A new dynamic increase factor for nonlinear static alternate path analysis of building frames against progressive collapse

This paper presents a new empirical method for calculating the dynamic increase factor (DIF) that is used to amplify the gravity loads on the affected bays of a building frame, when the nonlinear static alternate path analysis is carried out to predict the peak dynamic responses to sudden column removal. The new method defines the DIF as a function of max(Mu/Mp), where the maximum operator is applied to all beams within the affected bays immediately adjacent to and above the removed column, and Mu and Mp are the factored moment demand under original unamplified static gravity loads and the factored plastic moment capacity, respectively, of an affected beam. Therefore, 1 – max(Mu/Mp) directly, albeit approximately, measures the percentage level of the overall residual capacity of a building frame to remain essentially elastic while withstanding the dynamic effect of gravity loads upon sudden column removal, after the static effect of gravity loads has been resisted by the damaged frame. A step-by-step nonlinear static analysis procedure using the new DIF is described. As an illustration, empirical DIF formulas are derived from curve fitting data points generated by the nonlinear static alternate path analysis of three model steel moment frames originally designed to resist different levels of earthquake. It is found from the numerical examples that the new DIF is well correlated with max(Mu/Mp) for different column removal scenarios. Hence, the new DIF can be used with nonlinear static analysis in lieu of nonlinear dynamic analysis to assess the potential of building frames for progressive collapse.