A non-iterative progressive collapse design method for RC structures based on virtual thermal pushdown analysis

Disproportionate progressive collapse is a structural failure mode with low probability and high consequences. Due to this nature, progressive collapse design is usually treated as a secondary design; namely, a design check after the design for primary loadings. Various design procedures have been recommended, notably the alternate load path method through nonlinear pushdown analyses. However, most of these design procedures are iterative by nature to satisfy the design acceptable criteria. To improve the design efficiency, this study presented an innovative design technique that allows to directly determine the proper amount of reinforcement in beams and slabs of a reinforced concrete (RC) structure in order to withstand the gravitational loads under column removal scenarios. Inspired from fire-induced progressive collapse research, the proposed method employs a virtual thermal pushdown analysis, in which the temperature increase affects only the strength of reinforced steel. With carefully developed strength-temperature relationships of the rebars, the virtual thermal analysis produces a displacement-temperature curve that represents the genuine nonlinear relationship between the amount of reinforcement and structural performance (often represented by vertical displacement). This curve is then used to directly determine the amount of reinforcement at the prescribed performance target. Two beam-column sub-assemblage examples and the Alfred P. Murrah Federal Building were analyzed and redesigned to demonstrate the effectiveness of the proposed method. All three examples showed that the proposal virtual thermal pushdown method can accurately determine the appropriate amount of reinforcements to meet the performance target.