Displacement-based performance assessment of steel moment resisting frames

Transcription

1 Dsplacement-based performance assessment of steel moment resstng frames M. Ferraol, A. Lavno, A.M. Avossa, A. Mandara Seconda Unverstà d Napol, Dpartmento d Ingegnera Cvle, va Roma 9 Aversa (CE), Italy ABSTRACT: The assessment of nelastc sesmc behavor and performance of SMRF structures was developed. At ths am, some specfc performance crtera both for structural members and for non-structural components at the dfferent lmt state were used. An ncremental non-teratve nonlnear statc procedure based on adaptve capacty spectra method was used for performance assessment. The results obtaned were compared wth ncremental tme-hstory response. INTRODUCTION The estmaton of lateral dsplacement demands s of prmary mportance n performance-based earthquake-resstant desgn, especally, when damage control s the man quantty of nterest. In partcular, the steel moment resstng frames (SMRFs) are expected to be able to sustan large plastc deformatons n bendng and shear. However, so that the dsspatve capacty of the structure can be completely actvated, t s necessary to optmze the energy dsspaton and guarantee the formaton of a global plastc mechansm of collapse. Such obectves are persecuted not drectly through nonlnear response hstory analyss, but ndrectly through desgn procedures essentally based on capacty desgn. These tradtonal desgn provsons may be not effectve to obtan a global plastc mechansm and to avod that nterrupton or damage may far outwegh the cost of the structural system. It s, rather necessary a multlevel and mult-obectve desgn procedure based on the estmaton of the global behavor of the structure n terms of lateral dsplacement. At ths am, ths study develops a smplfed sesmc demand estmaton procedure n whch the spectral characterstcs of the ground moton are related to the nelastc deformaton capacty for the structure. DISPLACEMENT-BASED CAPACITY SPECTRUM METHOD. Adaptve and multmodal pushover Statc pushover analyss s usually employed to determne the deformaton demands wth acceptable accuracy wthout the ntensve modelng and computatonal effort of a dynamc analyss. The lateral force dstrbuton should be defned to reproduce the nerta forces dervng from the earthquake ground moton. As the damage progresses, the nerta forces are redstrbuted, the vbraton propertes of the structure change and local plastc mechansm may occur. As a consequence, also the orgnal partcpaton and dynamc amplfcaton of the mode shapes changes, and hgher mode effects may be sgnfcantly ncreased. Therefore, multmodal and adaptve pushover analyses may be requred to mprove the accuracy of the deformaton estmates. Several researchers have proposed adaptve force dstrbutons that attempt to follow more closely the tmevarant dstrbutons of nerta forces. These approaches can gve better estmatons of the nelastc response, but they are conceptually complcated and computatonally demandng for applcaton n structural engneerng practce. The Modal Pushover Analyss (MPA) (Chopra and Goel, ) allows for the change n load dstrbuton due to damage of the structure wthout resortng to an adaptve load pattern. Target dsplacement values are computed by applyng equvalent nonlnear procedures wth a SDOF system representatve of each modal load pattern and, fnally, response quanttes are combned wth the SRSS method. Other authors (Antonou and Pnho ) proposed adaptve pushover procedures: Force-based adaptve pushover () and Dsplacement-based adaptve pushover (). Partcularly, n the force-based adaptve pushover approach (), a modal analyss s performed step by step to update the force modal ratos. The lateral load dstrbuton s contnuously updated durng the process accordng to modal propertes, softenng of the structure, ts perod elongaton, and the modfcaton of the nertal forces due to spectral amplfcaton. The lateral load profles of each vbraton mode

2 are then combned by usng SRSS or CQC method. An ncremental updatng wth ncrement of load calculated accordng to the spectrum scalng s appled at each analyss step. Despte ts apparent conceptual superorty, the results obtaned through appear to be smlar to those from conventonal pushover analyss. Both types of analyss may gve very poor predcton of deformaton patterns. In the dsplacement-based adaptve pushover (), the modal shape s drectly mposed to the structure, usng a dsplacement control analyss. The maxmum nterstorey drft values are obtaned drectly from modal analyss, rather than from the dfference between not-necessarly smultaneous maxmum floor dsplacement values. However, the use of SRSS or CQC rules to combne modal results lead to load vector shapes whch neglect the possblty of sgn change n storey dsplacements from dfferent modes. Generally, the dsplacement-based adaptve pushover provdes much mproved approxmaton of hghly rregular dynamc deformaton profle envelopes, even f t assumes that all the nterstorey drfts are maxma at the same tme, whch s of course not realstc. Two shortcomngs of the modal combnaton rules can be ponted out: the frst one s that the result obtaned does not fulfll equlbrum; the second lmtaton s that sgns are lost durng the combnaton process elmnatng the contrbuton of negatve quanttes. In other words, an alwaysaddtve ncluson of hgher modes contrbuton s consdered.. Non-teratve Capacty Spectrum Method The result of the analyss s the pushover curve, whch plot a deformaton ndex (typcally roof dsplacement δ TOP ) aganst a force ndex (typcally base shear V). Ths capacty curve (CC) s the startng pont for all the NSP s based on Capacty Spectrum Method. In the case of adaptve pushover, the lateral load pattern s updated durng pushover analyss accordng to varaton n modal propertes as the stffness of the structure changes. Ths leads to varaton n lateral dsplacement pattern and n lateral force pattern. Therefore, also the equvalent SDOF system, whch s representatve of MDOF three-dmensonal model of the buldng n the Capacty Spectrum Method, changes durng pushover analyss. In order to consder such effect, an adaptve verson of the Capacty Spectrum Method (ACSM) s consdered n the analyses. At each step of the pushover analyss a dfferent equvalent SDOF system s defned as a functon of the actual lateral dsplacement pattern. Partcularly, the mass M eq and the stffness K eq of the equvalent SDOF system at the th step of pushover analyss can be expressed as a functon of the th storey dsplacement, as follows: M eq = N = N = m m K N m N = eq = F N = m = () where F s the th storey force at the th step. The transformaton from Capacty Curve (CC) to Capacty Spectrum (CS) n ADRS format (Acceleraton- Dsplacement Response Spectra) s carred out consderng the followng varaton of the spectral coordnates to every step of pushover analyss: a Δ S =ΔV N = m N ( m = ) ΔS N m = d = ΔdTOP N δ N m = () Fnally, the CS s approxmated wth an elastcperfect-plastc equvalent model (Blnear Capacty Spectra BCS). In partcular, the elastc stffness and the yeldng dsplacement S dy are defned from the pont of the CS correspondent to % of the yeldng acceleraton S ay. The sesmc demand s generally represented by means of the Inelastc Demand Response Spectra (IDRS S d versus S a ). In ths paper the IDRS are computed scalng the %- damped Elastc Demand Response Spectra (EDRS S de versus S ae ) as follows: S S ae de a = Sd R μ R μ μ S = () A reducton factor dependng on velocty and dsplacement elastc spectra s adopted (Ordaz et al. 998): R μ ( T ) α ( μ ) ( T ) β ( μ ) Sv Sd = + ( μ ) () PGV PGD where PGV s the peak ground velocty; PGD s the peak ground dsplacement; S d (T) s the elastc spectral dsplacement; S v (T) s the elastc spectral velocty; α(μ) and β(μ) are functons obtaned wth a statstcal data analyss on spectrum compatble earthquakes (Ferraol et al., ). R μ depends from the ductlty μ and, therefore, from the lateral dsplacement of the equvalent SDOF system. Consequently, an teratve procedure s usually requred n order to estmate the ntersecton between IDRS and BCS. Appled for the dsplacement-based assessment the capacty spectrum method may become non-teratve. In fact, the performance-based assessment s dsplacement-based snce the performance parameters used n the acceptance crtera are the plastc rotatons and the nterstorey drft damage ndex (IDI). As a consequence, the performance levels may be assocated to the dsplacement demand of the structure. Then, the equvalence between MDOF and SDOF system gves the lateral dsplacement of the SDOF system (S d,o S d, S d, ) at each performance level.

3 ance level. Consequently, the poston of the performance pont (PP) on capacty spectrum n ADRS format s defned (fg.). Ths greatly smplfes the estmaton of the ntensty levels of the earthquake ground moton. In fact, the poston of the PP gves the ductlty rato μ and ductlty reducton factor R μ wthout any teratve procedure. So the PGA may be ncreased untl IDRS ntersects BCS n PP. As a consequence, the problems n convergence and accuracy of the teratve graphcal procedures based on the Capacty Spectrum Method are avoded. DISPLACEMENT-BASED PERFORMANCE ASSESSMENT. Study cases Three dfferent steel frames are consdered n the analyses (tab.). The frames are desgned accordng to four dfferent desgn provsons: ) New Italan Code - (8); ) Eurocode 8 - EC8 (); ) Plastc Desgn PD (Mazzolan et al., 99); ) Plastc Desgn wth S Verfcaton -. In the last approach the desgn ultmate dsplacement s ncreased tll to satsfy the S verfcaton of Italan Code (nterstorey drft rato= ). The desgn sesmc acton s defned wth sol class A, dampng rato ξ=%, peak ground acceleraton PGA=.g, behavor factor q=.. Steel members are made from Italan S (f y = MPa). The nterstorey heght s.m for the frst floor and.m for the other floors. The bay length s. m. EC8 and gves very smlar results. On the contrary, PD gves a great overstrength of the steel members. Both dstrbuted plastcty-fber element model and plastc hnge model mplemented, respectvely, n Sesmostruct (SesmoSoft, ) and SAP non lnear computer programs are consdered n the analyses. Sources of geometrcal nonlnearty consdered are both local and global. The spread of plastcty along the element derves from an nelastc cubc formulaton wth two Gauss ponts to use for numercal ntegraton of the equlbrum equatons. A blnear model wth knematc stran-hardenng of.% s used for steel. The emprcal method of Kato- Akyama s used for the determnaton of local ductlty n plastc hnge model. The plastc rotaton and the resdual strength are defned wth FEMA. SPECTRAL ACCELERATION (Sa) BCS IDRS SPECTRAL DISPLACEMENT (Sd) EDRS PP S d,pp Fgure. Non-teratve capacty spectrum method Table. Study cases Desgn ELEMENT STOREYS BAYS Level Beams IPE IPE IPE Ext. HEB HEB HEB Int. HEB HEB HEB Level Beams IPE IPE IPE PD Ext. HEB HE8B HEB Int. HE8B HEB HEB Level Beams IPE IPE IPE Ext. HEB HEB HEB Int. HEB HEB HEB Level Beams IPE IPE IPE EC8 Ext. HEB HEB HEB Int. HEB HEB HE STOREYS BAYS Level 8 9 Beams IPE IPE IPE IPE IPE IPE IPE - - Ext. HEB HEB HEB HEB HEB HEB HEB - - Int. HE8B HE8B HE8B HE8B HE8B HE8B HE8B - - Level 8 9 Beams IPE IPE IPE IPE IPE IPE IPE - - Ext. HEB HEB HEB HEB HEB HEB HEB - - Int. HEB HEB HEB HEB HEB HEB HEB - - Level 8 9 Beams IPE IPE IPE IPE IPE IPE IPE - - EC8 Ext. HEB HEB HEB HEB HEB HEB HEB - - Int. HEB HEB HEB HEB HEB HEB HEB STOREYS BAYS Level 8 9 Beams IPE IPE IPE IPE IPE IPE IPE IPE IPE Ext. HEB HEB HEB HEB HEB HEB HEB HEB HEB Int. HE8B HE8B HE8B HE8B HE8B HE8B HE8B HE8B HE8B Level 8 9 Beams IPE IPE IPE IPE IPE IPE IPE IPE IPE Ext. HEB HEB HEB HEB HEB HEB HEB HEB HEB Int. HEB HEB HEB HEB HEB HEB HEB HEB HEB

4 . Lateral load pattern effects For structures n whch local plastc mechansm occurs the shear forces vs. story drft relatonshp may be very senstve to the appled load pattern. To nvestgate the lateral load pattern effects sx dstrbutons are consdered: ) Unform Dstrbuton (). The lateral load dstrbuton s proportonal to the floor masses m. ) Frst Mode Dstrbuton (). The vertcal dstrbuton s proportonal to the floor masses and the shape of the fundamental mode. ) Equvalent Frst Mode Dstrbuton (E). The lateral force dstrbuton s proportonal to an equvalent frst mode defned from SRSS combnaton of suffcent modes to capture at least 9% of the total mass. ) SRSS Dstrbuton. The vertcal dstrbuton s proportonal to the story shear dstrbuton calculated by combnng modal responses. ) Force-based adaptve pushover (); ) Dsplacement-based adaptve pushover (). In fg.- the comparson of capacty curves s reported. The 9- storey frame desgned accordng to EC8 or to Italan Code shows very lttle varaton wth the lateral load pattern. On the contrary, the steel frames desgned wth plastc desgn are very senstve to the lateral load pattern. Partcularly, tends to overestmate the lateral strength f compared to other pushover analyses. Ths result derves from the hgher mode contrbuton that n analyss gves a reducton of the axal force n the external column of the frst floor. Consequently, P-delta effects decrease and the plastc bendng moment consequently ncreases.. Statc versus dynamc pushover analyss Senstvty analyss of SMRFs loaded nto the plastc response range, s more complcated and computatonally ntensve because the state of nternal forces depends on the loadng hstory. In order to verfy the accuracy of non-lnear statc procedures and the senstvty to nput ground moton a seres of, and conventonal pushover analyses are compared wth the predctons of nelastc dynamc analyss, employng a set of artfcal earthquakes. Partcularly, a set of nput ground motons s generated to be consstent to %-damped EC8 elastc spectrum for sol class A. In fg.- the comparson between pushover analyses and Incremental Dynamc Analyses () s shown. For the 9-storey frame desgned wth Italan Code () the statc pushover seems to be conservatve snce t understmates the capacty. On the contrary, for the frame desgned wth plastc desgn and S verfcaton analyss gves much greater lateral strength SRSS CQC..9.. E CQC Fgure. Base shear versus roof dsplacement Pushover and Incremental Dynamc Analyss (-storey, desgn) Fgure. Base shear versus roof dsplacement Pushover and Incremental Dynamc Analyss (9-storey, desgn) SRSS Fgure. Base shear versus roof dsplacement Pushover and Incremental Dynamc Analyss (-storey, desgn) E CQC SRSS Fgure. Base shear versus roof dsplacement Pushover and Incremental Dynamc Analyss (9-storey, desgn)

5 . Performance-based assessment The dsplacement-based assessment s carred out for three dfferent levels of performance (Immedate Occupancy - IO, Lfe Safety, Collapse Preventon ). Two control parameters are montored to check the acceptance crtera: ) nterstorey drft damage ndex (IDI); ) plastc rotatons n columns and beams. The plastc rotatons are defned by tab.. of FEMA. The lmt values for the nterstorey drft damage ndex are: ) IDI=. for IO lmt state; ) IDI=. for lmt state; ) IDI=. for lmt state. Usng the non-teratve Capacty Spectrum Method gves the peak ground acceleratons correspondng to the three levels of performance (IO,,). In fg.-9 these performance ponts are reported n the plane PGA versus total drft rato (roof dsplacement/heght). In partcular, the performance ponts obtaned from non-lnear statc analyss are compared wth the performance ponts dervng from ncremental dynamc analyss. In the same fgures both the mean value and the maxmum value of the responses obtaned usng the generated accelerograms are reported. The plastc desgn wth S verfcaton () gves a great ncrease of the ntensty level of the earthquake ground moton at collapse. On the contrary, the ntensty levels of the earthquake ground moton correspondng to the other lmt states enoy very moderate ncreases.. MDOF Effects The dstrbuton of localzed demands n the MDOF system can dffer from those assocated wth the equvalent SDOF system, and the mportance of ths so-called MDOF Effects ncreases wth the amount of nelastcty n the structure and wth the occurrence of local plastc mechansm. In order to nvestgate these effects the nterstorey drft profles obtaned from pushover analyses are compared to the drft profles from nonlnear tmehstory analyss (fg.). The drft profle from pushover analyss are referred to the lmt state. The drft profle from dynamc analyss are referred to the nput ground moton correspondng to the maxmum total drft rato Fgure. Base shear versus roof dsplacement Pushover and Incremental Dynamc Analyss (-storey, desgn)..9.. IO..... Fgure 8. Base shear versus roof dsplacement Pushover and Incremental Dynamc Analyss (9-storey, desgn) Fgure. Base shear versus roof dsplacement Pushover and Incremental Dynamc Analyss (-storey, desgn). IO Fgure 9. Base shear versus roof dsplacement Pushover and Incremental Dynamc Analyss (9-storey, desgn)

6 STOREY 8 9 STOREY 8 9 STOREY 9 8 STOREY Fgure. Comparson of drft profles from Pushover Analyses wth the maxmum nterstorey drft from Dynamc Analyss Ths earthquake s scaled to have the same roof dsplacement obtaned from pushover analyss at the collapse preventon lmt state. The results obtaned show that the analyss systematcally understmates the nterstorey drfts f compared to dynamc analyss, whle the dstrbuton seems to be more effectve. All the nonlnear statc procedures understmates the nterstorey drfts of the -storey frame desgned wth the Italan Code. Ths result derves from the hgh strength requred to the roof columns by the capacty desgn crtera. CONCLUSIONS The comparatve evaluaton of desgn procedures confrmed that also recent codes based on the local ductlty condton and the capacty desgn rule are not able to assure the sutable plastc mechansm. On the other sde, the results demonstrated the effectveness of the plastc desgn n governng the collapse mechansm. The desgn procedure based on the control both of collapse mechansm and of lateral dsplacement requre an teratve desgn process to avod that the ncrease of structural overstrength produced by the damage lmt state provsons leads to undesred collapse mechansms. Furthermore, ther cost s often an uncontrollable overstrength of the structure. However, the same safety factor for the other lmt states (Immedate Occupancy and Lfe Safety) s not guaranteed. Fnally, the overstrength generally ncreases the sesmc demand and so reduces the benefts dervng from the control of collapse mechansm and lateral dsplacement. ACKNOWLEDGEMENT The paper s part of the research proect RELUIS -8 Lne Development of nnovatve approaches for desgn of steel and composte steelconcrete structures (Coordnators Prof. F.M. Mazzolan, Prof. R. Zandonn). The actvty was carred out by the members of Research Unt Desgn crtera of steel frame structures and methods of nonlnear analyss of the Second Unversty of Naples (Scentfc Responsable Prof. A. Mandara). REFERENCES Antonou, S. and Pnho, R.. Advantages and Lmtatons of Adaptve and Non-Adaptve Force-Based Pushover Procedures. Journal of Earthquake Engneerng 8:. 9-. Antonou, S. and Pnho, R.. Development and Verfcaton of a Dsplacement-Based Adaptve Pushover Procedure. Journal of Earthquake Engneerng 8:. -. CEN.. Eurocode 8. Desgn of structures for earthquake resstance. European Commttee for Standardzaton. Chopra, A.K. and Goel, R.K.. A modal Pushover analyss procedure for estmatng sesmc demands for buldngs. Earthquake Engneerng and Structural Dynamcs. :, -8. ECCS European recommendatons for steel structures n sesmc zones. Pubblcaton No.. Faggano, B., De Mattes, G. and Landolfo, R.. Comparatve study on sesmc desgn procedures for steel MR frames accordng to the force-based approach. Thrd Int. Conf. STESSA, Montreal, Balkema, Rotterdam. FEMA,. Prestandard and Commentary for the Sesmc Rehabltaton of Buldngs, prepared by the Amercan Socety of Cvl Engneers for the Federal Emergency Management Agency. Washngton, D.C. Ferraol, M., Avossa, A.M. and Malangone, P.. Approxmate method for evaluaton of sesmc damage of rc buldngs. Proc. of the th World Conf. on Earth. Eng. Vancouver. B.C., Canada. August -. Ferraol, M., Lavno, A., Avossa, A.M., Mandara, A. Dsplacement-based sesmc assessment of steel moment resstng frame structures. th World Conference on Earthquake Engneerng. October -. Beng, Chna. 8. Italan Code. 8. D.M...8, G.U. No Landolfo, R. and Mazzolan, F.M. 99. The consequence of desgn crtera on the sesmc behavor of steel frames. Proc. of IX Intern. ECEE, Moscow. Mazzolan, F.M. and Pluso, V. 99. Plastc Desgn of Sesmc Resstant Steel Frames. Earthquake Engneerng and Structural Dynamcs. :, -9. Ordaz, M. and Pèrez-Rocha, L.E Estmaton of strengthreducton factors for elastoplastc systems: New approach, Earthquake Engneerng and Structural Dynamcs. :9, SesmoSoft, 8. SesmoStruct. A computer program for statc and dynamc analyss for framed structures. (onlne) avalable from URL: