A Proposal for a General N-M-V Design Method

The performance of a steel reinforced, FRP strengthened or/and prestressed concrete element, subjected to normal force N, bending moment M and shear force V, has been object of many studies and reports. Many codes propose different models for reinforced, for prestressed and for FRP external strengthened concrete structures. For reinforced concrete elements, the shear strength, in presence of axial force N, has been discussed by many authors, but different models have been proposed to evaluate the shear-prestressing interaction, or obtaining the design formulations by experimental results, or accounting for the prestressing tendons by adding a strut-and-tie model to the traditional truss model by Ritter and Mörsch. Moreover, several analytical models have been proposed for predicting flexural and/or shear strength of beams and columns strengthened with FRP or CFRP sheets. However, relatively few studies have been conducted on shear-flexure interaction effect in concrete element strengthening with FRP sheets. These models take into account the non linear behavior of materials, incorporating in the framework of strut and ties models, and include the load transfer mechanism to reflect the plate-debonding phenomenon and associate cracking of concrete core. In the present paper a new approximate physical model, based on stress fields plasticity theory, is proposed for evaluation of the N-M-V interaction resistance domains of concrete cross-sections by generalizing a precedent one. This model that includes, now, the effect of prestressing tendons bounded and unbounded, has been modified, in order to take into account the strengthening effects of the FRP or CFRP sheets bonded to the tension face as well as the lateral faces, and it is able to take in account now the different mechanisms of failure, including those influenced by bond slip. Finally, it has been generalized to take into account N-M-V interaction for concrete reinforced columns of circular shape cross section.