Probabilistic analysis of interior reinforced concrete flat slabs

Four interior reinforced concrete flat slabs are analyzed deterministically using the finite element analysis (FEA) program ABAQUS. Using this verified FEA model, probabilistic FEA is performed considering uncertain material properties. Probabilistic FEA is executed using a new variance based method, namely, multiplicative dimensional reduction method (M-DRM). M-DRM is selected because it overcomes the computational cost limitation, which can be a barrier for these types of analyses; it provides the probability distribution of any structural response, e.g., distribution of punching shear strength; it conducts sensitivity analysis without requiring any further execution of the FEA code. M-DRM is automated in ABAQUS using python programing. First, this study examines how material uncertainty impacts the structural response of interior flat slabs, in terms of ultimate load and ultimate displacement. Then, sensitivity analysis is performed in order to prioritize the most influential input random variables with respect to these structural responses. Finally, probability distribution of the punching shear resistance is also derived, using the design equations from the American code (ACI 318) and Eurocode 2 (EC2), in order to examine the degree of conservatism associated with the current design practices.