LARGE DEFLECTION ANALYSIS OF INELASTIC PLANE FRAMES By T. Y. Kam 1 ABSTRACT: A general method for the large deflection analysis of inelastic plane frames is presented. The large deflection analysis is based on the Eulerian formulation in which a member tangent stiffness matrix is constructed with reference to the current deformed configuration. The exact differential equation and the moment-thrust-curvature relations of a member subjected to large relative deflection are used for deriving the member tangent stiffness matrix. A member tangent stiffness matrix for W-sections of elasto-plastic material is constructed as an example and its application to the large deflection analysis of inelastic frames is demon- strated by several examples. A simple form of the member tangent stiffness matrix is deduced from the above exact formulation by utilizing the assumption of small member relative deflections. It is shown that the simple one can yield excellent results compared to those obtained by the exact formulation. Hence it is reasonable to adopt the assumption of small member relative deflections in the large deflection analysis of inelastic framed structures. INTRODUCTION The evaluation of accurate ultimate loads of structures is an important task in the structural design and reliability analysis processes. In order to find the accurate ultimate loads, one has to consider both material and geometrical nonlinearities in the structural analysis. Therefore the nonlin- ear analysis of framed structures has become a subject of research for many years. A considerable amount of research was devoted to the analysis of inelastic frames based on the assumption of small deflections of the frames (Alvarez and Birnstiel 1969; Harung and Miller 1973; Kam et al. 1983; Oran 1973; Saafan 1963; Vijakklane 1974). Some researchers inves- tigated the large deflections of elastic frames (Lee et al. 1968; Meek and Tan 1984; Oran and Kassimali 1976; Qashu and Dadeppo 1983; Turner et al. 1960). Recently, the large deflection analysis of inelastic frames has been successfully treated by some authors (Argyris et al. 1982; Backlund 1976; Bathe and Ozdemir 1975; Cichon 1984). For instance, Kassimali (1983) presented a method for the analysis of inelastic frames in which rigid body displacements of members can be arbitrarily large while relative member deflections are considered to be small and yielding is restricted to concentrated points at member ends. El-Zanaty and Murray (1983) utilized the incremental viriational principles together with the finite element method to analyze inelastic frames subjected to large deflections. Never- theless it has been pointed out that the development of an efficient and effective method for the large deflection analysis of inelastic structures is 'Prof. Mech. Engrg. Dept., National Chiao Tung Univ., Hsinchu, Taiwan, R.O.C Note. Discussion open until June 1, 1988. To extend the closing date one month, a written request must befiledwith the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on September 10, 1986. This paper is part of the Journal of Structural Engineering, Vol. 114, No. 1, January, 1988. ©ASCE, ISSN 0733-9445/88/0001-0184/$1.00 + $.15 per page. Paper No. 22139. 184 J. Struct. Eng. 1988.114:184-197. Downloaded from ascelibrary.org by National Chiao Tung University on 05/01/14. Copyright ASCE. For personal use only; all rights reserved.