21 1 Vol.21 No.1 2004 2 ENGINEERING MECHANICS Feb. 2004 1000-4750(2004)01-0067-06 ( 100084) HBTA HBTA TU352.1 A NONLINEAR DYNAMIC ANALYSIS OF STRUCTURES WITH VISCOUS DAMPERS TANG Yu-chuan, ZHANG Yu-liang, ZHANG Tong-sheng (Department of Civil Engineering, Tsinghua University, Beijing 100084, China) Abstract: Based on the story model of spatial member, the supplemental damping matrix, dynamic balance equation and relative energy balance equation of structures with viscous dampers are derived. Nonlinear dynamic analysis of structures with viscous dampers is added into the computer program HBTA (highrise building time-history analysis). Examples are provided to validate the dynamic analysis method and observe the seismic mitigation effect of viscous dampers. The inner forces and deformation of structural members and viscous dampers can be given by HBTA. Efforts are made to conduct dynamic analysis including both displacement-dependent nonlinearity and velocity-dependent nonlinearity. Key words: structure with energy dissipation system; viscous damper; dynamic analysis; energy analysis 1 SAP2000 CANNY 2002 1 1 [1] [2] (GB50011-2001) 2002-09-11 2003-03-18 (1977) (1945) (E-mail: zhangyl@tsinghua.edu.cn) (1934)
68 C i C i ( x, y ) i (2) 1 xyz 1 (3) l xx x x (4) ( x 2, y 2 ) 2 (1) [3] C C ( x j, y j ) j (2) 2 x HBTA [4] (5) (3) (4) (5) (1) 2 xyz x 2.1 (6) xyz ui v i θ i u j v j θ j 1 (7) 1 2.2 Fig.1 Coordinate systems m τ = kγ& { F DP } τ γ& k m k m (8) [5] F [M] [C] x& Rayleigh [K] (1) c m =1 {d} m 1 Taylor { F g } 0.3 1.0 (8) i [ u & T i v& i θ & (9) i ] ui v i θ i [C] [K] i x y z (8) (9) 1 1 xyz (2) ) ( x1, y1 1 2.3
69 (i) (i) (i) (i) i (7) i (10) (16) [6] (11) (16) [ C ] e DP [ C DP ] HBTA (12) (12) (9) [5] 9.7 3.1 (13) [C] [K] 1.32m 1.32m 1 0.90m [ C DP ] 2 5 1.20m 2.4 15.55cm 2 8.39cm 2 1~4 578kg 5 596kg Wilson-θ X (13) c=10kn s/m m=0.6 Wilson-θ 3.2 [2] X El Centro NS Wilson-θ 341.7gal X 0.25s 2.5 0.02s 0.01s HBTA HBTA SAP2000 (8) X 2 X T T D ({ d( τ )} ) = { d& ( τ )} dτ 3 HBTA SAP2000 X 4(a) (14) X 4(b) ( { F ( τ )} = HBTA ) { F ( τ )} = [ t i, t i + 1 D R (14) Fig.2 Displacement response of top story ] (15) E K E D E R E DP 3 HBTA [7] 2 3
70 HBTA 24 9.6% HBTA 8 [6] 92m X 3 ( 8.6m) Y 4 ( 8.6m 10.0m) H HBTA 1 5 2 Q345B 4.30kN/m 2 1~9 6.00kN/m 2 6 10~24 4.2 (15) II Taft SE NE 6 SAP2000 II HBTA 6 SAP2000 6 HBTA (GB50011-2001) (a) (b) 4 Fig.4 Maximum response of each story 5 6 Fig.5 Damping force versus relative displacement in damper Fig.6 Time-history trace of energy dissipated by dampers HBTA SAP2000 3 0.5 Taft 3 ( : kn s/m) Table 3 Damping coefficients of dampers (Unit: kn s/m) HBTA 4 X 400gal Y 340gal 20s 0.02s 2~16 1/70 (JGJ99-98) 5.5.3 0.08 [8] X Y 1~20 X Y 8 1~2 3~14 15~18 19~20 X 1000 1600 1200 1000 4.1 Y 600 4000 800 500 HBTA 1/70 7 12 M 8 x 9 10 7 8 Fig.7 Maximum displacement angle between stories Fig.8 Moment response at the top of column
71 9 10 Fig.9 Time-history trace of energy in original structure 5 Fig.10 Time-history trace of energy in damped structure HBTA HBTA SAP2000 HBTA ( 158 )
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