Response Spectrum of Piecewise Linear Elastic Structures

Abstract

Response spectra are helpful in the structural engineering practice for the design with earthquake as an extreme load case. However, it is restricted to the linear analysis, except for the plastic behavior. The linear analysis uses a single stiffness only, and by this, the low-level nonlinearities, as the opening and closure of cracks in reinforced concrete structures, are neglected. In this paper, we investigate single-degree-of-freedom systems with two linear elastic states. The response of the piecewise linear elastic structure is compared to the linear response for artificial earthquake accelerograms confined to a design response spectrum. The analysis shows that a high difference in the stiffnesses of the two states may result in a considerable increase in the response. At the same time, states with small relative differences in their stiffness have a maximum response below or close to the response of the linear system. Thus, the neglect of the low-level nonlinearity, as the opening and closing of a crack does not affect the assessment of the structure.