# Design Provisions for Shear Walls

RESEARCH AND DEVELOPMENT BULLETIN RD028.01D

L.

# Design Provisions for Shear Walls

## by A. E. Cardenas, J. M. Hanson,

## W. G. Corley, and E. Hognestad

## Reprinted with permission from

Journal

## of

the American Concrete Institute,

## Proceedings Vol. 70, No. 3, March 1973, pages 221-230.

## PORTLAND CEMENT

## ASSOCIATION

**CODE BACKGROUND PAPER**

**Background material used in preparing ACI 318-71**

**Design Provisions for Shear Walls**

## by A. E. Cardenas, J. M. Hanson,

## W. G. Corley, and E. Hognestad

**The background and development of Section**

II. 16,

**Special Provisions for Walls, of the ACI**

**Building Code (ACI 318-7 I ) is discussed.**

**These provisions were found to predict satisfactorily the strength of six high-rise and seven low-rise shear walls tested at the laboratories of the Portland**

**Cement Association, as well as the strength of wall specimens tested by other investigators.**

**The results of the PCA experimental tions are summarized in an Ap endix.**

**investiga-**

**Thirteen rectangular shear walls were teste cl’ under combinations of lateral and axial loads.**

**One of the specimens was subiected to ten cycles of load reversals.**

**Keywords: strength; axial high-rise loads; building buildings; codes; reinforced shear strength; shear stress: sheer walls; cyclic loads; flexural concrete; reseerch; structural design.**

WALLS ARE DEEP, relatively thin, vertically cantilevered reinforced concrete beams. They are commonly used in structures to resist the effects of gravity loads and story shears due to wind or earthquake forces.

This paper summarizes background material for Section 11.16, Special Provisions for Walls, of the 1971 ACI Building Code.l The provisions are intended to ensure adequate shear strength. However, other considerations such as flexural strength, energy absorption, lateral stiffness and reinforcement details are equally important to obtain satisfactory structural performance.

There has been relatively little research on the strength and behavior of shear walls. Investigators in Japan2-4have been concerned primarily with the strength of low-rise shear walls surrounded by a reinforced concrete or steel frame and subjected to load reversals.

Japanese shear wall design provisions are described in the Standards for Calculation of Reinforced Concrete Structures.6 They are based on the philosophy that the entire shear force is to be carried by reinforcement, when a certain limiting concrete shear stress is exceeded.

In the early 1950’s, Benjamin and Williams,o-g at the University of Stanford, conducted extensive static tests on low-rise shear walls surrounded by a reinforced concrete frame. Their proposed design equations had limited practical use due to restrictions in their applicability. An extension of this investigation, dealing with dynamic loads, was conducted by Antebi, Utku and Hansen10 at the Massachusetts Institute of Technology.

Dynamic loads simulated were those due to, blast from atomic weapons rather than earthquakes.

Prior to publication of ACI 318-71,1 the only provisions for design of shear walls in the United

States were those contained in Uniform Buildihg

Code?l

Fig, 1 shows a graphical representation of the provisions for shear walls in Uniform Building

Code, Depending on the height-to-depth ratio of the wall, h,,,/lu,, the nominal total design shear stress, v,,, is assumed to be resisted either only by

*This paper was prepared as part of the work of ACI-ASCE

Committee426, Shear and Diagonal Tension.

**low t**

## em -

**./**

## ,/’

*/*

*/’*

/ ./

## /-

T

## —-

## T

## -- —.- ._

~ota,

~,bn

**shear stress,vu**

**_ Shear strms carried by Enforcement Nominal shear et ress**

**W e~**

**4~**

**-**

**-**

**Shsar strws oairled by concrete, Vc**

24 -

**o**

**I**

**I z**

**Height to depth ratio, hw/lw**

**Noto, @ English. 0,265 @M6trio**

**3**

**Fig.**

*I*

**— Provisions for shear walls in the 1970 Uniform**

**Building Code**

2

*Design Provisions for Shear Walls*

**AC I member**

**Development**

**Alex**

**Section.**

**E.**

**Cardenas**

**Currently,**

**ASCE**

**Committee**

**Committee 426, Shear**

442,

**Lateral F6rces.**

**is a consulting engineer,**

**Lima, from**

**Peru.**

**He raceived**

**Universidad National and his PhD his BS in civil engineering de Ingenieria, Lima, degree in 1965 and in 1963 and his MS**

1968

**from degree the University workad for PCA of Illinois, as a**

**From research**

**1968 to engineer**

**1972 Dr.**

**Cardenas in the Structural he is a member**

**Diagonal Tension of ACl and AC I**

**ACI**

**Structural member John**

**Development**

**Portland**

**Chairman**

**Secretary**

**Tension.**

**Cemant of of**

**AC**

**Section,**

**Association,**

**I Committee**

**ACI-ASCE**

**M.**

**Hanson**

**Committee is**

**Research**

**Skokie,**

**215, Fatigue**

**426, assistant of**

**Shear manager**

**Development**

**Ill.**

**Currently,**

**Concrete, and of**

**Div., he is and**

**Diagonal**

**ACI**

**Research member**

**Section,**

**Cemant**

**University**

W.

**Association, of Illinois**

**Gene**

**Resaarch**

**Corlay**

**Skokie, in 1961, is manager and Development of**

**Div.,**

**Structural**

**Portland**

**Ill.**

**He received**

**Dr.**

**Corlay has his done**

**PhD from research and was a development**

**Rasearch and he is Chairman**

**Development of AC I coordinator for**

**La b,, Ft.**

**Belvoir,**

**Committee 443,**

**U.S.**

**Va.**

**Army**

**Concrete**

**Eng.**

**Currently,**

**Bridge**

**Design,**

**Design.**

**and Secretary of AC I-ASCE Committee 428, Limit**

**ACI**

**Research, member Eivind**

**Raseerch and**

**Hognestad**

**Development is director**

**Div.,**

**Association, research**

**Skokie, papers**

**Ill.**

**as well**

**Dr.**

**Hognestad as collaborating**

**Portland has authored on of saveral**

**Engineering**

**Cement numerous technical committee mittea reports.**

**318, Standard**

**Currently,**

**Building of Board Committee he**

**Codas, on lnternatiWa is a member and**

**! Activities, of is also**

**AC a**

**I Commember**

tween deep beams and shear walls. First, deep beams are usually loaded through the extreme fibers in compression. Under these conditions, shear carried by the concrete in a member without web reinforcement is greater than the shear causing diagonal tension cracking. Shear walls, however, are deep members loaded through stubs or diaphragms. This type of member, if it does not contain web reinforcement, may fail at a shear equal to or only slightly greater than the shear causing diagonal cracking.l* Second, deep beams are not usually subjected to axial loads, whereas the consideration of axial compression or tension may be important in shear walls.

Recognizing the limitations of the existing information on the strength of shear walls, the

Portland Cement Association started an experimental investigation in 1968.The highlights of this investigation are described in the Appendix.

the concrete, or by the concrete and the horizontal reinforcement.

The nominal permissible shear stress carried

**by**

the concrete, v,, on shear walls with low

*hw/2w*

ratios is assumed similar to that in deep beams.

It is taken as the straight-line lower bound of results of shear tests on deep beams without web reinforcement reported by dePaiva and Siess.lz

This shear stress is limited to 5.4+~~ for walls with

*hJlw*

ratios of 1.0 or less. For

*hw/ lw*

ratios of

2,7 or more, v, is taken equal to 2+V~, the value recommended for reinforced concrete beams in

ACI 318-63,13

Shear stress carried by the reinforcement is based on results of shear tests on beams containing web reinforcement reported by Slater, Lord and Zipprodt~Aas well as those reported by de-

Paiva and Siess.12Based on these tests, it is assumed that vertical or horizontal web reinforcement in shear walls with

*hw/l,.*

ratios of 1.0 or less does not appreciably increase the value of v,, above that of Vc attributed to the concrete. Consequently, their total shear stress is limited to 5,4+

~~, Shear walls with

*h,,llw*

ratios of 2,0 or more are considered to behave as beams; Total design shear stress for these walls is taken equal to 10+

V7, as recommended in A~I 318-63,1’

While the UBC provisions represented an advancement in design, additional work, including that by Crist,15Leonhardt and Walther,lQCardenas and Magura17 and Cardenas, has led to separate provisions for deep beams and shear walls in

Chapter 11 of ACI 318-71.1These provisions recognize that there are important differences be-

**DEVELOPMENT OF DESIGN PROVISIONS**

**Flexural strength**

The experimental investigation demonstrated the importance of considering the flexural strength of a shear wall. In many designs of shear walls in high-rise buildings, use of the minimum amount of horizontal shear reinforcement required by the provisions of Section 11,16 of ACI 318-71,1

0.0025times the concrete area, will be adequate to develop the flexural strength of the wall.

Using assumptions that are in accord with those in Secti,on 10.2 of AC!I 318-71,the fIexural strength of rectangular shear walls containing uniformly distributed vertical reinforcement and subjected to combined axial load, bending and shear, can be calculated as: 17 where

**c iii= cl+a**

**2q + 0.85~1**

(1)

Mu = design resisting moment at section, in. lb

*A.*

*=*

total area of vertical reinforcement at section, f.

L sq in.

= specified yield strength of vertical reinforcement, psi

= horizontal length of shear wall, in.

distance from extreme compression fiber to neutral axis, in.

distance from extreme compression fiber to resultant of tension force, in, thickness of shear wall, in.

design axial load, positive if compression, lb specified compressive strength of concrete, psi

**0.85**

for strength jc’ up to

**4000**

psi

**(281.0**

kgf/ cm2) and reduced continuously to a rate of

**0.05**

for each

1000 psi

**(70**

kgf /cm2) of strength in excess of

**4000**

psi

**(281.0**

kgf/cm2) can be approximated as:

*M,, = 0.5 AJU1*

*‘(’+%)(1-8 ‘“*

Based on results of the PCA investigation, Eq.

(1) appears to satisfactorily predict the flexural equal to or greater than 1.0,

Fig. 2 shows a comparison of Eq. (1) and (2) for different amounts of Grade 60 uniformly distributed vertical reinforcement for f:= 4000 psi (281.0 kgf/cmZ) and for two ratios of axial compression, a = O and a = 0.25. The comparison shows that for the case of pure bending, a = O,

Eq. (2) is in good agreement with the more rigorous Eq, (1). In the case of a rather Iarge axiaI compression, a = 0.25, the greatest difference is about 5 percent. Accordingly, the use of the simplified Eq. (2) appears adequate for practical design.

**Shear strength**

The distribution of lateral loads on shear walls varies with their height.lo-zo For example, under a lateral wind loading, this distribution may vary from nearly uniform on a wall in a tall building to a single concentrated force on a wall in a low building, Differences in lateral load distribution, geometry, and wall proportions lead to conditions that may make shear strength the controlling criterion in the design of low-rise shear walls.

As pointed out in the report of ACI-ASCE Committee 326(426), Shear and Diagonal Tension,21

American design practice is based on the premise that shear capacity of concrete beams is made up of two parts. One part is the shear carried by concrete, and the other part is the shear carried by web reinforcement. Furthermore, these two parts are considered to be independent, so that web reinforcement is required only for that portion of the total shear that exceeds the limit of the shear carried by the concrete.

With the adoption of ACI 318-63, an additional premise became inherent in the shear design provisions. This premise is that the shear carried by the concrete is equal to the shear causing significant inclined cracking. This last assumption underscores the importance of the cracking shear.

**A,fy~**

**Floxural**

**Strength,**

**2.0**

**I**

**1**

**I**

**I**

**\**

**\**

\

\

**\**

\

1

**\**

1

**H**

**\**

\

**\**

**\**

*ICA Research and Development Bulletin 3*

**I**

t

**I r fy= 60,000 psi (4219 kgf/cml)**

**I**

1

**f~. 4,000 p$i (281 kgf/cml)**

**1**

**1.0 -**

**‘q’2$----::**

**E,.(2)**

**0**

,

**Amount of Uniformly [email protected] Vertical Reinforcement,**

*p,*

**parcont**

**Fig, 2 — Flexural strength of rectangular shear walls**

**Shear carried by concrete**

It is generally ‘recognized that inclined cracking

*in*

concrete beams is of two types. In recent years, these types of cracks have been described as either “web-shear” or “flexure-shear,” The way in which these cracks develop in reinforced and prestressed concrete beams has been described in detail elsewhere.22,23

The provisions of ACI 318-71 use Eq. (11-4) for computing the shear causing flexure-shear cracking in a reinforced concrete member. The limiting value of 3.5 ~~ for Eq. (11-4) serves as a measure of the shear causing web-shear cracking. In prestressed concrete beams, the shear causing flexure-shear or web-shear cracking is computed from Eq, (11-11) or (11-12), respectively. Eq. (11-

12) predicts web-shear cracking as the shear stress causing a principal tensile stress of approximately 4 V j: at the centroidal axis of the cross-section. Eq. (11-11) as originally deveIoped23 predicts flexure-shear cracking as the shear stress causing a flexural crack, corresponding to a flexural tensile stress of 6 ~ ~ to form at a section located distance d/2 from the section being investigated, plus a small stress, 0.6 V f:, intended to represent the shear required to transform the initiating flexural crack into a fully developed fIexure-shear crack.

It is important to recognize that Eq. (11-11) for prestressed concrete beams is applicable to reinforced concrete beams subject to axial compression. However, the results would be expected to be conservative, because the shear stress required to transform an initiating flexural crack into a flexure-shear crack will usually be considerably greater than 0.6 ~~, Recent worl#4 has attempted to take this into account. It follows, therefore, that a similar approach applied to shear walls would be conservative.

4

*[email protected] Provisions for Shear Walls*

**Iofi**

t

**———**

**=**

**———————**

**T.+al de,b” sheer $tress,vu**

**1**

flexural tensile stress of 6 w% at a section located a distance

*lw/2*

above the section being investigated. For shear walls, an expression for the value of nominal shear stress expected to cause flexureshear inclined cracking is Eq. (11-33) of ACI 318-

71:

**N:om;::l strew**

**_v_**

**0,6twh**

**6~**

**4~**

**-**

**-**

**Shear stress carried**

**Z%& -**

,~

**Moment to shear ratio, Mu/Vu**

**Note:~ English. 0.265 fiMotric**

*Fig. 3*

**—Shear carried bywcocrate in rectangular shear**

Web-shear cracking would be expected in a shear wall when the principal tensile stress at any interior point exceeds the tensile strength of the concrete. In an untracked rectangular section, the maximum shear stress due to a shear force,

*V,*

is:

3V

‘“” =

*21wh*

**(3)**

At the occurrence of a principal tensile stress of

4 ~~ on a section subjected to combined axial load, N, and shear, Eq. (3) becomes:

Eq. (4) can be closely approximated by: 25

3V

==4vT+o”3&-

*(5)*

*W*

Introducing into Eq. (5) the concept of nominal shear stress, v =

*V/hd,*

and assuming that the effective depth d, is equal to 0.81W,leads to:

*V*= 3.3 w+&*

*(6)*

where VOis the value of nominal shear stress expected to cause web-shear inclined cracking, The subscript u has been added to N to indicate total applied design axial load occurring simultaneously with

*Vu.*

Eq. (6), which is the same as Eq. (11-32) in ACI

318-71, will apply to most low-rise shear walls. In cases where the axial load, N,,, is small, the equation reduces to VO= 3,3 Vfi Limitations due to the assumption of

*d = 0,81W*

are discussed later.

Flexure-shear cracking occurs when a flexural crack, because of the presence of shear, turns and becomes inclined in the direction of increasing moment, It is assumed that the flexure-shear cracking strength of a shear wall may be taken equal to the shear from a loading producing a

The shear carried by the concrete therefore corresponds to the least value of v. computed from

Eq. (6) or (7). However, the value of v. need not be taken less than corresponding values for reinforced concrete beams. Therefore, v. may be taken at least equal to 2 VT if N. is zero or compression, or 2 (1 + 0.002

*N./Ar) v=*

with N. negative for tension, as given in ACI 318-71.

Fig. 3 shows a diagram of Eq. (6) and (7) as a function of the moment to shear ratio,

*Mu/VW,*

for selected values of axial compression, expressed as

*NJlwh,*

The upper horizontal portion represents the web-shear cracking strength, as given by Eq.

(6). The transition to the suggested minimum of

2 w% rep resents the flexure-shear cracking strength, as given by Eq.

**(7),**

**Shear carried by reinforcement**

The contribution of reinforcement to shear strength of concrete beams has traditionally been based on the “truss analogy.” This concept is dis.

cussed in the report of ACI-ASCE Committee 326

(426), Shear and Diagonal Tension.2’ Applied to shear walls, this contribution, expressed in terms of nominal shear stress, is: v* = phfv

**(8)**

where

*ph*

= ~= ratio of horizontal shear reinforcement

Shear reinforcement restrains the growth of inclined cracking, increases ductility, and provides a warning in situations where the sudden formation of inclined cracking may”lead directly to distress. Accordingly, minimum shear reinforcement is highly desirable in any main load-carrying member. In shear walls, the specified minimum reinforcement area of 0.0025 times the gross area of the shear wall, provides a shear stress contribution of about 2 VT to the strength of the wall.

For low walls, it is reasonable to expect that the horizontal shear reinforcement is less effective than indicated by Eq. (8). However, the vertical reinforcement in the wall will contribute to its shear strength, in accord with the concept of shear-friction.26 Because of insufficient test data to develop recommendations for walls with low

*PCA Research and Development Bulletin 5*

*1*

*I f*

*I*

*,*

*1*

**8X**

.“

**8hnor stre8s,vu**

**-**

**I v———————————————**

**~Tafal dw!qn**

**f =eo,ooo psi y (421 Ekgf/cma) f:. 5,000 psi**

**(352 kgf/cm’)**

**Minimum shear stress**

**Nominal shear stress**

**~**

**0,8 lwh**

**2Jz-**

**4a**

-.

**k**

o~

**.——**

**I**

**—-— _**

**\**

**\**

**\ .— ------**

**1225 Parssnt**

**Reinforcement**

**H**

**Concrete**

Moment

**@hear ratio, Mu/Vu**

**NotO, @ English. 0.265 ~Motric**

**+**

**{**

**I .0 -**

**0,s -**

**Fig.**

**4 — Minimum shear stt;gth of rectangular shear**

height to depth ratios, the amount of vertical reinforcement required is equal to the amount of horizontal reinforcement when hw/lWis less than

0,5. When

*hJL is*

greater than 2.5, the required minimum vertical reinforcement area is 0.0025.

Between hW/lWratios of 0.5 and 2.5, the required minimum is determined by linear interpolation, as expressed by Eq. (11-34) of ACI 318-71.

The shear capacity of rectangular shear walls containing minimum shear reinforcement is plotted in Fig. 4 as a function of the moment to shear ratio, The curves have been plotted for a concrete strength, f,’, of 5000 psi (350 kgf/cm2), and a yield stress of the horizontal reinforcement, ~V,of 60,-

000 psi (4200 kgf/cmz).

The diagram shows that for these conditions, the minimum shear strength of low-rise walls is of the order of 5.4~, that of high-rise walls is of the order of 4.1 ~.

and

**Definition of nominai shear stress**

In the design provisions, nominal shear stress is used as a measure of shear strength. Nominal shear stress, as defined by Eq. (11-31) of ACI

318-71, is given by:

# ““”m

## vu

**(9)**

where

*vu =*

***

*= h= d=*

total applieddesign shear force at section capacity reduction factor (Section

**9.2,**

ACI

318-71) thicknessof shearwall distancefrom extreme compressionfiber to resultantof tensionforce

In shear walls, the effective depth,

*d,*

depends mainly on the amount and distribution of vertical reinforcement. Fig. 5 shows the variation of the effective depth with these variables. The value of d = 0.8lWis also shown in Fig.

**5. This value is**

**Depth ratio**

**~ lw**

**0.6 -**

04–

**0.2 o**

**1**

**Fig.**

**5 — Variation**

**I**

**001**

**,**

**,..**

!

@@@”

**Reinforcement Oistributlons**

**,**

**0.02**

**Rat io of vertical reinforcement, 48/ lwh**

**I**

**003 of effective shear walls depth in rectangular**

not necessarily conservative or unconservative, because the equations for shear attributed to the concrete have been modified to account for the proposed value of d. The equation for shear attributed to the reinforcement depends on the ability to effectively reinforce for shear over the vertical projection of the assumed inclined crack.

**Limitation on uitimate shear stress**

A limitation on ultimate shear stress is generally considered to represent failure due to crushing of concrete “struts” in beam webs,

For reinforced concrete beams, ACI 318-631a limited the nominal ultimate shear stress to

10W* There is some indicationz~ that the shear strength of a beam without web reinforcement may decrease with increasing depth, Other testslo on beams with low a/d ratios indicate that the limiting shear stress may be less than 10~.

However, the tests reported in this paper indicate that shear stresses up to 10~ can be attained in walls with web reinforcement, even under load reversals. Attainment of shear stresses of this magnitude requires careful reinforcement detailing.

**Comparison OF DESiGN Provisions**

**TEST RESULTS**

**WiTH**

The proposed design provisions for shear strength of shear walls have been compared with experimental results reported by Muto and

Kokusho,2 Ogura, Kokusho and Matsoura~ Benjamin and Williams,6!7Antebi, Utku and Hansen,~O and the PCA Laboratories.17 In the computation of nominal shear stress, the effective depth,

*d,*

was taken equal to the distance from the extreme compression force to the resultant of the tension

*O was not included here, so that the value is comparable to stresses in

ACI

31S-71.

*6*

*Design Provisions for Shear Walls*

*20~*

**Measured vu**

**15~**

**Iofi**

**5&**

**A**

**A**

v

**Vv**

**AA**

❑

**n**

**A**

**Vn**

**A**

n al

**A**

**A**

**A**

❑

❑

❑

**A n**

**A**

❑

**A n c**

**Calculated vu**

**English= 0.265**

**~Metric Note*&**

**Fig.**

**6 — comparison of measured strengths and calculated**

force, or 0.8lW,whichever was greater, Results of the tests carried out by PCA are summarized in

Tables Al and A2 in the Appendix.

Fig. 6 compares calculated and measured shear strength for these test results. The solid line represents equality between calculated and measured shear stresses, and the dashed line represents consideration of the ACI capacity reduction factor, ~, equal to 0.85.

The two PCA test results plotted under the solid line are for specimens where the shear failure was observed to have been precipitated by loss of anchorage of the flexural reinforcement. The PCA test result marked with an

*R*

corresponds to the specimen subject to load reversals. Comparison of measured and calculated strengths in Fig. 6 indicates that the design provisions are satisfactory,

**OTHER CONSIDERATIONS**

v

~v

In the development of design provisions for shear walls, the main emphasis was on evaluation of flexural and shear strength under static loadings. However, considerations of energy absorption, where earthquake resistance is required, and lateral stiffness are also important factors influencing the behavior of walls. Properly detailed reinforcement is also essential to obtain satisfactory performance,

Based on results of a recent investigation,zsjze

Paulay has indicated that energy absorption and stiffness characteristics of a wall may be significantly improved if the shear reinforcement does not yield when the wall reaches its flexural capacity, The apparent reason for this is that the widths of the inclined cracks are restrained, thereby maintaining aggregate interlock across the crack, and doweling action of the main reinforcement, Paulay has suggested that the total shear in a wall subject to load reversals should be taken by shear reinforcement, This requirement appears reasonable where great energy absorption is required.

In cases where high ductility is essential, as may be the case in spandrels or piers, it may be desirable to physically divide the wall into two or more parts as suggested by Muto.s’JThis would have the effect of substantially increasing the

*M/V*

ratio of the wall elements thereby making flexure the predominant consideration. In any case, it is desirable to provide shear strength capacity in excess of the flexural strength.

The importance of careful detailing of shear walls must be emphasized. From experie~ce, many researchers have found it is sometimes difficult to apply. very large concentrated loads to walls, without experiencing local failures.

The possibility of tension in unexpected locations should also be given careful consideration.

When beam action begins to break down due to the formation and growth of inclined cracks, particularly in deep members, the steel stress at the intersection of the inclined cracking and the flexural reinforcement tends to be controlled by the moment at a section through the apex of the inclined cracking. These stresses can be quite different from those calculated on the basis of the moment at a section through the lower extremity of the crack. Consequently, adequate anchorage of main reinforcement at force application points is essential,

**CONCLUSIONS**

Results of tests summarized in this paper indicate that flexural strength, as well as shear strength, must be considered in an evaluation of the load-carrying capacity of a shear wall. For use in design, the flexural strength of shear walls with height to depth ratios, hW/tw,of 1.0 or more can be satisfactorily predicted using Section

**10.2,**

Assumptions, of ACI 318-71. Equations for determining the design flexural capacity of rectangular walls with uniformly distributed vertical reinforcement are presented in this paper,

For use in design, the shear strength of walls can be satisfactorily predicted using Section 11.16,

Special Provisions for Walls, ACI 318-71,

In the design of shear walls, considerations such as energy absorption, lateral stiffness, and detailing of reinforcement need special attention,

**ACKNOWLEDGMENTS**

This investigation was carried out at the Structural

Development Section, Portland Cement Association.

Mr. D, D. Magura, former PCA Research Engineer, initiated the experimental investigation.

Laboratory technicians B, J, Doepp, B. W. Fullhart, W. H. Graves,

W, Hummerich, Jr., and O. A. Kurvits performed the laboratory work.

**REFERENCES**

1, ACI Committee 318, “Building Code Requirements for Reinforced Concrete (ACI 318-71) ,“ American Concrete Institute, Detroit, 1971, 78 pp.

2. Muto, Kiyoshi, and Kokusho, $eiji, “Experimental

Study on Two-Story Reinforced Concrete Shear Walls,”

Tmn.sactions, Architectural Institute of Japan (Tokyo),

No. 4’7, Sept. 1953, ‘7 pp.

3. Ogura, K.; Kokusho, S,; and Matsoura, N., “Tests to Failure of Two-Story Rigid Frames with Walls, Part

24, Experimental Study No. 6,”

*Report No.*

**18,**

Architectural Institute of Japan, Tokyo, Feb. 1952.

4, Tsuboi, Y.; Suenaga, Y.; and Shigenobu, T., “Fundamental Study on Reinforced Concrete Shear Wall

Structures—Experimental and Theoretical Study of

Strength and Rigidity of Two-Directional Structural

Walls Subjected to Combined Stresses M, N. Q.,” T~an++ actions, Architectural Institute of Japan (Tokyo), No.

131, Jan, 1967.

*(Foreign*

Literattwe Stud~ No. 536, Portland Cement Association, Skokie, Nov. 1967.)

5. “Standards for Calculation of Reinforced Concrete

Structures,” Architectural Institute of Japan, Tokyo,

1962. (in Japanese)

6. Williams, Harry A., and Benjamin, Jack R., “Investigation of Shear Walls, Part 3—Experimental and

Mathematical Studies of the Behavior of Plain and

Reinforced Concrete Walled Bents Under Static Shear

Loading,” Department of Civil Engineering, Stanford

University, July 1953, 142 pp.

7, Benjamin, Jack R., and Williams, Harry A., “Investigation of Shear Walls, Part 6-Continued Experimental and Mathematical Studies of Reinforced

Concrete Walled Bents Under Static Shear Loading:’

Department of Civil Engineering, Stanford University,

Aug. 1954, 59 pp.

8. Benjamin, Jack R., and Williams, Harry A., “The

Behavior of One-Story Reinforced Concrete Shear

Walls,” P~oceedings, ASCE, V. 83, ST3, May 1957, pp.

1254-1 to 1254-49. Also, Transactions, ASCE, V.

124,

1959, pp. 669-708,

**No.**

9, Benjamin, Jack R., and Williams, Harry A., “Behavior of One-Story Reinforced Concrete Shear Walls

Containing Openings,” ACI

JOURNAL,

Proceedings V. 55,

5,

**Nov.**

1958, pp. 605-618.

10.: Antebi, J.; Utku, S.; and Hansen, R. J., “The Response of Shear Walls to Dynamic Loads,” DAS~-1 160,

*PCA Research and Development Bulletin 7*

Department of Civil and Sanitary Engineering, Massachusetts Institute of Technology, Cambridge, Aug. 1960.

11. Uniform Building Code, International Conference of Building Officials, Pasadena, 1967 and 1970 editions.

12, dePaiva, H. A. Rawdon, and Siess, Chester P.,

“Strength and Behavior of Deep Beams in Shear,”

Proceedings, ASCE, V, 91, ST5, Part 1, Oct. 1965, pp.

19-41.

13, ACI Committee 318, “Building Code Requirements for Reinforced Concrete (ACI 318-63) ,“ American Concrete Institute, Detroit, 1963, 144 pp.

14. Slater, W. A,; Lord, A. R,; and Zipprodt, R. R.,

“Shear Tests of Reinforced Concrete Beams,” Technologic

*Paper No, 314,*

National Bureau of Standards,

Washington, D. C., 1926, pp. 387-495.

15. Crist, Robert A., “Shear Behavior of Deep Reinforced Concrete Beams—V.

2: Static Tests,” AFWL-

TR-67-61, The Eric H. Wang Civil Engineering Research

Facility, University of New Mexico, Albuquerque, Oct.

1967. Also, Proceedings, RILEM International Symposium on the Effects of Repeated Loading on Materials and Structures (Mexico City, Sept. 1966), Instituto de

Ingenieria, Mexico City, 1967, V. 4, Theme 4, 31 pp.

16. Leonhardt, Fritz, and Walther, Rene, “Deep Beams

(Wandartige Traeger) ,“

Bulletin No.

178, Deutscher

Ausschuss fur Stahlbeton, Berlin, 1966, 159 pp.

17, Cardenas, A. E., and Magura, D. D., “Strength of

High-Rise Shear Walls—Rectangular

*Response*

Cross Sections,” of

Multistory Concrete Structures’ to Lateral

*Forces,*

SP-36, American Concrete Institute, Detroit,

1973, pp. 119-150.

18. Zsutty, Theodore, “Shear Strength Prediction for

Separate Categories of Simple Beam Tests,” ACI

JOURNAL,

*Proceedings*

V. 68, No. 2, Feb. 1971, pp. 138-

143.

19. Khan, Fazlur R., and Sbarounis, John A., “Interaction of Shear Walls and Frames,”

*Proceedings,*

ASCE,

V. 90, ST3, June 1964, pp. 285-335.

20, “Design of Combined Frames and Shear Walls,”

Advanced

*Enginee~ing*

Bulletin No. 14, Portland Cement

Association, Skokie, 1965.

21. ACI-ASCE Committee 326(426), “Shear and Diagonal Tension,” ACI

JOURNAL,

*Proceedings*

V. 59, No.

1, Jan. 1962, pp. 1-30; No. 2, Feb. 1962, pp. 277-334; and

No. 3, Mar. 1962, pp. 353-396.

22, MacGregor, James G., and Hanson, John M., “Proposed Changes in Shear Provisions for Reinforced and

Prestressed Concrete Beams,” ACI

JOURNAL,

*Proceedings*

V. 66, No. 4, Apr. 1969, pp. 276-288.

23. Sozen, Mete A., and Hawkins, Neil M., Discussion of “Shear and Diagonal Tension” by ACI-ASCE Committee 326 (426), ACI

JOURNAL,

Proceedings V. 59, No. 9,

Sept. 1962, pp. 1341-1347.

24.

Mattock, Alan H., “Diagonal

Tension Cracking in

Concrete Beams with Axial Forces,”

*Proceedings,*

ASCE,

V. 95, ST9, Sept. 1969, pp. 1887-1900.

25, ACI Committee 318, “Commentary on Building

Code Requirements for Reinforced Concrete (ACI 318-

63) ,“ SP-10, American Concrete Institute, Detroit,

1965, 91 pp.

26. Mast, Robert F.,

“Auxiliary Reinforcement in

Concrete Connections,” Proceedings, ASCE, V. 94, ST6,

June 1968, pp. 1485-1504.

27. Kani, G, N. J., “How

Safe Are Our Large Reinforced Concrete Beams?,” ACI

JOURNAL,

*Proceedings*

V. 64, No. 3, Mar. 1967, pp. 128-141.

28. Paulay, Thomas, “The Coupling of Reinforced

Concrete Shear Walls,”

*P~oceedings,*

Fourth World Con-

*8 [email protected] Provisions for Shear Walls*

ference on Earthquake Engineering, Santiago, Chile,

Jan, 1969, V. 1, 11. B2-75 to B2-90.

29. Paulay, Thomas, “Coupling Beams of Reinforced

Concrete Shear Walls,”

*Proceedings,*

ASCE, V. 97, ST3j

Mar. 1971, pp. 843-862.

30. Muto, Kiyoshi,

“Recent Trends in High-Rise

Building Design in Japan,”

*Proceedings, Third world*

Conference on Earthquake Engineering, New Zealand,

1965, V. 1, pp. 118-147.

**APPENDIX**

**PCA investigation**

In this investigation, thirteen large rectangular shear wall specimens have been tested under static combinations of axial load, bending, and shear. Six of the specimens, SW-1 through SW-6, represented walls in high-rise buildings,ls The remaining seven, SW-7 through SW-13, represented walls inlow-rise buildings.

One of the low-rise shear walls, SW-13, was subjected to ten cycles of load reversals.

All test specimens were rectangular reinforced concrete members with a thickness h=3 in. (7,92 cm) and a depth ZW= 8 ft 3 in. (1,90 m), For convenience, the specimens were tested as horizontal cantilevered beams.

However, in describing the specimens, reference is always made to the position of a wall in an actual building rather than its position during testing, Fig. Al shows the test setup for one of the high-rise walls.

Loading rods extending through the test floor were used to apply the simulated static lateral forces.

Postten~ioning rods, running horizontally in the photo, were used to apply the simulated gravity loads. The portion of the specimen to the right of the support represents a foundation providing full restraint to the base of the wall,

Shear wall specimens SW-1 through SW-6 represent the lower portion of a shear wall in a frame-shear wall structural system.zo!zl The height of the specimen corresponds to the distance between the base of the wall and its point of contraflexure.

It was assumed that 50 percent of the total shear force at the base of the wall would be applied at the point of contraflexure.

The remaining 50 percent was uniformly distributed between the point of contra flexure and the base of the wall.

Four of the six high-rise shear wall specimens SW-1,

SW-2, SW-3 and SW-6 had a height of 21 ft (6.40 m), the other two, SW-4 and SW-5, were 12 ft (4.09 m) high, An axial compressive stress of about 420 psi

(29,5 kgf/cmz) was applied, The main variable was the amount and distribution of the vertical reinforcement, Horizontal shear reinforcement equal to 0.27

percent of the concrete cross-sectional area was provided in each of the six specimens.

Six of the seven specimens representing low-rise shear walls,

SW-7 through SW-12, were subjectedto a

single static lateral force applied at the top of the wall.

These specimens had a height,

*hw,*

equal to their [email protected],

L, of

*6*

ft 3 in. (1,90 m). At the top of these specimens, the thickness of the wall was enlarged to simulate the effect of floor slabs framing into the shear wall. The enlarged section distributes the applied shear force along the top of the specimen.

No axial compression was applied to these specimens.

Variables investigated were the amount and distribution of vertical reinforcement and the amount of horizontal shear reinforcement.

The seventh of the low-rise shear wall specimens,

SW-13, was subjected to ten cycles of load reversals.

All of the characteristics of this specimen were similar to those of specimen SW-9 previously tested under static loads. The objective of the test was to evaluate the effect of the cyclic loading on the strength and behavior of low-rise shear walls.

Tables Al and A2 summarize material properties, variables investigated and test results for all 13 specimens.

A summary of the results of the PCA investigation is presented in Fig. A2 in the form of bar graphs.

Comparison of test results for specimens representing

*PCA Research and Development Bulletin 9*

high-rise shear walls SW-L SW-2, SW-3 and SW-6 shows that 0.27percent of horizontalreinforcement,an amount consideredto be nearly a practical minimum, is sufficient to develop the flexural strength of walls with varying amounts and distribution of vertical reinforcement.

Specimens SW-4 and SW-5 were designed to have the same flexural capacity as that of specimensSW-3 and SW-6. However,their height, h~, was less. For the appliedloads,the momentto shearratio,

*M./Vu,*

at section LJ2 from the base of the wall, was L for SW-4 and SW-5, and 21t0 for SW-3 and SW-6.

Minimum horizontal reinforcement was again sufficient to develop nearly the calculated flexural strength, even though the shear stresses were substantially higher.

This implies that a greater proportion of the shear was carried by the concrete at the lower

*Mu/Vu*

ratio.

In the group representinglow-rise shearwalls, specimens SW-7 and SW-8 also indicate that walls with minimumhorizontal shear reinforcementhave a high load-carrying capacity. Comparisonsof specimensSW-

11 and SW-12 with SW-7, and also SW-9 with SW-8,

**12W lo~**

**II**

**II**

**II**

**II**

II

**II**

**II**

**II**

**II**

**,1**

**~T**

**,1**

**II**

**SK**

:~

**Nominol Shear**

**Stress,**

**6&**

**‘=&h**

**44**

**2~ o**

**Mark**

Phlpercent

*Pvw,*

**percent**

**Mode of Failure**

**Nominal Shear**

**Stress Symbols**

*

**/**

**/**

**/**

**/**

**n**

*SW-1*

**SW-2 SW-3 SW-6**

**0.27**

**0.27**

**t?**

**0.27**

**Lo**

**0.27**

**3,0**

**0.27**

**Lo**

**SW-4**

**0,27**

**3.0**

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

**SW-5**

**0.27**

**1.0**

*** /**

**/**

**/**

**/**

**/**

**/**

**/**

**/**

**/**

**/**

**/**

**/**

**/**

**5**

**SW-7**

**0.27**

**Lo s**

**SW-B**

**0.27**

**30 s**

**MU IVU=21W**

**Nu /~h=420 psi w**

**Mu/vu .tw**

**Nu/~h.**

**420 psi**

**Measured**

at

**Yield**

**(29.5**

**kgf/c m2)**

**Meosureti at Ullimote r**

**(29.5**

**kgf/cm2)**

**‘-**

**Calculated**

**Flexural Strength**

**SW-9**

**1.0**

**Sw-lo**

**0**

**30**

**F-S**

**0 s v**

**Mu/vu =0.5 ~**

**Sw-1 I SW-12**

**0.75**

**1.0**

**0**

**S-A**

**0 s-A**

**Nu @=O**

**SW-13**

**I ,0**

**3,0**

**F-S**

*** Calculated**

**F,**

**Shear Strength S .**

**Flexure**

**F-S = Flexure-Shear**

**Shear**

**(+. 1.0}**

**S-13 : Shear-Anchorage**

**Note,fl English = 0.265fi**

**Fig. A2 —**

**Results of PCA investigation**

**Metric**

**10**

*Design Provisions for Shear Wads*

SW-I

**SW-2**

**SW-3**

**SW-4**

**SW-5**

**SW-6**

**Sw-’l**

**SW-8**

**SW-9**

**SW-IO**

**SW-U**

**SW-12**

**SW-13**

**TABLE Al**

**— DIMENSIONS**

Mark

**AND**

Concrete

Height

~

20mpre8sive strength f.’ psi

**MATERIAL**

21.0

21.0

21,0

12.0

12.0

21.0

8,25

8.25

6.25

6.25

6.25

8.25

6.25

7420

0880

6780

6740

5900

5950

6240

8180

6240

5850

5540

5570

8200

**590**

**630**

**565**

**820**

**585**

**535**

**530**

**630**

**860**

**650**

**615**

**535**

**565**

**PROPERTIES OF TEST SPECIMENS**

**0,0027**

**0.0100**

**0.0200**

**0.0200**

**o,0220t o.0230t**

**o.0230t**

**0!0300**

**0.0300**

**0.0185$**

**0.0230~**

**0.0230$**

**0.0300**

Ratio

~~*

Vertical

Reinforcement

Horizontal

Yield stress

J:i

Ratio pb

Yield stress

$s1

**60,200**

**65,400**

**88,000**

**60,000**

**60,000**

**63,000**

**65,000**

**65,000**

**85,000**

**65,000**

**65,000**

**85,000**

**04,500**

0.0027

0.0027

0.0027

0.0027

0.0027

0.0027

0.0027

0.0027

0.0100

None

0.0075

0.0100

0.0100

81,300

81,000

60,000

80,000

80,000

70,000

80,000

67;500

60,000

None

85,000

65,000

66,000

Axial stress

Nullwb psi

None

None

None

None

None

None

415

430

420

420

425

430

None

where *A. = *total area of vertical reinforcement, tw = 75 in. and h = 3 in.

tOne-third of total vertical reinforcement concentrated within a distance h /10 from either extremity of cross section (amount of reinforcement in interior region p.w = 0.01).

$One-half of total vertical reinforcement concentrated within a distance 2s0/10 from either extremity of cross section (oflW = 0).

To convert to S1 equivalen~: 1 ft & 0,305 m; 1 psi = 0,0703 kgf/cmz.

**TABLE A2 – TEST RESULTS**

Calculated parameters Flexural strength

Measured

Measured

~oment, Mu, at base kip-ft

3alculated* moment,

**M.**

**at base**

kip-ft

Shear, *V.,* at lw/2, kips

Shear strength

Mark

Moment to shear ratio

*M.IV.*

**at**

lW/2 from base

Ratio

*d/lw,*

at

Calcu-

Iatedt v. v, v%

Measured

Calculated

Moment at the base

Shear at lW/2 from base

Sw-1

**2.OIW**

**0.58**

**406**

**379**

**26.5**

1.7

**3.9**

1.07

0.44

**SW-2**

**SW-2**

**SW-4**

**SW-5**

**SW-6**

**SW-7**

**2.o110**

**2.OIW**

**I.olw**

**1.Olw**

**2.01+0**

**0.51W**

**0.62**

**0.71**

**0.71**

**0.78**

**0,76**

**0.74**

**876**

**1073**

**1077**

**1078**

**1178**

**729**

**850**

**1200**

**1139**

**1121**

**1154**

**880**

**41.4**

**66.0**

**108.6**

**108.6**

**72.5**

**118,7**

2.8

4.5

7.4

7.6

5.3

6.2

**4,0**

**4.0**

**6.6**

**6.8**

**4,4**

**5.3**

1.04

0.90

0,95

0.96

1.02

0.74

0.70

1.13

L12

1.15

1,20

1.55

**SW-8**

**SW-9**

**Sw-lo**

Sw-11

SW-12

SW-135

**o.5110**

**0.5110**

**0.51W**

**o,5110**

**0.51W**

**0.51W**

**—.**

**0.65**

**0.85**

**0s4**

**0!94**

**0.84**

**0.65**

**801**

**954**

**429**

**858**

**925**

**888**

**1009**

**1000**

**700**

**1000**

**1000**

**1000**

**128.1**

**152.7**

**88,7**

**137,0**

**146.0**

**142.1**

9.1

10.7

4.3

6.7

9.4

10.0

**5.6**

**10.0**

**3.3**

**9.8**

**10.0**

**10.0**

0.79

0!95

0.81

0.86

0.93

0.89

1,82

1,07

1.30

0.89

0,94

1.00

*Based on compressive concrete 14miting strain of 0.003, strain compatibilityy and measured material properties.

&d#ated from proposed shear strength equations.

ed is 0,8L0 or greater.

$SW-13 was subjected to 10 cycles of load reversals._

To convert to S1 equivalents: 1 kip = 453.6 kgf; Vfo’, U.S. = 0.285 Vfi metric.

Observed mode of failurd

Flexure

Flexure

Flexure-Shear

Flexure

Flexure-Shear

Flexure

Shear

Shear

Flexure-Shear

Shear

Shear-Anchorage

Shear-Anchorage

Flexure-Shear

indicate that additional horizontal shear reinforcement will further increase capacity.

Comparisons of SW-8 with SW-7, and SW-9 with SW-

12, show that the lateral load carrying capacity aIso increases with vertical web reinforcement.

However, these observations are qualified somewhat by the observation that specimens SW-9, SW-11 and SW-12 did not fail in shear.

In addition, at failure there was yielding of the vertical reinforcement in all of these specimens,

The ultimate shear stress of SW-10, a specimen with no horizontal or vertical web reinforcement, was

4.3 Vz.

Specimen SW-13 was subjected to a total of ten cycles of increasing levels of load reversals.

Comparison of this specimen with SW-9, a physically similar specimen that was subjected to one-directional loading, shows no significant decrease in strength, Both of these specimens developed shear stresses of the order of

10 I f.’.

**Notation**

= shear span, distance between concentrated load and face of support, in.

= gross area of section, sq in.

= total area of vertical reinforcement at section, sq in.

= area of horizontal shear reinforcement within a distance, s, sq in.

= distance from extreme compression fiber to neutral axis, in.

= distance from extreme compression fiber to resultant of tension force, in.

## ;

*q s*

**ph**

**W**

## p

172

~c’

**fll**

h

*h.*

*La*

*Mu*

*N.*

*‘UC vu*

**v**

## VW

## ‘#

*PCA R esearch and Development Bulletin 11*

= square root of specified compressive strength of concrete, psi

= specified compressive strength of concrete, psi

= specified yield strength of reinforcement, psi

= thickness of shear wall, in.

= total height of wall from its base to its top, in.

= depth or horizontal length of shear wall, in.

= design resisting moment at section, in,/lb

= design axial load at section, positive if compression, lb

= **A,~Vllwhfc’**

*=*

vertical spacing of horizontal shear reinforcement, in,

= nominal permissible shear stress carried by concrete, psi

= nominal total design shear stress, psi

= shear force at a section, lb

= total applied design shear force at section, lb

= fv./lwhfc’

= jv/87,000

= 0,85 for strength f.’ up to 4000 psi (281,0 kgf/cmz) and reduced continuously to a rate of 0.05 for each 1000 psi (70.3 kgf/cmz) of strength in excess of 4000 psi (281.0 kgf /

**cm2).**

**=**

capacity reduction factor (Section 9.2 ACI

318-71)

= **A.lsh**

*= A&)h*

**This paper was rece;ved by the Institute May 15, 1972.**

Thispublicationis basedon the facts,tests,andauthoritiesstatedherein.It isintended for the use of professionalpersonnelcompetentto evaluatethe significanceandlimitamaterialit contains.Obviously,the PortlandCementAssociationdisclaimsany and all

**I**

**1**

**I i**

!

I

**I**

1

I

**i**

**I**

I sourcesotherthanworkperformedor informationdevelopedby the Association.

~

-------------------------------

I

**I**

**I**

:

I

KEYWORDS: axial

**rise**

Provisions for Walls, of the

------------------

L

-------loads,buildingcodes,cyclicloads,flexuralstrength,highbuildings,reinforcedconcrete,research,shearstrength,shearstress,shear

ABSTRACT: Discusses background and development of Sec. 11.16, Special

AC!IBuildingCode (ACI 318-71). Theseprovisions were found to predictsatisfactorilythe strengthof six high-riseand seven low-riseshearwallstested at the PCA laboratories,as well as the

?

I

REFERENCE: Cardenas, A. E.; Hanson,

J. M.;

Corley,

W. G.; andHognestad,

E., Des&n

*Provisions for Shear Walls (RD028.OID),*

PortlandCementAssoci-

,

~ ation, 1975.Reprintedfrom

*Journal of the American Concrete Institute,*

Pro-

**I**

;

1 ceedingsVol. 70, No. 3, March1973,pages221-230.

**I**

**I i**

**I i --------------------------------------------------------i**

!

I

**I**

~

!

~

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**PCA**

**R/D Ser. 1494**

## PORTLAND CEMENT I

**ml**

## I ASSOCIATION

**An organization 01 cement manufacturers to improve and extend the uses of portfand cement and concrete through scientific research, engineering fiefd work, and market development.**

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