44 9 0 9 CHINA CIVIL ENGINEERING JOURNAL Vol. 44 Sep. No. 9 0. 0009. 0007 TU3. 3 TU35. A 000-3X 0 09-004-09 The seismic response prediction of long-period seismic isolated structures based on response spectrum theory Cao Jialiang Shi Weixing Liu Wenguang. Tongji University Shanghai 0009 China. Shanghai University Shanghai 0007 China Abstract Method for calculation of seismic structural response is necessary for the design of base-isolated structures. Reduction of earthquake hazard of isolated structures can be improved by taking account of long-period earthquake effects. Relative displacement spectrum relative velocity spectrum and absolute acceleration spectrum with appropriate damping ratio and natural period were constructed according to the code fortification intensity through selecting suitable strong motion records. Relevant spectral calculation formulas and peak value of ground motion were provided through statistical calculation. Double-mass simplified calculation model for base-isolated structures was set up based on the simplification principle of equivalent natural period. Simplified calculation formulas for the double-mass model parameters as well as the dynamic characteristics and seismic response were derived and seismic response prediction method was proposed. Keywords seismic isolated structure response spectrum long period simplified calculation model seismic response prediction seismic action E-mail jialiang9@ 63. com -3 4-5 973 007CB740 508784 006B37000 009-- 0s 00s
44 9 43 0 50 6-7 3 8-0 0 90 / -6. PEER 80 0. 05 ~ 0. 5Hz PGA Peak Ground acceleration 0. 0g Fig. Modeling of relative displacement spectrum Ⅳ 0. 0g PGA 0. 05g 0. 0 7 Newmark-β 8. η 0. 0 0. 0 0. 0 β D = { 0. 4 T 0 T. 0s 0. 6 T - + 0. 4. 0s T 6. 0s 0. 05 T - 6 +. 6. 0s T 0. 0s η Table Damping ratio adjustment factors 0. 0. 0. 3 0. 4. 0 0. 7734 0. 67 0. 5697 0. 0 3 S V = { 0. 8π PGD 0 T. 0s 0. 6π + 3 /T PGD. 0s T 6. 0s π 0. 05 +. /T PGD 6. 0s T 0. 0s
44 0 Fig. Comparison of average-site-class relative displacement spectrum with relative displacement spectrum considering adjustment effect of damping ratio 3 4 ~ 5 5. 6π PGD 0 T. 0s 3 T Fig. 3 Modeling of relative velocity spectrum derived from S A = + 3 0. 3π PGD. 0s T 6. 0s relative displacement spectrum T T + 4 0. π PGD 6. 0s T 0. 0s 3 T T 4. 5πPGV 0 T 0. 8s 3 4 0. 0769 S { A = ( + 5. ) πpgv 0. 8s T 6. 0s T. 5T 0 T 0. 8s β V = 0. 03846 T - 0. 8 +. 0 0. 8s T 6. 0s - 0. 05( - 54 ) πpgv 6. 0s T 0. 0s T - 0. 05 T - 6 +. 6. 0s T 0. 0s 5 3 Fig. 4 4 Modeling of relative velocity response spectrum 5 Fig. 5 Modeling of absolute acceleration spectrum derived from relative displacement and velocity spectrum 3. 3 PGD PGV
44 9 45 80 PGD /PGA PGV /PGA 9. 8-0 PGD PGV 3 4 Table Mean value of ratio of peak ground motion Ⅰ Ⅱ Ⅲ Ⅳ 6 PGD /PGA s 0. 05 0. 0995 0. 083 0. 64 PGV /PGA s 0. 0946 0. 476 0. 587 0. 3 3 Table 3 Design peak ground displacement m Ⅰ Ⅱ Ⅲ Ⅳ Ⅰ Ⅱ Ⅲ Ⅳ 6 7 8 9 0. 00889 0. 07658 0. 03536 0. 07063 0. 06487 0. 050769 0. 09939 0. 9865 0. 06803 0. 036 0. 9865 0. 3090 0. 0757 0. 0354 0. 0708 0. 4056 0. 05708 0. 003 0. 9766 0. 3953 0. 99 0. 96 0. 3953 0. 6493 0. 094 0. 03847 0. 076496 0. 599 0. 05737 0. 0996 0. 54 0. 4308 0. 3387 0. 3904 0. 4308 0. 66933 0. 08977 0. 057955 0. 59 0. 38 0. 08693 0. 666 0. 3599 0. 6596 0. 084 0. 36 0. 6596. 04 4-4 Table 4 Design peak ground velocity m /s M = m b 6 6 7 8 9 0. 06704 0. 033409 0. 06686 0. 3364 0. 050 0. 09605 0. 879 0. 37585 0. 693 0. 088 0. 37585 0. 58464 0. 06063 0. 058 0. 045 0. 085 0. 07887 0. 4986 0. 93 0. 58644 0. 844 0. 3579 0. 58644 0. 99 0. 0803 0. 056048 0. 0. 49 0. 084069 0. 63 0. 356 0. 63054 0. 966 0. 3509 0. 63054 0. 9808 0. 04085 0. 08653 0. 633 0. 366 0. 48 0. 3475 0. 4597 0. 9859 0. 8578 0. 503 0. 9859. 489 Fig. 6 6 Double-mass simplified calculation model of base isolated structures. 6 M = m s eq = K = k b = N K = k eq = ω s m s eq = m i i m i i k bi m i i m i i k i i 7 8 9 6 ~ 9 M M K K N n m i i k i i i
46 0 m b T eq = T s = π M K k b k bi T eq M > M K >> K μ = T eq T eq = T b = π m b + M /k b 0 M /M >> λ = T eq /T eq < T T { + /λ } + /λ + + /λ 4 { ( - + ) + /λ } μ T = T b / + μ / + /λ - + /λ 4 - + μ T = T b / + μ / X /X 4 4 3 = μ / μ + μ + λ - + λ 4 + λ μ - / μ + + 4 X /X = μ / μ + μ + λ - - λ 4 + λ μ - / μ + + 5 γ = m i X i m i X i = ( + μ + λ - ) + μ μa ( ( μ + λ - ) μa ) 6 γ = m i X i m i X + ( μ + λ - B ) + μ μ + λ - B 7 ~ 7 8 ~ 0. 3 T = T b + λ 8a T = λt b / + μ + μλ 8b X /X = / + λ 9a X /X = - μ + λ 9b γ = λ + 0a γ = - λ / + μ + μλ 0b 9 9 γ i X ij = 9 a 7 8 7 9 b λ 0. 3 μ 0 λ 0. 3 0. 05 7 μ 0 λ. 0 8 0 λ. 0 μ. 0 λ 0. 3
44 9 47 9 c λ 0. 3
48 0 Fig. 9 9 Application scope of simplified calculation model 3 M = m b M = m i K = k b = k eq i K ζ sub = ζ b = k eq i ζ eq i = ω s m i K ζ sub = 0. 0 ~ 0. 05 T = T b + λ T = λt b / + μ + μλ X /X = / + λ X /X = - μ + λ γ = λ + γ = - λ / + μ + μλ ζ = ζ sub e -λ/ μ+ j i F ji = m i S A j γ j X ji S A j j SRSS F ek = F + F 3a F ek = F + F + F + F ζ = λζ sub μ / + μ + ζ sub + μ 3 0s SRSS 3b F ek i F ik = ( G i H i / G j H j ) F ek 4 α i = F ik / G j 5 Δ i = F ik /k i 6 k i i 4 6 4
44 9 49 0s 7. J. 0. 0 ~ 0. 40 003 0-8 Xie Lili Ma Yuhong. The development process of the modern earthquake resistant design theory J. Recent Developments in World PGD /PGA Seismology 003 0-8 in Chinese PGV /PGA 8 FEMA 440 Improvement of nonlinear static seismic analysis procedures R. Washington DC FEMA 005 PGD PGV 9. 3 J. 004 4 5-8 Zhou Yongnian Zhou Zhenghua Yu Haiying. A study on long period portion of design spectra J. Earthquake Engineering and Engineering Vibration 004 4 5-4 8 in Chinese 0. J. 998 3 6 49-55 Wang Junjie Fan Lichu. Modification of code response spectrum in long period phase J. China Civil Engineering Journal 5 998 3 6 49-55 in Chinese. 000 J. 000-4. J. 000 30. et al. Review of the development of the perforcement-based J. 990 0-0 Xie Lili Zhou Yongnian Hu Chengxiang et al. Characteristics of response spectra of longperiod earthquake ground motion J. Earthquake Engineering and J. 000 30 6 Engineering Vibration 990 0-0 in Chinese 3-6. J. 4. push-over 007 30 3 96-30 Wu Di Luo Qifeng. 005 6. M. 006 469-5 Hu Yuxian. Earthquake engineering M. Beijing Seismological Press 006 469-5 in Chinese 4 9-5 Xie Xiaojian Jiang Yongsheng Liang Shuting seismic-design theory J. Journal of Southeast University Natural Science Edition 000 30 4 9-5 in Chinese 3. / J. 000 37-43 Luo Yongfeng. Development of long-period seismic wave Ye Liaoyuan Pan Wen. The principle of nonlinear static research J. Journal of Seismological Research 007 30 3 96-30 in Chinese analysis push-over and numerical examples J. Journal of Building Structures 000 37-43 in Chinese 3. 5. J. J. 000-8 Wang Yayong. 006 36 5-33 Zhou Xiyuan Yu A review of seismic response spectra time history analysis Ruifang. Development of seismic design method for and energy method J. Journal of Building Structures 000-8 in Chinese 4. M.. 006 Architectural Society of Japan. Recommendation for the design of base isolated buildings M. Liu Wenguang Translation. Beijing Seismological Press 006 in Chinese building structure J. Building Structure 006 36 S 5-33 in Chinese 6. J. 000 8 9-3 Shi Weixing Li Zhengsheng Wang Dasui. Calculation and application of displacement spectrum in base-isolated buildings J. Journal of Tongji University Natural Science 5. 00 Edition 000 8 9-3 in Chinese 50 M. 7. Matlab J. 009 9 88-94 Cao Jialiang. Discussion on adjustment of strong motion records by using Matlab built-in functions J. South China Journal of Seismology 009 9 88-94 in Chinese
50 0 8 Chopra A K. Dynamics of structures theory and applications to earthquake engineering M. New Jersey Prentice-Hall 004 9 GB 500 00 S. 00 GB 500 00 Code for seismic 5 64-70 Liu Wenguang Yan Weiming Huo Da et al. Computation model and shaking table test for isolated design of buildings S. Beijing China Architecture & MDOF tower structure J. China Civil Engineering Building Press 00 in Chinese Journal 003 36 5 64-70 in Chinese 0. 3. J. 999 9-36 Su Jingyu Han Miao Zhou Xiyuan et al. The practical calculating method of equivalent seismic action of J. 006 3 8 38-43 Wang Huanding Fu Weiqing Liu Wenguang et al. Research on equivalent simplified model of regular shock-insulation base isolation building using rubber bearings J. Journal of Vibration Engineering 999 9-36 in Chinese J. 005 5 6 4-45 Fu Weiqing Liu Wenguang Wang Jian et al. Research on equivalent simplified model of hing-rise. J. 00 isolated structure J. Earthquake Engineering and Engineering Vibration 005 5 6 4-45 in Chinese. J. 003 36 building J. Engineering Mechanics 006 3 8 38-43 in Chinese 4. 33-4 Li Zhongxi Zhou Xiyuan. Simplified analysis method of seismically isolated regular building J. Earthquake Engineering and Engineering Vibration 00 33-4 in Chinese 98-96- 968-