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

在抗震设计中，结构和结构构件的塑性变形起着重要的作用，但已知其量变化非常显著。在这一过程中，抗震设计与可靠性的概念是认真考虑。本项目的目的是（1）开发一种简单、系统的方法来估计钢建筑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。一个分析程序包括以下步骤：（1）选择可能的崩溃机制使用的Symplex方法，（2）估计塑性铰旋转通过求解刚度矩阵对应的崩溃机制的时刻，和（3）估计所获得的塑性铰旋转的变化通过应用FOSM方法。采用所提出的方法和蒙特-卡罗模拟方法对几种钢结构建筑框架的塑性铰转角变化进行了分析。结果发现，对于分配给构件塑性弯矩承载力的变异系数为0.1，极限荷载的变异系数约为0.03，而构件塑性转角的变异系数范围为0.3至0.7。研究结果表明，即使构件强度发生适度变化，构件塑性变形也会发生非常显著的变化，如果抗震设计形成考虑塑性变形的需求和能力，则必须以明确的方式引入较大的安全裕度。

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.