Design method of frame structures with effective length based on eigen value analysis

在现行的钢框架结构设计体系中，设计人员进行小位移分析，设计规范中考虑了几何非线性的影响。因此，设计规范是复杂和不全面的。对柱有效长度的规定是一个典型的例子。在本研究中，对于未来基于非线性结构分析的设计体系，诸如“必须进行何种非线性分析？或“设计规范必须规定什么？”被调查。首先，在保证设计安全性和经济性的前提下，将非线性分析转化为线性有限位移分析。研究了LFDA的设计方法。结果表明，对于面内问题，通过引入适当的有效初始缺陷，解决了分叉问题;对于面外问题，基于LFDA的设计方法存在诸多困难，基于强度曲线的设计方法在现阶段是可行的。然而，目前的设计方法在确定一般构件的有效柱长时存在模糊性。本文将有效长度解释为表征几何非线性程度的参数，并提出了一种确定有效长度的新方法。根据LFDA计算的附加弯矩计算有效长度。最后，对平面外问题的缺陷进行了分析，并对简单框架结构的三维性能进行了分析。结果表明，基于LFDA的设计对缺陷的方向和次构件的刚度敏感。指出了今后的研究方向，即建立基于LFDA的设计方法。

In the present design system for steel frame structures, the designers carry out the small displacement analysis and the design code covers the effect of geometrical nonlinearity. Hence the design code is complicated and incomprehensive. The provision on the effective column length is a typical example.In the present study, for the future design system based on nonlinear structural analyses, matters such as "what kinds of nonlinear analysis must be carried out?" or "what the design code must prescribe?" are investigated. Firstly, with a precondition that the safety and economy in the present design are maintained, the required nonlinear analysis is concluded to bo the linearized finite displacement analysis (LFDA). The design method with LFDA is investigated. It is shown that one of the problem in this method for bifurcation phenomena is solved by introducing appropriate effective initial imperfections for in-plane problem.For out-of-plane problem the design method based on LFDA is found to have numbers of difficulties to be cleared and the desing method based on the use of strength curve seems to be practical at this stage. However, the present design method includes ambiguity in the determination of effective column length of a general member. Here, the effective length is interpreted as a parameter shich represents the extent of the reometrical nonlinearity, and a new method to determine the effective length is proposed. The effective length is calculated from additional bending moment calculated by LFDA. The design with this method is shown to provide reasonable results.Finally, imperfections for out-of-plane problems are investigated, and 3-d befaviors of simple frame structures are analyzed. It is shown that the design based on LFDA is sensitive to the direction of the imperfections and the stiffness of the secondary members. The direction of the future study to establish design method with LFDA is pointed out.