EVALUATION OF STRUCTURAL PERFORMANCE BASED ON AN ENERGY BALANCE APPROACH
Kevin K. Wong, Steven L. McCabe
An analytical method is developed to investigate the potential energy of fully nonlinear framed structures and other energy characteristics due to earthquake ground motions. Since the potential energy relates to the stiffness of the structure, it consists of three components in a fully nonlinear system: (1) Strain energy representing the stored energy associated with the linear elastic portion of the structural response, which can be recovered after the earthquake; (2) Higher-order energy associated with the geometric nonlinear effect of the overall structural response, which is derived from the nonlinear stiffness matrix and can also be recovered if the axial load is removed; and (3) Plastic energy representing the energy dissipated by inelastic deformation of the structure, which cannot be recovered after the earthquake. The proposed analytical method uses a change in stiffness for handling the geometric nonlinearity and a change in displacement for handling material nonlinearity before solving the nist-equations of motion, thereby separating the effects of geometric nonlinearity and material nonlinearity when computing the stiffness force. This also leads directly to the integral representations of each energy form. A four-story moment-resisting framed structure is used as a numerical example to demonstrate the feasibility of the proposed analytical method in evaluating the energy response and the transfer among different energy forms throughout the nonlinear response history analysis.