The nonlinear three-dimensional response of structures to earthquake excitation

The three-dimensional response of structures, comprised of members possessing nonlinear constitutive relationships, subjected to earthquake excitation is investigated. The input involves consideration of the simultaneous horizontal translation of the structure in two mutually perpendicular directions in addition to torsional behavior; vertical ground motion has not been included. Material nonlinearities are represented in a simplified fashion by the use of a bilinear moment-rotation relationship, subject to the kinematic hardening rule, at each member end. Relevant concepts of structural theory are reviewed and expressed in a format allowing for the use of matrix algebra. A general form of the member stiffness matrix is presented, and a method of formulating and subsequently statically condensing the structure stiffness matrix is also presented. The interaction of axial loads with the nonlinear material behavior is included. For columns subjected to bending about two principal axes, the effect of including biaxial interaction effects on the yield surface is considered. A method of calculating the unbalanced forces resulting from nonlinear behavior is outlined. An energy balance is established whereby the energy input by the earthquake into the structure is accounted for by the various mechanisms with which the structure is able to dissipate or store this input energy. The importance of analyzing the variation of the various energy forms is stressed. The theory developed is applied to two structural examples. The problems encountered in attempting to apply this theory to various models of a structure intended to represent a typical midsized office building are discussed. This structure has a dual component structural system in which an eccentric shear core is designed to resist the horizontal loads and an exterior framing system is designed to resist vertical loads and to act as a second line of defense with respect to horizontal loads. The results obtained from an earthquake analysis of a structure, comprised of exterior five storey frames, are presented. Specific aspects of these results, such as the amount of energy dissipated by various mechanisms, are analyzed in detail. The effect of assumptions made concerning the structural response are discussed and suggestions for future developments in this field of analysis, which will be aided by advancements made in computer technology, are also given.Applied Science, Faculty ofCivil Engineering, Department ofGraduat