  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 set of internals forces includes the derivatives
of the in-plane components. The corresponding generalized strains are
determined using an extension of the equivalent section method, valid for
shells. The formulation yields through-the-thickness distributions of stresses
and strains and the spatial orientation of the concrete struts. Although some
simplifications are necessary to establish a practical first-order
approximation, higher-order solutions could be developed. Despite the fact that
constitutive matrices are not symmetric, because of the tension-softening
formulation, the equilibrium and compatibility conditions are satisfied, the
stiffness derivatives are explicitly calculated and the algorithms show good
convergence. The formulation predicts results that agree 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.
