A Cost Optimization Model for Seismic Design of Structures

Structures constructed in seismic regions are required to function properly in a forcing environment characterized by random earthquake 2209 2210 T H E BELL SYSTEM TECHNICAL JOURNAL, DECEMBER 1972 occurrences and intensities. The seismic environment including the expected earthquake-magnitude levels and the corresponding frequency of occurrence for different seismic-risk zones was described previously. 1 The study was based on a statistical analysis of nationwide seismic data and may be used as a guide for the development of seismic design requirements on a global basis. Under localized situations, however, the seismic requirement for structures that are expected to adequately withstand the earthquake environments should be based on costreliability studies. During an earthquake of given intensity, there exists a probability that the response of the structure is greater than its resistance capability and, therefore, a probability of damage to the structure. The cost associated with this probable damage may be referred to as the "earthquake risk cost". Increasing the design intensity of the structure reduces the probability of damage, but at an increased cost of construction. Therefore, an optimal design earthquake intensity can be determined by achieving an appropriate balance between the construction cost and the earthquake risk cost. This paper presents a new analytical approach to the determination of the economically optimal earthquake intensity or other design variables for structures.