Stochastic and seismic design response of linear and nonlinear structures
New methods for calculating the stochastic and seismic design response of linear and nonlinear structures are presented.
For linear structures, two approaches are developed: (1) the modified mode displacement approach for classically as well as non-classically damped structures, and (2) the generalized force derivative approach for classically damped structures. Both techniques improve the calculation of the pseudostatic contribution of the truncated modes without including them in the analysis. In particular, the modified mode displacement approach is a useful tool for the calculation of seismic design responses affected by the contributions or higher modes. It properly considers the modal correlations as well as the correlation between retained and truncated modes. It is as fast as the mode acceleration method of structural dynamics and it only requires the commonly used ground response spectra employed by the classical mode displacement approach. On the other hand, the generalized force derivative approach requires the input to be defined in terms of its power spectral density function, but it improves even further the estimation of the missing mass effect due to the trucation of modes.
For nonlinear structures, the stochastic equivalent linearization technique is employed to develop response spectrum approaches for hysteretic shear buildings and for two dimensional frames with plastic hinges. For this purpose, a generalized modal analysis technique is successfully employed. The proposed response spectrum approaches require the input be defined in terms of the response spectrum of first order oscillators as well as in terms of the commonly used ground response spectra. For shear buildings, the work is extended to include the calculation of floor response spectra. A simulation study is performed to compare the results obtained by the proposed approach.