An Approximate Analytical Formulation for the Rise-Time Effect on Dynamic Structural Response Under Column Loss

Abstract

Dynamic progressive collapse analysis of building structures is usually conducted under sudden column loss conditions. The time length required for disabling the failed column is defined as the rise time. The rise-time effect on the maximum dynamic response of building frames under column loss is investigated in this study. Based on the work-energy principle, an approximate analytical formulation for the maximum dynamic response is derived considering the rise-time effect. The force- and displacement-based dynamic increase factors (DIFs) of a single degree-of-freedom model and a clamped steel beam are used to assess the accuracy and validity of the proposed formulation. Analysis results indicate that the DIFs decrease with increased rise time. Also, the rise-time effect decreases with increased ductility demand. Practical application of the analytical formulation to regular building frames subjected to column loss is illustrated. Primary factors related to the extent of the rise-time effect on the column-loss response are identified for design consideration.

Progressive collapse analysis of steel frames via a nonlinear SDOF model

“…The estimation of the dynamic response of the system is possible by solving the ordinary differential equations considering the appropriate initial conditions as shown in equation (8).…”

“…Among the analysis methods found in the literature, the idealization of a collapsed substructure as a SDOF system has been a particularly attracting method due to its simplicity. Different researchers have used this approach either to estimate the Dynamic Increased Factors (DIF) which are needed for the LA and NLA ALP methods, or to study the effect of important parameters on the response of the structure [6][7][8][9][10] but also as the basis for simplified design methodologies [11].…”