Modeling of higher-mode effects using an optimal multi-modal pushover analysis

An accurate optimal pushover analysis is developed to predict the higher-mode influence in multi degree of freedom (DOF) buildings. Performance levels are determined and seismic demands are calculated using two different ground acceleration records. The methodology is based on elastic structural dynamics theory and retains the simplicity of standard pushover procedures that rigorous time history analyses do not provide. A variant inertial load pattern is determined by updating the building's vibration properties at each stage of yielding. Each load pattern is derived using one mode shape at every yielding stage thereby capturing the higher-mode effects (HME). Using the energy under the building's capacity curve then enables a single optimal mode shape to be determined; this defines a representative single-DOF system (R-SDOF). Towards this end, an optimization algorithm is written to minimize the target displacement error between the pushover and nonlinear time-history analyses of a few buildings for a certain ground record. Optimal capacity and demand parameters are then determined and used to combine the individual mode shapes from each stage of yielding into the single optimal mode shape. This approach enables HME and phenomena such as HME and P-Δ effects to be captured through the optimal parameter identification. These same parameters are then applied in a pushover analysis of other buildings. The results are shown to compare favorably to a separate nonlinear time-history analysis.