Optimum Design for Infrequent Disturbances

Sporadic disturbances such as earthquakes and tornadoes are idealized as renewal processes. Uncertainties are classified according to their time correlation into disturbance, structure, and analyst random variables. Only the latter admit Bayesian updating. In this light a result due to Hasofer is revised. Structures are idealized as having a single degree-of-freedom and as having potential limit states in cascade, i.e., limit states can be entered only in a fixed order. Equivalent second-moment (beta method) criteria are developed. Treatment is then specialized to earthquake resistant design, in which disturbances are idealized as generalized Poisson processes. Explicit optimal-design formulas are given for this case. Appendices include novel second-moment approximate treatment of uncertainties not requiring calculation of derivatives. Those variables whose distributions are evidently close to Gaussian or lognormal are given a treatment that is exact for these types of distribution.