The th World Conference on arthquake ngneerng October -,, Bejng, Chna OPTIMUM STRNGTH RATIO OF BUCKLING-RSTRAIND BRACS AS HYSTRTIC NRGY DISSIPATION DVICS INSTALLD IN R/C FRAMS Juan Andrés Ovedo A., Mtsumasa Mdorkawa and Tetsuhro Asar Graduate Student, Archtectural and Structural Desgn Dvson, Hokkado Unversty, Japan Professor, Archtectural and Structural Desgn Dvson, Hokkado Unversty, Japan Assstant Professor, Archtectural and Structural Desgn Dvson, Hokkado Unversty, Japan mal: ovedo@eng.hokuda.ac.jp, juanovedo@yahoo.com ABSTRACT : Ths paper focuses on the applcaton of bucklng-restraned braces (BRB) to renforced concrete (R/C) framed structures n order to reduce the sesmc damage n the man frame components. An attempt for a new drecton n defnng the mechancal propertes of hysteretc dampers s evaluated n whch the deformaton of dampers s drectly controlled. The range of strength levels requred to be gven to the dampers to mnmze the damage n the man frame s nvestgated. A parametrc study was carred out on -story R/C buldng structure wth damper strength rato and yeld drft rato ν as man parameters. quvalent sngle-degree-of-freedom (SDOF) model s also dscussed. Based on the numercal results t has been concluded that there s not a unque value that mnmzes the damage n the man frame; on the contrary, there s an applcable range. The range s found to be dependent on the sesmc nput level and tme-dependent characterstcs of ground motons. arthquake response shows the sgnfcant mprovement of the structural performance and the mplcaton of the yeld drft rato on the reducton of maxmum floor dsplacements and damage n the man frame. SDOF model demonstrated to provde suffcently accurate estmatons of floor dsplacements. KYWORDS: bucklng-restraned brace, equvalent SDOF system, hysteretc damper, optmum strength of hysteretc dampers, renforced concrete structure. INTRODUCTION Conventonal structural desgn focuses on the deformaton capacty of buldngs n the nelastc range, takng as condton the ductlty capacty n the structural components. Ths approach allows certan extent of damage n the case of severe earthquake motons. The damage s accepted as long as does not endanger the human lves and user s propertes. Sesmc response control technques have been mplemented as new methodologes of earthquake-resstant desgn n order to reduce the sesmc demand n the structural members by controllng ther deformaton; therefore, the damage. These technques complement the conventonal approaches ntroducng addtonal structural components whch are to dsspate most of the energy exerted by earthquake motons. In the case of hysteretc dampers such BRBs, sesmc response control stands for the attempt to keep the man frame n ether ts elastc range or wthn low nelastc response and, n the mean tme, the secondary structure gven by the BRBs undergoes n the nelastc range (Bozorgna and Bertero, Wada and Nakashma ). Snce the frst applcaton of BRBs nearly years ago n Japan, recently n USA and other countres, the use of ths type of hysteretc dampers has become very popular n the engneerng practce. Ths popularty s manly caused by the remarkable economcal benefts n the fabrcaton process and on-ste nstallaton, and relatvely smple modelng. Up to present, most of the applcaton cases of BRBs, steel members n the man structural system have been used; n contrast wth the number of projects appled to renforced concrete structures. Moreover, some studes have been reported wth the am of estmatng a unque value of damper strength that mnmzes the sesmc damage n the man frame (Inoue and Kuwahara, Yamaguch and l-abd ). Ths study s motvated by the need to observe the effect of addtonal strength and stffness gven by BRBs on
The th World Conference on arthquake ngneerng October -,, Bejng, Chna the structural performance and protecton of R/C man frames. An attempt for a new drecton n defnng the mechancal propertes of hysteretc dampers s evaluated n whch the deformaton of dampers s drectly controlled. Ths attempt s meant to observe ts drect mplcaton on possble reductons of structural response. SDOF model proposed by Ovedo et al. () for R/C buldngs wth hysteretc dampers s also nvestgated.. R/C BUILDING WITH BUCKLING-RSTRAIND BRACS The structure nvestgated s a -story moment-resstant renforced concrete buldng wth a par of BRBs nstalled at each story at the center bay as llustrated n Fgure. Frame-C was analyzed representng the behavor of the buldng. As seen n Fgure a, the symmetrc plan conssts of by bays of meters and typcal heght of. meters. BRBs (damper system) are nstalled n the R/C structure (man frame). Fgure c summarzes the structural propertes of the man frame. Unlke common practce, structural desgn of the R/C man frame was done pror nstallaton of BRBs to observe the nfluence of the strength level of BRBs on the structural performance of the entre system (man frame + damper system), whle R/C man frame was ntentonally kept unchangeable. Requred desgn sesmc loads were defned accordng to the Buldng Standard Law of Japan (BSLJ) (The Buldng Center of Japan ). Vertcal dstrbuton of equvalent forces was defned accordng to the sesmc lateral strength at -th story C and the sesmc lateral strength dstrbuton factor at -th story A (The Buldng Center of Japan ). The story drft under the desgn loads was lmted to /. Structural desgn of the R/C man frame represents the strong-column-weak-beam collapse mechansm. Floor load was assumed to be the same at each story and proportonal to the trbutary area of Frame-C. The total weght for ths -dmenson frame model s kn.. PARAMTRIC ANALYSIS The restorng force of the entre system can be dealzed as the combnaton of two systems (man frame and damper system) connected n parallel as shown n Fgure. Man frame can be consdered as elastc or plastc meanwhle the damper system s always consdered nelastc. Both systems and the entre system share the same deformaton. The skeleton curve for the damper system s regarded as b-lnear type, and for R/C man frame, t should nclude the effect of stffness reducton due to secton crackng correspondng to a tr-lnear curve or b-lnear approxmaton wth reduced stffness as n Fgure. Mechancal propertes of the hysteretc dampers have been usually defned n terms of strength and stffness n order to comply wth certan requred stffness of the entre system. However, ths defnton does not allow a drect control over the deformatons. Therefore, unlke prevous studes (e.g., Inoue and Kuwahara ), mechancal propertes of BRBs are defned from the yeld story drft and strength level. strength rato (hereafter strength rato) and yeld story drft rato ν (hereafter drft rato) are the man parameters varyng upon a fxed R/C man frame; defned from Fgure as: = + (.) S = S (.) = ( ) (.) S k = K D K eq (.) Where, S,,,, k are the yeld shear strength of the entre system, the yeld shear strength of the man frame, the yeld shear strength of the damper system, the strength rato and the stffness rato, respectvely. Fc,,, max, µ F, µ D are the crackng story drft, yeld story drft of the man frame, yeld story drft of the damper system, maxmum story drft of the entre system, man frame s ductlty and damper system s ductlty. α and ρ defne the shear at crackng pont Fc and the equvalent stffness for the man frame K eq, respectvely.
The th World Conference on arthquake ngneerng October -,, Bejng, Chna The stffness at each story was determned and confrmed by pushover analyss;, K eq were determned. Then, value of was vared by ntervals of. (<<.), n order to modfy the strength level of dampers. At each value of, the total shear ressted by the damper system S was dstrbuted along the heght alke the horzontal force dstrbuton used for the man frame s desgn to determne the story shear ressted by the damper system at -th story. Drft rato ν s ntroduced by qn.. and Fgure wthn the range of [-] and s ntended that the value of ν s constant for all stores and strength ratos; ν=. means that both damper system and man frame wll yeld at the same story drft level. ν=. can be understood as the lowest protecton provded to the man frame now that the damper system wll have the lowest stffness and requre more dsplacement to start to dsspate energy. Therefore, control over the story drft and unform dstrbuton of stffness rato s automatcally granted. Then the horzontal stffness and story drft at yeld level at the th story for the damper system gven by K D and, respectvely, are defned as follows: = ν (.) K D = (.) In Fgure, t can be clearly seen that when the damper strength ncreases from j to j+, product of a larger, the stffness of the damper system ncreases to meet j+ and the drft rato s kept constant for all stores and strength ratos; yet the stffness rato remans the same for all stores under a certan. Sesmc exctaton Roof Floor Floor Floor Floor Floor R/C buldng wth BRB: *Columns floor: (.x.) m Concrete strength: MPa. Renf.rato:.% *Columns floor: (.x.) m Concrete strength: MPa. Renf.rato:.% *Columns floor-roof: (.x.) m Concrete strength: MPa. Renf.rato:.% Floor Floor Floor *Beams - floors: (.x.) m Concrete strength: MPa *Beams -roof: (.x.) m Concrete strength: MPa Floor Floor Foundaton *lastc modulus for concrete: MPa for concrete strength of MPa MPa for concrete strength of MPa a) b) c) Fgure Renforced concrete frame wth BRB. a) plan b) elevaton c) structural propertes S KD = ntre System K K = ρ eq K Fc Fc = Fc Fc Man frame K eq ManFrame System System = ( ) S = S = α µ F Fc µ D j + j j + K D K eq jk D ν j = ν k k j = j system f SD ( ) f SF ( ) Fc max Fgure Scheme of restorng force characterstcs Fgure Scheme for the constant yeld story drft rato of -th story Fgure SDOF model (Ovedo et al. )
The th World Conference on arthquake ngneerng October -,, Bejng, Chna Ovedo et al. () carred out an analytcal study on the floor dsplacement predcton of R/C buldngs wth hysteretc dampers and proposed an SDOF model whch dfferentates the hysteress behavors and skeleton curves for the man frame and damper system. They showed good correspondence of the floor dsplacement predcton by the proposed SDOF model. Therefore, the model proposed by Ovedo et al. () was used for the non-lnear tme-hstory analyses as shown n Fgure, where f SF () and f SD () are the restorng force for the man frame and damper system, respectvely. xtended detals can be found n Ovedo et al. ().. NON-LINAR ANALYSIS PARAMTRS AND INPUT GROUND MOTIONS Input ground motons were defned and scaled to meet dfferent levels of sesmc ntensty, characterzed by peak ground velocty (PGV), from three sources: l Centro NS (), JMA- NS () and syntheszed BCJ-L. Table summarzes the characterstcs of the nput motons used for the non-lnear tme-hstory analyses. A total of ( MDOF and SDOF) non-lnear tme-hstory analyses were performed. All analyss cases correspond to the combnaton of strength ratos [.-.], drft ratos [.,.,., and.] and the nput motons n Table. MDOF tme-hstory analyses were carred out by the program Dran-DX wth element type for columns, element type for beams and element type for BRBs (Prakash et al. ). B-lnear skeleton curve was used as approxmaton to tr-lnear skeleton curve for R/C members. Consequently, stffness reducton coeffcents were appled accordng to the provsons and recommendatons gven by FMA- (FMA ). For the SDOF model, degradng tr-lnear Takeda model and b-lnear model were used for the R/C man frame and damper system, respectvely. Inherent vscous dampng rato was taken as. and ntegraton tme step s.. Post-elastc stffness rato s. for MDOF. Table Input ground motons arthquake Source Input Moton PGA (cm/s ) PGV (cm/s) Td (s) NS NS NS BCJ-L BCJ-L JMA NS. ARTHUAK RSPONS AND DISCUSSIONS Fgure presents the energy dsspated by man frame HF and damper system HD n relaton to the total energy dsspated by hysteress behavor HS. Horzontal axs denotes the strength rato. Almost all nput motons present a relatvely flat regon at whch partcpaton of man frame s mnmzed. For, for ν =., the lowest partcpaton of man frame s about % and t ncreases up to nearly % for ν =.; on the contrary, n the damper system, the partcpaton decreases from % to %. For BCJ-L, the lowest partcpaton of man frame s about % and the largest about % when ν changes from. to.. In the case of, the partcpaton of man frame s kept from % to %. PGV level for tends to ncrease the partcpaton of man frame for low drft ratos and decrease t for large drft ratos; PGV also tends to shft the relatvely flat range to the rght. The aforementoned clearly shows that for low drft ratos, the partcpaton of man frame n the total hysteress energy dsspaton s also low ndependently on the nput moton for.. In ths sense, lower drft ratos would grant more protecton. For strength ratos on the rght of the relatvely flat range, the damper system s less effcent n protectng the prmary structure. Fgure llustrates the rato of total nput energy to the total nput energy wthout BRBs o. It s clearly notced that there s not much relevant nfluence of drft rato wthn the same nput ground moton for strength ratos lower than.. The nput energy rato almost always ncreases wth the strength rato. Moreover, t s also seen a remarkable nfluence of nput moton characterstcs rather than nfluence of PGV level. Input energy rato s found to be manly dependent on characterstcs of ground motons and strength rato.
The th World Conference on arthquake ngneerng October -,, Bejng, Chna Fgure shows the rato of cumulatve plastc stran energy dsspated by the man frame ω F normalzed to whch the structure experences wthout dampers ω Fo. The cumulatve plastc stran energy rato s calculated by qn.., where HF,, and ω F are the hysteress energy dsspated, yeld shear strength, yeld story drft and cumulatve plastc stran rato at -th story n the man frame, respectvely. F HF ω = (.) Reducton of damage n the man frame characterzed by ω F s no less than % for., except n for whch s no less than %; ths s a very attractve reducton. For ν =. and., the reducton of the damage n the man frame s larger comparng to the reducton gven for ν =. and.. The nterval at whch the protecton of man frame s maxmzed tends to enlarge and become more unform as ν decreases. Ths effect has remarkable meanng n the engneerng practce; the concept of a unform range for the strength rato may be desrable as t would regard possble modfcatons of the real response due to uncertantes such as constructon process and materal strength relablty. Consequently, the strength rato should be preferably chosen wthn ths unform range so that the protecton to the man frame s less probable to be modfed. Reducton of cumulatve plastc stran energy n the man frame s more sgnfcant wth decreasng drft ratos. Fgure shows the floor dsplacement response. Horzontal axs represents the floor dsplacement δ normalzed to the floor dsplacement wthout braces δ o. Vertcal axs represents the floor number. In general, floor dsplacements are lower than the dsplacements wthout braces. Ths reducton of floor dsplacements suggests lower story nelastc response and therefore less damage. For. and all drft ratos, there s always reducton; on the contrary, for hgher strength ratos, there are some ncrease n the dsplacements for ν =. and.. Hgher PGV tends to slghtly ncrease the dsplacement ratos. It s mportant to menton that for moderate earthquakes, such as and, the reducton of floor dsplacements tends to be relatvely constant among all stores for. regardless the drft rato. Ths behavor may suggest the lkelness of predefnng a target dsplacement reducton of the floor dsplacements and therefore drect control over the maxmum floor dsplacements could be acheved. Fgure shows the estmaton of maxmum floor dsplacements of MDOF by the SDOF model of Fgure. Horzontal axs denotes the estmated floor dsplacements by the SDOF model and vertcal axs denotes the floor dsplacements of MDOF. Sold lne represents the lnear regresson among all estmated values for a certan ν; the slope s ndcated. For nput moton, t can be seen that the average lne has a slope very close to. meanng reasonable good correspondence of the predcted dsplacements to those of MDOF. Dsplacement rato (δsdof/δmdof) s very close to. for all and ν. For nput moton, a hgher varablty s seen especally for upper floors where hgher mode effect s more sgnfcant; however, most of the predcted values fall n the conservatve sde. In general, low drft ratos allow better estmatons. The varaton of the total hysteress energy demand s llustrated n Fgure. Vertcal axs denotes the rato of hysteress energy demand H over the hysteress energy demand wthout BRBs Ho. It can be seen that there s not a sgnfcant nfluence of drft rato for strong nput motons such as and. On the contrary, for, and BCJ-L, hgh varablty s presented wth ncreasng strength ratos. Another remarkable stuaton presented for and s that the hysteress energy demand always ncreases along wth the strength rato and s kept relatvely nvarable n terms of drft rato for.. Ths suggests that n the case of strong ground motons, the demand of hysteress energy does not vary n relaton to the drft rato and manly depends on the strength level gven to the damper system. On the other hand, no clear trend s observed for, and BCJ-L nput motons; a hgh varablty s presented for approachng to.. It s mportant to hghlght that low drft ratos provde hysteress energy demands as large as or lower than the demands n the case wthout BRBs for.. Ths reducton s even more relevant for hgher drft ratos wthn the same range of strength rato.
The th World Conference on arthquake ngneerng October -,, Bejng, Chna... HF HS ν=. ν=.... HD HS... o BCJ-L... o BCJ-L... ν=. ν=................. HF HS ν=. ν=.. a).. ν=. ν=............... HF HS ν=. ν=..... b) BCJ-L.. HD HS HD HS............... o...... a) ν =. b) ν =. BCJ-L...... c) ν =. d) ν =.......... o BCJ-L...... Fgure Input energy rato..... ν=. ν=................. HF HS ν=. ν=... ν=. ν=.................. HF HS ν=. ν=........ c)........ HD d) HS HD HS. ν=. ν=....... e) Fgure Hysteress energy partcpaton rato..... BCJ-L................. ωf ω Fo ωf ω Fo a) ν =. b) ν =. BCJ-L................ ω F ωfo ω F ωfo BCJ-L BCJ-L...... c) ν =. d) ν =. Fgure Normalzed cumulatve plastc stran energy rato for the man frame
The th World Conference on arthquake ngneerng October -,, Bejng, Chna.... =...... =...... =.. ν=. ν=. ν=. ν=. ν=. ν=........... BCJ-L ν=. ν=. ν=. ν=...... =. =. =...... ν=. ν=. ν=. ν=................ ` ν=. ν=. =. =. =. ν=. ν=. ν=. ν=. ν=. ν=. ν=. ν=..... =...... =...... =.. ν=. ν=. ν=. ν=. ν=. ν=. Floor No. ``..... =. =. =. ν=. ν=...... =. =. =. ν=. ν=...... Normalzed floor dsplacement:.......... Fgure Dstrbuton of floor dsplacement rato δ δ o ν=. ν=. δμdof - δ(cm) =. =. =. =. =. =. =.. =. =. =. =. =. =. =. =. =. =. =. =. =. =. Non-conservatve a) ν =.. Upper floors zone Conservatve δμdof - δ(cm) =. =. =. =. =. =. =. a) ν =... =. =. =. =. =. =. =. δsdof - δ(cm). b) ν =. c) ν =. d) ν =. =. =. =. =. =. =. =. =. =. =. =. =. =. =.. b) ν =. c) ν =. d) ν =. δsdof - δ(cm) =. =. =. =. =. =. =. Intermedate floors zone.. Fgure Comparson of maxmum floor dsplacements between MDOF and SDOF
The th World Conference on arthquake ngneerng October -,, Bejng, Chna... H Ho BCJ-L... H Ho BCJ-L... H Ho BCJ-L... H Ho BCJ-L..................................... CONCLUSIONS a) ν =. b) ν =. c) ν =. d) ν =. Fgure Hysteress energy demand rato The earthquake response of a -story weak-beam strong-column R/C buldng wth bucklng-restraned braces was evaluated by carryng out a seres of non-lnear tme-hstory analyses for dfferent cases accordng to the strength rato and drft rato. The analytcal results have demonstrated the mprovement of the structural performance when hysteretc dampers are nstalled. The followng man fndngs are drawn from ths study: ) The damper strength that mnmzes the damage n the man frame does not necessarly fall n a unque value; on the contrary, the damper strength rato tends to keep a relatvely stable range at whch the reducton of the energy dsspated by the man frame s maxmzed and kept relatvely constant. ) Reducton of the nelastc work n the man frame was obtaned for almost all strength ratos and drft ratos. However, lower strength ratos accompaned wth low drft ratos demonstrated the best mprovement to the structural response and protecton to the man frame. ) The smplfed model proposed (Ovedo et al. ) for the predcton of floor dsplacements of R/C buldngs wth hysteretc dampers demonstrated to provde suffcently accurate estmatons when BRBs are nstalled. The model s consdered useful for the sesmc evaluaton of R/C buldngs wth BRBs. ACKNOWLDGMNT The authors would lke to acknowledge the fnancal support gven by the Mnstry of ducaton, Culture, Sports, Scence and Technology of Japan. Ths support s greatly apprecated. RFRNCS Y. Bozorgna, V.V. Bertero. (). arthquake ngneerng: From ngneerng Sesmology to Performance-Based ngneerng, The Internatonal Code Councl and CRC press. Akra Wada and Masayosh Nakashma. (). From Infancy to Maturty of Bucklng Restraned Braces Research. th World Conference on arthquake ngneerng Paper, Vancouver, B.C., Canada. Kazuo Inoue and Susumu Kuwahara. (). Optmum Strength Rato of Hysteretc. arthquake ngneerng and Structural namcs :, -. Hrok Yamaguch and Ashraf l-abd. (). ffect of arthquake nergy Input Characterstcs on Hysteretc ffcency. arthquake ngneerng and Structural namcs :, -. Juan Andrés Ovedo A., Mtsumasa Mdorkawa and Tetsuhro Asar. (). Study on Dsplacement Response Predcton of R/C Buldngs wth Hysteretc s by SDOF Model. Proceedngs of AIJ Hokkado Chapter Archtectural Meetng, Paper. The Buldng Center of Japan: The Buldng Standard Law of Japan. (). V. Prakash, G. H. Powell and S. Campbell. (). Dran-DX Base Program and User Gude. Department of Cvl ngneerng, Unversty of Calforna Reports: UCB/SMM-/, UCB/SMM-/. Federal mergency Management Agency (FMA). (). NHRP Gudelnes for the Sesmc Rehabltaton of Buldngs. FMA Publcaton, Washngton.