Study on Linear and Nonlinear Dynamically P-delta Effects on Frame Structures under earthquake spectra, harmonic and stochastic excitations

In this paper the effect of axial load on dynamic behavior of a simple frame, subjected to harmonic, seismic and earthquake excitation is investigated. The equations of motion are considered for two types of small and large deformations. The method of multiple scales is applied to solve the differential equations of motion with harmonic loading and for small and large deformations. Then, the steady state response near one-to-one resonance condition is studied. The results show that the dynamic behavior of the frame under axial load is completely different in resonance and non-resonance cases. The equations of motion with earthquake loading is also considered and the effect of axial load in the frame behavior under the time history and the response spectrum of the model is studied. Although white noise as a stochastic loading is applied to the model and, the results are approximated using the method of stochastic differential equations so, the mean value and covariance are calculated and the effect of axial force on them is investigated.