Nonlinear Static Analysis for Frame2shear2wall Structures

30 6 2008 12 Earthquake Resistant Engineering and Retrofitting Vol130,No16 Dec. 2008 [] 100228412 (2008) 0620041208,, (,100084) [ ],,, Chopra, MPA MPA,18,,MPA,,MPA [ ] ;;;; [] TU375 ; TU313 [] A Nonlinear Static Analysis for Frame2shear2wall Structures Miao Zhi2wei, Ye Lie2ping, Lu Xin2zheng ( Tsinghua University, Key Laboratory of Structural Engineering and Vibration of China Education Ministry, Beijing 100084, China) Abstract:Nonlinear static analysis (or pushover analysis) has been widely used recently as a simplified method to evaluate the structural seismic performance and estimate inelastic structural responses under severe ground motions. But most traditional pushover procedures, which have fixed lateral load patterns that are major based on first structural modal, can not reflect the effect of the higher modal on the structural dynamic response. To overcome this problem, Chopra et al. has proposed a new pushover procedure which is referred as modal pushover analysis (MPA) based on the modal decoupling response spectrum method to consider the effect of the higher mode. Currently, most MPA research is focused on frame structures. In this paper, the problem of MPA when it is implemented in frame2shear2wall structures is high lighted together with proposed solution method. An eighteen2story reinforced concrete frame2shear2wall structure is used as an example to benchmark the accuracy of traditional pushover method and MPA method. The structural responses with MPA method and traditional pushover methods are compared with the results of incremental nonlinear dynamic time history analysis, which shows that MPA procedure gives better prediction for inelastic responses of the structure. Keywords :nonlinear static analysis ; nonlinear time history analysis ; Modal Pushover Analysis ; reinforced concrete ; frame2shear2wall structure 1 Π,,, ( Pushover ) [] 2008206230 [] (JC2007003) ATC240,FEMA273 274 356 [12 ], GB5001122001 [3 ] Pushover ATC240 [1 ],,,, Pushover,, Earthquake Resistant Engineering and Retrofitting Vol130,No16 2008

42 2008 12 [3,5,6 ],Chopra, (Modal Pushover Analysis, MPA ) [7 ] MPA, Pushover,,,,MPA [79 ],MPA,,, -,,MPA 18,MPA, (incremental nonlinear dynamic time history analysis, IDA ), Pushover MPA,,MPA Pushover 2 [3 ],PKPM 18 1, 415m, 316m, 6517m,8,,, 810kNΠm 2,210kNΠ m 2,1 9 C40,10 18 C35 ;C30 HRB400, HRB335, HPB235 3 2120s 0153s 0122s,1 68 %,2 85 %,3 92 % 1, Y,Y, Y,8,6,- 1157,, 2,,, 1 3 Pushover MPA MSC1MARC [10 ] [10 ] 2, Rayleigh,5 % Pushover, 2 : (1) ; (2) ( SRSS ) [2 ], Earthquake Resistant Engineering and Retrofitting December 2008

30 6,: 43 1 (mm) (mm mm) (mm 2 ) ( mm 2 ) (mm mm) (mm 2 ) 1 3675 2281 1964 940 940 940 940 2 3675 1964 1884 940 940 940 940 3 3675 1964 1884 940 940 1256 940 4 300 1452 800 800 1964 1884 300 700 1140 1018 1256 940 5 (C40) 1452 (C40) 1964 1884 (C30) 1140 1018 1474 940 6 1452 1964 1884 1256 1140 1474 940 7 1452 1964 1884 1256 1140 1474 940 8 1452 1964 1884 1256 1140 1520 940 9 1452 1964 1884 1256 1140 1520 940 10 1452 1964 1884 1256 1140 1520 940 11 1452 1964 1884 1256 1140 1520 940 12 1452 1964 1884 1256 1018 1520 940 13 300 1452 800 800 1964 1884 300 700 1256 1018 1474 940 14 (C35) 1452 (C35) 1964 1884 (C30) 1140 940 1474 940 15 1452 1964 1884 1140 940 1474 940 16 1452 1964 1884 1018 940 1474 940 17 1452 1964 1884 1018 940 1474 940 18 1452 1964 1884 940 940 1256 940 Pushover, MPA,: i i Pushover, i (SDOF ),i SDOF,i SDOF,i SDOF,T p i, i SDOF,T i MPA [7 ],T p i T i, 1,T p1 = T 1,2 3,T p2 T p3 T 2 T 3 2 3 MPA T p1 T p2 T p3 T 1 T 2 T 3 [11 ], K p i K i MPA 2 MPA T i (s) MPA T p i (s) ( %) 1 2. 20 2. 20 0. 9 2 0. 53 0. 65 23 3 0. 22 0. 42 93 Earthquake Resistant Engineering and Retrofitting Vol130,No16 2008

44 2008 12,MPA,, i { < i }MPA,i,L i (1),, [ m ], s,{ l i } i,,,,mpa [7 ], T i T p i L i = [ m ]{ < i } s = { l i } s (1),,,,, Pushover,,(1), { < i }, i,, MPA,MPA,, SDOF T p i T i, 2, 2 3,T p2 T p3 T 2 T 3, MPA,,, MPA,T p i T i 3, 2 3 MPA T i (s) MPA T p i (s) ( %) 1 2. 20 2. 21 0. 45 2 0. 54 0. 56 3. 8 3 0. 23 0. 26 15,,,, 2 3 T i,,,,,,,, Pushover MPA,,P2 4,,,, ( Incremental Dynamic Analysis, IDA, (Dynamic Pushover) [12 ] IDA,, IDA, Pushover MPA 5 (United States Geological Survey,USGS),4,S1 S2 S3 S4, 750mΠs 360750mΠs 180360mΠs 180mΠs S2 Earthquake Resistant Engineering and Retrofitting December 2008

30 6,: 45,S2 10 ( 4) IDA 10,, PGA,,PGA 10, [8,12 ], S a ( T 1 ), S a ( T 1 ) IDA T 1 = 2120s,,S a ( T 1 ) = 0136mΠs 2, S a ( T 1 ) = 1101mΠs 2, S a ( T 1 ) = 2101mΠs 2, S a ( T 1 ) 012mΠs 2 2101mΠs 2, 0125mΠs 2,, 4 10 PGA (g) PGV (cmπs) PGD (cm) Friuli, Italy 1976Π09Π15 03 :15 8014 Forgaria Cornino 0. 26 9. 3 1. 07 Landers 1992Π06Π28 11 :58 22170 Joshua Tree 0. 274 27. 5 9. 82 Livermore 1980Π01Π27 02 :33 57T02 Livermore2Morgan Terr Park 0. 252 9. 8 1. 3 Loma Prieta 1989Π10Π18 00 :05 58235 Saratoga2W Valley Coll. 0. 255 42. 4 19. 55 S2 Morgan Hill 1984Π04Π24 21 :15 57383 Gilroy Array # 6 0. 292 36. 7 6. 12 Northridge 1994Π01Π17 12 :31 90009 N. Hollywood2Coldwater Can 0. 271 22. 2 11. 69 Parkfield 1966Π06Π28 04 :26 1438 Temblor pre21969 0. 272 15. 0 3. 4 San Fernando 1971Π02Π09 14 :00 24278 Castaic2Old Ridge Route 0. 268 25. 9 4. 67 Victoria, Mexico 1980Π06Π09 03 :28 6604 Cerro Prieto 0. 621 31. 6 13. 2 Whittier Narrows 1987Π10Π01 14 :42 90009 N Hollywood2Coldwater Can 0. 25 14. 3 1. 11 : http :ΠΠpeer. berkeley. eduπsmcatπindex. html 6, 10 ( ),,MPA Pushover 611,, 1,5,9,12,15,18,3, 10, Pushover MPA (3 (a) ), Pushover, Pushover MPA,,,MPA,,MPA 3 5 (3 ( b) ), SRSS Pushover,Pushover MPA,,, MPA 3 Earthquake Resistant Engineering and Retrofitting Vol130,No16 2008

46 2008 12 3 9 (3 ( c) ), SRSS Pushover,Pushover MPA 3,, 20 %,MPA 3,3 12 (3 (d) ),Pushover, Earthquake Resistant Engineering and Retrofitting December 2008

30 6,: 47 Pushover,SRSS Pushover, 30 %MPA,,,,, 18 %,,MPA 3 15 18 (3 (e) 3 (f) ), 12,MPA 20 %, Pushover,,MPA 3,3,, MPA Pushover,MPA 3 612 [3 ], 70gal 200gal 400gal ( ), S a ( T 1 ) 0136mΠs 2 1101mΠs 2 2101mΠ s 2 4 4 S a ( T 1 ) 0136mΠs 2 (), Pushover, SRSS Pushover,,, MPA,,, S a ( T 1 ) 1101mΠs 2 (), Pushover, SRSS Pushover,, MPA,,,, Pushover S a ( T 1 ) 2101mΠs 2 (), Pushover, SRSS Pushover,, MPA,,,Pushover,MPA,,,Pushover,MPA 613 5 S a ( T 1 ) 0136mΠs 2 1101mΠs 2 2101mΠs 2, S a ( T 1 ) 0136mΠs 2 1101mΠs 2 ( ),, Pushover, MPA ; Earthquake Resistant Engineering and Retrofitting Vol130,No16 2008

48 2008 12, SRSS Pushover, S a ( T 1 ) 2101mΠs 2 (),,MPA,Pushover, 614 6 5 S a ( T 1 ) 0136mΠs 2 1101mΠs 2 2101mΠs 2,,,Pushover,MPA 3, 7 18 Pushover MPA, : (1) MPA,, MPA, Pushover, (2),MPA 6 Pushover, (3) MPA,, (4) MPA 3,, 3 ( 54 ) Earthquake Resistant Engineering and Retrofitting December 2008

54 2008 12,, (3),, (4),,, : [ 1 ] Spacone E, Ciampi V, Filliou F C. Mixed formulation of nonlinear beam finite element [J ]. Computers & Structures, 1996, 58 (1) :7183 [ 2 ] Menegotto M, Pinto P E. Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and nonelastic behavior of elements under combined normal force and bending [ C ]. Proc., IABSE Symp. on Resis2tance and Ultimate Deformability of Struct. Acted on by Well Defined Repeated Loads,1973 :1522 [ 3 ] Spacone E, Filippou F C,Taucer F F. Fiber beam2column model for nonlinear analysis of RC frames. I: Formulation [J ]. Earthquake Engrg. and Struct. Dyn., 1996,25 (7) : 711725 [ 4 ] Neuenhofer A,Filippou F C. Evaluation of Nonlinear Frame Finite2Element Models[J ]. J. Struct. Eng.,1997,123 (7) : 958966 [ 5 ] Hjelmstad K D, Taciroglu E. Variational Basis of Nonlinear Flexibility Methods for Structural Analysis of Frames [ J ]. Journal of Engineering Mechanics,2005,131(11) :11571169 [ 6 ],,. [J ].,1990,23 (4) :214 [ 7 ],. [J ].,1995,16 (3) : 5965 [ 8 ]. [J ].,2005,22 (3) :339365 [ 9 ]. [D]. :,2007 [10 ] Yu2Fei Wua, Deric J Oehlers, Michael C Griffith. Rational definition of the flexural deformation capacity of RC column sections[j ]. Engineering Structures,2004,26 : 641650 [11 ]. [M]. :,1981 [] (1969),,,,wgjyc @sina. com ( 48 ) : [ 1 ] ATC. ATC240. Seismic evaluation and retrofit of concrete buildings [ S ]. Red Wood City, Califonia : Applied Technology Council, 1996 [ 2 ] FEMA273, FEMA274, FEMA356, NEHRP guidelines for the seismic rehabilitation of buildings[ S]. Washington D. C. : Federal Emergency Management Agency, 1996 [ 3 ] GB5001122001,[ S] [ 4 ],. Π [J ].,2000,30(6) : 2326 [ 5 ],. [J ].,2001,17 (5) :813 [ 6 ],. Pushover [J ].,2004,24 (3) : 8997 [ 7 ] Anil K Chopra, Rakesh K Goel. A modal pushover analysis procedure for estimating seismic demands for buildings[j ]. Earthquake Engng Struct. Dyn. 2002,31 (3) :561582 [ 8 ] Sang Whan Han, Anil K Chopra. Approximate incremental dynamic analysis using the modal pushover analysis procedure[j ]. Earthquake Engng Struct. Dyn. 2006, 35 (15) :18531873 [ 9 ],,. pushover [J ].,2006,26(6) : 5055 [10 ],,. [J ].,2006,23(z2) : 131140 [11 ],. [J ].,2006, 23 (8) : 6973 [12 ] Dimitrios Vamvatsikos, C. Allin Cornell. Incremental dynamic analysis [ J ]. Earthquake Engng Struct. Dyn. 2002, 31 (3) : 491514 [] (1981),,,,E2mail :miaozhiwei00 @mails. thu. edu. cn Earthquake Resistant Engineering and Retrofitting December 2008