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Improved nonlinear plastic hinge analysis of space frame . Richard Liew a,*, H. Chen a, . Shanmugam a, . Chen ba Department of Civil Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singaporeb School of Civil Engineering, Purdue University, West Lafayette, IN 47907, USAReceived 5 January 1999; received in revised form 17 August 1999; accepted 25 August 1999AbstractThis paper is concerned with second-order plastic hinge analysis of three-dimensional frame structures. The beam–column formulationis based on the use of stability interpolation functions for the transverse displacements, and considers the elastic couplingeffects between axial, flexural and torsional displacements. The developed computer program can be used to predict accurately theelastic flexural buckling load of columns and frames by modelling each physical member as one element. It can also be used topredict the elastic buckling loads associated with axial-torsional and lateral-torsional instabilities, which are essential for predictingthe nonlinear behaviour of space frame structures. The member bowing effect and initial out-of-straightness are also considered sothat the nonlinear spatial behaviour of structures can be captured with fewer elements per member. Material nonlinearity is modelledby using the concentrated plastic hinge approach. Plastic hinge between the member ends is allowed to occur. Numerical examplesincluding both geometric and material nonlinearities are used to demonstrate the robustness, accuracy and efficiency of the proposedanalytical method and computer program. Ó 2000 Elsevier Science Ltd. All rights : Advanced analysis; Buckling; Nonlinear analysis; Plastic hinges; Space frames; Instability1. IntroductionTwo-dimensional (2-D) plastic hinge analysis of planeframes composed of members with compact section,fully braced out-of-plane, has been the subject for investigationin recent years. The theory for advanced inelasticanalysis of rigid and semi-rigid 2-D frames has beenwell developed and verified by tests [1,2]. These analysismethods fulfil the requirements for the prediction ofmember strength and stability, with some constraints,satisfying the conventional column and beam–columndesign limit-state checks. Although there have beenmuch work on the plastic hinge analysis of 3-D framestructures, the issues related to different theoretical andnumerical formulations and their accuracy and efficiencyin solving large frameworks are not addressed well. Theresearch presented in this paper is an extension ofadvanced analysis for 2-D frames [2] to 3-D frames [3–5], reflecting the current trend towards the rationalisationof advanced analysis procedures.* Corresponding改进非线性塑性铰空间框架结构的分析摘要：这份研究报告表明三维的框架结构与二维逻辑性塑性铰的关联，梁柱公式化的表述并嵌入横断面移动为基准，并考虑轴力、弯曲和扭力的移位之间的关系。发达的计算机程序作出通过每个物质成分作为一个基本部件做模型的塔器和框架可弯曲的负载量，它也能预报可弯曲负载量与轴向扭力和横向扭力的不稳定性的关联，这对预报非线性空间结构的作用是必不可少的，以便非线性空间结构的性能和部分成分一些原理能被输入计算机。重要的非线性通过使用浓缩的塑性铰方式被制作模型，塑性铰和成分末端是容许存在。数值的例子包括集合学和重要的非线性，两者习惯于证明目的的分析方法和电脑程序的稳定性，精确性。

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