Abstract
The random response of two-degree-of freedom systems having bilinear hysteretic restoring force characteristics, when subjected to stationary white noises, has been investigated by theoretical approach together with digital simulation. Special attention has been paid to the distribution of plastic energy absorbed in each story. The energy of the lower story normalized by the total energy, ε_1, depends on mass ratio μ, stiffness ratio κ, plastic stiffness ratio γ_i, strength ratio β and on nondimensional input intensity ξ. In this paper, however, μ is kept constant as unity, and in most cases, γ_i and ξ are fixed on 0.1. Therfore main variable parameters are κ and β. The relation between ε_1 and β has been numerically evaluated with the wide range of κ. It has been found that β, in particular, produces a strong effect on ε_1. Especially when ν, which is defined as the ratio between nondimensional accumulated plastic deformations, is close to unity, ε_1 varies to a great extent with the slight change of β. Supposed that the criterion of optimum design under seismic loadings is taken such that ν becomes unity, the high accuracy is required for the evaluation of actual β. The approximate relation between the optimum β and ε_1 or κ has been analytically derived. It has been proved that theoretical expressions obtained have been agreed well with digital estimates.
