Generalized plastic hinge concepts for 3D beam-column elements

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.