Non linear seismic response of asymmetric buildings.

The study presented in this thesis is an attempt towards a better understanding of the coupled lateral-torsional response of buildings subject to seismic ground motion. Some of the problems identified in the past studies are thoroughly investigated and some new areas of study are explored. Some of these problems encountered in the literature include (a) the existence of several definitions of uncoupled torsional to lateral frequency ratio (b) an arbitrary selection of structural parameters in a parametric analysis resulting in a physically inadmissible structure and (c) the effect of nonlinearity. Because of the simplified models with either eccentricity in one direction or the ground motion applied in only one direction, the effects of a bi-directional loading have not been investigated in detail. These effects may include the relative differences in the amplitude or phase components of the individual accelerograms and their orientation with respect to the building. The phase properties of accelerograms are of particular interest and these have not received much attention in the past. Using analytical methods such as Chasle's[16] and Gerschgorin's[39] theorems, the equation of motion of a bi-eccentric system is derived and all of the existing problems regarding the definition of structural parameters and their bounds are studied in depth. To facilitate nonlinear parametric study, a paraboloid non-linear elastic stiffness model is proposed. Fourier spectral methods are used to study the frequency domain characteristics of the accelerogram pair. The difference in phase and amplitude of the component frequencies in each direction are studied for their effects on the response. For phase difference, cross-correlation function is used as a comparative statistical indicator. USA earthquake records obtained from US National Geophysical Data Centre are grouped into four soil types and the analysis is performed for each group in order to explore the soil-dependency of the aforementioned effects on the response. Computer programs are written in FORTRAN for both parametric and numerical model analyses. The latter can handle any number and orientation of columns with the assumed nonlinear stiffness properties. Newmark's and Runge-Kutta methods of numerical integration with adaptive step size control have been used to calculate parametric and the hysteretic responses of the system. The response to harmonic ground acceleration is used as a preliminary investigation into the response to actual accelerogram frequency components. The study has developed relationships for different definitions of the uncoupled torsional to lateral frequency ratio. Detailed derivation of the Equation of Motion has clarified the confusion that produced different definitions in the past studies. Graphical descriptions of the admissibility bounds on system parameters are produced. The variation in the response quantities is studied for a range of amplitude and phase contents of the applied ground acceleration. The difference in phase and amplitude in x and y ground accelerations have been found to affect the response quite significantly. More generally, the relationship of these differences to the torsional mode amplification has been observed. The effects of structural frequency and eccentricity parameters are also studied. Graphs showing the relationship between, the angle of incidence of the accelerogram with respect to the principal axis of the building, and the phase difference in the accelerogram pair, have been produced. The proposed analysis involving the bi-directional ground acceleration on a bi-eccentric system is an improvement on the current methods employed in design practice. Further work is, however, required before simplified design recommendations can be made and some proposals for future research are given at the end of this thesis