Analytical Model of Two-Directional Cracking Shear-Friction Membrane for Finite Element Analysis of Reinforced Concrete




Mitchell, Jeffrey
Cho, Bum-Yean
Kim, Yoo Jae

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Multidisciplinary Digital Publishing Institute


There are a multitude of existing material models for the finite element analysis of cracked reinforced concrete that provide reduced shear stiffness but do not limit shear strength. In addition, typical models are not based on the actual physical behavior of shear transfer across cracks by shear friction recognized in the ACI 318 Building Code. A shear-friction model was recently proposed that was able to capture the recognized cracked concrete behavior by limiting shear strength as a yielding function in the reinforcement across the crack. However, the proposed model was formulated only for the specific case of one-directional cracking parallel to the applied shear force. This study proposed and generalized an orthogonal-cracking shear-friction model for finite element use. This was necessary for handling the analysis of complex structures and nonproportional loading cases present in real design and testing situations. This generalized model was formulated as a total strain-based model using the approximation that crack strains are equal to total strains, using the proportional load vector, constant vertical load, and modified Newton–Raphson method to improve the model’s overall accuracy.



shear friction, membrane, crack-opening path, finite element, modified Newton-Raphson method, Engineering Technology


Mitchell, J. P., Cho, B. Y., & Kim, Y. J. (2021). Analytical model of two-directional cracking shear-friction membrane for finite element analysis of reinforced concrete. Materials, 14(6), 1460.


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