Some aspects of energy methods for the inelastic seismic response of ductile SDOF structures

This paper explores some aspect of energy demands for single-degree-of-freedom (SDOF) systems. Energy response time histories for simple pulses or sine-wave ground excitations are constructed and the behaviour of each contributing factor to the energy balance is studied. Examples are used to illustrate the fundamental behaviour of the kinetic energy, strain energy, energy dissipated through normal damping, energy dissipated through permanent deformations, and total input energy, the latter always being equal to the sum of the others throughout the dynamic response. It is found that: firstly, energy methods produce good indicators of the nonlinear inelastic seismic structural performance; secondly, the absolute energy method has some practical shortcomings, particularly regarding the definition of input and kinetic energies; thirdly, the relative energy method has a closer relationship to the parameters of engineering interest; and finally, if only hysteretic energy is of interest, both the absolute and relative energy methods can be used, unless normalization by input energy is sought.