Analysis of reinforced concrete shells with transverse shear forces

TL;DR

This paper presents a new analytical approach for analyzing reinforced concrete shells under combined in-plane and transverse loads, incorporating layered shell elements and smeared crack models to predict stress and strain distributions.

Contribution

It introduces a novel formulation that accounts for through-the-thickness stress distributions and concrete strut orientations, improving upon existing methods for shell analysis.

Findings

Predicted results align well with experimental data

The formulation satisfies equilibrium and compatibility conditions

Algorithms demonstrate good convergence

Abstract

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.