Analytical model of compressive arch action for one-way RC beams and two-way framed substructures under column removal scenarios

This paper proposes a direct analytical model to evaluate compressive arch action (CAA) of reinforced concrete (RC) beam-column sub-assemblages under middle column removal scenario (MCRS), incorporating bending curvature of the double-span beam, and different horizontal and rotational restraint conditions at the beam ends. Based on the proposed approach, the structural engineer can easily obtain the CAA peak capacity and the corresponding CAA displacement by hand calculations. Unlike the previous models in which the accuracy highly relies on pre-assumed CAA displacement, this prediction approach directly derives the CAA displacement and CAA capacity through force equilibrium, geometric relationship, compatibility and boundary conditions, incorporating various horizontal restraint conditions, span-to-depth ratio and section profile of the bridging beam. Comparison with existing test results in available literature indicates that this model not only gives good predictions of peak capacity, displacement and maximum axial beam force in CAA, but also incorporates the effect of horizontal restraint stiffness and working stress of compression reinforcement. Besides, a further simplified explicit model is proposed to enhance usability in practical design, and sensitive studies are conducted to study how the simplification affects the prediction accuracy of vertical CAA capacity and displacement. Thereafter, the proposed model is extended to substructures with orthogonal beams in X- and Y- directions to predict CAA capacity under different column removal scenarios such as interior, penultimate, edge and corner column removal cases.