Sensitivity of Optimum Designs for Spatially Varying Ground Motions

Abstract

An optimization method is presented for long-span frames for specified seismic responses considering spatial variation of ground motions. The response is evaluated by using a response spectrum approach, where incoherency effect, wave passage effect, and local amplification effect are considered. Sensitivity coefficients of the optimum objective value with respect to the parameters defining spatial variation of the seismic motions are computed based on the parametric programming method or postoptimal analysis. It is shown that the second-order parametric sensitivity coefficients are easily obtained if the first-order coefficients vanish due to symmetry and antisymmetry conditions of structure and ground motions. In the examples, optimum designs are found for an arch-type frame and the results of postoptimal analysis are verified in comparison with the parametric sensitivity coefficients by the central difference method. It is shown that the spatial variation of ground motions leads to the increase of the optimal structural volume under constraints on member strains.