Transverse shear and normal stresses in the nonlinear analysis of reinforced shells

This research investigates the simultaneous effect of in-plane and transverse loads in reinforced concrete shells. The infinitesimal shell element is divided into layers with triaxial behavior that are analyzed according to the smeared rotating crack approach. The transverse shear strength of shell elements is associated to an "equivalent" surface, which takes into account the nonlinear material behavior, using traditionally accepted hypotheses for shells. The set of internal forces includes the derivatives of the in-plane components. Although some simplifications are necessary to establish a practical first-order approximation, higher-order solutions could be developed. The whole set of equilibrium, compatibility and constitutive equations are satisfied, the stiffness derivatives are explicitly calculated and the algorithms show good convergence. The formulation yields through-the-thickness distributions of stresses and strains and the spatial orientation of the concrete struts. The formulation satisfactorily predicts the ultimate capacity under different load combinations, agreeing with experimental data obtained by other researchers. Although comparative analysis with additional experimental data is still necessary, the proposed theory provides a promising solution for the design of reinforced concrete shells.