Plastic Deformation and its Variation Demanded of Structures and Structural Members in Steel Building

在抗震设计中，结构和构件的塑性变形起着重要的作用，但其数量变化非常大。在这一过程中，结合可靠度概念的抗震设计是需要认真考虑的问题。该项目的目的是：(1)开发一种简单、系统的方法来估计钢结构及其构件所需塑性变形的变化程度；(2)为抗震设计中应考虑的变化提供指导。开发了一个由以下步骤组成的分析程序；(1)使用Symplex方法选择可能的崩溃机构；(2)通过求解崩溃机构瞬间对应的刚度矩阵来估计塑性铰的旋转；(3)应用FOSM方法估计得到的塑性铰旋转的变化。采用本文提出的方法和蒙特卡罗仿真方法，对若干钢结构框架的塑性铰旋转变化进行了分析。研究发现，当构件塑性弯矩承载力的变异系数为0.1时，其极限荷载的变异系数约为0.03，而构件塑性转动的变异系数则在0.3至0.7之间。研究结果表明，即使构件强度变化适度，构件塑性变形也会发生非常大的变化，如果在需求和容量方面以明确的方式考虑塑性变形，则必须引入较大的安全余量。

In seismic design, plastic deformations of structures and structural members play an important role, but the quantities are known to vary very significantly. In this course, seismic design incorporated with the reliability concept is of serious consideration. The objective of this project is (1) to develop a simple, systematic method to estimate the degree of variation of plastic deformations demanded of steel building structures and their elements and (2) to provide a guideline as to the variation to be considered in seismic design. A analytic procedure consisting of the following steps was developed ; (1) to select likely collapse mechanisms by use of the Symplex method, (2) to estimate plastic hinge rotations by solving the stiffness matrix corresponding to the instant of a collapse mechanism, and (3) to estimate the variation of the obtained plastic hinge rotations by the application of the FOSM method. Several steel building frames were analyzed for the variation of their plastic hinge rotations, where the proposed method and Monte-Carlo simulation were employed. It was found that, for an coefficient of variation of 0.1 assigned for the member plastic moment capacities, the coefficient of variation of the ultimate load was about 0.03, whereas the coefficient of variation of the member plastic rotations ranged from 0.3 to as much as 0.7. The finding indicates that the member plastic deformation can vary very significantly even for a moderate variation of member strength and that a large margin of safety has to be introduced if seismic design is formed to consider the plastic deformation, in terms of both the demand and capacity, in an explicit manner.