Proceedings of the 11th WSEAS International Conference on Sustainability in Science Engineering

Transcription

1 4,50m 4,00m 4,00m 4,00m 4,00m 4,00m 4,00m 4,00m 4,00m 4,00m 40,50m 7,50m 7,50m 7,50m Proceedngs of the 11th WSEAS Internatonal Conference on Sustanablty n Scence Engneerng OERSTREGTH DEMADS I MULTISTOREY ECCETRICALLY BRACED FRAMES ADREI CRIŞA, AUREL STRATA Department of Steel Structures and Structural Mechancs Unversty POLITEHICA of Tmşoara Ioan Curea no.1 ROMAIA andre.crsan@ct.upt.ro, aurel.stratan@ct.upt.ro Abstract: The present paper compares overstrength demands on non-dsspatve memebers n three sesmc desgn codes: P100-1/2006 (RO), E 1998 (EU) and AISC (USA) based on the analyss of a multstory eccentrcally braced frame. The structural behavor was studed usng pushover and tme-hstory analyss. The nonlnear behavor of structural members was modeled usng plastc hnges defned accordng to FEMA 356, whle acceptance crtera specfed n the same document were used. Key-Words: Pushover, Eccentrcally braced frames, Sesmc overstrength P100, E 1998, AISC , FEMA Introducton The present paper analyzes the behavor of a multstory eccentrcally braced frame desgned n accordance wth the provsons of P100-1/2006, the Romanan sesmc desgn code, E 1998, the European sesmc desgn code and AISC , the Amercan sesmc desgn code. Three structures were desgned usng E and E 1998 provsons, but wth overstrength requrements for non-dsspatve members establshed accordng to the nvestgated codes. Evaluaton of sesmc performance was accomplshed usng pushover and tme-hstory analyss. The nelastc behavor was modeled usng elastc-plastc hnges based on recommendatons of FEMA 356 whch was used also for establshng acceptance lmts of plastc deformatons. demands of the three codes was done. The only dfference n desgn was concernng the non-dsspatve members. EBF Gravty Frames 2 The structure under study The structure that was analyzed conssts of a multstory eccentrcally braced frame of 9 stores of 4.00m, a base story of 4.50m, three spans of 7.50m of whch the central span s sesmc resstant and the two sde spans are gravtaty-only frames. On the other drecton, the three bays have the same conformaton, as presented n fgure 1. All nteror frames are gravty-only. The locaton of the structure was consdered to be a very actve sesmc zone (Bucharest, Romana), havng PGA=0.24g, T C =1.6s and β 0 =2.75. For the begnnng the structure was desgned n accordance wth Romanan desgn codes, all loads were appled (dead loads, lve loads, wnd and snow loads, sesmc load) and all the elements were desgned n accordance. After the gravty frames were desgn, the desgn of sesmc resstant frames n accordance wth the 7,50m 7,50m 7,50m Fg. 1 Plan vew and elevaton of structure ISS: ISB:

2 The dual-steel concept was used n order to reduce the cross-secton of the columns, so the S235 steel was used for lnks and beam outsde lnks and S355 was used for braces and columns. Short lnks were used n the eccentrcally braced frame. The condton for a lnk to be classfed as short s based on the formula: e 1.6M Pl, lnk / Pl, lnk. 3 The structural desgn Even f the formula for lnk shear force capacty s dfferent for P100 and E 1998 on one sde and AISC 341 on the other sde, the dfference s small enough for the dsspatve elements to have the same cross-secton for all the three desgned structures. Due to dfferent demands mposed by the sesmc desgn codes for the structural non dsspatve elements, the resultng structures dffer. The overstrength demands for the three codes are translated nto the followng formulas. For P100 and E 1998: M ed, G M ed, G ed, G ov ov ov ed, E M ed, E ed, E wth the only dfference n calculaton of the 1.1γ ov Ω term, more specfc Ω. So, n case of P100, Ω represents the maxmum strength reserve of the dsspatve elements (lnks) pl, lnk max(1.5 ). The same term, n ed, lnk case of E 1998 s consdered to be the mnmum strength reserve of the dsspatve elements, pl, lnk mn(1.5 ). In case of AISC 341, desgn forces ed, lnk for non-dsspatve members (columns, braces and columns) should correspond to fully yelded and stran hardened lnks. Dfferent factors to account for stran hardenng are used n case of braces (1.25) and beams and columns (1.1). In order to accomplsh ths requrements, accordng to chapter 15.2b, 15.6a, and 15.6b from AISC 341, a seres o lateral forces were appled on the structure n order to obtan a general falure mechansm (shear plastc resstance of all lnks, takng nto consderaton the overstrength). Addtonally, n certan condtons, columns need to be checked for amplfed sesmc loads obtaned from the expresson of the overstrength demand: ed ed, E The Ω factor s gven as a fxed value for a gven structural type; for eccentrcally braced frame, n ths case, the specfed value s 2. Fg. 2 The structure resulted from AISC desgn Fg. 3 The structure resulted from EC8 desgn ISS: ISB:

3 lnks, n case of EBF). Ths approach takes nto account the strength reserve of all lnks and gves a better estmate of the forces nto structural elements after the lnks yeld. In addton to ths, the use of a specfc value for Ω n case of AISC (very close to the Ω mn from EC8) have the same ssues as for EC8, but, AISC, uses ths load combnaton just n order to verfy the axal force n columns (no bendng moment consdered). The change n cross secton changes the response for each structure. For example the structure desgned n accordance wth P100 t has a perod of vbraton of 1,36s beng the more rgd structure. On the other sde the structure desgned n accordance to AISC provsons has a perod of vbraton of 1.52s. The dfferences n cross sectons for columns and braces are responsble for ths varaton n rgdty. In between these two, there s the structure desgned wth EC8 whch has a perod of vbraton of 1.48 s. When Fg. 4 The structure resulted from P100 desgn pl >0.4, wthout consderaton of the amplfed sesmc load, where desgn axal force and pl s the nomnal axal strength of the column, the requred axal compressve and tensle strength, consdered n the absence of any appled moment, shall be determned usng the load combnatons stpulated by the applcable buldng code ncludng the amplfed sesmc load. The resultng structures have the followng perods of vbraton: 1.36 s for P100, 1.48 s for E 1998 and 1.52 s for the structure desgned n accordance wth the AISC 341. The EC8 desgn code has smlar provsons to P100. The dfference comes from the Ω value. As a result of these approaches the fnal values of sesmc amplfcaton factor had the maxmum value for P100 (2.68) desgn code and close values for EC8 (2.09). The use of Ωmn n case of EC8 could lead to larger forces n columns and further to development of plastc hnges. In case of P100, Ω max could lead to larger overstrength demands, ncreasng the rgdty of the structure, but ths overstrength demand cannot guarantee a superor behavor for the structure (hgher demand for ductlty wth the ncrease of rgdty and decrease of the perod). Unlke P100 and EC8, AISC recommends the use of lateral forces that wll be appled to the structure n order to obtan a plastc falure mechansm (yeldng n all 4. Modelng of nonlnear behavor In order to be able to compare the overall behavor of the three structures, the same non-lnear model was adopted for the structures. The plastc hnges that were consdered to form due to post-elastc behavor were defned n accordance wth the provsons recommended by FEMA 356 Table C2-1 whch states that the formaton of plastc hnges for columns s due to an nteracton between bendng moment and axal force (the axal force reducng the bendng moment resstng capacty), for braces s due to axal force, for beams s manly due to bendng moment and for the lnk, takng nto consderaton that t was above calculated to be short, t s due to shear force. Three acceptance levels were consdered: IO mmedate occupancy, LS lfe safety and CP collapse preventon. Due to the fact that the braced frames were used wth gravtatonal frames (not wth moment resstng frames) sesmc force was ressted by the braced frames and as a result n the lower part of the columns the axal force exceeded the lmt mposed by FEMA 356 for a deformaton controlled hnge. The consequence s the use of force controlled hnges for whch there s no sgnfcant plastc deformaton, so n fact they exhbt a brttle behavor. Fg. 5 Force vs deformaton curve of hnges ISS: ISB:

4 (deformaton controlled and force controlled) Further on, on the type 1 curve were set the acceptance crtera IO, LS and CP, as showed n the followng fgure: AISC EC8 P100 Fgure 1: Generalzed component force-deformaton relatons for depctng modelng and acceptance crtera The plastc hnges propertes were calculated for each composed cross-secton (Malta-cross) and appled to the structural elements. The other elements plastc hnges were automatcally generated and appled to the elements. For columns and beams outsde lnk two plastc hnges were consdered (defned by an nteracton between axal force and bendng moment for columns and bendng moment for beams) and for lnks and braces one plastc hnge n the mddle of element (defned by axal force for braces and shear force for lnks). The formulae used can be found n FEMA 356. The consdered acceptance crtera levels are summarzed n the followng table: Table 1: The acceptance crtera Member SLS IO ULS LS (λ=0.4) (λ=1.0) LIK rad 0.11 rad COLUMS Ө y 0.50Ө y BEAMS 0.25Ө y 2.00Ө y BRACES 0.25Δ c 4.00Δ c Where Ө y s the yeld rotaton for the consdered member, and Δ c s the axal deformaton at expected bucklng load. 5 The pushover analyss results Even f the formula for lnk shear force capacty s dfferent for P100 and E 1998 on one sde and AISC 341 on the other sde, the dfference 1 refers to deformaton controlled plastc hnges. DOES OT apply n case of force controlled hnges Fgure 2: The pushover curves For the analyss a trangular dstrbuton of forces was used based on the assumpton that the structures wll respond n the frst mode of vbraton. Due to the fact that the structures dffer by very lttle the same lateral forces were consdered for the pushover analyss. The forces appled on the structure are summarzed n the followng table: Table 2: The lateral forces for PUSHOER Lateral Forces, k Level z= m F b = Desgn Code AISC EC8 P Table 3: PUSHOER summary Base POIT Shear STEP on graph Force <k> Dsp. <mm> Takng nto consderaton the pushover analyss the behavor of the three structures s mostly the same. The dfference, as can be observed, of maxmum base shear force, s slghtly bgger for the structure desgned n accordance wth P100 due to ts hgher rgdty. The dfference n rgdty reflects not only n maxmum base shear force, but also n top dsplacement of the structures. ISS: ISB:

5 The frst plastc hnges appear at levels 2 and 3, these beng the ones that wll fal at the maxmum base shear force. For all structures the falure mechansm s the desred one, the only structural element that forms plastc hnges s the lnk. In the followng table are summarzed the maxmum base shear force, total top dsplacement and the dsplacement for whch the frst plastc hnge forms. 6. The tme-hstory analyss results In order make a more accurate comparson, a nolnear dynamc analyss consderng 7 semartfcal accelerograms scaled to the desgn spectum was done. The performance "basc" level was chosen from P100-3, Table A.3 and the acceptance crtera was based on FEMA 356 provsons. Table 4: Used accelerograms Source - year Staton Dr rancea - 77 ICERC S rancea - 86 ERE 10W rancea - 86 ICERC S rancea - 86 Magurele S rancea - 90 ISPH/ARM S3E rancea - 90 ICERC S rancea - 90 Magurele S In all cases (all seven accelerograms) no plastc hnges formed n braces. Due to ths reason, they wll not make the subject of the further dscussons. The mean values of plastc rotatons for lnks of the three structures after the use of all 7 accelerograms are presented below for IO and LS: Table 5: Plastc rotatons for lnk IO LEEL Rato (Demand/Capacty) AISC EC8 P100 Lv Lv Lv Lv Lv Lv Lv Lv Lv GL Mean (%) 714% 654% 711% The lmt mposed by FEMA 356 for plastc rotatons n case of mmedate occupancy s very restrctve (0.005rad) and as seen n the above table the lnk rotaton demand s not satsfed and t s exceeded by far for all three structures. The three sesmc desgn codes do not offer a comprehensve method n order to obtan a structure that wll comply wth the mposed acceptance crtera. The SLS requrements for storey drfts lmtatons, n accordance wth P100 and EC8 demands were satsfed, but, as seen above, they dd not lmt the lnk plastc rotatons. Ths can be a consequence of the codes omsson to take nto consderaton the structural types, sway or nonsway, before settng a demand. In fact, code drft requrements are ntended to lmt non-structural damage, neglectng the structural one. Consequently, rgd frames (concentrcally or eccentrcally braced) can experence large nelastc demands at SLS (IO performance objectve), as shown by the prevous results. Table 6: Plastc rotatons for lnk LS LEEL Rato (Demand/Capacty) AISC EC8 P100 Lv Lv Lv Lv Lv Lv Lv Lv Lv GL Mean (%) 74% 75% 76% In case of Lfe Safety perforamnce objectve, the demand was fulflled by all three structures; the verfcaton was done n order to protect the nonstructural elements of the structures and to be able to respect the sesmc jont condton between two nearby structures. The verfcaton for drft n case of ULS, as n case of SLS, does not take nto account the structural system used. For beams and columns the mposed lmts were satsfed; the values are lsted below n table 7: Table 7: Plastc rotatons for columns LS Columns <mean values> Desgn Braced frame Unbraced frames code Demand Capacty Demand Capacty AISC EC P For plastc hnges n columns, the force controlled hnges were consdered havng the plastc rotaton ISS: ISB:

6 capacty equals to zero (no plastc capacty). The average plastc deformaton was calculated for each hnge of each beam/column and the consdered value s the maxmum value from the calculated averages. The only structure that exceeds the lmts mposed by FEMA 356 s the AISC structure. 7 Concluson Ths paper offers a comparson of overstrength demands for non-dsspatve members accordng to three sesmc desgn codes: AISC, EC8 and P100. Accordng to the pushover analyss the three structures had small dfferences between ther maxmum top dsplacement, maxmum base shear and the plastc hnge formaton (only n lnks) so that t can be consdered that the overall behavor (the collapse mechansm) was the desred one. For the tme-hstory analyss, the three structures, despte the fact that the falure mechansm was the expected one for all and for IO (SLS) none of the three structures formed plastc hnges n nondspatve elements, had some partculartes. For LS (ULS) load combnaton some plastc hnges formed n nondspatve elements. For the IO (SLS) even f the verfcaton for storey drft was done n desgn and the requrements of EC8 and P100 were met by all structures (demand for nonstructural members), the tme-hstory analyss revealed that storey drft requrements were exceeded. Ths fact s due to lnk plastc deformaton, aspect not taken nto account by the smplfed elastc analyss n the desgn codes. The plastc rotatons for lnks were exceeded by more than 650%. For LS (ULS) all the three structures had the expected behavor, the lnk plastc rotatons are below the lmt specfed by FEMA. Even f plastc hnges appeared n some nondsspatve elements (some beams and columns), they were small and met the requrements mposed by FEMA. The storey drfts exceeded the 2.5% value specfed by P100. The structures desgned n accordance wth the demands of P100 and EC8 satsfed the demands of FEMA356 (not consderng the IO case). The structure desgned n accordance wth AISC exceeded the demand for column plastc hnges as t can be seen table 7. The fact that all plastc rotatons were under the specfed requrements of FEMA ndcates that the sesmc load reducton factor q=6 was well chosen for the structural type under study. References: [1]Amercan Insttute Of Steel Constructon, Inc. Sesmc Provsons for Structural Steel Buldngs, March 9, 2005, ncl. Supplement o. 1. [2]Eurocode 8: Desgn of structures for earthquake resstance - Part 1: General rules, sesmc actons and rules for buldngs [3]P100-1/2006 Preveder de proectare pentru cladr, redactarea a I-a [4]P Preveder pentru evaluarea ş pentru proectarea consoldăr construcţlor vulnerable sesmc draft [5]Helmut Krawnkler, G.D.P.K Senevratna, Pros and cons of a pushover analyss of sesmc performance evaluaton [6]FEMA 356, Prestandard and Commentary for the Sesmc Rehabltaton of Buldngs [7]The Insttuton of Cvl, Engneers, Manual for the desgn of steelwork buldng structures to EC3 [8]Akshay Gupta and Helmut Krawnkler, Member, ASCE, Behavor of Ductle SMRFS At arous Sesmc Hazard Levels [9]Ahmed Elghazoul, Sesmc desgn of steel structures to EUROCODE 8, Department of Cvl and Envronmental Engneerng, Imperal college London, UK, 2007 ISS: ISB: