SINGLE-DEGREE-OF-FREEDOM HYSTERETIC MODEL FOR COLLAPSE ANALYSIS OF BUILDING STRUCTURES

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1 29 10 Vol.29 No Oct ENGINEERING MECHANICS (2012) ( ) P- 8 IDA P- TU375.4 A doi: /j.issn SINGLE-DEGREE-OF-FREEDOM HYSTERETIC MODEL FOR COLLAPSE ANALYSIS OF BUILDING STRUCTURES SHI Wei, LU Xin-zheng, YE Lie-ping, QU Zhe (Department of Civil Engineering, Tsinghua Universit, Ke Laborator of Structural Engineering and Vibration of China Education Ministr, Beijing , China) Abstract: A simplified single-degree-of-freedom (SDOF) hsteretic model for collapse analsis of building structures is proposed in this work. The simplified hsteretic model is capable of simulating strength deterioration under monotonic loading, pinching, strength and stiffness deterioration under cclic loading as well as P- effect, so that it can be applied to collapse analsis. To validate the applicabilit and effectiveness of the proposed SDOF hsteretic model, an eight-store RC frame structure is simplified as an equivalent SDOF sstem according to its fundamental mode of free vibration and the collapse fragilit analsis based on incremental dnamic analsis is implemented to the prototpe structure and the simplified SDOF sstem, respectivel. The results show that the collapse fragilit curves of the prototpe structure and the simplified SDOF sstem agree quite well with each other. Ke words: collapse fragilit analsis; single-degree-of-freedom; hsteretic model; strength deterioration; P- effect (Single Degree of FreedomSDOF) SDOF [12] SDOF Behrouz Shafei (Incremental Dnamic AnalsisIDA) (Collapse Fragilit Analsis) [3] Luis ( )( )(NCET ) (1960)( lp@mail.tsinghua.edu.cn). (1986)( shi-w05@mails.tsinghua.edu.cn) (1978)( luxz@mail.tsinghua.edu.cn) (1983) FRP ( m.quzhe@gmail.com).

2 6 Ibarra (First Order Second Moment FOSM) SDOF [4] SDOF SDOF SDOF SDOF P- SDOF 8 SDOF IDA [56] SDOF 1 SDOF ( ) 5 K e F s c F F D E s = s K e D c =D F c E c = c K e 2 (6 7)(3 4) ( ) 2 Fig.2 Basic hsteretic rule (510) [10] f d / ( D / max ff ref ) D / max F / ref f / (1 )D D / d per per ((5) (6) (7)) F ref F c F F f ref D c D D Dc D F f D d per D per D max F F c 1 Fig.1 Backbone curve 1.2 Clough [79] 3 Fig.3 Simulation of pinching propert 1.4 [10] [11]

3 7 i i [10] c Ei i i (1a) Et E j j1 Et FD (1b) E FD t c 1.0~2.0 [11] c=1.0 c=2.0 E i i [10] 1) ( 4(a))2) ( 4(b))3) ( 4(c))4) ( 4(d)) i c sc u a D D c,2 D c,1 c,0 K s,1 K s,0 K s,2 F,0 F,1 F,2 F F,1,0 K s,0 K s,1 D c,0 D c,1 (c) D 1 D 1 (d) 4 Fig.4 Simulation of deterioration propert 1) ( 4(a)) 0 F K (2)(3),i F s,i (1 ) F (2), i s, i, i1 s, i (1 s, i) Ks, i1 K (3) s,i i D c,0 D c,1 (a) F ref,0 F ref,1 F ref,0 F ref,1 (b) D c,1 D c,0 s c s (1) 2) ( 4(b)) F ref F ref 0 F ref (4) F (1 ) F (4) ref, i c, i ref, i1 c,i i c c c (1)

4 8 3) ( 4(c)) K (1 ) K (5) u, i u, i u, i1 (2)~(4) u,i u c u (1) 0 u s c [10] 4) ( 4(d)) 0 D max +DD D D (6) i a, i i1 a,i a c a (1) 1.5 P- P- 5 SDOF V 2 2 V WhW H (7) W h H ( 2 2 ) h H P- V V W 1 F (8) H 2 1 ( / H ) (7)(8)P- [12] F F- W 1 KP H 2 1 ( / H ) / H 1/5 W W 1 H H 2 1 ( / H ) 0.1% F- 2 2 h H h 2 2 H F- [1214] W / K e (9) H W P- F- P- H K e P- P- P- SDOF P- K ( 6 ) F e D F K e D H W h 5 P- Fig.5 Simulation of P-effect F 2 6 P- Fig.6 Simulation of P- effect RC SDOF 8 RC 8 II (x ) 7.5m

5 9 ( ) 7.5m 3.0m( 7) x GX GY 1 ~4 5 ~ C45 C40 HRB mm C40 10@ RC Fig.7 Plane laout of the 8-store RC frame structure Fig.8 Section size and reinforcement of the structural elements 1 Table 1 Store information of the frame structure /mm /kn C-1a GX-1 GY C-1b GX-1 GY ~ C-1b GX-1 GY ~ C-2 GX-2 GY C-2 GX-2 GY SDOF MSC.MARC TECS(Tsinghua Earthquake Collapse Simulation) [1516] RC l 0 /3 b+12t [17] l 0 b t BN [18] ( ) T 1 = s [19] ( M 1 M 1 ) 8 RC Y ( 9) 10 10(a) V b -D r (10)(11) S a -S d [20] Fig.9 Lateral force pattern applied in the nonlinear static analsis

6 ,P-,P-,P- SDOF SDOF RC D/mm r /mm (a) - Sa/(m/s 2 ) 11 P- Fig.11 Validation of P- effect (b) - 10 Fig.10 Pushover curve S S V (10) b a * M 1 D r d (11) 11r M * 1 1 1r 10 TECS [1516] 10 P- P- 11 P- ( ) P- SDOF S a -S d SDOF 12 SDOF Fig.12 Restoring force of the simplified SDOF sstem 2.3 RC SDOF IDA [5 6] FEMA El-Centro [6,21] S a (T 1 ) [22] [6,1516] [23] RC SDOF 13 SDOF

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