Report - PEER - University of California, Berkeley

-The effective period obtained by usingsµ in Eq.(38) is T e1 .The effective periodobtained by using Eq. (39) is T e2 . No damping is applied. As is seen in Table 2, T e1and T e2 are almost equal. In Fig. 4, V E -T e relationship is shown by using T e2 as T e .The value f ranges as follows.0.19 ≤f ≤ 1.61, mean value f=0.64(41)The solid lines in Fig. 4 is the energy spectrum of the elastic system with 10% ofdamping. As is seen in Fig. 4, the input energy of individual systems well correspondsto the solid lines and the effective period shown by Eq.(37) is shown to be adequate inorder to estimate the total energy input into the highly nonlinear systems.(a) El Centro record (b) Hachinohe record (c) Kobe recordFigure 4. Effective period of multi-mass system.6. CONCLUSIONThe effective period of the highly nonlinear systems is derived by considering thefundamental feature of the energy spectrum. The effective period is the mean value ofthe fundamental natural period and the instantaneous longest period of the system.The instantaneous longest period is obtained by knowing the averaged maximumdeformation of the system. The derived simple formula of the effective period wasascertained its effectiveness by the direct numerical analysis of ten storied shear typeframes.REFERENCESAkiyama, H. (1985). Earthquake-Resistant Limit-State Design for Buildings,University of Tokyo Press.Akiyama, H. (1999). Earthquake-Resistant Design Method for Buildings Based onEnergy Balance.396