This is a repository copy of Optimum seismic design of concentrically braced steel frames: concepts and design procedures.

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1 Ths s a repostory copy of Optmum sesmc desgn of concentrcally braced steel frames: concepts and desgn procedures. Whte Rose Research Onlne URL for ths paper: Verson: Accepted Verson Artcle: Moghaddam, H., Hajrasoulha, I. orcd.org/ and Doostan, A. (2005 Optmum sesmc desgn of concentrcally braced steel frames: concepts and desgn procedures. Journal of Constructonal Steel Research, 6 (2. pp ISSN X Artcle avalable under the terms of the CC-BY-NC-ND lcence ( Reuse Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton-NonCommercal-NoDervs (CC BY-NC-ND lcence. Ths lcence only allows you to download ths work and are t wth others as long as you credt the authors, but you can t change the artcle n any way or use t commercally. More nformaton and the full terms of the lcence here: Takedown If you consder content n Whte Rose Research Onlne to be n breach of UK law, please notfy us by emalng eprnts@whterose.ac.uk ncludng the URL of the record and the reason for the wthdrawal request. eprnts@whterose.ac.uk

2 Moghaddam H, Hajrasoulha I & Doostan A (2005 Optmum sesmc desgn of concentrcally braced steel frames: Concepts and desgn procedures. Journal of Constructonal Steel Research, 6(2, Optmum sesmc desgn of concentrcally braced steel frames: Concepts and desgn procedures H. Moghaddam, I. Hajrasoulha and A. Doostan Department of Cvl Engneerng, Sharf Unversty of Technology, Tehran, Iran ABSTRACT: A methodology s presented for optmzaton of dynamc response of concentrcally braced steel frames subjected to sesmc exctaton, based on the concept of unform dstrbuton of deformaton. In order to obtan the optmum dstrbuton of structural propertes, an teratve optmzaton procedure has been adopted. In ths approach, the structural propertes are modfed so that neffcent materal s gradually fted from strong to weak areas of a structure. Ths process s contnued untl a state of unform deformaton s acheved. It s own that the sesmc performance of such a structure s optmal, and behaves generally better than those desgned by conventonal methods. In order to prevent the cumbersome analyss of the frame models, an equvalent procedure s ntroduced to perform the optmzaton procedure on the modfed reduced ear-buldng model of the frames, whch s own to be accurate enough for desgn purposes. Keywords: optmal strength pattern, performance-based desgn, braced frames, sesmc loadng Introducton The prelmnary desgn of most buldngs s normally based on equvalent statc forces specfed by the governng buldng code. The heght wse dstrbuton of these statc forces (and therefore, stffness and strength seems to be based mplctly on the elastc vbraton modes []. However,

3 structures do not reman elastc durng severe earthquakes and they are expected to undergo large nonlnear deformatons. Therefore, the employment of such arbtrary heght wse dstrbuton of sesmc forces may not lead to the optmum utlzaton of structural materals. Many expermental and analytcal studes have been carred out to nvestgate the valdty of the dstrbuton of lateral forces accordng to sesmc codes. Lee and Goel [2] analyzed a seres of 2 to 20 story frame models subjected to varous earthquake exctatons. They owed that n general there s a dscrepancy between the earthquake nduced ear forces and the forces determned by assumng dstrbuton patterns. The consequences of usng the code patterns on sesmc performance have been nvestgated durng the last decade [3, 4]. Chopra [5] evaluated the ductlty demands of several ear-buldng models subjected to the El- Centro Earthquake of 940. The relatve story yeld strength of these models was chosen n accordance wth the dstrbuton patterns of the earthquake forces specfed n the Unform Buldng Code [6]. It was concluded that ths dstrbuton pattern does not lead to equal ductlty demand n all stores, and that n most cases the ductlty demand n the frst story s the largest of all stores. The frst author [7, 8] proportoned the relatve story yeld strength of a number of ear buldng models n accordance wth some arbtrarly chosen dstrbuton patterns as well as the dstrbuton pattern suggested by UBC997 [6]. It has been concluded that: (a the pattern suggested by code gudelnes does not lead to a unform dstrbuton of ductlty, and (b a rather unform dstrbuton of ductlty wth a relatvely smaller maxmum ductlty demand can be obtaned from other patterns. These fndngs have been confrmed by further nvestgatons [9- ], and led to the development of a new concept: optmum dstrbuton pattern for sesmc performance that s dscussed n ths paper. Concept of Optmum Dstrbuton Pattern for sesmc performance As dscussed before, the use of dstrbuton patterns for lateral sesmc forces suggested by codes does not guarantee the optmum performance of structures. Current studes ndcate that durng strong earthquakes the deformaton demand n structures does not vary unformly [- 4]. Therefore, t can be concluded that n some parts of the structure, the deformaton demand does not reach the allowable level of sesmc capacty, and therefore, the materal s not fully exploted. If the strength of these strong parts decreases, the deformaton would be expected to 2

4 ncrease [2]. Hence, f the strength decreases ncrementally, we ould eventually obtan a status of unform deformaton. At ths pont the materal capacty s fully exploted. As the decrease of strength s normally obtaned by the decrease of materal, a structure becomes relatvely lghter as deformaton s dstrbuted more unformly. Therefore, n general t can be concluded that a status of unform deformaton s a drect consequence of the optmum use of materal. Ths s consdered as the Theory of Unform Deformatons [0, ]. Ths theory s the bass of the studes presented n ths paper. Shear and Flexural Deformaton Recent desgn gudelnes, such as FEMA 356 [3] and SEAOC Vson 2000 [4], place lmts on acceptable values of response parameters; mplyng that exceedng of these lmts s a volaton of a performance objectve. Among varous response parameters, the nter-story drft s consdered as a relable ndcator of damage to nonstructural elements, and s wdely used as a falure crteron because of the smplcty and convenence assocated wth ts estmaton. Consderng the 2-D frame own n Fgure -a, the axal deformaton of the columns results n ncreased lateral story and nter-story drfts. In each story, the total nter-story drft ( t s a combnaton of the ear deformaton ( due to ear flexblty of the story, and the flexural deformaton ( ax due to axal flexblty of the lower columns. Hence, nter-story drft could be expressed as: = + ( t ax Flexural deformaton does not contrbute n the damage mposed to the story, though t may mpar the stablty due to the P- effects. Neglectng the axal deformaton of beams, rotaton at the top and bottom levels of the panel own n Fgure -b are gven by: U 5 U 6 = L θ (2 2 U 2 U 3 = L θ (3 3

5 where, U 5, U 6, U 2 and U 3 are vertcal dsplacements, as own n Fgure -b. H s the story heght, and L s the span length. The rotaton of the panel, α, could be approxmated by averagng θ and θ 2 as follows: θ + θ 2 ( U 2 + U5 U3 U 6 = 2 2L α (4 Hence, as ndcated n Fgure -b, the flexural deformaton ax s calculated as: H ax = α H = ( U 2 + U 5 U 3 U 6 (5 2L Consderng equatons (5 and (, the ear nter-story drft can be determned as follows [5]: H = t + ( U 3 + U 6 U 2 U 5 (6 2L For mult-span models, the maxmum value of the ear drft n dfferent panels would be consdered as the ear story drft. Modelng and Assumptons In the present study, three steel concentrc braced frames, as own n Fgure 2, wth 5, 0 and 5 stores have been selected. The buldngs are assumed to be located on a sol type S D and a sesmcally actve area, zone 4 of the UBC 997 [6] category, wth PGA of 0.44 g. All connectons are consdered to be smple. The frame members were szed to support gravty and lateral loads determned n accordance wth the mnmum requrements of UBC 997 [6]. In all models, the top story s 25% lghter than the others. IPB, IPE and UNP sectons, accordng to DIN, are chosen for columns, beams and bracngs, respectvely. To elmnate the over strength effect, conceptual auxlary sectons have been developed by assumng a contnuous varaton of secton propertes. In the code type desgn, once the members were sezed, the entre desgn was checked for the code drft lmtatons and f necessary refned to meet the requrements. For statc and nonlnear dynamc analyss, computer program Dran-2DX [6] was used to predct the frame responses. The Raylegh dampng s adopted wth a constant dampng rato 0.05 for the frst few effectve modes. A two-dmensonal beam-column element that allows for the formaton of plastc hnges at concentrated ponts near ts ends was employed to model the columns. The brace members are assumed to have an elasto-plastc behavor n tenson and 4

6 compresson. The yeld capacty n tenson s set equal to the nomnal tensle resstance, whle the yeld capacty n compresson s set equal to 0.28 tmes the nomnal compressve resstance as suggested by Jan et al [7]. Four strong ground moton records were used to evaluate and compare the sesmc performance of the frames, ( The 994 Northrdge earthquake NWH360 component wth a PGA of 0.59g, (2 The 979 Imperal Valley earthquake H-E06230 component wth a PGA of 0.44g, (3 The 992 Cape Mendocno earthquake PET090 component wth a PGA of 0.66g, and (4 A synthetc earthquake record generated to have a target spectrum close to that of the UBC 997 [6] code wth a PGA of 0.44g. All of these exctatons correspond to the stes of sol profles smlar to the desgn ste sol, S D, of UBC. Optmum Desgn of Bracngs for Sesmc Exctatons The theory of unform deformaton can be employed for evaluaton of optmum strength dstrbuton n concentrcally braced frames. As an example, a 5-story model desgned n accordance to UBC code [6], as own n Fgure 2, s consdered to be laterally loaded for the Northrdge earthquake 994 (NWH360. The queston s how to proporton and arrange the bracngs to mnmze the maxmum ear story drft. The followng condtons are also stpulated: a The cross sectons of beams and columns are not regarded as varables n the optmzaton procedures, and therefore they reman unchanged. b All columns are checked for stablty under the combnaton of gravtatonal loads and the dynamc sesmc forces (resultng from sesmc exctaton accordng to ASD [8], and are reszed f necessary to meet: f F a a + c mx ( f / F a f bx ex F bx (7 where f a and f bx are the calculated axal and bendng stresses; F a and F bx are the allowable compressonal and bendng stresses, respectvely. c mx s a coeffcent dependent on the column end moments, and F ex s the elastc bucklng stress dvded by a factor of safety as gven n [8]. To obtan the optmum dstrbuton of bracngs, the evolutonary optmzaton method s adapted as follows: 5

7 . The model already desgned for gravtatonal and any arbtrary lateral load pattern, that of UBC97 [6] here, s regarded as a prmary pattern for dstrbuton of structural propertes. Here, the cross secton area of bracngs s assumed to be the only key parameter controllng the structural sesmc behavor. However, as mentoned before, the columns have to be checked for stablty. Ths s ndeed a stpulatng condton for the optmzaton program. 2. The structure s subjected to the gven exctaton, the peak values of ear story drfts, (, and the average of those values, avg, are determned. Consequently, the COV, coeffcent of varaton, of ear story drfts s calculated. If COV s small enough, dstrbuton of bracng strength n each story can be consdered as practcally optmum. The COV of the frst pattern s determned as It s decded that the COV s hgh, and the analyss ould be contnued. 3. At ths step the dstrbuton of bracng cross secton areas, as a parameter monotoncally proporton to the ear strength of each story and hence to the total strength of the story, s modfed. Usng the theory of unform deformatons, the neffcent materal ould be fted from strong parts to the weak parts to obtan an optmum structure. To accompl ths, the cross secton of bracngs ould be ncreased n the stores wth peak ear story drft greater than the average of peak drfts, avg, and ould be decreased n the stores where peak ear drft s less than the average. The total cross secton areas of the all bracngs n the frame s kept unchanged n order for the structural weght of the frame to be constant. Ths alteraton ould be appled ncrementally to obtan convergence n numercal calculatons. Hence, the followng equaton was used n the present work A b ] = [( A ( [( n+ b ] n (8 avg where (A b s the total cross secton area of bracngs at th story, n denotes the step number. α s the convergence coeffcent rangng from 0 to. For the above example, an acceptable convergence has been obtaned for a value of α equals 0.2. Consequently, cross secton areas of the bracngs are scaled so that the total structural weght remans constant. Usng these modfed cross sectons; the procedure s repeated from step 2. It s expected that the COV of peak ear story drfts for ths pattern s smaller than the correspondng COV for the prevous α 6

8 pattern. Ths procedure s terated untl COV becomes small enough, and a state of rather unform ear story drft prevals. Fgure 3, llustrates the evoluton of ear story drft dstrbuton from the UBC 97 [6] model toward the fnal optmum dstrbuton. As t s own n ths Fgure, peak ear story drfts n the fnal step have become remarkably unform and the maxmum peak ear story drft has been decreased from 4.7 cm to 2.4 cm. Modfed Shear Buldng Model The modelng of engneerng structures usually nvolves a great deal of approxmaton. Among the wde dversty of structural models that are used to estmate the non-lnear sesmc response of buldng frames, the ear buldng s the one most frequently adopted. In spte of some drawbacks, t s wdely used to study the sesmc response of mult-story buldngs because of smplcty and low computatonal expenses [9], whch mght be consdered as a great advantage for a desgn engneer to deal wth. La et al. [20] have nvestgated the relablty and accuracy of such ear-beam models. In the present study, the ear-buldng model has been modfed to have a better estmaton for the nonlnear dynamc response of real framed structures. In ordnary ear buldng models, the effect of column axal deformatons s usually neglected, and therefore, t s not possble to calculate the nodal dsplacements caused by flexural deformaton, whle t may have a consderable contrbuton to the sesmc response of most frame-type structures. In the present study, the ear-buldng model has been modfed by ntroducng supplementary sprngs to account for flexural dsplacements n addton to ear dsplacements. Accordng to the number of stores, the structure s modeled wth n lumped masses, representng the stores. Only one degree of freedom of translaton n the horzontal drecton s taken nto consderaton and each adjacent mass s connected by two supplementary sprngs as own n Fgure 4. The stffnesses of these sprngs are equal to the ear and bendng stffnesses of each story, respectvely. These stffnesses are determned by enforcng the model to undergo the same dsplacements as those obtaned from a puover 7

9 analyss on the frame model. As own n Fgure 4, the materal nonlneartes may be ncorporated nto stffness and strength of supplementary sprngs. In Fgure 4, m represents the mass of th floor; and V and S are, respectvely, the total ear force and yeld strength of the th story obtaned from the puover analyss. (k t s the nomnal story stffness correspondng to the relatve total drft at th floor ( t n Fgure. (k denotes the ear story stffness correspondng to the relatve ear drft at th floor ( n Fgure. (k ax represents the bendng story stffness correspondng to the flexural deformaton at th floor ( ax n Fgure, and (α t, (α and (α ax are over-strength factors for nomnal story stffness, ear story stffness and bendng story stffness at th floor, respectvely. (k t and (α t are determned from a puover analyss takng nto account the axal deformaton of columns. Usng equaton (6, ear story drft corresponds to each step of prevous pu over analyss could be calculated and consequently (k and (α are determned. As transmtted force s equal n two supplementary sprngs, equaton ( could be rewrtten as: For V S we have V t ( k V = ( k V + ( k ax hence + ( k ( k ( k t = (9 ax For V > S we have S t V S + = (0 ( k ( α ( k ( k ( α ( k ( k ( α t t S V S Substtutng Equaton (9 n (0, (k ax and (α ax are obtaned as follows: ( α ax ( k ax ( α ( k ( k S ax V S ax ( k t = ( ( k ( kt ( α [( k ( k ] t t = (2 ( α ( k ( α t ( kt Calculatons ow that (α ax s almost equal to when columns are desgned to prevent bucklng aganst earthquake loads. The ear nter-story drft, that causes damage to the structure, can be separated from the flexural deformaton by usng the modfed ear-buldng ax 8

10 model. Moreover, ths modfed model represents the behavor of frame models more realstcally as compared wth the ordnary ear-buldng model. Fgure 5, llustrates the response of 5 story frame model and ts correspondng modfed ear-buldng model under Imperal Valley 979. It s own n ths Fgure that modfed ear-buldng model has a good capablty to estmate the sesmc response parameters of braced frames, such as roof dsplacement, total nter story drfts and ear nter story drfts. Ths concluson has been confrmed by further analyses on dfferent models and ground motons. Stffness and Strength Relatonp In the absence of over-strength, a specfc relaton exsts between stffness and strength of a story. Ths relaton depends on the type of structural members, and the frame geometry, and can be smply determned by usng a puover analyss. Numerous analyses were conducted usng the frames desgned for dfferent sesmc load patterns. These analyses ow that for each story, the ratos (k ax /(k and S /(k are not dependant on the type of strength dstrbuton pattern (Fgure 6, hence: ( k S ax = a = b ( k ( k (3 where a and b are constant multplers and S s the ear strength of the th story, respectvely. These parameters depend on the type of structural members as well as the frame geometry, and can be smply determned by usng a puover analyss. These observatons are fundamental and smlar assumptons about the stablty of the member yeld dsplacement have been adopted by others [2, 22]. Optmum Sesmc Desgn usng Modfed Shear Buldng Model As descrbed n prevous sectons, the theory of unform deformaton can be employed drectly to evaluate optmum lateral loadng patterns for braced frames. However, nonlnear dynamc analyss of frame models needs a great deal of computatonal effort, and therefore, t would be desrable to employ the ear buldng model for such analyss. Ths can be accompled by usng the aforementoned modfed ear-buldng model. The procedure s as follows: 9

11 . An arbtrary lateral load pattern (such as that of UBC 97 [6] s chosen and used for desgn of structure. 2. Blnear sprng parameters and constant multplers of equaton (3 are determned for each story by conductng a puover analyss on the desgned frame, as dscussed n prevous sectons. The correspondng modfed ear- buldng model s defned accordngly. 3. Nonlnear tme hstory analyss under the desgn earthquake s carred out on the modfed ear- buldng model. Arbtrary values for strengths, ear and flexural stffness satsfyng equaton (3 are consdered n analyss. The average and peak values of ear story drfts, ( avg and (, are determned, and the correspondng coeffcent of varaton (COV s calculated. The procedure contnues untl COV decreases down to an acceptable level. 4. Accordng to the theory of unform deformaton, the ear strength, ear stffness, and flexural stffness of the stores wth ear story drfts greater than the average drft, ( avg, ould be ncreased proportonally. On the contrary, these parameters ould decrease where the drfts are less than average. As a result, a rather unform dstrbuton of story drfts prevals. The followng relatonp has been employed to modfy the strength parameters: ( [( k ] n+ = [( k ] n (4 avg where, α s the convergence coeffcent chosen as equal to 0.2 n ths work. After modfyng the story ear stffness, for each story, the flexural stffness and strength are modfed accordng to equaton (3. In order to keep the weght of the model constant, the parameters [(k ] n+ and [(k ax ] n+ are scaled so that the domnant perod of the structure remans unchanged. The procedure contnues untl the COV of peak ear story drfts decreases down to a target value. At ths stage, the strength dstrbuton s regarded as the optmum. 5. Consderng the safety factors ncorporated n the desgn of lateral resstant system of the frame, the optmum lateral load can be calculated from the foregong optmum strength pattern. Now, the constant multplers of equaton (3 are recalculated, and the procedure s repeated. However, the present study ows that these multplers are nearly constant for each story, and the optmum soluton s not senstve to small varaton of those multplers. α Fgure 7 llustrates the steps of ths approach from the UBC 97 [6] desgned model toward the fnal desgn for a 0-story buldng subjected to the Imperal Valley 979. The convergence 0

12 effcency of the proposed method to the optmum desgn s emphaszed n Fgure 7. It s own n ths Fgure, havng the same structural weght, maxmum ear story drft s reduced almost 50% after only fve steps. Fgure 7 ows that reducton COV s always accompaned wth reducton of maxmum ear story drft. These results are n agreement wth the Theory of Unform Deformaton. As mentoned before, by usng modfed ear-buldng model, optmzaton procedure can be adapted on smple nonlnear sprng elements and there s no need to perform any nonlnear dynamc analyss on a full frame models. In Fgure 8, fnal results of two proposed methods are compared wth UBC 97 [6] desgn for 5-story braced frame subjected to Northrdge earthquake 994. As t s own n ths Fgure, usng modfed ear-buldng model s both smple and accurate enough for desgn purposes. Accordng to these results, the procedure ntroduced n ths paper seems to be a practcal alternatve to current desgn procedures for steel braced frames. Optmum Sesmc Desgn Load Pattern The foregong procedure has been used for optmum desgn of 5, 0 and 5-story braced frames, own n Fgure 2, subjected to dfferent strong ground motons. The results ndcate that optmum structures suffer relatvely less damage as compared wth structures desgned for conventonal sesmc loadngs. Fgure 9, ows the lateral sesmc desgn loads for the ffteenstory conventonally desgned and that of the optmum model under the Northrdge 994 earthquake. The results ndcate that to mprove the performance under ths specfc earthquake, the frame ould be desgned n complance wth a new load pattern dfferent from the conventonal UBC pattern. Effect of the Intal Pattern on the Optmum Load Pattern As descrbed before, an ntal heght wse strength dstrbuton s necessary to begn the optmzaton algorthm. In order to nvestgate the effect of ths ntal strength dstrbuton pattern on the fnal optmum load pattern, the desgn base ear was dstrbuted as follows; ( A concentrated load on the roof level, (2 Trangular dstrbuton accordng to UBC 97 [6], (3 Rectangular dstrbuton over the heght of the frame, (4 An nverted trangular dstrbuton wth

13 the maxmum lateral load on the frst floor and the mnmum lateral load on the roof floor. For each case, the optmum lateral load pattern was derved for the Imperal Valley earthquake 979. The comparson of the optmum lateral load pattern of each case s depcted n Fgure 0. As own n ths Fgure, the optmum load pattern s unque and does not depend on the ntal strength pattern; however, the speed of convergence s to some extent dependant on the ntal strength pattern. Ths concluson has been confrmed by further analyses on dfferent models and ground motons. Cumulatve Damage The peak ear story drft may not always be the best performance crteron for performance base desgn as t occasonally fals n predctng the state of structural damage n earthquakes. To nvestgate the extent of cumulatve damage, the damage crteron proposed by Bak et al. [23] based on the classcal low-cycle fatgue approach has been adopted. The story nelastc ear deformaton s chosen as the basc damage quantty, and the cumulatve damage ndex after N excursons of plastc deformaton s calculated as: D = N pj j= δ y δ c (5 where D s the cumulatve damage ndex at th story, rangng from 0 for undamaged to for severely damaged stores, N s the number of plastc excursons, δ p s the plastc deformaton of th story n j th excurson, δ y s the nomnal yeld deformaton, and c s a parameter that accounts for the effect of magntude of plastc deformaton taken to be.5 [24]. To assess the damage experenced by the whole structure, the global damage ndex s obtaned as a weghted average of the damage ndces at the story levels, wth the energy dsspated beng the weghtng functon. D g n = = n = DW W p p (6 where D g s the global damage ndex, W p s the energy dsspated at th story, D s the damage ndex at th story, and n s the number of stores. Usng ths equaton, the global damage ndex of 2

14 each frame desgned accordng to UBC97 [6] and the optmum lateral loadng related to each earthquake has been calculated and presented n Fgure. The results suggest that the damages experenced by the optmum frames are sgnfcantly less than those of the UBC s. Concluson. Ths paper presents a new method for optmzaton of dynamc response of concentrcally braced steel frames subjected to sesmc exctaton. Ths method s based on the concept of unform dstrbuton of deformaton. 2. It s own that t s possble to mprove the sesmc performance of a structure by ftng the materal from strong to weak parts. Ths eventually leads to an optmum dstrbuton of materal, correlated wth optmum performance of the structure durng the gven earthquake. It has been own that at ths stage, a state of unform dstrbuton of deformaton prevals. Therefore, n general t may be concluded that we need to reach a status of unform deformaton for optmum use of materal. Ths s consdered as the Theory of Unform Deformaton. 3. The Theory of Unform Deformaton has been employed for evaluaton of optmum strength dstrbuton n concentrcally braced frames. It s own that deformaton demand s reduced for optmum model compare to conventonal models. 4. The ear-buldng model has been modfed by ntroducng supplementary sprngs to account for flexural dsplacements n addton to ear drfts. It s own that ths model can be used for estmatng the sesmc response of braced frames wth acceptable accuracy. Instead of a drect employment of the theory of unform deformaton, t s own that the modfed ear-buldng model can be used to accompl the optmum sesmc desgn of braced frames. 5. It has been demonstrated that there s generally a unque optmum dstrbuton of structural propertes, whch s ndependent of the sesmc load pattern used for ntal desgn. 3

15 6. The cumulatve damage has been calculated for both optmum and conventonal models n dfferent earthquakes. It has been concluded that optmum structures suffer relatvely less damage as compared wth conventonal structures. REFRENCES. Green, N. B., Earthquake resstant buldng desgn and constructon, 2 nd Edton, Van Nostrand Renhold Company, New York, Lee, S.S. and Goel, S.C. Performance based sesmc desgn of structures usng target drft and yeld mechansm, U.S Japan Semnar on Advanced Stablty and Sesmcty Concept for Performance Based Desgn of Steel and Composte Structures, Kyoto, Japan, Martnell, L., Perott, F. and Bozz, A. "Sesmc desgn and response of a 4-story concentrcally braced steel buldng", Behavour of Steel Structures n Sesmc Areas, pp , Glmore, T.A. and Bertero, V.V. Sesmc performance of a 30-story buldng located on soft sol and desgned accordng to UBC 99, UCB/EERC-93/04, Berkeley: Earthquake Engneerng Research Centre, Unversty of Calforna, Chopra, A. K., Dynamcs of structures: theory and applcatons to earthquake engneerng, 2 nd Edton, Prentce Hall Inc., London, UBC. Structural engneerng desgn provsons. In: Unform Buldng Code. Internatonal Conference of Buldng Offcals, vol Moghaddam, H. Earthquake Engneerng, RTRC Publcatons, st Edton, Tehran, 995. (n Fars. 8. Moghaddam, H. and Esmalzadeh Hakm, B. On the optmum sesmc loadng of multstory structures, 3 rd Internatonal Conference on sesmology and earthquake engneerng, Tehran, Iran, pp , Moghaddam, H. and Karam, R. Towards a more effcent sesmc loadng for MDOF Structures, Accepted for Publcaton, ASCE Journal of Structural Engneerng, October

16 0. Moghaddam, H., Hajrasoulha, I. and Doostan, A., On the optmum strength dstrbuton n sesmc desgn of structures, Response of Structures to Extreme Loadng (XL2003, Canada, Toronto, Moghaddam, H. and Hajrasoulha, I. On the optmum performance-based desgn of structures, The th Internatonal Conference on Sol Dynamcs & Earthquake Engneerng, USA, Berkeley, T. Vdc, P. Fajfar and M. Fschnger, Consstent nelastc desgn spectra: strength and dsplacement, Earthquake Engneerng. And Structural Dynamcs, Vol 23., pp , FEMA 356, Prestandard and commentary for the sesmc rehabltaton of buldngs. Wangton, DC: Federal Emergency Management Agency, SEAOC. Vson 2000, performance based sesmc engneerng for buldngs. Sacramento, CA: Structural Engneers Assocaton of Calforna, Bertero, V.V., Anderson, J.C., Krawnkler, H. and Mranda, E., Desgn gudelnes for ductlty and drft lmts Report No. UCB/EERC-9/5, Earthquake Engneerng Center, Unversty of Calforna, Berkeley, CA, July Praka, V., Powell, G.H. and Flppou, F.C. DRAIN-2DX: Base program user gude, Report No. UCB/SEMM-92/29, Jan, A.K., Goel, S.C. and Hanson, R.D. Hysteretc cycles of axally loaded steel members, Journal of Structural Dvson, ASCE, VOL.06, No.8, pp , Amercan Insttute of Steel Constructon, Specfcaton for Structural Steel Buldng- Allowable Stress Desgn, Chcago IL, Daz, O., Mendoza E. and Esteva, L. Sesmc ductlty demands predcted by alternate models of buldng frames, Earthquake Spectra, Vol. 0, No.3, pp , La, M., L, Y. and Zhang, Ch. Analyss method of mult-rgd-body model for earthquake responses of ear-type structure, WCEE 0 th Conf., Madrd, Span, pp , Prestley, M.J.N. Performance based sesmc desgn, Proceedngs of the 2th world conference on earthquake engneerng, Auckland, New Zealand, Aschem, M. Sesmc desgn based on the yeld dsplacement, Earthquake Spectra, Vol. 8, No. 4, pp ,

17 23. Bak, S.W., Lee, D.G. and Krawnkler, H., A smplfed model for sesmc response predcton of steel frame structures The 9 th word Conference on Earthquake Engneerng, Japan, Vol. V., Krawnkler, H. and Zohre, M. Cumulatve damage n steel structures subjected to earthquake ground motons, Comp. and Struct., 6, pp ,

18 ax t = ax + (a U 5 U 4 t = U 4 -U ax θ 2 U 6 U 4 H α U 5 -U 6 U 2 U 3 U θ L U U 2 -U 3 (b Fgure. Defntons of total nter-story drft ( t, ear nter-story drft ( and the effect of axal flexblty of columns ( ax

19 3m = 5 m 3m = 30 m 3m = 45 m 6m = 30 m 6m = 30 m 6m = 30 m Fgure 2. Typcal geometry of concentrc braced frames Story Number UBC97 COV= 0.42 Step- COV= 0.27 Step-2 COV= 0.5 Step-3 COV= 0.08 Step-4 COV= Shear nter-story Story Drft drft Dstrvuton dstrbuton (cm Fgure 3. Shear story drft dstrbuton from UBC97 desgned model toward the Fnal answer, 5 story braced frame, Northrdge 994 (NWH360

20 m n- m n (k ax n (k n (k ax n- (k n- ` m (k ax (k V V V S (α t (k t S (α (k S (α ax (k ax (k t (k (k ax ( t ( ( ax Fgure 4. Usng pu-over analyss to defne equvalent modfed ear-buldng model 5 3 Total Drft Story Number Frame Model Modfed Shear Buldng Frame Model Modfed Shear Buldng Shear Drft Max total and ear nter-story drft (cm Fgure 5. : A comparson of frame model and modfed ear-buldng model for 5-story model subjected to Imperal Valley 979

21 (kax /(k Load Pattern Load Pattern Story Fgure 6. A comparson of (k ax /(k rato for two 5 story braced frames desgned for dfferent sesmc load patterns 0 Cov & Max Shear Story Drft (Cm Cov Max Shear Story Drft Step Fgure 7. COV of ear story drfts and maxmum ear story drfts from UBC97 desgned model toward the Fnal answer, 0story braced frame, Imperal Valley 979.

22 5 3 Story UBC desgned model Cov=0.42 Opt. on Frame model Cov=0.04 Opt. on Shear-Buldng Model Cov= Shear Story Drft (cm Fgure 8. Optmzaton on frame model and ear-buldng model compare to UBC desgned for 5-story model subjected to Northrdge earthquake Story UBC 97 Optmum Desgn Story Load (ton Fgure 9. Optmum and conventonal desgn loads for 5-story braced frame subjected to Northrdge earthquake 994

23 Story Concentrate Load Trangular Inverted Trangular Rectangular Story Force/ Base Shear Fgure 0. Optmum lateral load pattern for dfferent ntal strength patterns, 5 story braced frame subjected to Imperal Valley 979 Global Damage Index EQ: Earthquake UBC-97 Optmum Structure EQ( EQ(2 EQ(3 EQ(4 EQ( EQ(2 EQ(3 EQ(4 EQ( EQ(2 EQ(3 EQ( Story 0 Story 5 Story Fgure. Global damage ndces calculated for dfferent models desgned wth optmum and code-type load pattern under dfferent earthquakes