INELASTIC ANALYSIS OF SEMIRIGID FRAMEWORKS
Y. Liu1, L. Xu and D. E. Grierson
Civil Engineering, University of Waterloo, Canada
This article presents an efficient method for inelastic analysis of semirigid planar steel frameworks. A compound element comprised of a plastic-hinge element and a semirigid connection element is located at member ends that may potentially undergo inelastic deformation. Nonlinear inelastic flexural behaviour is modeled by an empirical relation between moment and rotation for which the parameters are available from experimental results. A four-parameter model is employed to simulate the nonlinear moment-rotation behaviour of semirigid connections. The member stiffness matrix involving the compound element is expressed explicitly in terms of stiffness degradation factors that vary depending on the loading level. This permits direct account for the combined influence of inelastic and nonlinear connection behaviour on structure stiffness. A semirigid steel portal frame is analyzed to illustrate the proposed analysis method, and the results are compared with those obtained from experiments involving the same frame.
Keywords: semirigid connection, inelasticity, compound element
Many studies have been devoted to developing practical methods of nonlinear analysis accounting for both semirigid connections and member plastic behaviour (Ziemian et al 1992; Chen et al 1994; Yau et al 1994; Chen et al 1996). However, little work has been done to investigate the interaction between the behaviour of semirigid connections and that of member plasticity. This study focuses on such interaction using the concept of a compound element, which is shown in Figure 1 and explained in detail in the following.
Figure 1. Connection and inelasticity model at a joint
Figure 1(a) is a typical beam-to-column connection joint involving member plasticity. Typically, the connection is semirigid and possibly includes bolts, welds and angles. The member plastic zone forms at the beam end due to concentrated internal loads. To facilitate nonlinear analysis, Figure 1(a) 1 Corresponding author: Y27liu@uwaterloo. ca
M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 317-328. © 2006 Springer. Printed in the Netherlands.
may be replaced by the analytical model shown in Figure 1(b), where one of the two springs represents the plasticity formed at the member end while the other spring represents the semirigid connection.
A method of analysis has been recently developed by the authors to deal with geometric and material nonlinearities (Grierson et al 2005, Xu et al 2005). The goal of this article is to extend this method to account for semirigid connections using a so-called compound-element approach. At each stage of the analysis, the combined-stiffness degradation due to semirigid connection and member plasticity behaviour is determined, and the corresponding tangent stiffness matrix for the structure is formed. The process ends when the specified external loads are completely applied on the structure or the limit loading state is reached.