SPREAD OF PLASTICITY: AN ADAPTIVE GRADUAL PLASTIC-HINGE. APPROACH FOR STEEL FRAMES
Department of Civil Engineering, Lakehead University, Thunder Bay, Ontario, Cnada P7B 5E1
E-mail: ygong@lakeheadu. ca
This paper presents a new plastic-hinge method for inelastic analysis of steel frames. The proposed plastic-hinge model employed two parameters in the modeling. The first parameter involves mimicking the spread of plasticity through a section depth, while the second incorporates the spread of plasticity along a member length. Procedures to determine the key parameters are developed using moment-curvature-thrust relationship for steel beam-columns. The proposed analysis method is especially advantageous when modeling the spread of plasticity along a member length using various discretization schemes. Two numerical examples are performed to demonstrate the accuracy and simplicity of the method.
Keywords: steel frames, nonlinear analysis, plasticity, plastic-hinge, beam-columns Introduction
Considerable studies have been undertaken on the inelastic analysis of steel frames in recent years (Chen and Toma 1994, Xu et al. 2005). The inelastic analysis methods are generally classified into two types: the distributed plasticity method and the plastic-hinge method. The distributed plasticity method discretizes frame members both along their length and through their cross section into many elements. The spread of plasticity is traced by the sequential yielding of the elements. This method is usually adopted to create benchmark solutions, as it is too computationally intensive and not suitable for practical design purposes. On the contrary, the plastic-hinge method usually involves using single or multiple elements to model a frame member, thus making it more efficient and the preferred method in engineering practice. The plastic-hinge method assumes that inelastic deformations are concentrated at plastic hinges at the end of elastic elements. The early studies used an elastic-plastic – hinge model, where the relationship between moment and curvature is linear up to the full plastic – moment of a section, after which the section becomes a perfect hinge. Though this approach is easy to implement, it often overestimates the ultimate strength of structural systems. More recently, refined – and quasi-plastic-hinge approaches (Liew et al. 1993, Attalla et al. 1994) with two-surface yielding criteria were proposed to account for the gradual plastification within steel members. Often, a model was constructed to simulate the gradual softening of plastic-hinges whose force point falls within the two yielding surfaces (Chen and Chan 1995, Hasan et al. 2002, Xu et al. 2005, Xu and Liu 2005).
This study proposes a new gradual plastic-hinge model for the inelastic analysis of planar steel frames. The analysis approach belongs to the domain of matrix displacement method. The plastic – hinge model is capable of mimicking the spread of plasticity both through the depth of a section and along the length of an element. The moment gradient of a frame member is directly taken into account in the plastic-hinge model. The model is unique and applicable to a general steel beam-column.
In this study, it is assumed that the cross sections are doubly symmetric and the stress-strain relation for steel material is elastic-perfectly-plastic. Only moment yielding is considered, while shear and axial yielding are ignored. Local plate, torsional, and lateral-torsional buckling are not considered.