DESIGN OF STEEL PLATE SHEAR WALLS CONSIDERING BOUNDARY FRAME MOMENT RESISTING ACTION. B. Qu 1 and M.Bruneau 2 ABSTRACT

Transcription

1 Proceedngs of the 9th U.S. Natonal and 0th Canadan Conference on Earthquake Engneerng Compte Rendu de la 9ème Conférence Natonale Amércane et 0ème Conférence Canadenne de Géne Parassmque July 5-9, 00, Toronto, Ontaro, Canada Paper No 306 DESIGN OF STEEL PLATE SHEAR WALLS CONSIDERING BOUNDARY FRAME MOMENT RESISTING ACTION B. Qu and M.Bruneau ABSTRACT Conventonal desgn of steel plate shear walls (SPSWs) assumes that 00% of the story shear s ressted by each nfll panel. Followng ths approach, strength provded by the boundary frame moment resstng acton, whch provdes the SPSW wth an overstrength, s neglected. Whle ths desgn assumpton has a postve mpact on sesmc performance of SPSWs, no analytcal work has been done to quantfy the magntude of ths overstrength n general terms. Such prelmnary work s conducted n ths paper. Based on plastc analyss of SPSWs, ths paper nvestgates the relatve and respectve contrbutons of boundary frame moment resstng acton and nfll panel tenson feld acton to the overall plastc strength of SPSWs, followed by a procedure to make use of the strength provded by the boundary frame moment resstng acton. Procedures for desgn of SPSWs havng weak nfll panels are also presented n ths paper. Then, results from a seres of tme hstory analyses usng valdated models are presented to compare the sesmc performances of SPSWs desgned usng dfferent desgn assumptons. Introducton A typcal steel plate shear wall (SPSW) conssts of nfll steel panels surrounded by columns, called Vertcal Boundary Elements (VBEs), on each sde, and beams, called Horzontal Boundary Elements (HBEs), above and below. Prevous tests and analytcal studes on sngle-story and multstory SPSWs (Berman and Bruneau 003, Berman and Bruneau 005 to name a few) recognzed that a SPSW's ultmate strength combnes the contrbutons of both the moment resstng boundary frame and the nfll panels. However, strength of the wall provded by the moment resstng acton of boundary frame s not explctly taken nto account n the desgn of SPSWs by codes (AISC 005 and CSA 000), typcally resultng n a conservatve but possbly more expensve SPSW desgn. To nvestgate the relatve contrbuton of boundary frames to the overall strength of SPSWs and possbly acheve an optmum desgn of SPSWs accountng for that contrbuton, ths Assstant Professor, Department of Cvl and Envronmental Engneerng, Calforna Polytechnc State Unversty, San Lus Obspo, CA 93407; Tel: ; Fax: ; E-mal:bqu@calpoly.edu Professor, Department of Cvl, Structural and Envronmental Engneerng, Unversty at Buffalo, Buffalo, NY 460; Tel: x403; Fax: ; E-mal: bruneau@buffalo.edu

2 paper revews knowledge on the plastc strength of SPSWs, and summarzes some desgn assumptons n current codes. Then, desgn procedures consderng boundary frame moment resstng actons are presented followed by a case study to compare the performances of SPSWs desgned usng varous assumptons on the relatve strength and desgn of boundary frames. Plastc Strength of Steel Plate Shear Walls Plastc collapse mechansms for SPSWs subjected to lateral loads have been nvestgated by Berman and Bruneau (003). From that work, equatons for the ultmate strength of SPSWs have been shown to agree well wth the results obtaned from tests. For the desred SPSW plastc mechansm (.e. the unform collapse mechansm), by equatng the nternal and external work, Berman and Bruneau (003) derved the followng general equaton for the overall plastc strength of a SPSW wth moment resstng HBE-to-VBE connectons: Fh M M R f Lh t t sn( α ) ns ns ns = ( + ) + ( ) + pl pr yp yp w w = = = Contrbuton of boundary frame Contrbuton of nfll panels () where F s the lateral force appled on the wall to develop the desred mechansm; h s the th story elevaton; M pl and M pr are the expected plastc moments at the left and rght ends of the th HBE respectvely; t w s the thckness of the nfll panel at the th story; R yp s the rato of expected to nomnal yeld strength of nfll panels; f yp s the nomnal yeld strength of nfll panels; L s the SPSW bay wdth; n s s the total number of stores; and α s the tenson feld nclnaton angle at the th story. As shown n Eq., lateral strength of the wall combnes the contrbuton of boundary frame and that of nfll panels. Current Desgn Requrements Based on Eq., one can obtan the followng equaton for calculatng the shear strength of a sngle nfll panel: V = Ryp fypltwsn( α) () where V s the expected strength of the consdered nfll panel. Dvdng the nfll panel strength determned from Eq. by an overstrength factor, as defned by FEMA 369 (FEMA, 00), and taken as. n ths case (Berman and Bruneau, 003), and also excludng the R y factor used for calculatng the expected plate strength, one can obtan the followng nfll panel nomnal shear strength: V = 0.4 f Lt sn( α ) (3) n yp w where V n s the nomnal strength of the consdered nfll panel. Eq. 3 s mplemented n the AISC Sesmc Provsons and the CSA S6 Standard, and s

3 used for szng the thckness of nfll panels of SPSWs. Thus, by neglectng the contrbuton from the boundary frame moment resstng acton on the SPSW strength, and solvng for t w from Eq. 3, one can obtan the followng desgn equaton to select thckness of the nfll panel. Vn tw = (4) 0.4 f Lsn( α ) yp Then, the AISC Sesmc Provsons and the CSA S6 Standard requre that the boundary frame members be desgned usng capacty desgn procedures to ensure that the boundary frame members can anchor the nfll panel yeld forces developed by the nfll panel thckness determned from Eq. 4. As such, followng ths approach, strength provded by the boundary frame moment resstng acton provdes the SPSW wth an overstrength (whch has a postve mpact on sesmc performance). At the tme of ths wrtng, no analytcal work has been done to quantfy the magntude of ths overstrength n general terms and to nvestgate how to make use of t to acheve an optmum desgn of SPSWs. Such work s presented n the followng secton. Steel Plate Shear Wall Overstrength and Balanced Desgn In order to best understand the SPSW overstrength resultng from the desgn approach nferred by current desgn codes, whch assumes that all the lateral forces appled on the wall are ressted by the nfll panel tenson feld actons alone, ths secton nvestgates the overstrength of SPSWs desgned consderng that varous percentages of the lateral desgn forces are ressted by the nfll panels. Both sngle-story and multstory SPSWs are consdered. Sngle-Story SPSWs A sngle-story SPSW s frst studed here because ths smple case provdes some of the buldng blocks necessary to understand the more complex scenaro (.e. multstory SPSWs) presented later. Consder the sngle-story SPSW shown n Fg. and assume that ts VBEs are pnned to the ground. VDesgn L Fg. Sngle-Story SPSW Example α h Ω L/h=0.8 L/h=.0 L/h=.5 L/h=.0 L/h=.5 Overstrength due to capa cty desgn of boundary frame Balanced desgn cases Desgn force to be assgned to boundary frame Fg. The Relatonshp between Ω Κ and (assumng α=45º and η=.0 ) Assumng that the percentage of the total lateral desgn force assgned to the nfll panel s, the requred nfll panel thckness s determned by solvng for t w from the followng

4 equaton: Vdesgn = Ryp fypltw sn( α) (5) where V desgn s the lateral desgn force appled on the wall. Consderng the plastc strength of the wall, V p, based on the procedure developed by Berman and Bruneau (003), and also assumng the top beam s szed usng the capacty desgn procedure gven by Van and Bruneau (005), the rato of V p to V desgn, whch s denoted as Ω and s used to descrbe the overstrength of the SPSWs desgned usng dfferent values of, can be determned as L η ( α) h + η Ω = + tan where η s the plastc secton modulus reducton rato accountng for the presence of reduced beam secton (RBS) connectons and other terms have been defned prevously. Please note that detaled dervatons of Eq. 6 are presented n Qu and Bruneau (009) Explctly shown n Eq. 6, the factor, Ω, depends on a seres of varables ncludng,, α, Lh, and η. The effects of those terms can be nvestgated based on Eq. 6. Here, a parametrc study s conducted to dscuss the mpact of on Ω for the gven values of other terms. Note that, for smplcty, the nclnaton angle of the tenson feld acton s assumed to be 45º and η s assumed to be unty (.e. no RBS connectons are used n the HBEs). Note that results are not expected to vary substantally for other values of α. In addton, n the parametrc study, the nfll panel aspect rato (.e. Lh) was chosen to vary between 0.8 and.5, whch are the lmts allowed by the AISC Sesmc Provsons (AISC 005). The correspondng results are llustrated n Fg.. As shown, a hgher percentage of the lateral desgn forces assgned to the nfll panel (.e. greater value of ) results n a greater overstrength of the wall (.e. greater value of Ω ). Under the desgn assumpton presented n the AISC Sesmc Provsons and the CSA S6 Standard (.e. when =.0 ), the wall has a sgnfcant overstrength varyng from.4 to.5 over the code-complant range of nfll panel aspect ratos of 0.8 Lh.5. Note that the example wall assumes that the VBEs are pnned to the ground. It s recognzed that, for the SPSWs that wth VBEs fxed to the ground, the overstrength would be even greater. Also observed from Fg., when s reduced to certan level, showed by the crcles on that fgure, the lateral force ressted by the boundary frame of the SPSW s exactly equal to that whch wll be requred f that frame s desgned to resst the nfll panel yeld forces per capacty desgn prncples. Therefore, at that partcular pont, the boundary frame does not provde any overstrength for the system as the dvson of the lateral load resstance, and the overstrength ( Ω ) s therefore equal to unty. Such a desgn case s termed "" desgn case n ths (6)

5 paper. For ths case, the value of can be determned by settng the constrant Ω =.0 nto Eq. 6 and solvng for. The resultng value of for the case, desgnated as, s therefore: L η tan ( α) h + η = + As shown n Fg., when reducng to a value below (7), the SPSW plastc strength s not suffcent to resst the lateral desgn force. In other words, the boundary frame desgned only to resst the nfll panel yeld forces, per capacty desgn prncples, has to be strengthened to fll the gap between the avalable strength of the wall and the expected lateral desgn demand. Incdentally, detaled nformaton about the desgn of such SPSWs wll be presented later. Fgs. 3 and 4 respectvely plot, based on (7), the relatonshps between and η for varous values of Lh, and and Lh for varous values of α. As shown n Fg. 3, the value of ncreases when η reduces. Ths observaton s reasonable because the reserved strength of the wall due to the moment resstng acton of the boundary frame decreases when RBS connectons are ntroduced n the HBE (.e. when η.0 ), whch means that, n ths case, a hgher percentage of lateral desgn force should be ressted by the nfll panel tenson feld acton. Note that, when η reduces to zero, whch physcally corresponds to smple HBE-to-VBE connectons, becomes unty, ndcatng that 00% of the lateral force s ressted by the nfll panel. Fg. 4 llustrates the trends n for the code-complant range of nfll panel aspect ratos and the typcal range of tenson feld nclnaton angles. As shown, the value of decreases when the aspect rato ncreases. Ths s also reasonable snce a bgger HBE member has to be used to anchor the tenson feld acton n a "squat" wall (whch has a greater aspect rato) n comparson wth a slender wall (whch has a smaller aspect rato), resultng n a hgher strength of the wall provded by the moment resstng acton of the boundary frame L/h=0.8 L/h=.0 L/h=.5 L/h=.0 L/h= η Fg. 3 The Relatonshp between and η (assumng α=45º) α=38 o α=40 o α=4 o α=45 o α=48 o L/h Fg. 4 The Relatonshp between Aspect Rato and (assumng η=.0)

6 Mult-Story SPSWs Followng the same logc used for sngle-story SPSWs, one can obtan the followng equaton for of mult-story SPSWs: L η tan ( α ) + η = + h To have a better understandng of the lateral forces respectvely ressted by the nfll panels and the boundary frame n the desgn case for a multstory SPSW, consder a four-story SPSW wthout RBS connectons as an example. Assume that the lateral desgn forces lnearly dstrbute along the heght of the wall as shown n Fg. 5 and the story heghts and nfll tenson feld nclnaton angles (45º) are constant n all stores. Fg. 6 llustrates the percentage of the story shear ressted by the nfll panel at each level (.e. to be consdered to sze the nfll panels at each story). For comparson purpose, the results for the case when 00% of the story shear s ressted by each nfll panel (.e. the desgn case mpled by the AISC Sesmc Provsons) are also provded. As shown, the story shears assgned to the panels are reduced n the desgn case. For example, when the panel has an aspect rato of.5, 78% of the base shear s ressted by the frst-story panel when the wall develops the desred plastc mechansm. 0.40Vbase 0.30Vbase 0.0Vbase 0.40Vbase 0.70Vbase 0.90Vbase Story level 4 3 (8) Code L/h=0.8 L/h=.0 L/h=.5 L/h=.0 L/h=.5 0.0Vbase Vbase (a) Lateral Desgn Forces (b) Story Shear Story shear assgned to nfll panel (normalzed by base shear, %) Fg. 5 Descrpton of Example Four-Story SPSW Fg. 6 Modfed Desgn Forces of an Example Four- Story SPSW Boundary Frame Desgn of SPSWs Havng Weak Infll Panels When the nfll panel thckness s smaller than that correspondng to the desgn case, the SPSW wll not have a suffcent strength to resst the lateral desgn force f the boundary frame s only proportoned usng capacty desgn procedures (.e. desgned only to resst the nfll panel yeld forces). Here, such walls wll be termed SPSWs havng weak nfll panels. Three HBE desgn equatons, whch lead to dfferent desgns but same global plastc strength of the boundary frame, are presented n Table. What conceptually dffers n the three methods consdered below s that each case assumes a dfferent dstrbuton of HBE strength

7 along the heght of the SPSW for whch the global plastc strength s satsfed but the local storyby-story strength s not necessarly satsfed. Detaled dervatons of the equatons for Methods I to III are provded n Qu and Bruneau (009). Note that these three methods are based on plastc analyss and the yeldng sequence of members and nfll panels of the SPSW under the lateral forces s out of the scope of the work presented here. Table Desgn Equatons of HBEs n SPSWs wth Weak Infll Panels Desgn Methods Plastc secton modul of HBE cross-sectons s I = ( ) n s b D y η = = Z F h f II = ( ) Z F h f η b D y n s b j Dj s y j= III = ( ) Case Study Z F h f η Pror sectons presented dfferent approaches for SPSW desgn. To be able to determne the relatve merts of any of those desgns whch wll provde the same overall lateral load resstance, t s mportant to conduct nonlnear tme hstory analyses to compare the sesmc performances of the walls respectvely desgned assumng varous dstrbutons of the lateral loads between the boundary frame and nfll panels as well as varous dstrbutons of HBE strength that satsfy the total plastc strength of the structure. Such a study s conducted n ths secton. The followng brefly descrbes assumptons, desgn results, and the performances of those dfferently desgned SPSWs n the nonlnear tme hstory analyses. Assumpton and Desgn Summary An eght-story sngle-bay SPSW was used as the prototype structure n ths study. The VBEs were assumed to be pnned to the ground and the frst-story nfll panel was assumed to be anchored to the ground rather than to an anchor HBE at that level. The bay wdth and constant story heght were assumed to be 8 ft and 0 ft, respectvely, resultng n an nfll panel aspect rato of.8, whch s wthn the range allowed n the 005 AISC Sesmc Provsons. The structure was assumed to be located on class B sol n Northrdge, CA. Its weght was assumed to be kps dstrbuted as 65.5 kps at all levels except at the roof where t was 55 kps. Sesmc desgn loads were calculated usng FEMA 450 (FEMA, 003) and the assocated spectral acceleraton maps. Desgn short and -second spectral ordnates, S DS and S D, were respectvely calculated to be.43 g and 0.50 g. The perod of the structure was estmated (usng the FEMA procedures) to be 0.54 second, and usng a response modfcaton factor, R, of 7, and an mportance factor, I, of, the base shear was found to be kps. The correspondng lateral forces up the heght of the structure along wth the nfll panel thcknesses determned from dfferent desgn procedures are presented n Table n

8 The AISC desgn procedure, the desgn procedure, and the desgn procedure assumng that 40% of the story shear s ressted by the nfll panel at each story (.e. the procedure for the SPSWs havng weak nfll panels) are consdered to select the SPSW nfll panel thcknesses. Note that t s assumed that the calculated nfll panel thcknesses are avalable n all cases. Story Level Table Summary of Desgn Story Shears and Infll Panel Thcknesses Lateral Modfed Story Shear (kp) Infll panel thckness (n) Elevaton Force (ft) Balanced Weak Balanced Weak (kp) AISC AISC desgn nflls desgn nflls For the desgn usng weak nfll panels, all three HBE desgn methods were consdered for desgn of the boundary frame. As a result, a total of fve SPSW desgns were obtaned,.e. one from the AISC desgn procedure, one from the desgn procedure, and three from the procedure for SPSWs havng weak nfll panels (respectvely usng Methods I, II and III). Please note that detaled nformaton of the boundary frame members from those fve desgns are lsted n Qu and Bruneau (009). Analytcal Model and Artfcal Ground Motons Acceleraton (g) Acceleraton (g) Acceleraton (g) Realzaton-3 Realzaton- Realzaton Tme (Second) (a) (b) (c) PSa (g) realzaton- realzaton- realzaton-3 Target desgn spectrum Perod (Second) Fg. 7 Dual Strp Model and Ground Moton Informaton (a) Dual Strp Model (b) Ground Moton Hstores (c) Pseudoacceleraton Spectra To quantfy the sesmc performance of those SPSWs desgned usng dfferent procedures, nonlnear tme hstory analyses were conducted on models constructed followng the

9 dual strp procedure descrbed and valdated aganst cyclc test results (Qu et al. 008). Note that n these models the nfll steel plates were represented by two seres of nclned tenson-only members (.e. strps) to replcate the behavor of SPSWs under cyclc loads. Three realzatons of the target desgn spectra compatble ground motons were obtaned usng the computer program, TARSCTHS, by Papageorgou et al. (999) and were used as exctatons for the nonlnear tme hstory analyses. The dual strp model, ground moton realzatons and acceleraton spectra are shown n Fg. 7. Result Comparson The maxmum drft of each story was obtaned from the nonlnear tme hstory analyses to compare the sesmc performances of the 5 dfferent SPSWs. Fg. 8 presents the correspondng results along the heght of the walls for each consdered earthquake. HBE Level EQ- EQ- EQ-3 AISC Balanced Method-I Method-II Method-III Maxmum drft (rad) Maxmum drft (rad) Maxmum drft (rad) Fg. 8 Results from Tme Hstory Analyses As shown, the wall from the desgn exhbts smlar performance to that of the wall desgned usng the AISC Sesmc Provsons. For example, the average of the maxmum frst-story drfts of the wall desgned usng the desgn procedure for the three earthquake realzatons s.48%, whch s close to the correspondng result of.30% from the wall desgned usng the AISC Sesmc Provsons. For comparson purpose, the correspondng averages of the maxmum frst-story drfts the SPSWs havng weak nfll panels and desgned usng methods I, II and III are calculated to be.98%, 3.% and.65%, respectvely. It should also be mentoned that although the desgn procedure could lead to a SPSW that exhbts satsfactory responses accordng to the lmted analytcal data provded here, such a procedure should not be used wthout further confrmaton from expermental studes on the system performance of SPSWs. Another observaton from Fg. 8 s that the maxmum story drfts are dstrbuted n a unform pattern along the heghts of all SPSWs except for the wall havng weak nfll panels and desgned usng method II. As shown, sgnfcant deformatons concentrated n the lower stores of that SPSW although smaller responses are observed n ts upper stores.

10 Conclusons Ths paper nvestgated the lateral load resstance of SPSWs respectvely provded by the boundary frame moment resstng acton and the nfll panel tenson feld acton. A desgn procedure consderng the contrbutons of these two actons to the overall SPSW strength (.e. a procedure to acheve a desgn) was developed. Desgn of SPSWs havng weak nfll panels was also studed and three dfferent methods that assume dfferent HBE strength dstrbutons along the SPSW heght were presented. A seres of nonlnear tme hstory analyses were conducted to evaluate the sesmc performance of SPSWs desgned usng these dfferent procedures (.e. respectvely desgned usng the AISC Sesmc Provsons, usng the developed desgn procedure, and usng the three methods for the SPSWs havng weak nfll panels). It was shown that the SPSW desgned usng the desgn procedure exhbts smlar performance to that desgned usng the AISC Sesmc Provsons. Acknowledgement Ths work was supported by the EERC Program of NSF under Award Number ECC to MCEER. However, any opnons, fndngs, conclusons, and recommendatons presented n ths paper are those of the wrters and do not necessarly reflect the vews of the sponsors. References Amercan Insttute of Steel Constructon. (005). Sesmc Provsons for Structural Steel Buldngs. Amercan Insttute of Steel Constructon, Chcago, Illnos. Berman, J.W., and Bruneau, M. (003). Plastc Analyss and Desgn of Steel Plate Shear Walls. Journal of Structural Engneerng, Vol. 9(), Berman, J.W., and Bruneau, M. (005). Expermental Investgaton of Lght-Gauge Steel Plate Shear Walls Journal of Structural Engneerng, 3(), Canadan Standards Assocaton (CSA). (000) Lmt States Desgn of Steel Structures. CAN/CSA S6-0. Wllowdale, Ontaro, Canada. Federal Emergency Management Agency (FEMA). (00) NEHRP recommended provsons for sesmc regulatons for new buldngs and other structures, Part commentary, FEMA 369, Buldng Sesmc Safety Councl for the Federal Emergency Management Agency, Washngton, D.C. Federal Emergency Management Agency (FEMA). (003). NEHRP Recommended Provsons for Sesmc Regulatons for New Buldngs and Other Structures FEMA 450. Prepared by the Buldng Sesmc Safety Councl for FEMA, Washngton, D.C. Papageorgou, A., Halldorsson B., and Dong G., 999. Target Acceleraton Spectra Compatble Tme Hstores. TARSCTHS - User's Manual, Engneerng Sesmology Laboratory, State Unversty of New York, Buffalo. Qu, B., Bruneau. M., Ln, C.H., and Tsa, K.C. (008). Testng of Full Scale Two-story Steel Plate Shear Walls wth RBS Connectons and Composte Floor., Journal of Structural Engneerng, 34(3), Qu and Bruneau (009). Desgn of Steel Plate Shear Walls Consderng Boundary Frame Moment Resstng Acton, Journal of Structural Engneerng, 35(). Van D.and Bruneau M.(005). Steel Plate Shear Walls for Sesmc Desgn and Retroft of Buldng Structure, Techncal Report MCEER , Multdscplnary Center for Earthquake Engneerng Research, Buffalo, N.Y.