An analytical model is presented for predicting the response of reinforced concrete to in-plane shear and normal stresses. The model is based on conditions of equilibrium and compatibility, and utilizes realistic stress-strain relationships for the reinforcement and for the concrete. Stresses and strains are considered in terms of average values, 'smeared' over a finite area of a reinforced concrete element.

A bi-linear average stress-strain relationship is assumed for the reinforcement. To determine appropriate average stress-strain relationships for concrete, thirty reinforced concrete panels were tested under well defined, uniform stresses. While most of the panels were tested in pure shear, other load cases included combined shear and biaxial compression, and combined shear and biaxial tension.

The test results reveal that the average principal compressive stress-strain behaviour of cracked concrete differs substantially from that of a cylinder loaded in uniaxial compression. The presence of large average tensile strains can result in a significant deterioration in both the strength and stiffness of concrete. A simple expression is given which describes well the observed behaviour.

The panel tests also indicate that the average tensile stresses acting in the concrete can be significantly greater than zero, even after extensive cracking has occurred. Expressions are given relating the average principal tensile stress in the concrete to the average principal tensile strain and to the stress conditions in the reinforcement.

The analytical model is used to predict the observed response of the test panels. Good agreement is obtained in terms of failure stresses, and in terms of deformations at all stages of loading. The model is also used to make a theoretical study of factors influencing the shear strength of concrete.

As an example of its possible application in predicting the behaviour of more complex structures, the model is used to predict the response of reinforced concrete beams in shear. The predictions are compared to experimental results reported by other investigators. Good agreement is obtained. It is believed that the model will form the basis for future non-linear finite element analyses of reinforced concrete structures.