Nonlinear dynamic analysis of frames with plastic hinges at arbitrary locations

Abstract

This paper presents a method for nonlinear dynamic analysis of frames subjected to distributed loads, which is based on the semi-rigid technique and moving node strategy. The plastic hinge is modelled as a pseudo-semi-rigid connection with nonlinear hysteretic moment-curvature characteristics at element ends. The stiffness matrix with material and geometric nonlinearities is expressed as a sum of products of the standard and geometric stiffness matrices with their corresponding correction matrices based on the plasticity-factors developed from the section fl exural stiffness at the plastic hinge locations. Each beam member is modelled by two elements. The moving node strategy is applied to the intermediate node to track the exact location of any intermediate plastic hinge that may be formed. Equilibrium iterations and geometry updating are carried out in every time step. Stiffness degradation is adopted to describe the deterioration of plastic hinges, and the effects of various parameters in the degradation model are evaluated. Examples are used to illustrate the applicability and excellent performance of the proposed method. practical design, nonlinear dynamic analysis is still essential, especially to those structures that are irregular and those of which the higher mode effects cannot be ignored. Besides, the strong-motion peculiarity is also a problem that the pushover analysis needs to overcome (Elnashai, 2002). Therefore, dynamic analysis is still important to frames with nonlinearities.Under lateral loading, the frame members subjected to distributed load may have plastic hinges formed at intermediate locations besides the member ends. To capture the behaviour of the intermediate plastic hinges, an effi cient method for elasto-plastic large defl ection analysis of steel frames using an element with plastic hinges at mid-span and two ends was proposed (Chen and Chan, 1995). As the intermediate plastic hinges can only be formed at mid-span, the results obtained are subject to certain errors. Later, the moving node strategy was presented for the elasto-plastic analysis of frames subjected to loads including linearly varying distributed load (Wong, 1996). In addition, certain applications of the moving node method in the second-order inelastic analysis of two-and three-dimensional steel frames were reported (Kim et al., 2004;Kim and Choi, 2005). However, the above research on the intermediate plastic hinge was only for the static analysis of frames. Such plastic hinges are often formed when the frame is subjected to strong seismic excitations, and therefore, the corresponding dynamic problem warrants further study.The material and geometric nonlinearities in beam-column elements may be simulated by either the plastic hinge element or the fi bre element. Although the fi bre element model can handle the residual stresses and better simulate the yielding process, it is rather computation intensive. On the other hand, the plastic hinge element model can simulate nonlinearities well and it is computationally effi c...

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Behaviour of uni-axially loaded concrete-filled-steel-tube columns confined by external rings

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