ASSESSMENT OF THE COLLAPSE RESISTANCE OF STEEL MRFs EQUIPPED WITH FLUID VISCOUS DAMPERS

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1 ASSESSMENT OF THE COLLAPSE RESISTANCE OF STEEL MRFs EQUIPPED WITH FLUID VISCOUS DAMPERS Choung-Yeol Seo Bechtel Power Corporaton, Frederck, MD, USA T.L. Karavasls School of Engneerng, Unversty of Warwck, Coventry, UK James M., Rcles & Rchard Sause Department of Cvl and Envronmental Engneerng, Lehgh Unversty, Bethlehem, PA, USA SUMMARY: Ths paper evaluates the resstance aganst collapse of steel moment resstng frames (MRFs) wth flud vscous dampers. A smplfed desgn procedure s used to desgn four dfferent systems of steel MRFs wth flud vscous dampers where the strength of the steel MRF and the added dampng rato are vared. The combned systems are desgned to acheve a performance that s smlar or hgher than that of conventonal steel MRFs desgned accordng to current sesmc desgn codes. Based on the results of ncremental nonlnear tme hstory analyses, the probabltes of collapse of the frames wth dampers are calculated and compared wth those of conventonal steel MRFs. The analytcal frame models used n ths study are relably able to smulate global frame collapse by consderng full geometrc nonlneartes as well as the cyclc strength and stffness deteroraton of the structural steel members. The results of the study show that supplemental dampng reduces the probablty of collapse of a steel MRF wth a gven strength. However, t s also shown that supplemental dampng does not guarantee a better collapse performance when the strength of the steel MRF wth dampers s lower than 75% of the strength of a conventonal MRF. Keywords: Collapse fraglty, Steel structure, Flud vscous damper, Incremental dynamc analyss 1. INTRODUCTION Passve dampng systems can sgnfcantly mprove the sesmc performance of buldngs by reducng drft and nelastc deformaton demands on the prmary lateral load resstng system, n addton to reducng the velocty and acceleraton demands on non-structural components (Chrstopoulos and Flatrault 2006). Among the dfferent types of passve dampng systems, vscous dampers have been extensvely studed and used for the sesmc desgn of new structures and the sesmc upgrade of exstng vulnerable structures (Symans et al. 2008). These dampers contan a closed cylnder flled wth a flud such as slcone ol, and a stanless steel pston wth a pston rod and a pston head. Indvdual flud vscous damper tests have been performed and models to predct damper behavor under earthquake loadng have been developed (Seleemah and Constantnou 1997). These studes have shown that the hysteress of flud vscous dampers can be accurately descrbed by a nonlnear dashpot: a F C v sgn(v) (1) d where F d s the damper force output, C s the dampng coeffcent, α s the velocty exponent and sgn s the sgnum functon. The exponent α typcally ranges from 0.3 to 1.0. The frst desgn procedures for new buldngs wth passve dampers were publshed by the Structural Engneers Assocaton of Northern Calforna (Whttaker et al. 1993). These gudelnes were developed on the bass that dampers wll be located n a lateral force resstng system that already satsfes the strength and drft crtera of the current sesmc code, wth the goal of reducng earthquake

2 damage. The 2000 NEHRP provsons (BSSC 2001), however, allow a reduced desgn base shear force for the sesmc desgn of buldngs wth passve dampng systems where the expected performance s smlar or hgher than that of buldngs wth conventonal lateral force resstng systems. Past research (e.g., Lee et al. 2009, and Karavasls et al. 2012) confrmed that steel MRFs equpped wth vscous type dampers can perform better under the desgn earthquake than a conventonal steel MRF, even when the MRF wth dampers s sgnfcantly lghter than the conventonal MRF. The recent ATC-63 document presents a new methodology for collapse assessment of structures under maxmum consdered earthquake (MCE) ground motons, wth the am to assess desgn crtera and sesmc performance factors adopted n sesmc codes (ATC 2009). A well desgned structural system should provde a low probablty of collapse (.e., lower than 10%) under the MCE earthquake. In ths methodology, the collapse margn rato (CMR) s defned as the rato of the ground moton ntensty (.e., spectral acceleraton at the fundamental perod of the structure) that causes one-half of the structures to form lfe-threatenng collapse to MCE ground moton ntensty. The acceptable value for the CMR vares dependng on the sesmc behavoral characterstcs. The ATC-63 document hghlghts the need of applyng the proposed collapse assessment methodology for structures equpped wth dampng systems n order to evaluate the damper desgn crtera of sesmc provsons. Ths paper evaluates the sesmc resstance aganst collapse of steel MRFs wth flud vscous dampers. A smplfed desgn procedure s used to desgn four dfferent systems of steel MRFs wth flud vscous dampers n whch the strength of the steel MRF and the added dampng rato are vared. The combned systems are desgned to acheve a performance that s smlar or hgher than that of conventonal steel MRFs desgned accordng to current sesmc codes. Based on the results of ncremental dynamc analyses, probabltes of collapse of the frames wth dampers are calculated and compared wth those of conventonal steel MRFs. The analytcal results n the paper do not account for the effect of spectral shape at the fundamental perod of the buldng, uncertantes n structural component propertes, and the lmt states of vscous dampers whch can affect the collapse probabltes; these aspects and ther effect on collapse are the subject of ongong research by the authors. 2. PERFORMANCE BASED SEISMIC DESIGN OF STEEL MRFS WITH FLUID VISCOUS DAMPERS 2.1 Current Sesmc Desgn Crtera Current sesmc provsons (e.g., BSSC 2001) specfy that the desgn base shear force for the prmary lateral force-resstng system of a buldng wth dampers can be reduced to 75% of the desgn base shear of a conventonal system wthout dampers. A steel MRF desgned for a reduced base shear force would normally exceed the 2% drft lmt of the sesmc provsons. However, supplemental dampers are used to control drft demands on the flexble MRF and acheve a performance smlar to that of a conventonal frame (.e., expected drft lower or equal to 2%) or hgher performance (.e., desgn drft sgnfcantly lower than 2%). Ths desgn phlosophy offers sgnfcant benefts such as the reducton n steel weght of the MRF due to a reduced desgn base shear and hgher performance due to the potental of passve dampers to reduce structural response. 2.2 Smplfed Sesmc Desgn Procedure for Buldngs wth Flud Vscous Dampers Ln and Chopra (2003) studed the peak dsplacement of an elastc SDOF system wth a natural perod T n equpped wth a vscous damper n seres wth a brace of stffness K b. The results of the study showed that the relaton τ/t n <0.02 s satsfed for the practcal range of values for the bracng stffness K b and the dampng coeffcent C, where τ s the relaxaton tme,.e., τ =C/K b. Ramrez et al. (2002) studed the relatonshp between the peak dsplacements of nelastc blnear systems and correspondng lnear elastc systems of the same perod of vbraton for hgh values of the vscous dampng rato. Ther results showed that for systems wth a perod of vbraton longer than 0.5 sec. that the equal-dsplacement rule s vald.

3 Chrstopoulos and Flatrault (2006) proposed a dstrbuton of dampng coeffcents proportonal to the stffness of the frame. In partcular, the dampng coeffcent at each story s calculated equal to C =εk o,, where K o, s the horzontal story stffness of the frame wthout dampers and ε s a constant. Gven the dampng coeffcents C at each story of the buldng and by assumng lnear dampers (α=1) postoned n a horzontal confguraton, the equvalent dampng rato ξ eq at the fundamental perod of vbraton T 1 under elastc condtons can be estmated accordng to the equaton presented n Whttaker et al. (2003): eq T1 4 C φ φ m φ (2) where φ and φ -1 are the frst modal dsplacements of stores and -1, respectvely, and m s the mass of story. Based on the above dscusson and gven the propertes of the MRF wthout dampers, a modfed verson of the smplfed desgn procedure (SDP) developed by Lee et al. (2009) was adopted to desgn buldngs wth lnear flud vscous dampers and dagonal braces to acheve a target desgn drft. The modfed SDP s gven shown n Fgure 1. A more detal descrpton of the procedure can be found n Seo et al. (2012a) Establsh the performance objectves and desgn crtera Select an approprate value (rato of total brace stffness per story n the horzontal drecton to the MRF story stffness) Select an approprate dampng coeffcent C value for each story, based on the selected value Calculate the equvalent dampng rato and correspodng dampng reducton factor Perform elastc analyss usng the equvalent lateral load procedure and estmate nelastc story drft No Check whether the desgn crtera are met Yes Desgn dampers based on the requred dampng coeffcent C Fgure 1. Modfed smplfed desgn procedure for MRF s wth flud vscous dampers 2.3 Prototype Buldng Fgure 2(a) shows the plan vew of the 4-story, 7-bay by 7-bay prototype offce buldng used for the study. The buldng s assumed to be located on a stff sol ste and has eght dentcal two-bay permeter steel MRFs (two at each sde) to resst lateral forces. The MRF s desgned ether as a conventonal specal moment resstng frame (SMRF), as defned n the 2003 Internatonal Buldng Code, IBC (ICC 2003), referred to heren as IBC 2003, or as an MRF equpped wth lnear flud vscous dampers. In the latter case, dampers connected to the frame through chevron braces are added to the two bays of the MRF, as shown n Fgure 2(b). The gravty (dead and lve) loads consdered n the desgn are those descrbed n IBC A determnstc lmt spectrum wth parameters S S =1.5g and S 1 =0.6g represent the maxmum consdered earthquake (MCE), accordng to IBC2003. The desgn bass earthquake (DBE) has an ntensty that s two-thrds that of the MCE. The permeter MRF of Fgure 2(b) s desgned as a conventonal SMRF usng the equvalent lateral force procedure from IBC Ths conventonal SMRF wthout dampers, referred to heren as SMRF, satsfes the member strength crtera of the IBC 2003 wth a response modfcaton coeffcent (.e., strength reducton factor), R, equal to 8 and the 2% story drft lmt of IBC 2003 wth a deflecton amplfcaton factor, C d, equal to 5.5. The desgn of the SMRF was controlled by drft.

4 W14x311 W14x342 W14x342 (a) Typcal permeter MRFs (shown n red) (b) W21x50 Same members as exteror columns W21x50 (c) W18x55 W18x55 Brace Damper m 3.66 m W14x193 W27x94 W30x116 W27x94 W30x m W14x257 W30x108 W33x130 W30x108 W33x130 W14x257 W33x130 W33x130 W33x141 W33x m 4.57 m Same members as exteror columns m m m Fgure 2. (a) Plan vew of the prototype buldng, (b) Elevaton of MRF wth dampers and (c) Elevaton of SMRF Table 1. Summary of frame desgn Desgn Column sectons Beam sectons W s (kn) T 1 (sec) C (kn mm -1 s.) * ξ eq (%) 1 st story : W14x342 1 st floor :W33x141 SMRF 2 nd story: W14x342 2 nd floor:w33x130 3 rd story: W14x257 3 rd floor: W30x N.A N.A 4 th story: W14x257 4 th floor: W18x55 CP100VLD 1 st story : W14x311 2 nd story: W14x311 3 rd story: W14x193 4 th story: W14x193 1 st floor:w33x130 2 nd floor: W30x116 3 rd floor: W27x94 4 th floor: W21x50 CP75VLD Same as CP100VLD Same as CP100VLD HP100VHD Same as CP100VLD Same as CP100VLD HP75VHD Same as CP100VLD Same as CP100VLD st story: nd story: rd story: th story: st story: nd story: rd story: th story: st story: nd story:3.4 3 rd story: th story: st story: nd story: rd story: th story: 2.00 For the MRFs wth dampers, two dfferent versons of the permeter MRF were desgned ntally wthout dampers to have desgn base shears equal to 1.00V and 0.75V (where V s the desgn base shear of the SMRF) and wthout the 2% drft crtera. In partcular, only the MRF wth a desgn base shear equal to 1.00V was desgned. The MRF wth a desgn base shear equal to 0.75V was acheved by havng the same cross sectons wth those of the MRF wth a desgn base shear equal to 1.00V n conjuncton wth the sesmc weght equal to (1/0.75) tmes the sesmc weght of the MRF wth a desgn base shear equal to 1.00V. The two resultng MRF desgns are lghter than the SMRF and do not comply wth the 2% story drft desgn lmt of IBC The supplemental lnear flud vscous dampers are then desgned to control the story drft n these lghter MRFs usng the smplfed desgn procedure descrbed above. The maxmum story drft estmates for the damped MRFs are based on an equal dsplacement rule for checkng complance wth the story drft desgn lmt. For each of the two lghter MRFs, two dfferent damper desgns were obtaned wth the am to acheve a performance smlar to that of the SMRF (.e., desgned for 2% story drft lmt) or hgher performance (.e., desgned for 1.5% story drft lmt). The two resultng hgh-performance (hghly damped) MRF desgns wth dampers are referred to heren as HP100VHD and HP75VHD whle those wth a conventonal performance (lghtly damped) are referred to heren as CP100VLD and

5 CP75VLD. The HP100VHD and CP100VLD MRFs wth dampers result from the MRF wth a desgn base shear equal to 1.00V, whle the HD75VLD and CD75VLD MRFs wth dampers result from the MRF wth a desgn base shear 0.75V. The last two letters n the notaton for the desgns relate to the amount of dampng added to the frame, where HD and LD stand for hgh and lghtly damped, respectvely. Table 1 ncludes a summary of the propertes of the SMRF and the four MRF desgns wth dampers (HP100VHD, HP75VHD, CP100VLD and CP75VLD). The table lsts n sequence the column crosssectons, beam cross-sectons, sesmc weght (W s ), fundamental perod of vbraton of the structure wthout the dampers (T 1 ), dampng constant (C) at each story, and equvalent vscous dampng ( eq ). The dampng constant (C) at each story s arrved at by satsfyng the target story drft lmt at each story level. 3. ANALYSIS AND DETERMINATION OF COLLAPSE STATE 3.1 Ground Moton Ensemble A set of 22 recorded far-feld ground moton pars developed n the Appled Technology Councl Project 63 (ATC 2009) s used n ths study for nonlnear tme hstory analyss. In ths set, twenty-two record pars were taken from 14 events whch range n magntude from 6.5 to 7.6, where the records were recorded on stff sol (or soft rock) and do not exhbt pulse-type near-fault characterstcs. It should be noted that the ground moton set used n ths study does not represent extreme rare ground motons that have unque spectral shapes n the vcnty of the fundamental structural perod (Baker and Cornell 2005) and, as a result, the performance assessment usng the ground moton set can be conservatve. 3.2 Analytcal Frame Model Ground motons along only one prncple axs of the buldng s floor plan are consdered. The analytcal model n the study s a 2-D model of one-half of a permeter frame of the 4-story buldng, consderng two bays of the MRF and the assocated trbutary gravty load frames and sesmc mass. The OpenSEES program (Mazzon et al. 2006) s used to develop the analytcal frame model n ths study. The columns of the frame are modeled wth a dstrbuted plastcty force-based beam column element wth fve fber sectons along the element length. Each fber s assgned a blnear materal model wth a small postve post-yeldng stffness. The columns n the analytcal model are assumed to exhbt stable cyclc behavor (.e., no deteroraton of strength or stffness under cyclc loadng), under large drft levels. Ths modelng assumpton s reasonable snce a typcal sesmcally compact column secton (e.g., W14 secton) exhbts a large post-cappng plastc rotaton capacty for the full range of axal force expected n a column (Newell and Uang 2008). The beams are modeled as elastc elements wth a zero length plastc hnge rotatonal sprng at ther ends. The cyclc deteroraton model developed by Lgnos and Krawnkler (2007) was assgned to the zero length plastc hnge rotatonal sprngs. In ths model, a backbone curve defnes a reference skeleton for strength and deformaton bounds of a structural component as well as a set of rules governng the hysteretc behavor between the bounds defned by the backbone curve. Cyclc deteroraton characterstcs n the model are defned by yeld strength, post-cappng strength, unloadng stffness, and reloadng stffness. The monotonc backbone curve for the moment rotaton relatonshp s llustrated n Fgure 3 (a), where ths curve s characterzed by the elastc stffness (K e ), a plastc rotaton capacty and correspondng capped maxmum strength ( p.c and M c ), a post-cappng plastc rotaton capacty and correspondng resdual strength branch ( pc.c and M r ), as a fracton κ of the model yeld strength (M y ), and a vertcal branch ndcatng fracture. A typcal hysteretc response showng cyclc strength and stffness deteroraton for the deteroraton element s llustrated n Fgure 3 (b). To account for P- effects, the gravty frame s modeled as a lean-on column wth elastc beamcolumn elements ncorporated wth the co-rotatonal formulaton avalable n OpenSEES. The floor mass s assgned to the lean-on column at each floor level n the model. A four sded planar element s used to capture mportant panel zone deformaton modes ncludng shear and symmetrc column

6 bendng deformatons (Seo et al. 2012b). The damper and brace elements for the MRF wth dampers are modeled wth a lnear elastc truss element. Lnear vscosty s assgned as a materal property for the damper element. Fgure 3. (a) Backbone curve, and (b) Cyclc moment rotaton behavour for the cyclc deteroraton model Raylegh dampng proportonal to the mass and the tangent stffness s assgned at the 1 st and 3 rd modal perods of the structure to account for structural nherent dampng n the nonlnear tme hstory analyss (NTHA). The same dampng assumed n the desgn procedure s assgned at these perods. It should be noted that the current analytcal model can capture the cyclc deteroraton of beam stffness and strength, whch can contrbute to the global frame collapse. In the current analytcal models, the dagonal braces are assumed to be strong enough not to buckle before the frame reaches ts collapse capacty. In the analytcal model, the damper lmt states caused by ther stroke lmt are not consdered, whch may be an mportant consderaton n the assessment of collapse fraglty of frames equpped wth flud vscous dampers wth lmted stroke. Typcal damper stroke lmts n the dampers avalable n the market range from ±80 to ±130 mm, however, strokes can be extensble up to ±900 mm upon request (Taylor Devce Inc.). Wth an extended stroke lmt, the dampers n the prototype buldngs would not reach ther lmt states before the frame reaches laterally nstablty. Therefore, the analytcal model n ths study s stll vald to assess collapse fraglty of the frames wthout consderng damper lmt states n the model. 3.3 Incremental Dynamc Analyss Incremental dynamc analyss (IDA) (Vamvatskos and Cornell 2002) s employed for assessng the collapse potental of the frames n ths study. IDA s used to detect the collapse capacty of the frame assocated wth a partcular ground moton. In ths method nonlnear tme hstory analyses are performed, where the ground moton ntensty measured by 5% damped spectral acceleraton at the fundamental perod of the structure, Sa,s systematcally scaled up n small ncrements untl the frame model becomes globally unstable under the lateral sesmc forces. The frame collapse capacty ntensty to a partcular ground moton, denoted as Sa COL, s defned by the Sa value equal to the maxmum Sa value for the frame to have been stable but less than the mnmum Sa value for the frame to cause collapse. A lmt of 15% transent story drft was used to defne an upper bound value for Sa COL. The results of the IDA usng a large number of ground moton records are presented as a plot of Sa versus the frame response quantty of nterest (e.g., peak story drft) and used for the probablstc evaluaton of the collapse capacty. 4. ASSESSMENT OF COLLAPSE FRAGILITY 4.1 Statc Pushover Analyss Statc pushover analyses are ntally performed to nvestgate the lateral load-roof drft relatonshp for the frames consdered n ths paper. These analyses are performed usng a statc lateral force dstrbuton derved from the equvalent lateral force procedure descrbed n the IBC Fgure 4 (a) shows the relatonshp between the normalzed base shear (V/W s ), and roof drft ( roof ). It s shown that the SMRF exhbts the hghest base shear strength and ntal stffness, snce members n the SMRF are larger and heaver than the MRFs wth dampers. Wth the ad of supplemental dampng, these MRFs are desgned to have a smaller V/ W s (.e., the frames are weaker and more flexble). It s shown

7 that the MRFs wth a smaller V/W s exhbts a smaller roof drft assocated wth the complete loss of the statc lateral load resstance (a) SMRF CP100VLD and HP100VHD (b) 0.15 CP75VLD and HP75VHD V / Ws roof SMRF CP100VLD and HP100VHD column end plastc rotaton beam end plastc rotaton (symbol sze ndcates the relatve magntude of plastc rotaton) CP75VLD and HP75VHD Fgure 4. (a) Backbone curve, and (b) Cyclc moment rotaton behavour of the of the cyclc deteroraton model The post-yeldng stffness n the pushover curve becomes negatve for the MRFs wth dampers and ts absolute value s larger for the MRFs wth smaller V/W s, ndcatng that the P- effect s more pronounced for the weaker and more flexble MRFs wth dampers. Fgure 4 (b) llustrates the sde sway mechansm of the frames consdered n ths study and relatve magntude of plastc hnge rotaton at 9% roof drft predcted by pushover analyss, where plastc hnges form n the beam ends at all floor levels and n the column bases. As ndcated n the fgure, the frame desgn fulflls the strongcolumn-weak-beam (SCWB) phlosophy under statc lateral loads n accordance wth AISC sesmc specfcaton (AISC 2005). 4.2 Collapse Fraglty Results of the IDA for the SMRF are plotted n Fgure 5 (a), where a data pont representng S a and the correspondng maxmum story drft s s shown at each ncrement for each ground moton record. It s obvous that there s large varablty n s between records, even for the same frame at a specfc ground moton ntensty level. The slope of the IDA curve n general rapdly decreases and flattens out at some S a level, meanng that at such ntensty level, the story drft becomes very large wth a small ncrease n ground moton ntensty. For an ndvdual record, the collapse capacty ntensty (S acol ) of the frame model s defned as the S a value at the end of the correspondng IDA curve. Fgure 5 (a) llustrates that most of the IDA curves n general flatten out as s exceeds 10% and, n many cases, the IDA curves termnate at a much lower story drft level. S acol from the IDA curves are ranked n ascendng order. The collapse fraglty curve s obtaned by fttng a cumulatve dstrbuton functon, assumng a lognormal dstrbuton, to the ranked S acol data ponts, as llustrated n Fgure 5 (b) for the SMRF. It shows the cumulatve dstrbuton functon fts well wth the data ponts and valdates the legtmacy of a lognormal dstrbuton assumpton. Although t s not shown n the paper, the lognormal dstrbuton assumpton stll holds for S acol of the MRFs wth dampers consdered n ths study. Ftted collapse fraglty curves for all frames consdered n ths study are llustrated n Fgure 5 (c), where Sa COL s normalzed by S a at the MCE level, denoted as Sa MCE. To quantfy the structural safety margn aganst collapse n an earthquake, the collapse margn rato (CMR) was calculated for each frame, where CMR s the rato of the medan Sa COL ( Ŝ acol ), to Sa MCE. Assessment of the collapse potentals of all frames consdered n ths study s summarzed n Table 2. Fgure 5 (c) shows that the collapse fraglty curves for all frames studed, except for CP75VLD, are shfted to the rght wth respect to that for the SMRF (.e., have a hgher CMR than the SMRF). From ths observaton, t can be concluded that addtonal dampng n general mproves sesmc resstance to frame collapse. In comparsons of the MRFs wth dampers desgned for the same target desgn performance level (.e., CP100VLD versus CP75VLD or HP100VHD versus HP75VHD), the collapse fraglty curves for the weak and more flexble MRFs (CP75VLD or HP75VHD) are shfted to the left wth respect to the stronger and stffer MRFs (CP100VLD or HP100VHD). Ths observaton s confrmed by comparng the CMR values and the collapse probabltes at the MCE level for each

8 Sa (T 1 ) Probablty of Collapse frame n Table 2. As noted above, the CMR for CP75VLD s lower than that of the SMRF; Table 2 ndcates that the CMR for CP100VLD s hgher than that of the SMRF, as s the CMR for HP75VHD where the maxmum desgn drft s 1.5%. Ths result mples that the beneft of added dampng on the frame collapse resstance cannot be fully utlzed for relatvely weak or flexble frames, and wth frames whose desgn drft s too large. When a frame experences sgnfcant lateral sway moton, the P- effect can play an mportant role n cumulatng drft. For a weak and flexble frame, ths geometrc nonlnearty effect s more pronounced n drftng the frame n one drecton, where supplemental dampng does not effectvely help reduce the drft (a) (b) (c) SMRF Probablty of Collapse CP75VLD CP100VLD HP75 VHD HP100VHD s Sa COL Sa COL /Sa MCE Fgure 5. (a) Relatonshp between S a and peak story drft s resultng from IDA for SMRF, (b) Cumulatve dstrbuton of Sa COL wth a ftted curve for SMRF, and (c) Ftted cumulatve dstrbuton of S acol for SMRF and MRFs wth dampers consdered n ths study Table 2. Summary of collapse analyss Desgn Ŝ acol, g Sa * Sa COL MCE, g CMR Prob. of collapse gven Sa MCE Ŝ acol, g SMRF CP100VLD CP75VLD HP100VHD HP75VHD * Sa exp ln, where s the standard devaton of logarthm of Sa COL COL Sa col lnsa col In order to examne how the SCWB phlosophy avods the concentraton of damage n the column at a partcular story at ncpent collapse of a frame, the collapse mechansm and the locaton of the plastc hnges was examned. Fgure 6 llustrates typcal ncpent collapse modes predcted by nonlnear tme hstory analyss of each frame. The ncpent collapse mode to a ground moton s captured at a slghtly hgher level than Sa COL. Sold and hollow crcles ndcate beam and column plastc hnges, respectvely. The relatve magntude of damage s ndcated by the dameter of the crcles. A typcal collapse mode n the SMRF conssts of a sway mechansm, characterzed by large levels of plastc rotaton at all floor beams and column bases as shown n Fgure 6 (a). Ths collapse mode s well captured by statc pushover analyss. In some cases, a mechansm characterzed by plastc rotatons at the column ends at some floor levels as shown n Fgure 6 (b) wth plastc hnges also formng n the beams. The formaton of a dstnct soft story mechansm, characterzed by the formaton of plastc hnges at the both ends of all columns at a partcular story level, s not observed n the SMRF. A typcal collapse mode observed n the MRFs wth dampers s a sway mechansm, as shown n Fgure 6 (c). In some cases, the collapse mode conssts of a combnaton of beam and column plastc hnges. A collapse mode characterzed by a dstnctve soft-story mechansm s observed n the MRFs wth dampers, as llustrated n Fgure 6 (d). Out of 44 records, a soft-story mechansm occurs n HP100VHD for three ground moton records, n HP75VHD for two records, and n CP100VLD for one record. However, a soft-story mechansm does not occur n CP75VLD. The formaton of a softstory mechansm s partly attrbuted to hgh axal force demand on the columns of the MRFs wth dampers. The axal force demand n columns s relatvely hgh for a stffer frame and the dampng force transferred to the columns n an MRF wth dampers tends to ncrease the axal force demand on the columns. Hence, the stff and hgher damped MRFs wth dampers are more lkely to develop a

9 soft-story mechansm. Snce CP75VLD has the lowest CMR among all frames consdered n ths study, ths observaton may mply that frames wth a soft-story collapse mechansm do not necessarly have a lower CMR than the frames wth a sway mechansm wth hnges n the beams and at the base of the ground floor columns. (a) (b) (c) (d) column end plastc rotaton beam end plastc rotaton (symbol sze ndcates the relatve magntude of plastc rotaton) Fgure 6. Typcal ncpent collapse modes (a) and (b) predcted for SMRF, and (c) and (d) predcted for MRFs wth dampers. 5. SUMMARY AND CONCLUSIONS In order to assess the collapse potental of steel moment resstant frames (MRFs) wth and wthout flud vscous dampers to selected ground moton ntensty levels, analytcal studes were performed usng a set of ground moton records representatve of a typcal Calforna earthquake. The MRFs wth dampers consdered n ths study were desgned wth less steel weght and wth the use of supplemental flud vscous dampers to acheve a performance smlar to, or hgher than that of a conventonal specal steel moment resstant frame (SMRF). The analytcal frame models are able to smulate global frame collapse relably by consderng geometrc nonlneartes and usng a phenomenologcal element that can capture cyclc deteroraton n strength and stffness of the structural components. Damper lmt states were not, however, consdered n the analytcal models developed n ths study. Through a number of nonlnear tme hstory analyses (NTHA), the collapse ntensty level were obtaned and examned to nvestgate the beneft of addng supplemental dampng to the MRFs to enhance ther sesmc performance and ncrease ther margn aganst collapse. Record to record varablty was consdered n the estmate of the response by usng multple ground moton records. Uncertanty, however, due to unknown structural component propertes and ther varaton were not consdered n the analyss, whch would otherwse ncrease the dsperson n the calculated response dstrbuton. The ground moton records were used to represent a wde range of ground moton ntensty levels by scalng them up or down. Consequently, the calculated response can substantally overestmate actual response, especally when t represents the response to a rare extreme earthquake. The conclusons drawn from the comparsons and the observatons made n ths study, however, stll hold as follows: MRFs wth supplemental dampng can be desgned wth less weght to acheve smlar or better performance than conventonal SMRFs. Ths addtonal dampng effectvely decreases the probablty of collapse. The reducton n strength can ncrease the probablty of collapse (.e., a frame wth reduced strength would be less reslent to frame collapse) when the desgn drft t too large snce the weak and more flexble frame s more vulnerable to P- effects. Reducng the strength further below 75% of the mnmum base shear capacty would not guarantee the levels of safety margn aganst collapse that are acheved by conventonal SMRFs unless the drft s adequately controlled. An SMRF tends to form a sway mechansm wth beam plastc hnges at ncpent collapse and the strong-column-weak-beam phlosophy n the desgn reduces the chance of havng damage concentrated at a partcular story (.e., soft-story mechansm). Smlarly, a typcal ncpent collapse mode n the MRFs wth dampers s also a sway mechansm wth beam plastc hnges. In

10 the MRFs wth dampers a soft-story mechansm occurred and the lkelhood of formng a softstory mechansm ncreases for the stffer or larger supplementally damped MRFs. The chance of havng a soft-story mechansm at the ncpent collapse s, however, stll small for all frames consdered n ths study. REFERENCES AISC. (2005) Sesmc Provsons for Structural Steel Buldngs, Amercan Insttute of Steel Constructon, Chcago, IL. Appled Technology Councl (2009). Quantfcaton of buldng sesmc performance factors, ATC-63 Project Report. Baker JW, Cornell CA. (2005) A vector-valued ground moton ntensty measure consstng of spectral acceleraton and epslon. Earthquake Engneerng and Structural Dynamcs, 34:10, Buldng Sesmc Safety Councl (2001) NEHRP recommended provsons for sesmc regulatons for new buldngs and other structures, Report FEMA 450, Federal Emergency Management Agency, Washngton, D.C. Chrstopoulos C, Flatrault A. (2006) Prncples of supplemental dampng and sesmc solaton. IUSS Press, Mlan, Italy. Internatonal Code Councl (2003). Internatonal Buldng Code. Falls Church, VA Karavasls TL, Sause R, Rcles J. (2012) Sesmc desgn of steel MRFs wth compressed elastomer dampers. Earthquake Engneerng and Structural Dynamcs, 41:3, Lee KS, Rcles J, Sause R. (2009) Performance based sesmc desgn of steel MRFs wth elastomerc dampers. (ASCE) Journal of Structural Engneerng, 135:5, Lgnos DG, Krawnkler H. (2007) A database n support of modelng of component deteroraton for collapse predcton of steel frame structures. ASCE Structures Congress, SEI nsttute, Long Beach CA. Ln W-H, Chopra AK. (2003) Earthquake response of elastc sngle-degree-of-freedom systems wth nonlnear vscoelastc dampers. (ASCE) Journal of Engneerng Mechancs 129:6, Mazzon, S., McKenna, F., Scott, M. H., and Fenves, G. (2006) OpenSEES user s manual, Avalable from: Myamoto HK, Glan AS, Wada A, Aryaratana C. (2010) Lmt states and falure mechansms of vscous dampers and the mplcatons for large earthquakes. Earthquake Engneerng and Structural Dynamcs, n press. Newell JD, Uang C-M. (2008) Cyclc behavor of steel wde-flange columns subjected to large drft. (ASCE) Journal of Structural Engneerng 134:8, Ramrez OM, Constantnou MC, Whttaker AS, Krcher CA, Chrysostomou CZ. (2002) Elastc and nelastc sesmc response of buldngs wth dampng systems. Earthquake Spectra 18:3, Seleemah A, Constantnou MC. (1997) Investgaton of sesmc response of buldngs wth lnear and nonlnear flud vscous dampers. Report No. NCEER , Natonal Center for Earthquake Engneerng Research, State Unv. of New York at Buffalo, Buffalo, N.Y. Seo C-Y., Karavasls TL, Rcles J, Sause R. Probablstc assessment of the sesmc collapse resstance of steel MRFs wth vscous flud dampers. In preparaton for submsson to Earthquake Engneerng and Structural Dynamcs Seo C-Y., Rcles J, Sause R., Ln YC, Analytcal models for 0.6 scale self-centerng MRF wth beam web frcton devces. In preparaton for submsson to Earthquake Engneerng and Structural Dynamcs Symans MD, Charney FA, Whttaker AS, Constantnou MC, Krcher CA, Johnson MW, McNamara RJ. (2008) Energy dsspaton systems for sesmc applcatons: current practce and recent developments. (ASCE) Journal of Structural Engneerng, 134:1, Taylor Devces nc. North Tonawanda, NY. Accessble to Whttaker AS, Aken ID, Bergman D, Clark PW, Cohen JM, Kelly JM, Scholl RE. (1993) Code requrements for the desgn and mplementaton of passve energy dsspaton systems, Proceedngs, Semnar on Sesmc Isolaton, Passve Energy Dsspaton, and Actve Control, Report No. ATC-17-1, Appled Technology Councl, Redwood Cty, CA. Whttaker AS, Constantnou MC, Oscar MR, Johnson MW, Chrysostomou CZ. (2003) Equvalent lateral force and modal analyss procedures of the 2000 NEHRP Provsons for buldngs wth dampng systems. Earthquake Spectra 19:4, Vamvatskos D, Cornell C. A. (2002) Incremental dynamc analyss. Earthquake Engneerng and Structural Dynamcs, 31:3,