longer

required to resist exure and axial force. For this purpose,

ACI 318 § 21.9.2.3 refers to ACI § 12.10, which denes bar

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

cutoff requirements for beams, but with 0.8l

substituted for

beam effective depth d. Hence, the basic requirements are

that (a) terminated bars must be developed beyond points of

maximum stress and (b) terminated bars must extend 0.8l

beyond the point at which they are no longer required to resist

exure and axial force; the 0.8l

extension is because diagonal

shear cracks may shift exural tension upward.

Figure 5-9 illustrates strict application of ACI § 12.10 to a

wall, using a moment envelope as suggested in Figure 3-1.

Bars a provide design strength

sufcient to resist M

at the critical section for exure and axial force. If bars b

are to be terminated, the requirements are (i) bars b must be

developed for 1.25f

above the critical section requiring these

bars (1.25 factor required by ACI 318 § 21.9.2.3c); and (ii) bars

b must extend at least 0.8l

above the elevation where they are

no longer required to resist exure and axial force (in this

case, 0.8l

above the point where continuing bars c provide

design strength

= M

). This process can be continued

up the wall height, as in (iii) bars d must be developed for

above the critical section for bars c; and (iv) bars d must

extend at least 0.8l

above the point where continuing bars

e provide required strength. In most cases, bar cutoffs will

be controlled by the requirement to extend bars 0.8l

past the

point where they are no longer required to resist exure and

axial force, thereby simplifying design.

Figure 5-9

– Bar cutoffs for vertical reinforcement for idealized M

moment diagram.

The aforementioned procedure seems unnecessarily onerous,

especially considering that the wall moment diagram for a

building responding to future earthquake shaking is not

accurately known. A practice used by many design ofces is

to extend bars l

above the oor where the bars are no longer

required. This practice is not strictly in compliance with the

aforementioned Building Code requirement, but it serves

the intent to extend bars well past the point where they are

no longer required for exure, and seems to be a reasonable

approach for design. This requirement is being evaluated by

ACI 318 at the time of this writing.

ACI 318 § 12.10.5 addresses exural reinforcement terminated

in tension zones. Although not specically exempted by the

Building Code, it is understood that this provision is intended

for beams. Common engineering practice does not apply this

provision to the design of special structural walls.

5.4 Shear

Unlike the design of ordinary reinforced concrete structural

walls, the design of special structural walls for shear does not

consider the interaction of axial force and shear. ACI 318 §

21.9.4.1 denes the nominal shear strength as:

where A

= l

is 3.0 for h

≤ 1.5, is 2.0 for h

≥ 2.0,

and varies linearly between these limits; and

= 0.75 for all-

lightweight concrete, 0.85 for sand-lightweight concrete, and

1.0 for normalweight concrete. For design of an entire wall,

the ratio h

refers to the overall dimensions from base to

top of wall. For design of a vertical wall segment within a

wall, the ratio refers to the overall dimension of the wall or

the dimensions of the vertical wall segment, whichever ratio

is greater. The intent is that a vertical wall segment never be

assigned a unit strength greater than that for the entire wall,

although it can be assigned lower unit strength if its h

greater than that of the entire wall.

The basic design requirement is

≥ V

. Strength reduction

factor

is discussed in Section 5.1. This expression and the

expression for V

(ACI 318 Eq. 21-7) can be combined and

solved for

, the required horizontal reinforcement ratio.

Reinforcement composing

must be placed in two curtains

if V

> 2A

√f ’

, which is almost always the case. (This Guide

recommends always using two curtains within the hinge

region of a slender wall.) The reinforcement must provide a

web reinforcement ratio not less than 0.0025 with maximum

vertical spacing of 18 inches.

ACI 318 § 21.9.4.4 denes upper limits for shear strength

of special structural walls. For all vertical wall segments

resisting a common lateral force, combined V

shall not be

taken greater than 8A

√f ’

, where A

is the gross combined

area of all vertical wall segments. For any one of the individual

vertical wall segments, V

shall not be taken greater than

10A

√f ’

, where A

is the cross-sectional area of concrete

of the individual vertical wall segment. It is acceptable to

interpret the common lateral force as either (a) the entire story

shear, in which case the combined area refers to all walls or

vertical wall segments in the story, or (b) the shear resisted by

a single wall or a line of walls in a single plane, in which case

the combined area refers to the area of walls or vertical wall

segments in that plane.

If a special boundary element is required, ACI 318 § 21.9.6.4

(e) requires the horizontal shear reinforcement to extend to

(ACI 318 Eq. 21-7)

= A

(

√f ’

)

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

within 6 inches of the edge of the wall and to be anchored to

develop f

in tension within the conned core of the boundary

element using standard hooks or heads (Figure 5-3a).

One option is to extend the web horizontal reinforcement

continuously to near the wall edge. Another option is to lap

the web horizontal reinforcement with the boundary element

horizontal reinforcement such that the boundary element

reinforcement serves as the wall shear reinforcement within

the boundary element. This is only permitted if there is

sufcient lap length and if the boundary element horizontal

reinforcement provides strength A

/s parallel to the web

reinforcement at least equal to the strength of the web

horizontal reinforcement A

/s. In this case, it is permitted

to terminate the web horizontal reinforcement without

a standard hook or head. According to this alternative,

the required reinforcement A

parallel to the web is the

maximum of that required for connement (ACI 318 Eq. 21-

5) or shear (ACI 318 Eq. 21-7). It is not necessary to sum the

two requirements.

5.5 Shear-Friction

The shear-friction provisions of ACI 318 § 11.6 are applicable

where shear is transferred across an interface of two concrete

volumes cast at different times. These provisions are intended

to prevent sliding shear failure at such interfaces. This is a

commonly applicable condition at the connection between

walls and foundation and, for multi-story structural walls cast

oor-by-oor, at the horizontal cold joint at each oor.

According to the shear-friction concept, the sliding resistance

depends on interface roughness and the clamping force across

the interface. Where reinforcement is perpendicular to the

sliding plane, nominal shear strength is:

(ACI 318 Eq. 11-25)

= A

refers to the distributed vertical reinforcement in the

wall web; in a wall with boundary elements, A

can be

conservatively calculated as if the distributed vertical web

reinforcement continues uninterrupted into the boundary

elements. Alternately, nominal shear-friction strength can be

calculated per the equation given in ACI 318 R11.6.3. Where

permanent net compression force N

acts perpendicular to the

sliding plane, the sliding shear strength is V

)

with N

positive in compression. Where transient net tension

force T

u,net

acts perpendicular to the sliding plane, the sliding

shear strength is V

= (A

–

u,net

)

The basic design requirement is

≥ V

. Strength reduction

factor

is discussed in Section 5.1. Wall vertical reinforcement

sized and located for P-M interaction resistance can serve double

duty as shear-friction reinforcement. If that reinforcement

proves insufcient to resist the interface shear, additional

distributed vertical dowels can be placed along the wall

centerline, developed for f

above and below the interface.

ACI 318 also contains provisions for inclined bars, which can

be more effective at resisting sliding, although bars would

need to be inclined in both directions to resist alternating load

directions.

is not permitted to exceed the least of 0.2f ’

, (480 + 0.08f ’

and 1600A

In addition to reinforcement, ACI 318 § 21.9.9 requires that

the interface be clean and free of laitance. If the surface is

intentionally roughened to a full amplitude of ¼ inch, the

friction coefcient can be taken as

= 1.0

. Shear keys

are an effective alternative where surface roughening to ¼

inch amplitude cannot be achieved. Otherwise, frictional

resistance is reduced and

= 0.6

5.6 Squat Walls

As noted at the beginning of Section 3, low-aspect-ratio

(or squat) walls tend to have high inherent exural strength

compared with shear strength, such that it can be difcult to

achieve a exural yielding mechanism for aspect ratio h

less than approximately 1. Furthermore, squat walls tend to

resist lateral forces through a diagonal strut mechanism that

differs considerably from the exural mechanism of a slender

wall. For these reasons, the design approach and the required

details for squat walls differ from those of more slender

walls. Design usually begins with shear design (Section 5.4),

followed by checking for shear-friction (Section 5.5) and then

combined exure and axial force (Section 5.3).

Nominal shear strength is dened by ACI 318 Eq. 21-7

(See Section 5.4). In Eq. 21-7,

is 2.0 for h

≥ 2.0,

is 3.0 for h

≤ 1.5, and varies linearly between these

limits. The basic design requirement is

≥ V

. For many

squat walls, especially those having h

< 1, it will not

be feasible to achieve shear strength greater than the shear

corresponding to development of exural strength, in which

case the strength reduction factor is

= 0.6. The required

horizontal reinforcement ratio

is determined from these

expressions. As with slender walls, reinforcement composing

must be placed in two curtains if V

> 2A

√f ’

. In addition,

the distributed horizontal reinforcement must provide web

reinforcement ratio not less than 0.0025 with maximum

vertical spacing of 18 in. Finally, the upper limits of wall

nominal shear strength (8A

√f ’

and 10A

√f ’

) apply as noted

in Section 5.4.

In a squat wall, distributed vertical reinforcement is as

important as distributed horizontal reinforcement in resisting

shear (Figure 3-6). ACI 318 § 21.9.4.3 requires reinforcement

ratio

for distributed vertical reinforcement to be at least

equal to reinforcement ratio

for distributed horizontal

reinforcement if h

≤ 2.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

Once the shear reinforcement design is completed, the next

step is to check for shear-friction resistance at any construction

joints where concrete is placed against hardened concrete. If

additional reinforcement is required, either reinforcement

ratio

can be increased or dowels can be added at the

construction joint. See Section 5.5.

Next, the wall is checked for combined exure and axial force

using the procedures of Section 5.3. If vertical reinforcement

is required in addition to the distributed reinforcement

provided for shear, then either add additional distributed

reinforcement or add vertical reinforcement at the boundaries.

These two approaches (distributed reinforcement or

concentrated boundary reinforcement) are equally efcient

in resisting moment, but distributed reinforcement is

more effective in resisting sliding at construction joints.

Requirements for boundary elements, if any, are illustrated

in Figure 5-6.

ACI 318-11 versus IBC 2009 Wall Pier

Provisions

This Guide follows wall pier provisions of ACI 318-11,

which differ from those of IBC 2009. It is likely that

future editions of the IBC will adopt the ACI 318-11

provisions. This Guide recommends checking with the

local jurisdiction to determine applicable provisions.

5.7 Wall Piers

A wall pier is a relatively narrow vertical wall segment that

is essentially a column, but whose dimensions do not satisfy

requirements of special moment frame columns. According

to ACI 318 §21.9.8, a vertical wall segment is to be considered

a wall pier if l

≤ 6.0 and h

≥ 2.0, where b

, l

, and

refer to dimensions of the vertical wall segment. Design

of wall piers follows the usual requirements for vertical wall

segments, but additional requirements apply as noted below.

ACI 318 requires wall piers to satisfy the special moment

frame requirements for columns contained in ACI 318 § 21.6.3,

21.6.4, and 21.6.5, which address splice type and location,

connement reinforcement, and shear strength requirements

applicable to special moment frame columns. Alternatively,

wall piers with l

> 2.5 can be designed as follows.

Design shear force V

is either the shear corresponding

to development of M

at both ends or Ω

times the shear

determined by analysis of the structure for design load

combinations including earthquake effects. Design

strength

is calculated according to the usual provisions

for walls (Section 5.4). Although not required by ACI 318,

it would be prudent to reduce shear strength if the section

has net tension, similar to requirements for columns.

Transverse reinforcement is required to be in the form of

hoops except where only one curtain of distributed shear

reinforcement is provided (permitted only if V

≤ 2A

√f ’

in which case it is permitted to use single-leg shear

reinforcement with 180° bends at each end engaging

boundary vertical reinforcement). Maximum spacing

of transverse reinforcement is 6 inches. Transverse

reinforcement must extend at least 12 inches above and

below the clear height of the wall pier.

Special boundary elements are to be provided if required

by ACI 318 § 21.9.6.3.

For wall piers at the edge of a wall, ACI 318 requires horizontal

reinforcement in adjacent wall segments above and below

the wall pier, proportioned to transfer the design shear force

from the wall pier into adjacent wall segments (Figure 5-10).

First, determine the design shear force V

in the wall pier.

Then determine the nominal unit shear strength

(force per

unit length) of the adjacent wall segment. The total length of

the required horizontal reinforcement is V

ϕv

, where

is the

applicable strength reduction factor for shear (Section 5.1).

•

Figure 5-10

– Reinforcement required above and below wall pier.

5.8 Coupled Walls and Coupling Beams

Design of coupled special structural walls introduces design

complexities beyond those encountered for uncoupled walls.

Coupling beams often have relatively low aspect ratios and

high deformation demands, requiring special details to

achieve ductile performance. Coupling between walls results

in axial force variations complicating their design. Coupling

beam-wall connections require additional attention to avoid

conicts in reinforcing bar placement.

5.8.1 Coupling Beams

ACI 318 § 21.9.7 classies coupling beams into three

categories based on aspect ratio l

/h and shear demand. As

a practical matter, a fourth category for very deep beams is

added here. Figure 5-11 illustrates the design options for

these categories.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

Figure 5-12

– Details for conventionally reinforced coupling beams.

Coupling beams with l

/h ≥ 4 must satisfy proportioning

and detailing requirements specied for beams of special

moment frames, except certain dimensional limits are

exempted. Such beams are considered too shallow for

efcient use of diagonally placed reinforcement as allowed

for deeper beams. Instead, exural reinforcement is

placed horizontally at top and bottom of the beam.

Coupling beams with l

/h < 2 and V

> 4

√f ’

are

required to be reinforced with two intersecting groups of

diagonally placed bars symmetrical about the midspan,

unless it can be shown that loss of stiffness and strength

of the coupling beams will not impair the vertical load-

carrying ability of the structure, post-earthquake egress

from the structure, or the integrity of nonstructural

components and their connections to the structure.

Implicit in the exception is the requirement for the

engineer to demonstrate that the seismic force-resisting

system satises code strength and drift requirements in

the absence of the excepted coupling beams.

Other coupling beams not falling within the limits of

the preceding two bullets are permitted to be reinforced

as either conventionally reinforced special moment frame

beams or diagonally reinforced beams. In Figure 5-11,

beams falling to the right of the dashed line likely can

be designed efciently as special moment frame beams,

whereas those to the left probably are better designed with

diagonal reinforcement.

Very low aspect ratio beams are better designed using

the strut-and-tie model of ACI 318 Appendix A. Design

of these beams is not covered in this Guide.

The darkly shaded area of Figure 5-11 denes the upper

limit on beam design shear stress. The lightly shaded area

indicates designs that are permitted by ACI 318 but that may

have constructability problems because of reinforcement

congestion.

Figure 5-11

– Seismic coupling beam design space.

Beams designed as special moment frame beams (ACI 318

§ 21.5) must have exural reinforcement placed horizontally

at top and bottom of the beam and hoop reinforcement that

connes the end regions. Figure 5-12 illustrates typical

details. Because l

/h is relatively small, longitudinal bars

cannot be lapped and it may be easier to use closed hoops

over the entire beam span rather than only 2h at each end.

Skin reinforcement, if any, typically is terminated after short

extension into the wall (~6 inches); alternatively, it can be

developed into the wall in which case it contributes to beam

exural strength.

For beams reinforced with top and bottom longitudinal

reinforcement, exural and shear strengths are calculated

according to conventional procedures. For exure, the design

requirement is

≥ M

, where M

is determined from

building analysis under design load combinations, and

= 0.9.

For shear, the requirement is

≥ V

, where V

is determined

from equilibrium of the beam assuming it develops M

both ends with distributed load w

acting along the span

(Figure 5-13). M

is probable moment strength, calculated

using conventional ACI 318 assumptions except longitudinal

reinforcement yield strength is assumed equal to 1.25f

Within 2h from member ends, shear strength is based on

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

= 0, that is, V

= V

= A

d/s, with an upper bound of

= 10√f ’

(ACI 318 § 21.9.4.5). Strength reduction

factor for shear is

= 0.75 (ACI 318 § 9.3.2.3).

Figure 5-13

– Design shear for conventionally reinforced coupling

beam. Reversed loading case also must be considered.

Figure 5-14 shows typical details for a coupling beam

reinforced with two intersecting groups of diagonally placed

bars symmetrical about the midspan. Each group of diagonal

bars consists of a minimum of four bars provided in two or more

layers. The diagonal bars are required to extend straight into

the wall a distance at least 1.25 times the development length

for f

in tension. A challenge is avoiding interference between

the diagonal bars and the boundary element transverse and

longitudinal reinforcement. If an adjacent wall opening or

edge (for example, at the top of the wall) requires the diagonal

bar extension to be bent, additional reinforcement is required

to resist the unbalanced force resulting from the change in

reinforcement direction, similar to the requirement for offset

bars in columns (ACI 318 § 7.8.1.3). This detail should be

avoided where practicable. The minimum wall thickness to

accommodate both wall and coupling beam reinforcement is

around 14 inches, although 16 to 18 inches is more practical.

ACI 318 § 21.9.7.4 prescribes requirements for two reinforcement

options. The rst option is to conne individual diagonals using

hoops and crossties such that corner and alternate diagonal

bars are restrained in a hoop or crosstie corner (Figure 5-14a).

Connement reinforcement along the entire diagonal length

must satisfy the volumetric ratio requirements that apply

at ends of special moment frame columns, assuming each

diagonal as an isolated column with minimum cover over

the diagonal cage. Maximum permitted hoop spacing along

the diagonal is the smaller of s

and 6d

of the diagonal bars,

where s

= 4 + (14 – h

)/3. Connement reinforcement can be

difcult to place along the free lengths of the diagonals and

even more difcult where the diagonals intersect or enter the

wall boundaries. See Section 7 for additional discussion.

The second option is intended to ease construction difculties

commonly encountered with the rst option. By this

option, hoops and crossties conne the entire beam cross

section (Figure 5-14b). Connement reinforcement along

the entire beam length must satisfy the volumetric ratio

requirements that apply at ends of special moment frame

columns, with maximum spacing along the beam span not

exceeding 6 inches or 6d

of the diagonal bars, and with

spacing of crossties or legs of hoops around the beam cross

section not exceeding 8 inches. Although the total amount of

connement reinforcement may be greater with this second

option, the increased material costs are often more than offset

by reduced labor costs.

Regardless of the option selected for the diagonally reinforced

beam, longitudinal and transverse reinforcement is required

around the beam section (Figure 5-14). The longitudinal

reinforcement, typically No. 4 or No. 5 bars, should extend

only a short distance into the wall boundary so that it will

not develop signicant tensile stress due to beam exure.

Transverse reinforcement varies depending on the option selected

for connement reinforcement. See ACI 318 § 21.9.7.4.

A diagonally reinforced coupling beam can be idealized as

a truss with tension and compression diagonals along the

axes of the diagonally placed reinforcement (Figure 5-15).

Vertical equilibrium of the truss denes the shear strength

as:

The inequality at the right side of Equation 21-9 is not from

equilibrium but instead expresses the upper bound permitted

by ACI 318, similar to the limit on wall shear (Section 5.4).

Equation 21-9 requires determination of the reinforcement

angle

. At least two layers of reinforcement are required

in each diagonal bundle, so more than minimum cover is

required to the centroid of the bundle. A good starting point

is to assume the centroidal depth at the critical section is jd =

h – 8 inches, from which

can be determined.

The basic strength design requirement for a diagonally

reinforced coupling beam considers only shear; moment

resistance is automatically provided by the idealized truss

(Figure 5-15). The design requirement is

≥ V

, where

is determined from building analysis under design load

combinations, and

= 0.85 (ACI 318 § 9.3.4(c)).

The main reinforcement must be fully developed in adjacent

wall segments. For conventionally reinforced beams, ACI 318

§ 21.7.5.2(b) typically governs for straight bars. For diagonally

reinforced beams, the anchorage must be designed to develop

1.25f

in tension. Headed reinforcement sometimes is used

to shorten development lengths and facilitate construction.

It should be noted that slip of reinforcement from adjacent

wall segments is an important component of the overall

deformation capacity of a coupling beam. Consequently,

short headed bar anchorage can reduce deformation capacity

of a coupling beam. Extending the headed bar beyond

minimum development length l

will improve coupling beam

deformation capacity.

(ACI 318 Eq. 21-9)

= 2A

sin

≤ 10√f ’

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

Figure 5-14

– Alternative details for diagonally reinforced coupling beams.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

Figure 5-15

– Free-body diagram of half-span of a diagonally reinforced

coupling beam. (Gravity loads not shown.)

5.8.2 Coupled Walls

Under lateral loading, coupling between walls causes variations

in wall axial force in addition to moment and shear (Figure

5-8). The resulting combinations of moment and axial force

produce increased exural tension demand on some regions

of the cross section (at a in Figure 5-8) and reduced exural

tension demand on others (at c in Figure 5-8). Similarly,

exural compression demands differ for the two coupled walls

(d versus b in Figure 5-8). Individual walls designed for these

combinations may have asymmetric boundary elements such

as shown in Figure 5-16).

Alternative Coupling Beam Details

This Guide presents details prescribed by ACI 318.

Several alternative detailing approaches have been

proposed for use, including: hybrid beams combining

elements of conventionally reinforced and diagonally

reinforced beams; alternative arrangements of

diagonally oriented reinforcement, and steel coupling

beams. This Guide recommends checking with the

local jurisdiction to determine acceptability of alternative

designs.

5.9 Geometric Discontinuities

Where vertical discontinuities occur in multi-story walls, P-M

interaction analysis must explicitly account for the change

in vertical force paths. A common example occurs at a wall

opening with solid panels above and below (Figure 5-18). For

the design of the solid panel immediately above and below

the opening, the P-M interaction check must exclude the

portion of wall stacked with the opening. However, since this

Figure 5-16

– Characteristic coupled wall cross sections.

Figure 5-17

– P-M

capacity check for coupled walls.

Redistribution of Internal Moments and Shears

Special structural walls and coupling beams are

designed to have inherent ductility. As such, the

designer should be able to take advantage of some

moment redistribution relative to values obtained from

elastic analysis without detrimental effect on building

performance. For example, considering the coupled

walls in Figure 2-9, elastic analysis will produce equal

wall moments and shears for both the tension and

compression walls. There may be some benet (e.g.,

reduced reinforcement congestion or more economical

foundation design) of redistributing moment from the

tension wall to the compression wall. Likewise, coupling

beam moments and shears will vary continuously over

height, whereas there is some benet to uniform beam

design over several contiguous levels. Some building

codes (e.g., Eurocode 8, 2004) permit wall moments in

any vertical wall segment to be decreased by up to 30 %,

provided the moment and proportional shear are picked

up by other wall segments. Furthermore, coupling beam

moments can be decreased up to 20 % at any level,

provided the total coupling force over building height is

not reduced. This approach is not explicitly recognized

by U.S. building codes, but is deemed reasonable for

design of coupled special structural walls.

Tests of coupled walls show that the compression

wall is stiffer than the tension wall, such that moment

(and shear) naturally “migrates” from the tension wall

to the compression wall during earthquake shaking.

Therefore, designing for force redistribution is both more

efcient and more realistic.

Figure 5-17 illustrates the P-M capacity check for a pair of

coupled walls symmetric about the system centerline. The

solid curve corresponds to the P-M nominal strength, with the

right side applicable to the compression wall and the left side

applicable to the tension wall. The dashed curve is design

strength (nominal strength reduced by strength reduction

factor

). Finally, the range of P-M demands under design

load combinations including earthquake load is shown by the

two inclined lines. This is an example of a well-designed wall

with axial force well below the balanced point.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

Figure 5-20

– Strut-and-tie model.

In addition to transferring axial and exural forces around

the opening, designs need to consider transfer of shear forces

around the opening. The procedure, illustrated in relation to

Figure 5-10, is to determine how much shear is to be carried by

the vertical wall segments on either side of the wall opening,

and then design horizontal reinforcement to drag the required

horizontal shears from these segments into the solid segments

above and below.

Rows of openings in coupled walls sometimes are interrupted

by solid wall segments at the roof level, at mechanical

stories, or at basement walls, and these solid segments can

be subjected to large demands. Figure 5-19 illustrates the

case where coupled walls transmit moments and axial forces

to a basement wall, which in turn distributes the forces into

the foundation elements. Very large shear forces can develop

in the basement wall between the two wall piers. This

region should be analyzed to determine the shear forces on

this “horizontal wall segment.” Boundary element vertical

reinforcement should be well anchored into this segment,

preferably full depth, and the panel should be well conned

and generously reinforced for shear. Alternatively, if it is

found to be benecial to system performance, the designer

should consider adding an opening to such areas to eliminate

the discontinuity. These openings can have nonstructural inll

to restore the programmatic intent.

Figure 5-18

– P-M analysis at irregular opening.

(a) Wall elevation (b) Sections for P-M analysis

Strut-and-tie models can be useful to understand the ow of

forces around wall irregularities. Figure 5-20 illustrates a

highly irregular condition at the base of a wall for which a

strut-and-tie model is useful. Wall moment and axial force

from above are resisted primarily by tension and compression

resultants at a and c. Shear from above is resisted primarily

by panel bcef, producing diagonal compression strut bf,

which requires tension tie be. The horizontal component

of strut bf requires tension tie def, for which appropriate

tension reinforcement should be provided. Panel degh resists

the majority of shear in the rst story. ACI 318 Appendix

A prescribes stress limits for struts, ties, and nodes of the

strut-and-tie model. Given the irregular geometry, and lack

of a clearly dened plastic-hinge region, determination of

connement requirements would have to be according to ACI

318 § 21.9.6.3 (described as Method II Section 5.3.3).

Figure 5-19

– Forces in solid wall below or above row of openings.

is a solid panel, it can be assumed that plane sections remain

plane. The effect of the opening likely is negligible beyond

approximately l

above and below the opening, where l

is the

width of the opening (Figure 5-18).

5.10 Columns Supporting Discontinuous

Walls

A column or wall pier supporting a discontinuous structural

wall (for example, member  in Figure 5-20) can be subjected

to compressive overload due to axial force and moment transfer

from the discontinuous wall. For columns, ACI 318 § 21.6.4.6

requires full-height column connement for all stories beneath

the discontinuous wall if the axial force related to earthquake

effect exceeds A

f ’

/10. The connement reinforcement

must extend upward into the discontinuous wall at least the

development length of the longitudinal reinforcement. If the

column terminates at a wall, the connement reinforcement

must extend the same distance downward into the wall below.

If it terminates at a footing or mat, extension 12 inches into

the footing or mat is required, unless it terminates within one

half the footing depth from an edge of the footing, in which

case it must extend at least l

(calculated for f

) of the largest

column longitudinal reinforcement. Similar requirements

apply for wall piers (ACI 318 § 21.9.8).

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

6.1 Special Inspection

Proper construction of special structural walls is essential to

ensuring that a building, once constructed, complies with the

requirements of the code and the approved design. To foster

proper construction, the IBC requires special inspections for

most concrete buildings.

IBC Table 1704.4 requires periodic inspection to verify size

and placement of reinforcing steel. Periodic inspection includes

inspection of all completed reinforcing steel placement.

Concrete also requires special inspections, including:

Verifying use of required design mixture

Inspecting formwork for location, dimensions, and debris

Sampling fresh concrete for strength test specimens,

performing slump and air content tests, and determining

concrete temperature at time of placement

Placing of concrete and shotcrete

Curing temperature and techniques

The design professional for a building must prepare a statement

of special inspections identifying the required inspections

for construction of the building. The statement is to include

the materials, systems, components, and work required to

have special inspection; the type and extent of each special

inspection; the type and extent of each test; additional

requirements for seismic or wind resistance; and clarication

of which inspections shall be continuous and which shall be

periodic. The statement of special inspections must include

inspection requirements for seismic force-resisting systems in

structures assigned to Seismic Design Category C, D, E, or F.

The only exception to this last requirement is for reinforced

concrete buildings that are less than 25 ft in height above the

grade plane and that are located on a site with design spectral

response acceleration at short periods, S

, less than or equal

to 0.5 g.

The special inspector must be a qualified person who

demonstrates competence to the satisfaction of the building

official for inspection of the construction. The special

inspector is to furnish inspection reports to the building ofcial

and the design professional indicating whether work inspected

was completed in conformance with approved construction

documents. Discrepancies are to be brought to the immediate

attention of the contractor for correction. If not corrected,

they are to be brought to the building ofcial and design

professional prior to completion of that phase of the work.

A nal report documenting required special inspections and

correction of any discrepancies noted in the inspections also

is to be submitted.

6.2 Materials

6.2.1 Concrete and Shotcrete

ACI 318 § 21.1.4 requires specied compressive strength,

f ’

, of at least 3000 psi for structural concrete. Additional

requirements apply where lightweight concrete is used (see

ACI 318 § 21.1.4). Where high-strength concrete is used, the

value of √f ’

is restricted to an upper-bound value of 100 psi for

any shear strengths or anchorage/development lengths derived

from Chapters 11 and 12 of ACI 318. Chapter 21 of ACI 318

does not include this upper-bound value for determining the

shear strength of structural walls or coupling beams, but this

Guide recommends including it. Some jurisdictions impose

additional restrictions on the use of high-strength concrete.

For some structures, specied concrete strength of structural

walls is higher than that of the diaphragm/oor system, resulting

in a weak slab sandwiched between two stronger wall sections.

ACI 318 § 10.12, which allows column concrete compressive

strength to be 1.4 times that of the oor system, is intended

to apply only for axial force transmission in columns. Some

jurisdictions deem this applicable for structural walls. This

Guide, however, recommends that it be applied for moment

and axial force transmission only where the wall is conned

by slabs on all sides. Applying this for shear goes beyond the

code intent and is not recommended. The higher wall strength

can be maintained using a jump core or ying form system for

the wall construction to precede the oor construction. Where

concrete for the portion of the wall through the thickness of the

oor system is placed with concrete for the oor system, the

higher strength concrete should be puddled at these elements

and extended 2 ft into the slab as allowed for columns in ACI

318 § 10.12.1.

Use of shotcrete for structural walls is governed by IBC §

1913. Where wall reinforcement is larger than No. 5 bars, or

reinforcement spacing is less than 2½ inches for walls with

single curtain or 12d

in walls with two curtains of steel, the

IBC requires preconstruction tests to demonstrate adequate

encasement of the reinforcing bars.

6.2.2 Reinforcement

Deformed reinforcement resisting earthquake-induced exural

and axial forces in special structural walls and coupling beams

must conform to ASTM A706 Grade 60 (ACI 318 § 21.1.5).

Alternatively, ASTM A615 Grades 40 and 60 are permitted if

A706 stress and strain requirements are met. The optional use

of A615 reinforcement sometimes is adopted because it may

6. Additional Requirements

•

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

be more widely available and may be less expensive. Higher-

strength longitudinal reinforcement, including ASTM A706

Grade 80, is prohibited by ACI 318-11 because of insufcient

test data to demonstrate its use and concerns about higher bond

stresses and increased buckling tendency. ACI 318 § 21.1.1.8

permits alternative material such as ASTM A706 Grade 80 if

results of tests and analytical studies are presented in support

of its use and approved by the building ofcial.

Higher-strength reinforcement up to 100,000 psi nominal yield

strength is permitted for design of transverse reinforcement.

This reinforcement can reduce congestion problems especially

for members using higher strength concrete. Where used,

the value of f

used to compute the amount of connement

reinforcement is not to exceed 100,000 psi, and the value of f

used in design of shear reinforcement is not to exceed 60,000

psi except 80,000 psi is permitted for welded deformed wire

reinforcement (ACI 318 § 11.4.2). The intent of the code

requirement is to limit the width of shear cracks.

6.2.3 Mechanical Splices

Longitudinal reinforcement in special structural walls is

expected to undergo multiple yielding cycles in prescribed

locations during design-level earthquake shaking. If

mechanical splices are used in these locations, they should be

capable of developing nearly the tensile strength of the spliced

bars. Outside yielding regions, mechanical splices, if used,

can have reduced performance requirements.

ACI 318 classies mechanical splices as either Type 1 or Type

2, as follows: (a) Type 1 mechanical splices conform to ACI 318

§ 12.14.3.2, that is, they are to be capable of 1.25f

in tension

or compression, as required; (b) Type 2 mechanical splices are

required to develop the specied tensile strength of the spliced

bar. Where mechanical splices are used in special structural

walls, only Type 2 mechanical splices are permitted within a

distance equal to twice the member depth from sections where

yielding of the reinforcement is likely to occur as a result

of inelastic lateral displacements. Either Type 1 or Type 2

mechanical splices are permitted in other locations.

6.2.4 Welding

Welded splices in reinforcement resisting earthquake-induced

forces must develop at least 1.25f

of the bar and are not to

be used within a distance equal to twice the member depth

from sections where yielding of the reinforcement is likely to

occur as a result of inelastic lateral displacements. Welding of

stirrups, ties, inserts, or other similar elements to longitudinal

reinforcement that is required by design is not permitted

because cross-welding can lead to local embrittlement of the

welded materials. Welded products should only be used where

test data demonstrate adequate performance under loading

conditions similar to conditions anticipated for the particular

application.

6.3 Additional System Requirements

Structures assigned to Seismic Design Categories D, E, or F

must also satisfy certain other ACI 318 Chapter 21 requirements,

as summarized below.

6.3.1 Anchoring to Concrete

Anchors resisting earthquake-induced forces must conform to

the seismic design requirements of ACI 318 § D3.3, which aim

to provide either a ductile yielding mechanism in the anchor or

attachment, or sufcient overstrength to reduce risk of failure.

The provisions of D3.3 do not apply to the design of anchors

in portions of structural walls that are intended to yield during

design-level shaking.

6.3.2 Diaphragms

Structural diaphragms are required to satisfy requirements of

ACI 318 § 21.11. For elevated diaphragms in buildings without

vertical irregularities, the diaphragm forces are predominantly

associated with transferring inertial forces from the diaphragm

to the vertical elements of the seismic force-resisting system.

ASCE 7 contains requirements for determining these

diaphragm forces. For elevated diaphragms in dual systems

or for buildings with vertical irregularities, the diaphragms

also resist transfer forces associated with interaction among

the different elements of the seismic force-resisting system.

For buildings with a podium level (Figure 2-5), the diaphragm

transmits overturning forces from above-grade structural walls

to the basement walls or other stiff elements of the podium.

Diaphragm design should aim to produce a diaphragm capable

of transmitting forces to vertical elements of the seismic force-

resisting system without signicant inelastic response in the

diaphragm. For this reason, ASCE 7 requires collectors of

diaphragms to be designed for forces amplied by the factor

, which is intended to account for structural overstrength of

the building. ACI 318 § 9.3.4 contains additional requirements

related to the strength reduction factor for diaphragm shear.

Moehle et al. (2010) presents guidance for cast-in-place

diaphragms.

6.3.3 Foundations

ACI 318 § 21.12.1 presents requirements for foundations,

including specic requirements for the foundation elements

as well as requirements for longitudinal and transverse

reinforcement of walls framing into the foundation. Slabs-on-

ground that resist seismic forces from walls must be designed

as diaphragms according to ACI 318 § 21.11.

6.3.4 Members Not Designated as Part of the

Seismic Force-Resisting System

Common design practice designates only some of the building

framing to be part of the seismic force-resisting system. The

remainder of the structural framing not designated as part

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

of the seismic force-resisting system, sometimes referred

to as “gravity-only” framing, needs to be capable of safely

supporting gravity loads while the building sways under

maximum expected earthquake ground motions. Failure to

provide this capability has resulted in building collapses in

past earthquakes.

ACI 318 § 21.13 species design requirements for members

not designated as part of the seismic force-resisting system.

The requirements apply to columns, beams, beam-column

connections, slab-column connections, and wall piers of

“gravity-only” framing. In some cases, the requirements

approach those for special moment frames designated as part of

the primary seismic force-resisting system. In some buildings

it may be more economical, and may improve performance,

to spread the seismic force resistance throughout the building

rather than concentrating it in a few specially designated

elements.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

7. Detailing & Constructability Issues

A special reinforced concrete structural wall relies on carefully

detailed and properly placed reinforcement to ensure that it

can maintain strength through multiple cycles of deformation

beyond yield. Although a structural wall is considered a

singular element, reinforcement modules within the wall are

typically pre-tied and hoisted into the place as separate pieces

(Figure 7-1). The pre-tied modules are spliced to create

a fully interlocked reinforcement cage prior to closing the

forms and casting the wall. Aspects of detailing to improve

constructability and performance are described below.

Figure 7-1

– Pre-tied modules (some modules encircled).

7.1 Boundary Element Connement

As discussed in Section 5.3.4, the extent of a boundary element

is integrally linked to the size and spacing of the vertical

reinforcement within. Furthermore, a vertical bar is required

in the corner of each hoop or crosstie bend. For this reason, it

may be convenient rst to determine the desired connement

layout prior to selecting vertical reinforcement. Fortunately,

the connement quantity and layout are dened by a closed-

form equation that is independent of design forces.

The connement variables typically at the designer’s discretion

are the connement bar size, and the horizontal and vertical

spacing of connement hoop legs and crossties. Large diameter

conning bars are desirable to reduce congestion, but bars

larger than No. 5 are impractical because of required space

for bar bends and hook tails. For higher strength steel, there

also can be a limit to what bar size is bendable with locally

available equipment.

Horizontal spacing of connement legs, and hence the spacing

of vertical reinforcement within the boundary element, will

typically be much tighter (4 to 8 inches) than desired for the

remainder of the wall. It is common to select vertical bar

spacing within a boundary element that is a divisor of the

vertical bar spacing in the unconned portion of the wall.

For example, if 12-inch spacing of vertical reinforcement is

considered practical for the unconned wall, the spacing of

vertical bars within the boundary element should be 6 inches

or 4 inches. This is benecial because as vertical boundary

bars drop off at higher elevations, the remaining bars align

with and can be spliced to the 12-inch grid.

Boundary element reinforcement very much resembles a

ductile column within the structural wall. A representative

boundary element at the end of a planar wall is shown in Figure

7-2. Note that each crosstie has a 90° and a 135° hook, and

these must be alternated end for end along both the length

and the height.

Figure 7-2

– Boundary connement for planar wall.

Some anged walls require connement throughout the ange,

in which case connement must extend at least 12 inches into

the wall web (Figure 7-3). For very long conned boundary

regions, one approach is to provide closely spaced connement

reinforcement in both directions at wall ends, with only closely

spaced through-wall crossties along the middle extent of

the wall. In this case, more widely spaced horizontal shear

reinforcement in the web satisfying ACI 318 Eq. 21-5 can

adequately conne the wall lengthwise.

Structural wall longitudinal reinforcement must extend into

supporting elements and be fully developed for f

or 1.25f

in tension. See Section 5.3.3 for details. Where boundary

elements are provided, equivalent horizontal connement

must be extended into the support. For structural walls on

shallow foundations, this connement must be extended 12

inches into the footing or mat. For structural walls supported

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

by all other elements, or where the edge of the boundary

element is within one-half the footing depth from an edge of

the footing, the connement must extend into the support a

distance equal to the development length of the largest vertical

bar in the boundary. The critical subset of this category is

boundary elements landing ush with the edge of a foundation

or signicant foundation step. This commonly occurs for

structural walls that enclose elevator cores. The elevator

pit dimensions commonly require a signicant depression

on one side of the structural wall. For this condition, it is

recommended that the base of the depression be considered

as the base of the structural wall. Vertical bars are therefore

developed below the depression, and connement is continued

through the depth of the depression.

Figure 7-3

– Boundary connement for wall ange.

7.2 Bar Compatibility

The critical location for detailed consideration of bar placement

is the interface of wall ends with coupling beams. The main

coupling beam reinforcement must extend into the wall end a

length sufcient to fully develop the bar capacity (see Section

5.8.1). Bar compatibility becomes especially challenging where

diagonal bars must extend into a heavily conned section. Full-

scale pre-construction mockups can help identify solutions for

particularly challenging designs (Figure 7-4).

To be reliably anchored, coupling beam longitudinal

reinforcement must be placed inside the wall vertical

reinforcement. For conventionally reinforced beams, this

results in side cover over beam longitudinal reinforcement

around 3 inches (Figure 5-12, Section A-A). Transverse

reinforcement must be detailed for this increased cover so that

the corner longitudinal bars are rmly placed in stirrup and

crosstie bends. This decreased available width must also be

considered when verifying clear horizontal spacing between

longitudinal bars, a necessary measure to facilitate concrete

placement and consolidation.

Figure 7-4

– Anchorage of diagonal reinforcement in heavily reinforced

boundary element.

7.3 Anchorage of Web Reinforcement

To engage the full wall length to resist shear, horizontal shear

reinforcement must be anchored at wall ends to develop

the yield strength of the bar. For wall ends without special

boundary elements, this requires hooking the horizontal

reinforcement around the end vertical bars, or enclosing the

wall end with U-stirrups having the same size and spacing

as the horizontal reinforcement. For wall ends detailed as

special boundary elements, horizontal reinforcement must be

anchored to develop f

within the conned core of boundary

element, and extended to within 6 inches from the wall end.

See Figure 5-3.

7.4 Bar Splices

According to ACI 318 § 21.9.2.3, reinforcement in structural

walls is required to be developed or spliced for f

in tension

in accordance with ACI 318 Chapter 12, with some noted

exceptions. At locations where yielding of longitudinal

reinforcement is likely to occur as a result of lateral

displacements, development and lap splice lengths of

longitudinal reinforcement are required to be 1.25 times values

calculated for f

in tension. Lap splices, mechanical splices,

and welded splices are permitted, with laps splices being the

most common. As for all elements of concrete construction,

reinforcing bars larger than No. 11 may not be lap spliced in

structural walls. Mechanical and welded splices are required

to satisfy ACI 318 § 21.1.6 and 21.1.7.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

The rst splice of vertical reinforcement typically occurs

immediately above the foundation, where wall longitudinal

reinforcement laps with dowel bars. These dowels provide

the critical mechanism of transferring tension and shear

forces from the structural wall to the foundation. All vertical

reinforcement must be extended into the foundation a depth

sufcient to be fully developed for tension. For constructability

purposes, it is recommended that dowels with 90° hooks extend

to the bottom of the foundation where they can be tied rmly

the foundation bottom reinforcement.

For structural walls with two curtains of reinforcement, it

is preferred for the vertical reinforcement to be inside the

horizontal reinforcement. This arrangement improves splice

strength and buckling restraint for the verticals.

Horizontal reinforcement is always treated as “top-cast”

reinforcement, requiring

= 1.3 for all development and

lap splice length calculations. Splice locations might not be

nalized until the contractor has determined the breakdown of

pre-tied segments and the overall erection sequence including

formwork operability. For structural walls with pre-tied

segments, the horizontal reinforcement has the additional

function of tying the pieces together in the nal arrangement

(Figure 7-1).

7.5 Miscellaneous Detailing Issues

As signicant obstructing elements, structural walls must be

closely coordinated with mechanical, electrical, and plumbing

designs to enable the routing and distribution of these systems.

Although it is preferable to spatially separate structural walls

from the nonstructural components introduced by other

trades, it is often necessary to provide blockouts and sleeves

to allow for minor penetration of the structural walls. It is

recommended to identify early those areas that are not available

for penetrations, typically boundary elements, coupling beams,

and the development zone of coupling beams in wall ends.

Where penetrations occur, it is important to provide trim

reinforcement around all edges. The exact layout and size of

trim reinforcement should be selected to provide a complete

load path for all local forces and to inhibit cracking of the walls

along the sides of the penetrations.

The transfer of diaphragm forces between slabs and structural

walls is ideally detailed in a distributed manner. Where this

cannot be accomplished, due to large slab openings or very

large transfer forces, horizontal collector elements must be

created. At the wall-to-slab interface, this generally takes

the form of large quantities of longitudinal reinforcement.

Collector forces must be fully resolved into the wall end,

requiring embedment in excess of a typical development

length when the wall horizontal reinforcement is insufcient

to provide a complete splice.

When steel elements are framed to structural walls, the

connection detail typically takes the form of an embedded

steel plate with deformed bars or headed studs welded to that

plate and developed into the backing structural wall. This is a

frequent occurrence for structural walls enclosing and forming

an elevator core. Steel members will be required to separate

multi-bank elevators, and to support elevator and counterweight

rails. These members must be attached to the structural walls

in very precise locations. To allow for tolerance in placement

of the embedded steel connection plates, it is recommended

to oversize the plates to allow for misplacement up to 3 inches

without compromising the integrity of the connection.

7.6 Concrete Placement

Similar to column construction, the placement of structural

wall concrete in high-aspect-ratio (height/width) forms

inevitably includes the issues of concrete drop height, blind

vibration, practical lift heights, and selection of a mixture

with appropriate owability. These issues need to be clearly

discussed and coordinated with the contractor to ensure that the

nal product is fully consolidated, monolithic, and isotropic.

The intersection of slabs and structural walls is a region in

which the placement sequence and resulting concrete strength

needs to be closely considered. For multi-story construction,

structural walls are typically cast to the underside of the slab

above. The slab is cast over the top of the wall, and the wall

construction resumes above. This results in a plane of slab

concrete placed through the structural wall. The standard

remedy is to place higher strength concrete in the slab over

the top of the structural wall, extending two feet beyond the

face of the wall. This method, typically called puddling, must

be carefully scheduled with the slab pour to ensure that the

high strength concrete is well integrated with the remainder

of the slab.

The slip-form method of constructing structural walls

eliminates this weakened plane at the structural wall-to-slab

intersection. In this and other similar wall forming techniques,

the structural wall is cast continuously through the depth of

the slab, construction joints notwithstanding. Although this

method avoids the potential for insufcient concrete strength

in the structural wall, the slab-to-wall connection must be

detailed to accommodate all force transfers. This critical

location must transfer vertical shear from gravity forces in the

slab and in-plane horizontal shear from diaphragm forces, and

it must maintain integrity during drift-induced rotation of the

slab-to-wall connection. Shear keys can help transfer shear

forces at this otherwise smooth interface. Reinforcement

details must be selected with due consideration of anticipated

local deformations during earthquake shaking.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

ACI (2011). Building code requirements for structural concrete (ACI 318-11) and commentary, American Concrete Institute,

Farmington Hills, MI.

ASCE (2010). Minimum design loads for buildings and other structures (ASCE/SEI 7-10), American Society of Civil

Engineers, Reston, VA.

ATC (2010). Modeling and acceptance criteria for seismic design and analysis of tall buildings, Report No. ATC 72-1,

Applied Technology Council. Also available as Report No. PEER 2010/111, Pacic Earthquake Engineering Research

Center, University of California, Berkeley.

DBI (2009). “Structural bulletin SB 09-09,” Department of Building Inspection, City and County of San Francisco.

Deierlein G.G., Reinhorn A.M., and Willford M.R. (2010). “Nonlinear structural analysis for seismic design: A guide for

practicing engineers,” NEHRP Seismic Design Technical Brief No. 4, produced by the NEHRP Consultants Joint Venture, a

partnership of the Applied Technology Council and the Consortium of Universities for Research in Earthquake Engineering,

for the National Institute of Standards and Technology, Gaithersburg, MD, NIST GCR 10-917-5.

Eurocode 8 (2004). Eurocode 8: Design of structures for earthquake resistance, part 1, general rules, seismic actions and

rules for buildings, Comité Européen de Normalisation, European Standard EN 1998-1:2004, Brussels, Belgium.

IBC (2009). International Building Code, International Code Council, Washington, DC.

Moehle J.P., Hooper J.D., Kelly D.J., and Meyer T.R. (2010). “Seismic design of cast-in-place concrete diaphragms, chords,

and collectors: A guide for practicing engineers,” NEHRP Seismic Design Technical Brief No. 3, produced by the NEHRP

Consultants Joint Venture, a partnership of the Applied Technology Council and the Consortium of Universities for Research

in Earthquake Engineering, for the National Institute of Standards and Technology, Gaithersburg, MD, NIST GCR 10-917-4.

Osterle, R. G., Aristizabal-Ochoa, J. D., Shiu, K. N. and Corley, W. G. (1984). “Web crushing of reinforced concrete

structural walls,” ACI Journal, American Concrete Institute 81 (3), pp. 231-241.

SEAW (2009). “Special reinforced concrete shear walls as building frame systems for mid- and high-rise buildings,” White

Paper 1-2009, Earthquake Engineering Committee, Structural Engineers Association of Washington.

SEAOC (2008). “Reinforced concrete structures,” Article 9.01.010, SEAOC blue book – Seismic design recommendations,

Seismology Committee, Structural Engineers Association of California.

UBC (1997). Uniform Building Code, International Conference of Building Ofcials, Whittier, CA.

8. References

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

9. Notations and Abbreviations

g,be

A ’

s,be

f ’

, F

gross area of concrete section bounded by web

thickness and length of section in the direction of

shear force considered, in.

area of concrete section of coupling beam resisting

shear, in.

effective cross-sectional area, in.

gross area of concrete section, in.

gross area of wall boundary containing longitudinal

reinforcement A

s,be

, in.

area of longitudinal tension reinforcement in

boundary element, in.

area of longitudinal compression reinforcement in

boundary element, in.

total area of longitudinal reinforcement at wall

boundary, in.

cross-sectional area of transverse reinforcement

within spacing s and perpendicular to dimension b

in.

total area of longitudinal reinforcement, in.

area of shear reinforcement within spacing s, in.

total area of reinforcement in each group of diagonal

bars in a diagonally reinforced coupling beam, in.

area of shear-friction reinforcement, in.

width of compressive face of member, in.

cross-sectional dimension of member core measured

to the outside edges of the transverse reinforcement

composing area A

, in.

web width or wall thickness, in.

distance from extreme compression ber to neutral

axis, in.

exural compression force, lb

deection amplication factor dened in ASCE 7

coefcient for upper limit on calculated period

dened in ASCE 7, or exural compression force, lb

distance from extreme compression ber to centroid

of longitudinal tension reinforcement, in.

nominal diameter of bar, in.

the effect of dead load

eccentricity of axial load relative to geometric

centroid of section, measured in the plane of the wall,

in.

effects of earthquake, or related internal moments and

forces

modulus of elasticity of concrete, psi

the horizontal seismic load effect dened in ASCE 7

effect of vertical seismic input

specied compressive strength of concrete, psi

specied yield strength of reinforcement, psi

specied yield strength of transverse reinforcement,

psi

horizontal and vertical forces in squat wall, lb

design lateral force of level i, lb

gravity acceleration, in./s

shear modulus of concrete, psi

overall thickness or height of member, in.

height from base to roof, in.

the story height below Level x

height of entire wall from base to top, or clear height

of wall segment or wall pier considered, in.

maximum center-to-center horizontal spacing of

crossties or hoop legs on all faces of the boundary

element, in.

effects of soil, water in soil, or other materials

effective moment of inertia, in.

moment of inertia of gross concrete section about

centroidal axis, neglecting reinforcement, in.

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

IDR

, j

n,CS

pr,CS

, M

u,CS

, S

factored axial force normal to cross section

occurring simultaneously with V ’

, to be taken as

positive for compression and negative for tension,

axial force due to dead load D, lb

nominal axial strength of cross section, lb

nominal axial strength at zero eccentricity, lb

factored axial force; to be taken as positive for

compression and negative for tension, lb

value of P

at the critical section for exure and

axial force, lb

effect of horizontal seismic (earthquake-induced)

forces

response modication coefcient

center-to-center spacing, in.

center-to-center spacing of transverse

reinforcement, in.

the effect of snow load

spectral acceleration, g

spectral displacement, in.

section moduli of gross section about x and y axes,

in.

design, 5-percent-damped, spectral response

acceleration parameter at short periods

design, 5-percent-damped, spectral response

acceleration parameter at 1-second period

fundamental period of the building, seconds

approximate fundamental period of the building,

seconds

period at intersection of constant acceleration

and constant velocity regions of design response

spectrum dened in ASCE 7

tensile force in distributed vertical reinforcement in

wall web, lb

inter-story drift ratio

coefcients dening horizontal distances between

centroids of exural compression force and

exural tension forces T

, T

and T

length of boundary element, in.

development length in tension of deformed bar, in.

development length in tension of deformed bar

with a standard hook, measured from critical

section to outside end of hook, in.

development length in tension of headed

deformed bar, measured from the critical section

to the bearing face of the head, in.

width of opening, in.

length of clear span measured face-to-face of

supports, in.

unsupported length of compression member, in.

length of entire wall or length of wall segment or

wall pier considered in direction of shear force, in.

the effect of live load

nominal exural strength at section, in.-lb

value of M

at the critical section for exure and

axial force, in.-lb

probable exural strength of member, with

or without axial force, determined using the

properties of the member at the joint faces

assuming a tensile strength in the longitudinal

bars of at least 1.25f

and a strength reduction

factor,

, of 1.0, in.-lb

value of M

at the critical section for exure and

axial load, in.-lb

factored moment at section, in.-lb

values of M

about x and y axes, in.-lb

value of M

at the critical section for exure and

axial force, in.-lb

number of stories from base to roof

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

u,net

V ’

u,CS

Abbreviations

ACI American Concrete Institute

ASCE American Society of Civil Engineers

ATC Applied Technology Council

IBC International Building Code

SEAOC Structural Engineers Association of California

SEI Structural Engineering Institute

net tensile strain in extreme layer of longitudinal

tension steel at nominal strength

modication factor reecting the reduced mechanical

properties of lightweight concrete, all relative to

normalweight concrete of the same compressive

strength

coefcient of friction dened by ACI 318

a redundancy factor based on the extent of structural

redundancy present in a building

ratio of area of boundary element longitudinal

reinforcement to gross area boundary element

ratio of area of distributed longitudinal reinforcement

to gross concrete area perpendicular to that

reinforcement

ratio of area of distributed transverse reinforcement

to gross concrete area perpendicular to that

reinforcement

normal stress used to determine required boundary

elements by Method II, psi

strength reduction factor

exural overstrength factor

ultimate curvature, in.

-1

factor used to modify development and lap splice

length based on reinforcement location

dynamic amplication factor

amplication factor to account for overstrength of the

seismic force-resisting system dened in ASCE 7

tensile force in boundary element vertical

reinforcement, lb

exural tension force, lb

factored transient net tension forces on section, lb

nominal unit shear strength of wall, dened as

, lb/in.

seismic base shear calculated according to the

equivalent lateral force procedure of ASCE 7

nominal shear strength provided by concrete, lb

nominal shear strength provided by shear

reinforcement, lb

design shear force for load combinations including

earthquake effects, lb

nominal shear strength, lb

factored shear force at section, lb

factored shear force at section after application of

dynamic amplication and exural overstrength

factors, lb

value of V

at critical section, lb

factored load per unit length of beam

effective seismic weight of building, lb

horizontal distance between centroids of exural

compressive force and wall axial force, P

, measured

in plane of wall, in.

angle dening the orientation of reinforcement

relative to longitudinal axis

coefcient dening the relative contribution of

concrete to nominal wall shear strength

factor relating depth of equivalent rectangular

compressive stress block to neutral axis depth dened

by ACI 318

design displacement, in.

nominal compressive strain capacity of plain concrete

strain at f

for reinforcing steel

Seismic Design of Cast-in-Place Concrete Special Structural Walls and Coupling Beams: A Guide for Practicing Engineers

10. Credits

Cover photo Image courtesy of John Wallace, University of California, Los Angeles

Figure 2-4 Image courtesy of National Information Service for Earthquake Engineering -

Pacic Earthquake Engineering Research Center

Figure 3-3 Image courtesy of Ken Elwood, University of British Columbia

Figure 3-4 Image courtesy of W. Gene Corley

Figure 5-11, 7-1, 7-2, 7-3 Images courtesy of Magnusson Klemencic Associates

Figure 5-14 Image courtesy of the American Concrete Institute

“reprinted with permission from the American Concrete Institute”

All other images courtesy of Jack Moehle, University of California, Berkeley