Three-dimensional inelastic dynamic structural analysis of frame systems

The first objective of this dissertation is the development of a three-dimensional hysteretic model capable of representing the behavior of typical frame members. A macro-modeling approach is adopted, the essence of which is to define the constitutive relations at a control section directly in terms of stress resultants and strains. The derivation relies on the premise that the underlying material behavior can be represented by a parallel-plasticity model. The connection between the fundamental stress-strain law and the section stress resultant-strain relations is rationalized from that perspective. The model is designed as a constitutive relation with internal variables. The evolution equations are postulated using non-associated flow rule with the ultimate-yield locus of the section serving as a plastic potential function. The latter is represented by an axial force-biaxial moment interaction surface in hysteretic force space. A new parametric equation of a general interaction surface is introduced to provide a versatile tool for modeling triaxial effects in frame members. It is also demonstrated that several popular one- and two-dimensional hysteretic models can be regarded as particular cases of the proposed model. The loading/unloading criteria of the two-dimensional versions are shown inadequate and a new loading/unloading criterion is proposed.; The constitutive model is then used to define the behavior at the control sections of a nonlinear beam-column element. The principle of virtual forces is employed to derive the nodal force-displacement relationship embodied by the flexibility matrix. This approach exploits the internal determinancy of frame members under any boundary conditions---a quality allowing exact interpolation of the element force field from the nodal actions. The element is developed in the setting of a stiffness-based incremental solution of the governing equations. The specific contribution is the introduction of a novel aspect in the state determination procedure. The main idea is to merge the equilibrium unbalances at the control sections from the current global iteration with the incremental internal forces in the next one.; Another goal of the dissertation is the conceptual design of an algorithm for solving finite-element problems in state space. The key concept is to solve the structure equations of motion and the element constitutive relations simultaneously in time. Specific advances are made toward systematizing the task of defining the state of a general element and postulating its evolution. Guidelines are provided for selection of state variables for various combinations of formulation types and constitutive models. The concepts involved in the creation of a new element are illustrated through the definition of an inelastic frame member model, operating in the setting of the state-space method.; The final chapter of this dissertation presents analytical studies of a typical long multi-span highway bridge for spatially varying ground motion of the 1994 Northridge earthquake. The primary objective of the study is to qualify and quantify the effects of the non-synchronous excitation. The numerous cases involved in the study are analyzed using the modeling and analysis tools of the computational platform IDARC-BRIDGE. Based on these results, the relative importance of factors that have been shown to affect the behavior of highway bridges is weighed and the dominant influence on the response is identified.