Interaction between longitudinal shear and transverse bending in prestressed concrete box girders

In box girder bridges, the quantity and distribution of reinforcement to be put in concrete elements of sections can be evaluated only by considering the deformation of the cross section in addition to the longitudinal analysis of the static scheme, establishing the entire state of stress of box sections. This leads to a need to evaluate the interaction between internal forces obtained by the global analysis and the ones obtained by the local analysis of the cross sections. The frame effect implies the elastic deformation of slabs and webs, whereas eccentrically applied loads lead to cross-section distortion with the loss of the box shape. Hence, the reinforcement is strongly influenced by a significant interaction between longitudinal shear and transverse bending moments, because the same reinforcement bars, although acting on different planes, face these two stress resultants. Moreover, the longitudinal reinforcement in the webs plays an important role in the failure model. In this paper, an analytical model of interaction between longitudinal shear and transverse bending is presented, based on the stress field theory and on the application of the static theorem of plasticity. The proposed model allows engineers to establish the effective quantity of transverse and longitudinal reinforcements of box girder elements, both for ordinary and prestressed concrete girders. In the model, the variation of stress field inclination between the limit state of first cracking (serviceability) and the ultimate limit state is considered, and the related consequences are discussed. Interaction domains of longitudinal shear and transverse bending are sketched and supplied through dimensionless graphs to be used by designers for actual cases of engineering practice. A case study of a prestressed girder bridge is presented to show the reliability of the proposed approach. The analytical model is validated through comparisons with experimental data; finally, the influences of prestressing, warping phenomena, and cross-section distortion are discussed.