Modeling of higher-mode effects in structural frames using a probabilistic dynamic pushover analysis

Under a dynamic load environment, traditional methods of quantifying inelastic responses typically rely on step-by-step procedures. With the current advent of various nonlinear static pushover techniques, however, the inelastic displacement level of a representative SDOF system can be found, and the target displacement of the MDOF structure can be eventually determined and the performance objective defined along with any local responses. This is accomplished through the gradual push of the structure in a displacement- controlled environment. The premise of the analysis has insofar been contingent on the system's independence of higher-mode effects while employing a single mode shape to represent the entire MDOF response. However, since the analysis is effective primarily in the first mode of vibration, it does not allow for a redistribution of inertial loads once a plastic hinge has formed, which thus limits the imposed demand on the structure. In the present work, a pushover procedure defined on fundamental structural dynamics theory is used to provide insight into the seismic demands as incurred through ground motion input. Pushing the MDOF system and charting the constitutive relationship through hinge developments, the model is able to adjust to the behavior of the structure as opposed to forcing the structure to behave according to the model; ultimately, the degree of accuracy hinges on the accountability of the higher mode effects. This approach utilizes several fundamental mode shapes in a probabilistic sense and provides the flexibility for inertial force redistribution through the updating of the dynamic characteristics of the structure at sequential hinge formations all leading towards the target displacement. The results of this modeling procedure have been shown to conform well to a nonlinear time history analysis.