Application of the work-energy principle to assess the risetime effect on the dynamic response amplification under column loss

Abstract

Progressive collapse analysis of building structures is usually performed under sudden column loss conditions. This means that the bearing capacity of the targeted column disappeared instantaneously. Hence, a time length less than one tenth of the natural period in the gravitational direction of the damaged structure has been recommended for disabling the targeted column in the numerical analysis. The time length required for disabling the postulated column in dynamic progressive analysis is defined as the rise time. Most seismically designed structural members may have a minimum ductility capacity as regulated in design codes. When the column is subjected to a devastating abnormal loading, it may gradually lose its load-carrying ability with increased deflection. Thus, the column strength is completely lost within a finite rise time. In other words, the dynamic loading for progressive collapse analysis of the remaining structure is increased gradually rather than instantaneously. This study intends to apply the work-energy principle to investigating the rime-time effect on the dynamic response amplification under column loss. A single-degree-of-freedom (SDOF) model is used to derive the analytical formulation with consideration of the rise-time effect. It is constructed with an assumption that the maximum imposed loading can be attained before yielding. Analytical procedures for calculate the force- and displacement-based dynamic increase factors (DIFs) are proposed. Nonlinear time-history analyses are then carried out to evaluate the accuracy of the proposed approach. The analysis results indicate that the dynamic amplification will decrease with increased finite rise time. The rise-time effect decreases with increased plastic demand. For practical application, the rise-time effect may be reasonably neglected as the ductility demand is larger than 5.0 and the normalized loading is larger than 1.5 for the force- and displacementbased DIFs, respectively. Its influence on the column-loss response may vary with the ratio of the rise-time length to the natural period and the extent of plastic deformation.