Accuracy of expressing the effects of hysteretic energy in terms of equivalent viscous damping according to ATC 40 and FEMA 440

Abstract A numerical study is carried out to evaluate the precision of expressing the dissipated energy by hysteretic behavior of the material (HBM) in terms of viscous damping (VD), as specified in the Capacity Spectrum Method (CSM)(ATC 40, FEMA 440) and in modal seismic analysis (MSA), by using nonlinear time history analysis (NTHA). Initially, the equivalent viscous damping (ζE1) is estimated according to the CSM. Then, by using NTHA, the reductions of several response parameters produced by HBM and VD are calculated. Based on these results, the equivalent viscous damping (ζE2) is calculated. It is shown that the values of ζE1 significantly vary with the strong motion without showing any trend; the range of variation goes from 5% to 18% tending to decrease as the height of the building increases. Results of NTHA indicate that the maximum and minimum reductions of the elastic responses produced by HBM occur for interstory shears (IS) and axial loads; they can be up to 330% and 79%, respectively, greater than the inelastic ones. The implication of this is that seismic analysis simplified procedures, in which elastic interstory shears and forces acting on members are reduced by the same amount, can lead to non-conservative designs. The maximum reductions of the elastic responses produced by VD are larger for axial loads and are quite similar for bending moments, displacements, and IS. In seismic codes the dissipated energy produced by HBM is usually expressed in terms of a fixed amount of viscous damping (5%). Results of NTHA indicate that this practice is appropriate for interstory and roof displacements, very conservative for IS and bending moments, but non-conservative for the case of axial loads; for the case of IS, the values of ζE2 range from 5.8% to 10.5%. Starting from the fact that NTHA is the most accurate analysis procedure, the results of this research indicate that expressing the effect of dissipated energy by HBM in terms of VD according to the CSM and MSA may result in non-conservative and conservative designs, respectively. If IS is the parameter of interest, a value of 8% can be reasonably used in both the CSM and MSA.