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

在现有的钢框架结构设计体系中，设计人员进行了小位移分析，设计规范涵盖了几何非线性的影响。因此，设计规范是复杂和不全面的。对有效柱长度的规定就是一个典型的例子。在本研究中，对于未来基于非线性结构分析的设计体系，探讨了“必须进行什么样的非线性分析”或“设计规范必须规定什么”等问题。首先，在保证现有设计的安全性和经济性的前提下，总结出所需的非线性分析，得到线性化有限位移分析（LFDA）。研究了LFDA的设计方法。结果表明，该方法通过引入适当的面内问题有效初始缺陷，解决了分岔现象的一个问题。对于面外问题，发现基于LFDA的设计方法有许多困难需要解决，基于强度曲线的设计方法在现阶段似乎是可行的。然而，目前的设计方法在确定一般构件的有效柱长度时存在歧义。本文将有效长度解释为表征几何非线性程度的参数，提出了一种确定有效长度的新方法。有效长度由LFDA计算的附加弯矩计算得到。应用该方法进行设计，得到了合理的结果。最后，研究了平面外缺陷问题，分析了简单框架结构的三维性能。结果表明，基于LFDA的设计对缺陷的方向和次级构件的刚度敏感。指出了利用LFDA建立设计方法的未来研究方向。

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.