Inverse reliability-based design of shear buildings supported by springs with stochastic stiffnesses

A straightforward and efficient stiffness design method is developed for a shear building supported by a pair of swaying and rocking springs with stiffnesses given as statistically independent normal variates. The story stiffnesses are determined with the use of the closed form stiffness solution for specified fundamental frequency and translational eigenmode so that the probability of the seismic mean maximum interstory drifts not exceeding prescribed values would coincide with the specified value. The proposed method consists of two steps: (1) find the stiffnesses of swaying and rocking springs that can achieve the constrained nonexceedance probability by derived approximate formulas; (2) determine the story stiffnesses of the shear building so that the mean maximum interstory drifts would coincide with the prescribed values. The validity and good accuracy of the proposed method are demonstrated by use of Monte Carlo simulation.