Mechanical model for the shear capacity of R/C beams without stirrups: A proposal based on limit analysis

• Physically based model for the shear capacity of reinforced concrete beams without shear reinforcement.
• The model provides a rational explanation regarding influence of important design parameters.
• Good agreement with a wide range of tests and other existing models.
• The model forms a solid base for further development into different loading scenarios.

In this paper a rational model for the shear capacity of beams without shear reinforcement is presented, relating to the basic case of a straight beam subjected to combined shear and bending. The model is established using the upper bound principle derived from the Theory of Plasticity, and rests upon the observation that shear failures in slender beams typically evolve from already existing cracks, developed due to the influence of bending, and shaped under the combined influence of shear and bending. In the model, this observation is formalised into a characteristic crack pattern and a characteristic pattern of failure lines along existing cracks and within uncracked concrete. The influence of crack widths is taken into account using a relation between the crack failure condition and the crack width. The estimates of the model are shown to be in good agreement with a wide range of tests as well as with existing models.