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Shear Wall

Design Shear Wall

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247 views12 pages

Shear Wall

Design Shear Wall

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thongchai_007
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© © All Rights Reserved
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SHEAR WALL 1, Tentative wall thickness: ffom top- 4m below —> — ,=0.10m for every 9m below increases” +0.02 m also for bearing wall ty 2 max( min (thy25, 125), 100mm ) see. 1453.1 for non-bearing wall ty 2 msx( by/30, 100mm ) soo. 14.6.1 for ext. basement wall and foundation Wall te 2 200 rama 2. Check shear (.=085 ACESS, e= 0.75 ACEO ) 2.4 websshear mek ves 088 yf, 1081) + 022, 1129 Coshere Py is +foreompression & - fr tension ) 2.2 flexural-shear crack 7 ly (033yRi +0.2R, a.) ves 40.1696) + ght eg tro M,/V, —0.51, 23 bsumshear crack ves os3cieome Py JF ane (eis fortension) oy, 11-8 (Wut 4P YA forcomp.) eq 1-4 os fF any Poa 2.4 maximum shear V, 3. Reinforcement B1EVS V2 then for d, S I6mm p, = 0.0020 see 1432 p.™ = 0.0012 for d>1émm — p,™ = 0.0025 00.14.3.3, p,m = 0.0015 32 if PWV S G.Ne then P,D® = 0.0025 see, 11.10.92 W= 4%, 33 if be 0.65 ot 085. for <= 280s © = (Anh (let) and ) 5, Steel spacing: horizontal rit s iy/S ,3t, 450mm ) see, 11.10.93 vertical rf. s 1/3 .3t, 450mm ) sec 111095 Project : Sample No. swt INPUT DATA conc.strength fc’ steel yield fy wall thickness t wall length | ul.moment Mu ultshear Vu ultcomp. Pu total height SHEAR WALL DESIGN ( USD ) ( use 0=0,70 and at least 10% eccentricity ) Reo {if ind mistakes please inform ajar thaksin for corrections) ‘ant Date: 15 Oct 10 Floor 15 ENG. TTC output 280. kse. thickness 25.0 cm, 4000 kse. Ash: ph = 0.0025 25.0 om. Ash = 63 cm2im = 350.0 om. use 2DB 12 @ 0.360 315.0 tm Asv: py = 0.0053 60.0 ton Asv = 13.2. omaim = 100.0 ton use 2DB 16 @ 0,00 = 350 m. 12.08@0.360 16 DB@O.300 3.50 Shear wall.xls | ACI JOURNAL / MARCH 1873 (ODE BACKGROUND PAPER CODE BACKGROUND PAPER _______ Background material used in preparing ACI $1971 TITLE NO. 70-23 7 Design Provisions for Shear Walls 7 By ALEX E, CARDENAS, JOHN M. HANSON, W. GENE CORLEY, and EIVIND HOGNESTAD The background and development of Section 11.18, Special Provisions fer Walls, of the ACI Building Code {ACI 316-71) is discussed. Those pro~ visions found to predict saticfactorily the Strength of six high-rise “and seven low-rise shear walls tested at the laboratories of the Portland Coment Assotiation, as well as the sirength of wall specimens tested by other investigators. ‘The results of the PCA experimental investiga- fions ate summarized in an Appendix. Thirteen rectangular shear walls were tested under combina- tions of lateral and axial loads, One of the spe mens was subjected to ton cyclos of load reversals 1 building codes; cyclic loeds: enrol ‘taingss relorced concrete: reseorch: SA. Rear sees shear wall: strvetucal design. BL SHEAR WALLS ake peep, relatively thin, vertical ly cantilevered reinforced concrete beams. They are commonly used in structures to resist the effects of gravity Joads 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.’ The provisions are intended to ensure adequate shear strength. How- ever, 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. Inves- tigators in Japan? have been concerned primarily with the strength of low-rise shear walls sur- rounded by a reinforced concrete or steel frame and subjected to load reversals. Japanese snear wall design provisions are described in the Standards for Calculation of Re- inforced Concrete Structures* 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, at dhe Univ £ five static tests en low-rise chear walls surroxncied by a reinforced concrete frame, ‘Theit 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 Hansen at the Massachusetts Institute of Technology. Dy- namie loads simulated were those due to blast from atomic weapons rather than earthquakes. Prior to publication of ACI 318-71, the only provisions for design of shear walls in the United States were those contained in Uniform Building Code™ Fig. 1 shows a graphical representation of the provisions for shear walls in Uniform Building Cote. Depending on the height-to-depth ratio of the wall, hty/le, the nominal total design shear stress, v,, is assumed to be resisted either only by i paver wes prepared se part of the work of ACI-ASCE comiils"fie,"Shebr dnd Disgonal ‘eneion, oi] - ove | iE ‘ner sas cre sew Jitancaes ft wove Fig. 1 —Provisions for shear walls in the 1970 Uniform Building Code mm ¢ i j j } i ACI mambar Ales E. Cardanss it 9 contuling onginee Limo. Pere: Ho tocsived his 8S in chil engineering in ftom Universidad Necionel da Ingorieca, Lins, and Ni MS Gegine ard his PhD. degree in 1965 ond 1968 from the Usivonity of liinots, From 1968 to 1972 Dr, Cardenes worted for FCA ass retearch engineer in tho’ Siucloral Bevelopmant Socti he is 0 member of ACI. ASCE “Comite Common 42. Ce ACI momber Joka M. Hansen is opsilent manager of Sirscivral Doveloomant Suction, Research Davelcoment Ds, Portlond Camant” Association, Shotie. Il. Currant he ip Chatman of AC! Committee 215, Faligue of Concrsle, and ‘tary of ACLAGCE Commitioe 426, Shear ond Diagonal ACI mambor W. Gene Corlay ie manager of Sieucosal Research Soci ‘ond Dovolopment. Div. Povlend fol, He Us. Army En, it, Va. Currently ‘Concrete Bridge n, end. Secriaty ef ACLASCE Commivioe 48, Lit Design toe of Exginwstng Portland Cement ‘fen, Sista. Dr Hognetad hoy nsthored sumorovt seently, hy fs 8 mambo the concrete, or by the conerete and the horizontal reinforcement. The nominal permissible shear stress carried by the conerete, v., on shear walls with low h,/le 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. ‘This shear stress is limited to 5.46 for walls With Rv/le Fatios of L0 or less. For it./l, ratios of 27 or more, vis taken equal to 24 fi, the value recommended for reinforced concrete beams in ACT 318-63. Shear stress carried by the reinforcement is bbased on results of shear tests on beams contain. ing wed reinforcement reported by Slater, Lord and Zipprodt as well as those reported by de- Paiva and Siess.? Based on these tests, it is as- sumed that vertical or horizontal web reinforce- ment in shear walls with h,/l, ratios of 1.0 or less does not appreciably increase the value of v, above that of v, attributed to the concrete, Conse- quently, their total shear stress is limited to 5.44 Vie. Shear walls with he/be ratios of 2.0 or more are considered to behave as beams. Total design shear stress for these walls is taken equal to 10g Viv, as recommended in ACI 318-63. While the UBC provisions represented an ad- vancement in design, additional work, including that by Crist," Leonhardt and Walther, Cardenas and Magitsa™” aad Cardenas," has led to separate provisions for deep beams and shear walls in Chapter 11 of ACT 318-71! These provisions rec- ognize that there are important differences be- 222 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 with- out 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’ 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 in- formation on the strength of shear walls, the Portland Cement Association started an. experi- mental investigation in 1968. The highlights of this investigation are described in the Appendix. OF DESIGN PROVISIONS Flexural strength The experimental investigation the importance of considering the fiesu: strength of a shear wall, In many desi: ‘walls in high-rise buildings, use of the minim amount of horizontal shear reinforcemen: req) by the provisions of Section 11.16 of ACT 318-11.! 10,0025 times the concrete area, will be adequate to develop the flexural strength of the wall. Using assumptions that are im accord “with those in Section 10.2 of ACI 318-71, the flexural strength of rectangular shear walls containing uniformly Gistributed vertical reinforcement and subjected to combined axial load, bending and shear, can be caleulated as:1? ssn[ (+3) qa lesign resisting moment at section. jotal area of vertical reinforcement sq in, fy = specified yield strength of vertical reinforce ment, pst te = horizontal length of shear wall, in. fannlae “Ghost” Secuigee’ ip Se Yublchea ES Ethent Assocation, Skeide, I ACI JOURNAL / MARCH 1973, “stgneth of Low-Rise, Shes P = distance from extreme compression fiber to neutral axis, in. - d= distance from extreme compression fiber to resultant of tension force, in. thickness of shear wall, in, esign axial Joad, positive if compression, 1b specified compressive strength of concrete, psi 0.85 for strength fe’ up to 4000 psi (281.0 kgt/ com!) and reduced continuously to a rate of ‘045 for each 1000 psi (70 kgf/em?) of strength fin excess of 4000 pai (281.0 kgt/em?) Eq, (1) can be approximated as: 05 Adfsbe (: + EG 2 é) @ Based on results of the PCA investigation, Eq. (2) appears to satisfactorily predict the flexural strength of rectangular walls with an he/l, ratio equal to or greater than 1.0. Fig. 2 shows a comparison of Eq. (1) and 2) for different amounts of Grade 60° uniformly tributed vertical reinforcement for fé = 4000 psi 2810 kgf/em!) and for two ratios of axial compression, «= 0 and «= 0.25, The comparison shows that for the case of pure bending, a= 0; Eq. (2) is in good agreement with the more rigor- ous Eq. (1). In the case of a rather large axial compression, «= 0.25, the greatest difference is about 5 percent. Accordingly, the use of the sim- plified Eq. (2) appears adequate for practical de- sign. Shear strength ‘The distribution of lateral loads on shear walls varies with their height." 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 eti- terion in the design of low-rise shear walls. ‘As pointed out in the report of ACI-ASCE Com- mittee 326(426), Shear and Diagonal Tension,” 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 con crete, 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 conerete is equal to the shear causing sig- nificant inclined cracking. This last assumption underscores the importance of the cracking shear. ACI JOURNAL / MARCH 1973 tyr o,000pH (A2DKat ent) Fo 4,009 (et ibe ° 15 35 Fig. 2—Flexural strength of rectanguler shear walls Shear carried by concrete It is generally recognized that inclined crack~ ing in concrete beams is of two types. In recent years, these types of cracks have been descriced as either “web-shear” or “flexure-shear.” The way in which these cracks develop in reinforced and prestressed conerete beams has been described in detail elsewhere." ‘The provisions of ACI 318-71 use Eq. (11-4) fo computing the shear causing flexure-shear crack: ing in a reinforced concrete member. The limiting value of 3.5 Vf? for Eq, (11-4) serves as a meas. ure 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 « principal tensile stress of ep-_” proximately 4VJ/ at the centroidal axis of the” cross-section. Hq. (11-11) as originally developed": predicts flexure-shear cracking as the shear stres causing a flexural crack, corresponding to 2 flex ural tensile stress of 6 Vf, to form at a section, Jocated distance d/2 from the section being in: vestigated, plus a small stress, 06 "72 intended: to represent the shear required to transform the. initiating flexural crack into a fully developed flexure-shear crack. It is important to recognize that Eq. (I1-11) for prestressed conerete beams is applicable to rein- forced concrete beams subject to axial compres- sion. However, the results would be expected to bbe conservative. because the shear stress required to transform an initiating flexural crack into a flexure-shear crack will usually be considerably greater chan 0.6 Vj. Reet * has atte to take this into account. It follows, therefore. “kat a similar approach applied to shear walls would bbe conservative, 2B woe ad Ng ahe1000 | L ien 1 LEE pap es ai veh pom eve] te + a sen /iE Engin 0808, /1E met Fig. 3— Shear carried by concrete in rectangular shear walls 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 uneracked rectangular sec- tion, the maximum shear stress due to a shear oree, V, is: av, Pmt = SER @ At the occurrence of a principal tensile stress of 4 fF on a section subjected to combined axial load, N, and shear, Bq. (3) becomes: Ni anaes fi +e ® Eq. (4) can be closely approximated by: 3V Ea vR +095, © Introducing into Eq. (8) the concept of nominal shear stress, 0 == V/hd, and assuming that the ef- fective depth d, is equal to Oily, leads to: ro @ ar. Ne ves 88VIE + Te where v; is the value of nominal shear stress ex- pected to cause web-shear inclined cracking. The subscript u has been added to WN to indicate total applied design axial load occurring simultaneously with Ve 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 equa- tion reduces to v= 33 V7? Limitations due to the assumption of d= 0.6L, are discussed later. Plexure-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 24 7 flexural tensile stress of 6-V Jv at a section located a distance 1/2 above the section being investigat- ed. For shear walls, an expression for the value of nominal shear stress expected to cause flexure- shear inclined eracking is Eq. (11-33) of ACI 318- n: be (1.26 VIF + 0.2N/ beh) Mle oe The shear carried by the. concrete therefore corresponds to the least value of », computed from Eq. (6) or (7). However, the value of v, need not be taken less than corresponding values for rein- forced concrete beams. Therefore, ». may be taken at least equal to 2 V fv’ if Nu is zero or compression, or 2 (1-4+0.002N,/A,) VJ- 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, M,/V., for selected values of axial compression, expressed as ,/I,h. The upper horizontal portion represents the web-shear cracking strength, as given by Eq (6). The transition to the suggested minimum of 2Vie represents the flexure-shear cracking strength, as given by Bq. (7). v= 06 Vie + mM 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?" Applied to shear walls, this contribution, expressed in terms of nominal shear stress, ist Piby @ where pr= At= ratio of horizontal shear reinforcement, Shear reinforcement restrains the growth of inclined cracking, increases ductility, and provides a warning in situations where the sudden forma- tion of inclined cracking may lead directly to dis- tress. Accordingly, minimum shear reinforceme: 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 contri- bution of about 2'VJ/ to the strength of the wall. For low walls, it is reasonable to expect thet the horizontal shear reinforcement is less effective than indicated by Eg. (8). However, the vertical reinforcement in the wall will contribute w its shear strength, in accord with the concept of shear-friction.*® Because of insufficient test date to develop recommendations for walls with low ACI JOURNAL / MARCH 1973 BEERS ER EE Ee EE EEE EE Eee ee eee atte | evi] Fig. 4—Minimam sheor strength of rectengular sheor height to depth ratios, the amount of vertical re- inforcament required is equal to the amount of horizontal reinforcement when h/t, is less than. 0.8, When fte/ly is groater than 23, the required minimum vertical reinforcement area is 0.0025. Between hy/ly ratios of 05 and 25, the required minimum is determined by linear interpolation, as expressed by Eg. (11-34) of ACI 318-71 “The shear capacity of rectangular shear walls, containing minimum shear reinforcement is plot- ted in Fig, 4as a function of the moment to shear ratio. The curves have been plotted for a concrete strength, j, of 5000 psi (350 kgf/cim?), and a yield Stress of the horizontal reinforcement, f,, of 60. 000 pst (4200 kgf/em*). ‘The diagram shows that for these conditions, the minimum shear strength of low-rise walls Is of the order of 54V fi, and that of high-rise walls Js of the order of 4.1 VJ¥. Defi ition of nominal shear stress Ini 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: Ve gna @) = total applied design shear force at section eapacity reduetion factor (Section 9.2, ACT 318-71) thickness of shear wall @ = distance {rom extreme compression fiber to resultant of tension foree 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=08le is also shown in Fig, 6. This value is ACI JOURNAL / MARCH 1973 1 fot of eres tse A / teh Fig. 5—Variation of effective depth in rectongular shear walls : not necessarily conservative or unconservative, because thé equations for shear atiributed to the concrete have been modiised to account f proposed value of d. The equation for shea tributed to the reinforcement depends on ability lo effeclively reinforce for shear over the vertical projection of the assumed inclined crac Limitation on ul jate shear stress ‘A limitation on ultimate shear stress is gen- erally considered to represent failure due to rushing of concrete “struts” in beam webs. For reinforced concrete beams, ACI 318-63" Timited the nominal ultimate shear stress to 10 Vf. There is some indication that the shear strength of a beam without web reinforeer:ent may decrease with increasing depth. Other tests! fon beams with low afd ratios indicate that the limiting shear stress may be less than 10YF7. However, the tests reported in this paper indicate that shear stresses up to 1077 can be attained in walls with web reinforcement, even under load reversals. Attainment of shear stresses of this magnitude requires careful reinforcement de- tailing. COMPARISON OF DESIGN PROVISIONS WITH TEST RESULTS ‘The proposed design provisions for shear strength of shear walls have been compared with experimental results reported by Muto and Kokusho? Ogura, Kokusho and Matsoura? Ben- jamin and Williams" Antebi, Utkw and Hansen,” land the PCA Laboratories.” In the computation ‘of nominal shear stress, the effective depth, d, was taken equal to the distance from the extreme compression force to the resultent of the tension “Was not inghied here, so that the value 1s com: able to Sette’ KEE ST 5 20 ———_—5 Maosured tov 4 Pea Stanford Mir vooon ave oe Caleta vy English: 0.265,/%0 Fig. 6—Compatison of measured and calculated strengths trie force, or 081,, 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 rep- resents consideration of the ACI capacity reduc- tion factor, ¢, equal to 0.85. The two PCA test results plotted under the solid lime are for specimens where the shear failure was observed to have been precipitated by loss of anchorage of the flexural reinforce. ment. The PCA test result marked with an R corresponds to the specimen subject to load re- versals. Comparison of measured and calculated strengths in Fig. 6 indicates that the design pro- visions are satisfactory. OTHER CONSIDERATIONS In the development of design provisions for shear walls, the main emphasis was on evaluation 226 of flexural and-shear strength under static load- ings, However, considerations of energy absorp- tion, where earthquake resistance is required, and lateral stiffness are also important factors in- fluencing the behavior of walls. Properly detailed reinforcement is also essential to obtain satisfac. tory performance. Based on results of a recent investigation,382 Paulay has indicated that energy absorption and stiffness characteristics of a wall may be signifi- cantly improved if the shear reinforcement does not yield when the wall reaches jts flexural ca- pacity. The apparent reason for this is that the widths of the inclined cracks are restrained, thereby maintaining aggregate interlock across the erack, and doweling action of the main rein- forcement. 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 absorp- Tn eases where high ductilt La may be the case in spandrels ‘or piers, it may be desirable to physically divide the wall into two ar mara parts as suggested by Muto." This ‘would have the effect of substantially increasing the M/V ratio of the wall elements thereby mak- ing flexure the predominant consideration, In any case, it is desicable to provide shear strength capacity in excess of the flexural strength. ‘The importance of careful detailing of shear walls must be emphasized. From experience, 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 loca- tions should also be given careful consideration, When beam action begins to break down due to the formation and growth of inclined cracks, par- ticularly in deep members, the steel stress at the intersection of the inclined cracking and the flex- ural reinforcement tends to be controlled by the moment at a section through the apex of the in- clined cracking. These stresses can be quite di ferent 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 Resntts of tests summarizs4 in this paper indi. cate 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, he/le, of 1.0 or more can be satisfactorily predicted using Section ‘ACT JOURNAL / MARCH 1973 502, Assumptions, of ACI 318-71, Equations for determining the design flexural capacity of rec tangular 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 detail- ing of reinforcement need special attention. ACKNOWLEDGMENTS ‘This investigation was carried out at the Structural Development Section, Portland Cement Association. ‘Ms. D. D. Magura, former PCA Research Engineer, tiated the experimental investigation, Laboratory technicians B. J, Doepp, B. W. Pullhart, W. Hi, Graves, W. Hummerich, Jz, and O, A. Kutvits performed the laboratory work. ~ REFERENCES Avi Ce 2, Colle Requirements fox Peintoreed Canerate (ACT 818-71),” American Con- crete Institute, Detroit, 1971, 78 pp. 2, Muto, Kiyoshi, and Kokusho, Seiji, “Experimental study on Two-Story Reinforced Conerete Shear Walls,” Transuetions, Arehitecturst Institute of Japan (Tokyo), No. 41, Sept. 1959, 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, Archi- tectural Institute of Japan, ‘Tokyo, Feb. 1952, 4, Touboi, ¥ Suenaga, ¥.; and Shigenobu, ., "Fun damental Study on Reinforced Concrete Shear Wall Structures—Experimental and Theoretical Study of Strength and Rigidity of Two-Directional Structural Walle Subjected to Combined Stresses M. N, Q.” Trans eections, Architectural Institute of Japan (Tokyo), No. 131, Jan. 1967. (Foreign Literature Study No. 536, Port- Tana Cement Association, Skokie, Nov. 1967.) 5, “Standards for Caleulation of Reinforced Concrete Structures,” Architectural Institute of Japan, Tokyo, 1862, (in Japanese) 6, Williams, Harry A, and Benjamin, Jack R,, “In- vestigation of Shear Walls, Part 3—Experimental and Mathematical Studies of the Behavior of Pain and Reinforced Conerete Walled Bents Under Static Shear Loading.” Department of Civil Engineering, Stanford University, July 1953, 142 pp. 7, Benjamin, Jack R,, and Williams, Harry A., “In- vestigation of Shear Walls, Part 6—Continued Experi- mental 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 Ay “The Behavior of One-Story Reinforced Concrete Shear Walls,” Proceedings, ASCE, V. 8, STS, May 1957, pp. 1Bk-l to 1254-48. Also, Trensuctions, ASCE, V. 124, 1959, pp. 669-708, ‘8. Benjamin, Jack R, and Williams, Harry A, “Be- havior of One-Story Reinforced Concrete Shear Walls Containing Openings," ACI Jouxwat, Proceedings V. 85, No. 5, Nov. 1958, pp. 605-618. 10, Antebi, J.; Utku, Sand Hansen, RJ, “The Re~ sponse of Shear Walls to Dynamic Loads," DASA-1160, ACL JOURNAL / MARCH 1973 Department of Civil and Sanitary Engineering, Massa~ ‘chusetts 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, sgtrength and Behavier of Deep Beams in Shear’ Proceedings, ASCE, V, 91, STS, Part 1, Oct. 1965, pp. 19-41. 3. ACI Committce 218, “Tuilding Code Requirements for Reinforced Concrete (ACI 318-03)," American Con~ ereie Institute, Detroit, 1963, 144 pp. 14, Slater, W. Ag Lord, A. Ri: and Zipprodt, R. R., “shear ‘Tesls of Reinforced Concrete Beams.” Tech- nologie Paper No. 314, National Bureau of Standards, Washington, D.C. 1926, yp. 387-495, 15, Crist, Robert A., “Shear Behavior of Deep Rein forced Concrete Beams—V. 2: Static Tests," AFWL- "DR-57-61, The Erie 11, Wang Civil Engincering Research Facility, University of New Mexico, Albuquerque, Oct 1967, Also, Proceediigs, RILEM International Sym- posiam on the Bffects of Repeated Loading on Materials dnd Structures (Mexico City, Sept, 1966), Instituto de Ingenieria, Mexico City, 1987. V. 4, Theme 4, 31 pp. 16, Leonhardt, Fritz, and Walther, Rene, “Deep Beams (Wondartige ‘Traeger),” Bulletin No. 178, Deutscher ‘Ausschuss fir Stablbeton, Berlin, 1986, 139 pp. 31. Cardenas, A. Ey and Magura, Dy W “teeta High-Rise Shear Walls—Rectangular Cross Section: Response of Multistary Concrete Structures to Late Forces, SP-86, American Concrete Tnstitute, Detroit, 1073, pp. 119-150. 18, Zsutty, Theodore, “Shear Strength Prediction for Separate Categories of Simple Beam Tests,” ACT TournaL, Proceedings V. 68, No, 2, Feb. 1971, pp. 133 143, 19, Khan, Fazlur R, and Sbarounis, Jobn A., “Inter action of Shear Walls and Frames,” Proceedings, ASCE, ¥V_ 90, ST3, June 1964, pp. 285-335, ‘20. “Design of Combined Frames ané Shear Wall “Advanced Engineering Bulletin No. 14, Portland Cement ‘Association, Skokie, 1965. 21, ACI-ASCE Committee 326(426), “Shear and Di agonal Tension,” ACI Jourxat, Proceedings V. 58, 1 Jan, 1962, pp. 1-30; No. 2, Feb, 1962, pp. 277-934) No. Mar. 1962, pp. 353- ol 22, MacGregor, James G., and Hanson, John M., “Pro posed Changes in Shear Provisions for Reinforced end Prestressed Concrete Beams," ACI Jovaxat, Proceed ings V. 63, No. 4, Apr. 1969, pp. 276-288. 23, Sozen, Mete A, and Hawkins, Neil M., Discussion ‘of "Shear and Diagonal Tension” by ACI-ASCE Com Tnitter 326 (426), ACI JouRKaL, Proceedings V, 59, No. 8 ‘Sept. 1862, pp. 2341-1347. 24, Mattock, Alan HL, “Diagonal Tension Cracking it Concrete Beams with Axial Forces.” Proceedings, ASCE, V. 95, ST9, Sept. 1969, pp. 1887-1900 25. AC Committee 318, “Commentary on Building Code Requirements for Reinforced Concrete (ACI 318- 3)." SP-10. American Concrete Institute, Detreit, 3965, 91 pp. 26. Mast, Robert F, “Auxillary Reinforcement in Concrete Connections.” Proceedings, ASCE, V. 94, STé, June 1968, pp. 1485-1504 27, Kani, GN. J, “How Sate Are Our Large Rein~ forced Concrete Beams?,” ACT Jounsat, Proceedings Y¥. 64, No, 8, Mar. 1967, pp. 128-141, ‘98, Paulay, ‘Thomas, “The Coupling of Reinforced Concrete Shear Walls.” Proceedings, Fourth World Con- 2 ference on Earthquake Engineering, Santiago, Chile, Jan, 1969, V. J, 11. B25 to B2-00 29. Paulay, Thomas, “Coupling Beams of Reinforced Conerete Shear Walls,” Proceedings, ASCE, V. 97, ST3, ‘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, 1955, V. 1, pp. 118-247. APPENDIX PCA investigation In this investigation, thirteen Jarge rectangular shear wall specimens thave been tested under static combi nations of axial Toad, bending, and shear, Si of the specimens, SW-1 through SW-6, represented walls in igh-rise “buildings.” The remaining seven, SW-7 through SW-13, represented walls in low-rise buildings, ‘One of the low-rise shear walls, SW-12, was subjected to ten eycles of load reversals. All test specimens were rectangular veinforced con- rete members with 2 thickness h=3 in, (7.92 om) and @ depth lo = 6 ft 3 in. (1.90 m). For convenience, the specimens were tested as horizontal cantilevered beams Ie Susshiag the specimens, reference is always made to the pasition of a wall in an actual buslding rather than its position ducing 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 Interal forces. Post~ tensioning rods, running horizontally in the photo, were used to apply the simulated geavity 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 {rame-shear wall structural system.2h°1 The height of the specimen eor- responds to the distance hetween the base of the wall and its point of contraflexure, It was assumed that 50 pereent of the total shear force at the base of the wall would be applied at the point of eontraflexure, ‘The remaining 50 percent was uniformly distributled bee tween the point of contrafiexure and the base of the wall. Four of the six high-rise shear wall specimens SW=t, 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 & (4.09 m) high, An axial compressive stress of about 420 psi (205 kgf/cm?) was applied. The main variable was the amount and distribution ‘of the vertical reinforee ment. Horizontal shear reinforcement equal to 027 erent of the concrete cross-sectional area was provid ed In ench of the sie eperimene Six of the seven Jhaae walls, SW-7 specimens representing low-rise though SW-12, were subjected to a Fig. Al—Test setup for shear wall investigation 208 ACI JOURNAL / MARCH 1973 single static Interal force applied at the top of He wall. sinete secjmens hada height, hay equal to thelr dep Tee gin, (190 m=). At the top of these spectne, toot Chess of the wall was enlanged to cimelaie 8 | the thleFrfjoor sabe framing into the shear, wall. "ye effect ei ection, distributes the applied shear, fers cra ee te top ot the speckmen, No axial compressor |, Mone to these specimens, Variables investigated {7 was applied mount and. distribution of vertical Felo- | ere AM, and the amount of horizontal shear reinforce ment. The seventh of the sw-i3, was subjected to ten cycles of | SWor'the characteristics of this specimen were A ene of apecimen SW-9 previously tested woder te tro de, The objective of the test was to evsluate siatic toot the eyelic Toading on the strength, 270 the toe of low-rise shear wolls. Tables AL and. bene ge material properties, variables investigated snd test results for all 13 specimens. sd torr mary of the results of the PCA investigation vs uctuunted in Fig, AZ in the form of bar graphs ~ Gouiparison of test results for specimens TeprescooNe 1 Gampartenear walls SW-1, SW-2, SWS and SWS Nigh pat 0.27 percent of horizontal reinforcemen’, 2 Shows treonsidered to be nearly a practical aint | ttielent to develop the flexural streng\h of is 3s suttieering, amounts and distribution of vertical rreinforerment. oGimens SW-A and SWS were designed 9 Hove ease Flewural capacity as that of specimens SW" te sari. However, their height, he, was less, For he see ied loads, the moment to shear ratio, MG/Vo 9505) applied roma. the base of he wal, was te for SW4 Bed Gw-5, end Zhe for SW-3 and SW-t Migimem and Guia veinforcement was again. sufficient to Ge shear wall. specimens, Toad reversals. similar Jow-rise afi where A Jone tinea of total vortleal reinforcement elo, Sele Nein Tarun of reinforsene em ert to ak equivalents: 1 ACL JOURNAL / MARCH 1873 tn velop nearly though the shear Tee taplies that a greater proportion of the shesr was carried by the concrete at the In the group representing 10 mens SW-7 me cm horizontal. shear reinforcement have @ ie ra ing capacity. Comparisons of specimens 51 Mi and SW-12 with SW-7, sc00 65,000 000 | 63500 tal area of vertical relaforeement, fe = oncontrated within 2, distance iS ntetor reson pe = at ro cue remtzcement eapceniaad matin » chance Ze/t¢ from SNE he calculated flexural strength, even Stresses were substantially higher, Tower Ma/Vu ratio. rise shear walls, spec! adieate that walls with ‘and SW-8 sls0 ‘and also SW-9 with SW- sv ten 030 mae Fig. A2—Reslts of PCA investigation TABLE Al — DIMENSIONS AND MATERIAL PR PERTIES OF TEST SPECIMENS PePeeo eee eee eeeee sane | eter 5 [omovies] meppe| Verte : "§ | stone | tenet|———7 | ve | tw | mane | BSS vst pa |e a qa [ome | wm | gio | conn | ena sea | a | am | so | ene | oe crm | as | ecaro | e500 ‘0000 somo camo 000 200 200 100 100 15 im and 1388 m; 3 pel = 9.8709 Restle TABLE AZ—TEST RESULTS Catone seronetes Frocera areneth Shear arenes ees eax | 2 hen | carved vation | “Ratio | Measured | coteuateat ‘mode ee | ee ee ease "| snese rtoment | shear ne | IE trom J unin | ae | iba | sc a te | tert seam sw 2te ose 406 st 5 ar a9 107 oa [Ploxure swe | 2m | oo es oo | aa | 20 | so) aoe | om |rtexore sw | sae | on | tos | ww fee | as [> 4a | om | ras |rexurnsheor swt | toe | om wr | ae | aus | ae | as | ot | te |roxure sw | uae | om | ioe | ona | ams | ore | on | eos | ats Irtexatesne swe | tae | om | nm | nse | ms | sa | ts | oaee | a0 mesure suet | oste | ont 0 so | ner | nz | 52 | on | uss |snear swe | ase | oss si_| som | amr | or | se | em | am |snear sws | cate | oss 4 wo |* asx | 12 | woo | oss Fiexero-shear swe | ase | ost a m-| oz | 4a | a2 | om snear swan | ose | oat we | rom | ato | ar | on | ome | snear-anchosnge swir | ose | oat 2s wo | ase | se | oo | om | aoe |snearanctorne swiss] 05te oss a2 1060 wea 200 yop | 989 | 100 | FlexuresShesr son eamnoressive concrete limiting st SGiicdigSte ibn rapased shear ‘trons saunter SWEET Wat fubseett fo Tb cyetes of toad rove ‘Po convert to St eguivatenter 1 Kip = A%0 in indicate that additional horizontal shear reinforcement ‘will further inerease eapacity. Comparisons of SW-8 with SW-1, and SW-9 with SW- 12, show that the lateral load carrying cepacity also increases with vertical web reinforcement. However, these observations are qualified somewhat by the ob- servation 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 wit no horizontal or vertical web reinforcement, wes 43K. Specimen SW-13 was subjected to a total of ten cycles of increasing levels of load reversals. Compart son of this specimen with SW-9, a physically similar specimen thet was subjected to one-directional loading. shows no significant decrease in strength. Both of these specimens developed shear stresses of the order of 10 VF Notation a shear span, distance between concentrated. load and face of support, in, Ag ross area of section, sq in. Av = atea of horizontal shear reinforcement within a distance, s, sq in. © = distance from extreme compression fiber to neutral axis, in. istance from extreme compression fiber to resultant of tension force, in. in of 9000, strain compatibility and messured material properties. 265 VF metric, Vie = square root of specified compressive strength of concrete, psi | fe = specified compressive strength of concrete, | si . ty specified yield strength of reinforcement, h of shear wal, in. fy total height of wall from its base to its top, in. tw iepth or horizontal Yength of shear wall, in, Ma design resting moment at section, in/ib Ny = design axial load at section, positive if com= pression, Ib - Ad yMlahte 5 vertical spacing of horizontel shear rein- forcement, in. ve = nominal permissible chear stress earried by conerete, pel v cominal total design shear stress, psi v Shear force at a section, Ib V. =total applied design shear force at section, b B 9/87, 000 Bi 85 for strength 4 up to 4000 psi (281.0 kkgi/em®) and reduced continuously to a rale of 0.05 for each 1000 psi (70.3 kgtiem®) of | This paper wat feceivad by the Institue May 16, 1972 AC\ JOURNAL / MARCH 1973 ! FEA WD ser. 1908 |

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