Optimum Assessment of Irregular Three‐Dimensional Seismic Buildings

A structural optimization algorithm based on an optimality criteria approach is presented for three‐dimensional, statically and dynamically loaded steel or reinforced concrete structures. The theoretical work is presented in terms of scaling, sensitivity analyses, optimality criteria, and Lagrange multiplier determination. The structures can be subjected to a combination of static and dynamic displacement and stress, and natural frequency constraints. The dynamic analyses are based upon the ATC‐03 provisions for equivalent lateral force and modal analysis procedures, or multicomponent response spectra modal analyses. Using the algorithm presented, a computer program called ODRESB‐3D was developed for analysis and design of various building systems. In this paper, only the design examples of vertically irregular building systems are provided to illustrate the rapid convergence and the practicality of the presented method as well as the effects of ATC‐03 provisions on the optimal structural parameters. Interesting results are: ATC‐03 modal analysis and equivalent lateral force procedures produce similar stiffness distributions but different magnitudes for the irregular structural configurations, and ATC‐03 stability function values are much less than the upper bound value of 0.1 in the provisions.