Viscous damping in seismic design and analysis

The characterisation of viscous damping in time history analysis is discussed in this paper. Although it has been more common in the past to use a constant damping coefficient for single-degree-of-freedom time history analyses, it is contended that tangent-stiffness proportional damping is a more realistic assumption for inelastic systems. Analyses are reported showing the difference in peak displacement response of single-degree-of-freedom systems with various hysteretic characteristics analysed with 5% initial-stiffness or tangent-stiffness proportional damping. The difference is found to be significant, and dependent on hysteresis rule, ductility level and period. The relationship between the level of elastic viscous damping assumed in time-history analysis, and the value adopted in Direct Displacement-Based Design is investigated. It is shown that the difference in characteristic stiffness between time-history analysis (i.e. the initial stiffness) and displacement based design (the secant stiffness to maximum response) requires a modification to the elastic viscous damping added to the hysteretic damping in Direct Displacement-Based Design.