Nonlinear SDOF Model for Progressive Collapse Responses of Structures with Consideration of Viscous Damping

Abstract

The effect of damping on progressive collapse responses of structures is typically ignored. However, the margin of conservatism resulting from ignoring damping is not well known. Therefore, in this paper, a nonlinear single-degree-of-freedom (SDOF) model is developed with a piecewise linear resistance function, viscous damping, and a loading function consisting of a ramp part and ensuing constant load. The closed-form analytical solutions are derived with Laplace transform techniques and verified with experimental results of steel beam-column assemblies under column-removal scenarios (CRS). The model is then used to investigate the damping effect on the dynamic displacement responses of structures under CRS with different initial conditions, structural resistance types, and levels of applied load. The results indicate that the effect of damping on displacement responses depends not only on the structural resistance but also on the level of applied load. For structural responses involving elastic and plastic hardening resistance, ignoring conventional global damping (e.g., a damping ratio of 3–5%) is reasonably conservative, but it is suggested that for structures with severe plastic softening resistance (e.g., softening stiffness greater than 10% elastic stiffness) and high damping ratio (e.g., more than 10%), the damping should be explicitly considered in the progressive collapse analysis; otherwise, it is too conservative, resulting in unnecessary cost.