Investigation of nonlinear seismic response, dynamic instability and dynamic buckling for column-supported structures

In this thesis, a simplified model is analyzed for column-supported structures in which both material and geometric nonlinearities can be considered. To investigate material nonlinearity, three widely-used hysteretic models are considered: bilinear, Clough's and Takeda's models. The differential equations of motion are derived for this simplified model subjected to seismic multi-component excitations, which are solved by using the fourth-order Runge-Kutta method.; The purpose of this thesis is to study three different failure mechanisms for column-supported structures, (i) 'Dynamic Instability'; (ii) 'Elastic Dynamic Buckling of Columns'; and (iii) 'Inelastic Dynamic Buckling of Columns'. Two intuitive criteria for dynamic instability are proposed for column-supported structures: pseudo-dynamic moment and dynamic energy approaches. The Euler-Bernoulli-Beam model has been used for dynamic buckling analysis of simply-supported uniform columns, excited by arbitrary end axial forces, end moments, and support motions. The end axial forces and end moments are derived via numerical nonlinear response analysis of column-supported structures. The support motions are represented by given earthquake excitation.; Criteria for dynamic buckling failure are established on the basis of different Euler buckling patterns. Since we consider the second-order effect of column transverse vibration on its longitudinal vibration, the differential equations of motion are highly nonlinear and cannot be solved analytically. Galerkin variational approach is employed to solve them numerically. Then end axial force and moment responses are calculated to enable dynamic buckling analysis for uniform columns.; Numerical examples show that dynamic instability failure times increase with increasing length of column, stiffness ratio, yield level of structure, but decrease with increasing structural damping ratio. Both elastic and inelastic dynamic bucklings of column can occur locally before the dynamic instability of the whole structure. As column slenderness ratios increase, local dynamic buckling of columns becomes a more dominant factor than dynamic instability. Dynamic buckling times of columns decrease, but the time intervals between column buckling and structural instability increase gradually with increasing column slenderness ratio.