Simplified evaluation of the N-M-V ultimate domain of R.C. rectangular members with shear reinforcement

This paper describes a simple analytical tool for the calculation of the shear strength of r.c. rectangular members with shear reinforcement and subjected to only truss mechanism. The proposed method considers simplified stress fields and evaluates the shear strength of members subjected to axial force, bending moment and shear force by means of the application of the static theorem of limit analysis. Unlike most of the formulations proposed in codes and in other research studies, the proposed method considers a single physical model to explain the resistance to axial force, bending moment and shear force, and simultaneously satisfies the equilibrium under all the above internal forces. The paper identifies basic points of the N-M-V ultimate domain and reports relations and procedures to calculate the values of the internal forces of these points as well as the internal forces of the points in between. The method is applied to a set of beam and column members and a comparison is drawn between the shear strength resulting from the simplified method and that from a more complex non-linear mathematical program proposed in the past by the same author. Finally, to prove the value of the method and define the field of reliable application, the proposed method is applied to members tested in laboratory by other researchers and characterised by different geometric and mechanical properties. The obtained results are also compared with those deriving from other methods present in the literature.