Shear strength of RC beams with stirrups using an improved Eurocode 2 truss model with two variable-inclination compression struts

Abstract

The shear strength of reinforced concrete beams with stirrups can be assessed with strut-and-tie models based on the truss analogy. The Eurocode 2 formulation exploits such a possibility with a variable-angle inclination of the compression struts that is determined through the lower-bound theorem of plasticity. This approach tends to underestimate the shear capacity of lightly shear-reinforced beams where the concrete contribution, which is neglected in this formulation, is more significant. Based on this consideration but adopting an identical theoretical framework without adding a concrete contribution explicitly, this paper presents an upgrade of the EC-2 truss model incorporating two variable-inclination compression struts, whose inclination angles are determined through equilibrium conditions and the theory of plasticity. In this model, the upper compression strut may have lower inclination than the lower compression strut, which is mechanically motivated by the increase of shear stresses observed in the upper portion of the beam, in the neighborhood of the crack tip, following the trend of the principal compressive stress direction. This improved truss model enables the construction of a wider class of statically admissible solutions compared to the EC-2 single-strut approach. Closed-form expressions are derived for a variant of this model in which the two compression struts extend equally for half of the inner lever arm, which allows a simple and compact formulation for practical design purposes. Based on comparison with the well-established ACI-DafStb databases including more than 200 tests, the proposed model leads to values of the shear strength that are in very good agreement with experimental results and more accurate than the values obtained from the EC-2 procedure, despite the relatively comparable simplicity.