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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.

Irregular structures are known to be more prone to disproportionate collapse (DC) than structures with regular horizontal and vertical layouts. Despite this, many public, commercial and institutional buildings have to be designed with various irregularities in structural layout due to architectural and aesthetic considerations. While extensive experimental and numerical studies have been carried out to advance the basic understanding of DC behaviors of regular structures, limited research has been carried out on irregular structures. On the other hand, alternate load path method has been recommended by several design codes and standards for DC design, but the large number of potential column removal scenarios involved poses a real challenge for the wide use of the method. This paper presents a quantitative measure referred to as irregularity index, or Π , that can be used to quickly identify the worst column removal scenarios for design check of DC resistance of reinforced concrete (RC) frame structures. Based upon a solid understanding of various competing failure mechanisms and DC resistance of RC frame structures, the irregularity index was derived from the maximum load factors between the yielding load and the limit load at the end of tensile membrane action stage. For verification and validation of the proposed Π , a 3D nonlinear finite element model was developed in OpenSees and calibrated by beam-slab sub-assemblage experiments. Various numerical experiments were carried out to verify the effectiveness of the Π . The very high correlation coefficient between the calculated irregularity indices and DC resistance obtained from finite element analyses showed that the proposed irregularity index can quickly identify the worst column removal scenarios in various irregular structures including setback buildings and large-bottom-space structures. Sensitivity analysis further verified the reliability of the proposed irregularity index.