Mean maximum values of non-normal distributions for different time periods

摘要

To perform the reliability analysis for structures, it is necessary to determine the statistical parameters of loads and resistance. However, these statistical parameters are time-dependent variables; therefore, Mean Maximum Value (MMV) should be properly deliberated. If distributions of the load and resistance behave as normal distributions, by taking advantage of normal probability paper, MMV can be estimated using extrapolation of the Cumulative Distribution Function (CDF). However, there are many phenomena in nature in which the CDFs are not normally distributed. Furthermore, the upper/bottom tails of the distributions of the load and resistance do not necessarily behave as normal distributions. Therefore, in order to determine the statistical parameters for non-normal distribution, there is a need to propose a different methodology to analytically compute MMV for non-normal distributions. The main contribution of this paper is to derive a mathematical formula for elaboration of the time-dependent MMV for non-normal distributions. Accordingly, for engineering application, this paper introduces MMV factor, f_(mm), which represents the required safety margin for MMV at the intended time period for load/resistance. Eventually, as a practical example standpoint in structural engineering domain, MMV and f_(mm) for weigh in motion data are determined.