The effect of strain hardening in limiting the forces developed in structures subjected to earthquake motions below those of the elastic behavior is investigated by treating a single degree of freedom system. Response spectra for El Centro earthquake, May 1940 are generated from an idealized bilinear strain hardening resisting force-displacement relation for different values of the strain hardening coefficient and ductility factor. Optimum response spectra are presented in terms of the yield displacements and the maximum displacements. For a system with the optimum yield displacement, the maximum displacement response is always less than that of the elastic system, and thus the optimum response spectra may be used as a guide in selecting members for a displacement constrained design.

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