Simplified design and capacity calculations of shear strength in reinforced concrete membrane elements

This paper presents a simple rational method for the design, capacity calculation and identification of mode of failure of membrane elements subjected to combined in-plane shearing and normal stresses. The non-iterative method named SMCS (simple model for combined stress-resultants) is based on a simplification of the results of the modified compression field theory (MCFT). The simplification leads to equations similar in format to the Plasticity Theory equations except that the contribution of reinforcement larger than the “balanced” reinforcement is neglected, and the maximum attainable shearing stress is limited to a crushing strength that is based on experimental data from normal and high strength concrete (100 MPa) membranes. A comparison with test results from 84 reinforced concrete membrane elements subjected to in-plane shearing and normal stresses gives an average of the experimental to calculated shearing strength of 1.03 and a coefficient of variation of 11.3%. For the original iterative MCFT, these values are 0.99 and 11.1% respectively. The results of the proposed method are also compared with those of the ACI code, the Simplified MCFT and the Plasticity Theory, and favorable results are obtained. The proposed SMCS was also capable of calculating the correct mode of failure in 45 out of 49 panels where the mode of failure was available. The simplicity of the model is illustrated using a design and a capacity calculation example.