Simplified model for shear strength of orthogonally RC membrane elements subjected to in-plane normal and shear stresses

•The behavior of RC membrane elements subjected to in-plane stresses is evaluated.•Failure is shown to be preceded by formation of two or more major critical cracks.•These cracks propagate in a direction normal to concrete principal tensile stress.•These cracks are shown to open at an angle that assumes least shearing resistance.•At failure, the contributions of both reinforcements to resist shear are the same.•Simple expressions are provided to compute strength and angles of major cracks.

A simplified model is proposed for the shear strength of reinforced concrete (RC) membrane elements subjected to in-plane normal and shear stresses. The shear strength of these elements is evaluated at various stages of loading and can be computed by direct simple expressions. Failure in these elements is shown to occur in four different modes and to be preceded by the formation of two or more major critical cracks. At each stage of loading, the major critical cracks are shown to open at an optimum angle that supplies least shearing resistance to external loading. Consequently, these major cracks are shown to form when the contribution of the reinforcement in the x-direction to resist shear stresses is equal to that of the reinforcement in the y-direction. A unique normalized relationship is derived for the shear strength as a function of a ratio defined in terms of the amounts and yield strengths of reinforcements. Experimental results of 70 RC membrane elements subjected to in-plane normal and shear stresses obtained from literature are used to validate the proposed model. Numerical examples are provided for the computations of shear strength and modes of failure by the proposed model.