Bending Moment–Shear Force Interaction Domains for Prestressed Concrete Beams

The performance of a prestressed concrete beam, subjected to bending moment $M$ together with shear force $V$ , has been the object of many studies and is an important aspect to take into account in the design. Some models, proposed by researchers and international codes, evaluate the shear strength of prestressed beams by modifying the truss model by Morsch, so as to account for the different slope of stress fields in the web due to the prestressing action. More recent approaches add a strut-and-tie model to the traditional truss model. This paper generalizes a model that was previously proposed for box and I-shaped reinforced concrete cross sections of structural elements. The model, that now includes the effect of prestressing tendons, considers variable-depth stress fields applied to the cross section, subdivided into layers, and allows evaluation of normalized $m\text{–}v$ design domains depending both on the web and flange reinforcement and on the slope of the prestressing steel tendons. The reliability of the method has been validated by comparing its numerical results to the strength provided by tests on reinforced concrete beams and on thin-webbed prestressed concrete beams, referred to in the literature. Finally, it has been used in the design of a pretensioned bridge beam to evaluate the additional reinforcement necessary in the flanges, as a function of the reinforcement provided to the web.