Cyclic Plastic Hinges with Degradation Effects for Frame Structures

Abstract

A model of cyclic plastic hinges in frame structures including degradation effects for stiffness and strength is developed. The model is formulated via potentials in terms of section forces. It consists of a yield surface, described in a generic format permitting representation of general convex shapes including corners, and a set of evolution equations based on an internal energy potential and a plastic flow potential. The form of these potentials is specified by five parameters for each generalized stress-strain component describing: yield level, ultimate stress capacity, elastic and elasto-plastic stiffness, and a shape parameter. The model permits gradual changes in stiffness and strength parameters via damage-based degradation. The degradation effects are introduced in the energy and flow potentials and result in additional evolution equations for the corresponding strength and stiffness parameters. The cyclic plastic hinges are introduced into a six-component equilibrium-based beam element, using additive element and hinge flexibilities. When converted to stiffness format the plastic hinges are incorporated into the element stiffness matrix. The cyclic plastic hinge model has been implemented in a computer program and used for analysis of some simple structures illustrating the characteristic features of the cyclic response and the accuracy of the proposed model.

Minkowski plasticity in 3D frames: Decoupled construction of the cross‐section yield surface and efficient stress update strategy

“…This is the reason why this strategy is not commonly employed in practical contexts. The second approach formulates the cross‐section yield criterion in terms of generalized stresses, that is, axial force and bending moments . This is, therefore, more useful from an engineering point of view, being theoretically able to provide synthetic results in an extremely short time, and also making it possible to afford parametric studies on the design parameters.…”

“…They consist of sophisticated methodologies to obtain the cross‐section strength domains accounting for the limit in the maximum strain, different stress‐strain relationships, and prestressed conditions . Most of these approaches are, however, limited to the strength check of local sections, whereas a complete nonlinear analysis is carried out only in a few works as, for instance, in the work of Tidemann and Krenk …”

“…The geometric nonlinearity under large displacements can be accounted for by means of corotational formulations . The geometric interpretation of the Minkowski sum together with the proposed analysis procedures opens, however, new attractive possibilities to account for the strength decrease due to damage or fire exposition without the need to reconstruct the yield surface. The proposed approach, in fact, allows us to obtain the new yield surface by simply contracting the ellipsoid of each cross‐section region accounting for its strength reduction.…”

“…The second approach formulates the cross-section yield criterion in terms of generalized stresses, that is, axial force and bending moments. 2,[8][9][10] This is, therefore, more useful from an engineering point of view, being theoretically able to provide synthetic results in an extremely short time, and also making it possible to afford parametric studies on the design parameters. However, the accurate and efficient evaluation of the yield surfaces of steel or RC sections under axial force and biaxial bending as well as their use in elastoplastic analysis is not an easily resolved problem.…”

“…18,19 Most of these approaches are, however, limited to the strength check of local sections, whereas a complete nonlinear analysis is carried out only in a few works as, for instance, in the work of Tidemann and Krenk. 9 For the steel and confined RC section, however, as proposed in many building standards, 20,21 the strain limit is sufficiently large to allow an alternative approach based on the classical plasticity theory. 22 In particular, an accurate approach for the yield surface construction has been recently proposed in the works of Bleyer and De Buhan 2 and Leonetti et al 23 It consists in evaluating a point cloud of generalized yield stresses by assigning the corresponding collapse mechanisms, that is, position and orientation of the neutral axis.…”