Simplified analytical model for moment–axial force domain in the presence of shear in R.C. members externally strengthened with steel cages

Equations for a hand calculation of moment–axial force domain in the presence of shear for R.C. beam/column externally strengthened with steel angles and strips are developed. The analytical derivation is made assuming, for axial load and flexure, the equivalent stress-block parameters for internal forces, considering the confinement effects induced in the concrete core by external cages both in the cases of strips or angles yielding. Limit states due to bond failure, concrete crushing and yielding of steel angles and strips in flexure and in shear, including moment-to-shear interaction, are considered. The proposed model gives results in a good agreement with available experimental data and it allows a hand control of the influence of the main parameters governing the problem (angle and strip geometry and mechanical properties of constituent materials).