Seismic Response of Reinforced Concrete Diagonal- Braced Frames

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1 Seismic Response of Reinforced Concrete Digonl- Brced Frmes 1 Vrdhmn R. R., 2 Kore P. N., 3 Swmi P. S. 1, 2, 3 Assistnt Professor 1 Civil Engineering Deprtment, 1 Pune Institute of Computer Technology, Pune, Indi Astrct Brced frmes widen their resistnce to lterl forces y the rcing ction of inclined memers. The rces stimulte forces in the ssocited ems nd columns so tht ll work s one like truss with ll memers sujected to stresses tht re for the most prt xil. This xil rection results in less moments nd in turn smller sizes of ems nd column sections compred to moment resisting frmes. This pper presents the elstic seismic response of reinforced concrete frmes with reinforced concrete rcing memer in digonlly rced pttern which re nlyzed numericlly for twelve storey uilding with 5-y structures. This pproch focuses on the rrngements of digonl rces in prticulr y, level nd comintions thereof to reduce the lterl displcement ultimtely to chieve n economy in comprison with similr moment resisting frmes. Results re concluded from grphs nd discussed comprehensively. Index Terms Bre Frmes; Bywise Brced Frmes; Levelwise Brced Frmes; Digonlly Brced Frmes; Concentriclly Brced Frmes (CBF); Outriggers I. INTRODUCTION In order to mke multi-storey structures stronger nd stiffer, which re more susceptile to erthquke nd wind forces, the cross sections of the memer increses from top to ottom this mkes the structure uneconomicl owing to sfety of structure [5]. Therefore, it is necessry to provide specil mechnism nd/or mechnisms tht to improve lterl stility of the structure. Brced frmes develop their confronttion to lterl forces y the rcing ction of digonl memers. Fully rced frmes re more rigid. From sving view point ritrrily rced ones hve lest forces induced in the structure nd t the sme time produce mximum displcement within prescried limits [10]. Frmes cn e nlyzed y vrious methods [8]. However, the method of nlysis dopted depends upon the types of frme, its configurtion of (portl y or multi-y) multi-storey frme nd degree of indetermincy [8]. The structurl nlysis ws sed on structurl models plotted in the STAAD - structurl nlysis nd design commercil softwre. The frme shll e designed to resist the effect of grvity nd erthquke lodings for strength nd serviceility without id of digonl rces first, to ultimtely represent proposl of n introduction of digonl rces hving economicl structure with good ehvior nd convenient rchitecturl distriution. Shn Hu Xu & Di To Niu [1] hd worked on seven reinforced concrete (RC) rced frme, one reinforced concrete frme nd one reinforced concrete sher wll re tested under verticl loding nd reversed cyclic loding. They focused minly on the filure mechnism, strength, degrdtion in stiffness, nd hysteresis loop of the RC rced frme. According to their study, in rced frmes, not only lterl resistnce nd stiffness enhnced, ut lso energy dissiption mount incresed significntly. A.R. Khloo nd M. Mhdi Mohseni [2] hd worked on nonliner seismic ehvior of RC Frmes with RC Brces. This study focuses on evlution of strength, stiffness, ductility nd energy sorption of reinforced concrete rced frmes nd comprison with similr moment resisting frmes nd frmes with sher wll. J. P. Desi, A. K. Jin nd A. S. Ary [3] hd worked on two-y, sixstory frme designed y limit stte method sujected to rtificil erthquke nd iliner hysteresis model ws ssumed for girders, elsto-plstic model ws ssumed for columns nd simple tringulr hysteresis model ws ssumed for reinforced concrete rcing. It is concluded tht the inelstic seismic response of X nd K rced concrete frmes with intermedite rcing memers is stisfctory. M.A. Youssef, H. Ghffrzdeh, M. Nehdi [4] hd worked on the efficiency of using rced RC frmes is experimentlly evluted. Two cyclic loding tests were conducted on moment frme nd rced frme. The moment frme ws designed nd detiled ccording to current seismic codes. A rtionl design methodology ws dopted to design the rced frme including the connections etween the rce memers nd the concrete frme. II. DESCRIPTION OF STUDY BUILDING STRUCTURES Bre nd Fully Brced Frmes In order to study the ehvior of moment resisting digonl rced frmes (re, fully, prtilly y rced nd prtilly level rced nd outrigger frmes) 5 y 12 storey structures re modeled nd nlyzed numericlly. The sections of columns re reduced from top to ottom which is sme for every 3 storey (1-3, 4-6, 7-9, nd 10-12) in order to chieve n economy in re frmes itself. In ll cses, spn length nd story elevtion re 4 nd 3 meters, respectively. A typicl frme of this type is shown in Fig. 1. IJSDR Interntionl Journl of Scientific Development nd Reserch (IJSDR) 100

2 Fig.1 The specific worst loded memer considered for the nlysis of vrious frmes Bywise nd Levelwise Brced Frmes To study the ehvior of ywise nd levelwise rcing pttern 5 y 12 storeyed structures re modeled nd nlyzed numericlly. A typicl rcing pttern of this type is shown in Fig. 2 ( & ). A numer of structures nd their different ptterns with nd without rces hve een nlyzed. The responses of rced frmes of different configurtions hve een compred with re frme nd the sme lso hve een compred with ech other. Behviors of fully rced frmes with the prtilly rced frmes lso studied. Fig.2 5-y 12 storey structures with prticulr By () & Level () Brced lgorithms Outrigger i.e. Prtilly Brced Frmes The logic of plcing the rces ywise nd levelwise shre the lgorithm which llows for comining them evolving rced frme with outrigger i.e. prtilly rced frme which results the new comintion of ove two scenrios. To study the ehvior of such outrigger frmes 5 y 12 storeyed structures re modeled nd nlyzed numericlly. A typicl frme of this type is shown in Fig. 3. III. PARAMETRIC STUDY Fig.3 5-y 12 storey structures with Outrigger Brced lgorithms. Numers of cses re tried for Bywise nd Levelwise Brced Frmes. The following Tle 1 shows totl numer of cses for Bywise nd Levelwise rced frmes for considered structures. In cse of levelwise rced frmes it is wise to restrict ourselves up to for higher level comintions since it will not going to procure ny economy. Prtilly rced frmes hving comintion of ove two types i.e. ywise nd levelwise rced frmes shll e nlyzed to study nd compre the response of such frmes. For this work 5 By 12 storeyed with 350 mm em depth structure ws used. IJSDR Interntionl Journl of Scientific Development nd Reserch (IJSDR) 101

3 Tle 1 No. of cses considered for Bywise & Levelwise rced Frmes for 12 storey structures. No. of Bys Brced No. of Bys Brced t time One Two Three Four Five Totl 5-y No. of Levels Brced No. of Levels Brced t time One Two Three Four Five Totl 5-y Totl No. of Cses Studied 328 Check Digit Algorithems Nturl logrithm of reference numer N s dimensionless prmeter hs een used s sciss with respect to considered prmeters. The reference numer used here is pure numer, which is uniquely specified for the frme nd rcing pttern tried. The check digits specil lgorithms re used for lph nd/or lphnumeric chrcter fields. Ech chrcter is ssigned numeric equivlent. The numeric equivlents re weighted nd the products re summed. The totl is divided y the modulus to determine the reminder. The reminder is compred to pre-ssigned index to determine the check digit. Internl Forces Forces induced viz. xil force, sher force nd ending moment in one prticulr worst loded column segment is considered for this purpose s shown in Fig. 2 ( & ). In order to fcilitte the direct comprison etween re nd fully nd/or prtilly rced frmes the ltter hve een nlyzed for the sme geometry of mutully perpendiculr/orthogonl memers for the sme loding comintion for which the re frme yielded the mximum design force in the memers so selected. However, once the design forces re evluted for fully nd/or prtilly rced structures ll individul segments re redesigned nd the minimum required cross sections nd steel percentge ws clculted. Ultimtely cost comprison is crried out to compute economy. Optimum Bywise Loction for Brcing Frmes 5 y 12 Storey Structures Fully rced frmes descried previously, when nlyzed, exhiit the vlues of forces nd displcements which re chnging with the vrition of numer of prmeters. However, it ws noticed tht the frmes underwent very smll lterl displcement thn ws permissile. It is ut ovious tht, when such frmes re prtilly rced i.e. rced ll long the height in prticulr or comintion of numer of ys which is less thn totl numers of ys for the frme, similrly when rced ll long the level or comintion of numer of levels concerned, will produce lrger displcement compred to re nd fully rced frmes ut within permissile limit i.e H [9]. Hence it ws decided to find out such possiility of developing prticulr pttern for prtilly rced frmes, which would produce smller forces for worst lod comintions. It goes without sying tht the rcing pttern tried lwys stisfied strength s well s serviceility criterion. Fig.4 Optimum y rcing pttern for 5 y 12 storey structures Here dimensionless prmeter (R ) i.e. rtio of xil force which is the rtio of vlue of xil force in memer C1 for ll cses of ys rced to xil force in sme memer of re frme s shown in Fig. 1 ove. Sme is pplicle to rtio of sher force (R s ) nd to rtio ending moment (R m ). The vlue of internl forces in worst loded column segment (C 1 ) of re frme s shown in Fig. 4 ove is chosen s reference vlue for rtio R /R s /R m. It seen clerly tht every grph shows two lines prllel to the x-xis. If these re considered s the upper nd the lower limits s my e pproprite to prticulr dimensionless prmeter, one finds tht mny times in cse of prtilly rced frmes the dimensionless prmeters oserved exceeds the upper limits nd/or is less thn the lower limit so considered. From which it concludes tht some of the rced frmes my llow reduction in effect of considered prmeters hence; it would e dvntgeous to suggest certin working rnge from specified/ccepted minimum to mximum for vrious internl forces concerned within which numer of rcing ptterns/cses produce the force eing considered for different cses. However, numer of cses my e IJSDR Interntionl Journl of Scientific Development nd Reserch (IJSDR) 102

4 found common to ll of them re the optimum cses s fr s force levels re concerned. The frmes which pper etween those cceptle rnges were further tken into ccount for the nlysis nd design purpose. Often symmetricl cses re tken into ccount nd tried in cse of ywise rcings only. Tle 2 Showing percentge of Economy chieved in optimum Bywise nd Levelwise loction of rcings Cse No. 5 y 12 storey structures Percentge of Sving 6.91% For Bywise rced Pttern 3.22% c 8.22% For Levelwise rced Pttern d 7.11% All memers of the frme re designed nd sving in mteril is found out. Amongst ll the so clled est choices there is only one or more thn one choice/choices is mde ville which reduce the totl cost of structures compred to re frmes, when ll memers re designed to crry the most criticl comintion of the lrgest developed forces. This rcing pttern/ these rcing ptterns is/re the optimum solution/solutions. It is found tht such rcing pttern is most economicl thn fully rced one. Following Fig.5 shows the vrition of internl forces of 5 y 12 storey structures nd Fig. 4 shows exmples of optimum ywise rced frmes for 5 y 12 storey structures. c Fig.5 Vrition of internl forces i.e. R, Rs, Rm of 5 y 12 storey structures for Bywise comintions Optimum Levelwise Loction for Brcing Frmes 5 By 12 Storey Structures The sme is repeted for levelwise rcing for previously mentioned structures nd is represented in the Fig. 6 elow. The grphs show vrition of xil force, sher force nd ending moment in memer C1 s the rcing pttern chnges. Overll, these grphs show the increment in the vlues of rtios of R s the rcing level nd comintions of floor increses, Fig. 6 () show step vrition except the cses which lie elow nd ove the limit of re nd fully rced frmes respectively, nd Fig. 6 (c) show the step vrition except the cses which lie elow the limit of re frmes. c Fig.6 Vrition of internl forces i.e. R, Rs, Rm of 5 y 12 storey structures for Levelwise comintions Hence, it seems resonle to ccept certin working rnge for xil force; sher force nd ending moment from specified/ccepted minimum to mximum for vrious internl forces concerned within which numer of rcing ptterns/cses produce the force eing considered different cses. However, numer of cses my e found common to ll of them. These re most optimum cses s fr s force levels re concerned. Fig. 7 shows exmples of optimum levelwise rced frmes for 5 y 12 storey structures nd the economy is tulted in tle nd the respective comintions re shown in Tle 2 ove. IJSDR Interntionl Journl of Scientific Development nd Reserch (IJSDR) 103

5 Optimlly Brced Frmes with Outriggers Fig.7 Optimum level rcing pttern for 5 y 12 storey structures To egin with nd to rrive t the outrigger orienttion, comintion of optimum cses of ywise rcing nd levelwise rcing pttern re tried. c Fig.8 Optimum rcing ptterns for 5 y 12 storey structures It my e noted tht when numer of ys or levels rced simultneously re increses then normlly the cost effectiveness is lost, s the numer of memers increse which compenste the sving climed due to reduction in the internl forces induced in the structures nd the reduced cross sections commensurte with the sme. Tle 3 Showing percentge of economy chieved in optimlly rced frmes with outriggers. Cse no. (For 5 y 12 storey structures) Percentge of Sving B (3) + L (1) 5.84% B (3) + L (1 + 3) 4.78% B (2 + 4) + L (1) 2.17% In order to reduce the mteril cost, optimum cses of ywise, levelwise nd prtilly rced re considered nd the section sizes re reduced to get minimum mteril cost nd yet displcement remin within permissile limits. The following Fig. 8 (, & c) shows the prtilly rced frme for the comintion of specific ys nd levels rced. The respective comintions nd economy is tulted s shown in Tle 3 ove. Storey Drift The lterl displcement of frme ws oserved t common point t specific position in 5 y 12 storey structures. The comprison is mde etween re, fully rced, prtilly rced i.e. optimum y rced nd level rced nd outrigger. It ws checked whether the structure stisfies mximum permissile reltive lterl drift criterion s per IS: (Prt-I) which is 0.004H [11]. IJSDR Interntionl Journl of Scientific Development nd Reserch (IJSDR) 104

6 Tle 4 showing vrition of lterl displcement long height of structure for 5 By 12 storey structure with 350 mm em depth Anlyzed Structures of 5 By 12 storey structures for 350 mm em Depth Ht. From Bre Frme Fully Brced Frme Optimum By Optimum Level Frme with Bse (m) (mm) (mm) Brced (mm) Brced (mm) Outrigger (mm) Fig.9 Vritions of lterl displcement long height of structure for 5 By 12 storeyed with 350 mm em depth for L/C (1.5 D.L E.Q.) For re frmes the lterl drift is well within the permissile one, ut it is incresing s one move towrds the top most point of structure. Also the lterl displcements for fully rced frmes re getting sustntilly reduced s compred with re frme, ut these re uneconomicl structures from sving point of view. For optimlly y rced frmes nd for outriggers the lterl displcements re getting reduced y ner out hlf nd more s compred to the re frmes. There is no vlule reduction in the lterl displcement for optimlly levelwise rced frmes tulted s shown in Tle 4 ove. Conclusion It concludes tht optimlly rced frmes re stiff, strong, nd n economicl structurl system. Fully rced frmes re very conservtive in so fr s lterl drift is concerned ut uneconomicl nd t the sme time optimlly rced one hve lest forces induced in the structure nd produce mximum displcement ut within prescried limit. However, further work is needed in order to chieve more economy y developing new scenrio i.e. cellwise rced frmes. This work is importnt, ecuse rced frmes re very efficient nd effective system for resisting lterl forces. References [1] Shn Hu Xu & Di To Niu, Seismic Behvior of R.C. Brced Frmes, ACI Structurl journl, No.1, 100, Jn Fe [2] R. Khloo & M. Mhdi Mohseni, Nonliner Seismic Behviour of RC Frmes with RC Brces Asin Journl of Civil Engineering, Vol. 9, No. 6, [3] J.P. Desi, A.K. Jin nd A.S. Ary, Seismic response of R.C. Brced Frmes, Computers nd Structures Vol. 29, No. 4, [4] M.A. Youssef,, H. Ghffrzdeh, M. Nehdi Seismic performnce of RC frmes with concentric internl steel rcing, Deprtment of Civil nd Environmentl Engineering, Shirz University, Shirz , Irn, 23 Octoer [5] Kulkrni J. G., Kore P. N., Tnwde S. B., Seismic Response of Reinforced Concrete Brced Frmes, Interntionl Journl of Engineering Reserch nd Applictions (IJERA) ISSN: Vol. 3, Issue 4, Jul-Aug 2013, pp IJSDR Interntionl Journl of Scientific Development nd Reserch (IJSDR) 105

7 [6] S. I. Khn, Prof. P. O. Modni Seismic Retrofitting of RC Building y Using Different Brcing Systems Interntionl Journl of Engineering Reserch & Technology (IJERT) Vol. 2 Issue 7, July 2013 [7] Dr. V. L. Shh nd Dr. S.R. Krve, (Fe. 2005), Illustrted design of reinforced concrete uilding, 5th Ed., structure puliction. [8] V.N. Vzirni nd M.M. Rtwni, (1985) Anlysis of structures, 10th Ed., Khnn Pulishers. [9] Wever Jr. nd Gere J.M., (1986) Mtrix nlysis of frmed structure, CBS Pulishers nd distriutor, New Delhi. [10] I.S , Indin stndrd code of prctice for plin nd reinforced concrete (fourth revision), Bureu of Indin stndrds, New Delhi. [11] I.S (Prt 1)-2002, Criteri for erthquke resistnt design of structure, generl provision nd uilding, Bureu of Indin stndrds, New IJSDR Interntionl Journl of Scientific Development nd Reserch (IJSDR) 106