Critical seismic load inputs for simple inelastic structures

Abstract

The modelling of earthquake loads as design inputs for inelastic single-degree-of-freedom structures is considered. The earthquake load is modelled as a deterministic time history which is expressed in terms of a Fourier series that is modulated by an enveloping function. Subsequently, the coefficients of the series representation, and, the parameters of the envelope function are determined such that the structure inelastic deformation is maximized subject to a set of predefined constraints. These constraints include bounds on the total energy of the earthquake signal, peak values on ground acceleration, velocity and displacement and upper and lower bounds on the Fourier spectra of the ground acceleration. Additional mathematical limits on the envelope parameters are also considered. The quantification of these constraints is obtained based on numerical analysis of a set of past recorded ground motions at the site under consideration or other sites with similar soil conditions. The structure force–displacement relation is taken to possess an elastic–plastic behavior. The resulting nonlinear optimization problem is tackled by using the sequential quadratic optimization method. The study, also, examines influences of the structure yield strength and damping ratio on the derived earthquake load and the associated structure response. Issues related to the time-variation of various energy forms dissipated by the inelastic system are also explored. The proposed formulation is demonstrated with reference to the inelastic response analysis of a frame structure driven by a single component of earthquake load.