On the computation of seismic energy in inelastic structures

The explicit computation of energy balance for structures subjected to seismic excitation is useful to assess the accuracy with which dynamic equilibrium is achieved in each time-step. Examples on the use of the energy balance concept are presented in the first part of this paper for simple inelastic structures excited by various ground motions. It is shown how the energy approach can guide the designer in appreciating the nonlinear behaviour of the structure, the hierarchy of mechanisms that occur in time, and the ductility requirements of the various components. This was achieved using an unconditionally stable time marching algorithm with no algorithmic damping. A parametric study is then presented on the influence of algorithmic damping on seismic energy response of multi-degree-of-freedom structures. Finally, the Newmark-Beta method, with and without algorithmic damping, and the Alpha method are used in comparative analyses to evaluate the response of bilinear hysteresis models of multi-degree-of-freedom structures.