A Cost Optimization Model for Seismic Design of Structures

Abstract

Considering the earthquake susceptibility of structures located in seismic regions, the question arises as to what level of protective measures should be provided in order to achieve a certain degree of reliability against possible damage. To address this question, engineering risk and optimal design of structures located in a seismic area are studied. The basic concept is to obtain a tradeoff between the cost of providing a protective measure and the expected cost of earthquake damage. A simple mathematical approach is presented to determine the optimal earthquake intensity which the structure is designed to withstand. The objective is to minimize the total construction cost of the structure plus the expected cost of earthquake damage throughout the entire service life of the structure. For the case of deterministic structural resistance, and for structural response processes having Poisson (independent) crossings, an objective function is derived in terms of the building and earthquake variables. The optimal design intensity can then be determined by minimizing the objective function with respect to the intensity variable. The resulting equations are relatively simple and can be easily handled for numerical studies and sensitivity analysis. Generalizations of the results for nondeterministic structural resistance and for structural response processes different from those having Poisson crossings are also indicated. As an illustration of the proposed approach, a hypothetical building with realistic seismicity and structural parameters is analyzed for its optimal design earthquake intensity. The construction, damage and total costs are obtained in terms of the intensity variable. The implications and sensitivity of the results are also discussed.