An algorithm for the automatic design of concrete shell reinforcement

Abstract

An algorithm developed for the design of reinforcement in concrete shells is presented in this text. The formulation and theory behind the development is shown, as well as results showing its robustness and capability of application on fairly large-scale structures. The design method is based on the three-layer model for reinforced concrete shell elements. A material model is also proposed in order to improve the numerical stability of the algorithm. Comparisons of single element design show that the modifications made to the material model don't effect significantly the final results while making for better numerical stability.

Design and verification of reinforced concrete shell elements

“…Given the great applicability of shells in civil and industrial structures, it is important to compare the existing methods for designing and verifying reinforced concrete shell elements. In this context, the objective of the work is to describe the methodology developed by Colombo et al [12] for designing reinforced concrete shells and to present a methodology based on the idea proposed by Kollegger et al [13] for verifying such shells. The work will be developed through the presentation of formulations and numerical examples as well as comparisons between the two methodologies.…”

“…The formulation proposed by Colombo et al [12] for designing reinforced concrete shells will be presented below. It can be applied to both thin and thick shells, requiring only that the loads are obtained accordingly.…”

“…The two outer layers are responsible for resisting the moments and the membrane forces, and the central layer is responsible for resisting transverse shear. Colombo et al [12] were also based on this three-layer method to develop an algorithm for reinforced concrete shell design.…”

“…Colombo et al [12] propose a model for the concrete that is based on the experimental results obtained by Vecchio and Collins [17]. Such model assumes that the maximum compressive strength f cmax of the concrete decreases as the maximum tensile strain ε 1 increases.…”

“…Colombo et al [12] consider that for cases I, II and III, in which the concrete is cracked, f c can be interpolated between the values of f cd1 and f cd2 through Equation 33. For the case IV, Equation 30 is valid because the concrete is uncracked.…”