地震作用下钢框架最大弹塑性层间变形的概率统计特性

Probability distribution of the elastoplastic maximum story drift of steel frames subject to earthquake load

近年来基于功能的结构抗震设计思想逐渐被世界各国地震工程界所接受,与现行抗震规范相比,它在遵循"投资-效益"准则的基础上,更加注重结构在进入弹塑性状态后的表现,并且采用具体的量化指标(结构最大层间变形)来衡量。由于结构抗震设计中存在着大量不确定性,结构可靠度分析成为结构设计中的一个重要工具。本文以钢框架结构为例,考虑了结构抗震设计中的各种不确定性,包括地震作用、结构构件面积、材料弹性模量、恒荷载和活荷载的随机性,采用概率统计理论中的K-S检验法,对最大弹塑性层间变形的概率统计特性进行了分析。结果表明,在给定烈度的地震作用下钢框架结构的最大弹塑性层间变形,在其均值较小时服从极值 型分布,在均值较大时服从极值 型分布。以上结论可为研究钢结构弹塑性变形可靠度的近似分析提供参考。

The concept of performance based seismic design is gradually accepted by the earthquake engineering profession recently. Compared with the current seismic design codes, performance based seismic design takes cost\|effectiveness criterion as its important principle, and pays more attention to the structural performance at the elastoplastic stage, which is always evaluated by the maximum story drift. There are many uncertainties in structural seismic design. Engineers must deal with the uncertainties in the structural design process, and structural reliability analysis is the useful tool to help the designers realize such a purpose. Therefore, the reliability analysis of the structural performances usually expressed by the elastoplastic deformation is a major procedure in performance based seismic design. However, structural reliability analysis is usually a procedure with costly computation because the limit state function is the highly nonlinear implicit function of the basic design variables, especially for the complex largescale structures with dynamic and nonlinear analysis. Thus to develop efficient approximate approaches of reliability analysis with the accepted accuracy is an important task and challenge to the researchers and engineers, and the study on probability distribution of the structural elastoplastic deformation is helpful to develop such an approximate method. The present paper studies the probability distribution of the maximum elastoplastic story drift of steel frames subject to earthquake load with the KS test method, considering the uncertainties of earthquake action, structural member area, material elastic module, dead load and live load. The results show that the probability distribution of the maximum elastoplastic story drift of steel frames is related to the mean value of the maximum elastoplastic story drift. It follows the probability distribution of extreme value type I when the mean value is small, and extreme value type II when the mean value is relatively large.