Shear strength of deep beams: a mathematical model and design formula

This paper presents a proposal for estimating the shear capacity of reinforced concrete deep beams. The proposed model is based on the fixed-angle softened truss model and utilizes a newly proposed formula for the effective transverse compressive stress acting on the beam web. The proposed formula is developed using a stepwise multiple linear regression analysis of the reported shear capacity values of 445 experimental deep beams. The validity of the mathematical model is examined by comparing its response with the experimental results as well as the predictions of other formulas available in the literature, and it results in the one best fitting the measured shear strengths. The mathematical model leads to an explicit single closed-form expression for computing the shear strength of deep beams. The proposed expression is dimensionless and contains four variables that express the horizontal and vertical reinforcement ratios, the concrete strength and the shear span-to-depth ratio. On the basis of the results of this paper, a design formula is proposed with predictions that are more consistent and also more reliable than those of the ACI Code and the Eurocode.