Beam‐column elements in which plastic hinges may form are commonly used for elastic‐plastic analysis of frames. The concept of a zero‐length plastic hinge (lumped plasticity) is a mathematical abstraction, because it implies infinite strains. Nevertheless, the concept is convenient computationally, and can be sufficiently accurate for many practical applications. For simple beams, plastic hinges can be introduced easily into a mathematical model. For 3D beam‐columns, however, the concept of a “generalized” hinge is needed, accounting for interaction among axial, torsional and biaxial bending effects. A theory and computational procedure based on plasticity concepts are presented. Numerical examples indicate how the element might be used, and show that results in agreement with more elaborate models can be obtained. Because the lumped plasticity assumption is not necessarily accurate, caution is advised in use of the element.

3D Beam‐Column Element with Generalized Plastic Hinges

Steel plate shear walls have been used in buildings in North America and Japan. Until recently, the design practice has been to limit the strength of the wall to the buckling strength of the plate. The post-buckling strength of thin plates subjected to shear has been recognized for more than 60 years, since it was outlined by Wagner in the early 1930s. Tests of a quarter and one third scale specimens of thin steel plate shear walls under cyclic loading were performed; the tests are described and the results are summarized. An analytical model to determine the behavior of thin steel plate shear walls was developed and is given. The model is capable of depicting the behavior of walls with plates welded or bolted to the surrounding beams and columns of the building frame. Comparisons between the analytical and experimental results are made.

Thin steel plate shear walls behavior and analysis

Finite element models of reinforced concrete beam columns often fail to behave in a stable manner near the point of maximum resistance. Simple numerical examples presented indicate that the conventional displacement formulation when used at the section or member level is unable to establish solutions associated with softening behavior. Thus, such analysis models are often limited in their applicability or necessitate the use of unrealistic material laws. A mixed finite-element scheme is proposed herein that exhibits stable numerical behavior even when critical regions become ill-conditioned. It is demonstrated that enforcing equilibrium within the member during state determination provides the necessary constraint to obtain a stable solution. Examples are presented to demonstrate the reliability and realism of this approach for members subjected to generalized excitations even where severe deformation softening occurs.

Analysis of Reinforced Concrete Beam-Columns under Uniaxial Excitation

A formulation for modeling links in eccentrically braced steel frames (EBFs) subjected to random inelastic cyclic loading is presented. The formulation is plasticitybased, and includes shear and fl...

Inelastic Link Element for EBF Seismic Analysis

The tapered-plate energy absorber (TPEA) has been accepted as an effective energy dissipator to absorb earthquake-induced energy and improve seismic resistance of a structure. Previous analytical studies associated with the TPEA device were primarily based on simple methods to predict its behavior. In this study, a more complex model, based on plasticity theory, and a finite-element formulation for the TPEA device are developed. The proposed model predicts effectively the device behavior under wind and earthquake loadings. Analytical results obtained by the proposed model are in good agreement with the experimental observations from the tests of the TPEA devices. Furthermore, numerical simulations of a 10-story building equipped with TPEA devices and subjected to earthquake ground motions show that the energy-dissipation capacity of the structure increases, and that its responses to earthquake loadings are significantly reduced when the TPEA devices are employed.

TPEA Device as Seismic Damper for High-Rise Buildings

Two basic procedures may be used for modeling the inelastic behavior of beams and columns. In the "fiber" type of model, the element cross section is divided into a number of small areas (fibers), and the behavior is governed by the stress-strain characteristics of the fiber material. Detailed and accurate results can be obtained, but the computational cost is high. In the "section" type of model, inelastic behavior is defined for the cross section as a whole, not for individual fibers. Actiondeformation relationships for the cross section must be devised, considering the stress-strain characteristics of the cross section material. Models of this type are less accurate than fiber models, but more efficient computationally. The purpose of the research has been to explore in depth the theory and computational techniques for the "section" type of model. In developing the model, inelastic interaction between bending moments, torque and axial force has been considered by means of yield interaction surfaces and a flow-rule type of plasticity theory. Emphasis has been placed on the ability to consider arbitrary loading-unloading cycles of the type likely to be induced by an earthquake. The study has considered both stable hysteretic action-deformation characteristics and relationships involving stiffness degradation. Three separate inelastic beam-column elements, which share similar concepts, have been developed, as follows. (a) An element with distributed plasticity and nondegrading stiffness, for the computer programs ANSR and WIPS. This element is most suitable for modeling inelastic behavior in piping systems. (b) An element with lumped plasticity and nondegrading stiffness, for the ANSR program. This element is most suitable for modeling inelastic steel beams and columns in buildings. (c) An element with lumped plasticity and degrading stiffness, for the ANSR program. This element is most suitable for modeling inelastic reinforced concrete beams and columns in buildings. The theory and computational procedure are described in detail for each element. Five example structures have been analyzed to test the elements and to assess their acceptability for different applications. The examples include a steel tubular beam-column; a steel tubular braced frame; a reinforced concrete cantilever beam under biaxial bending; a reinforced concrete frame subjected to earthquake excitation; and a pipe undergoing large displacements following pipe rupture.

P. F. S. Chen

Papers

Generalized plastic hinge concepts for 3D beam-column elements