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.

The design of reinforced concrete structures starting from a linear analysis is allowed by design codes and leads to safe solutions. The structural model built for the analysis may be composed not only of bar and shell elements, but also solid elements. In the present work, the formulation of the Reinforced Solid Method (RSM) was reviewed and applied to the Ultimate Limit State design of a reinforced concrete member, with the computation of the required reinforcement and concrete check of each individual solid element within the structural model. The results were visualized in a post-processor and validated by numerical simulations. The RSM effectively allows for the design of concrete structures with general geometry and loading conditions, whilst identifying local effects throughout the volume of the structure.

The ultimate limit state design of reinforced concrete members usually derives from the analyses of structural models composed of unidimensional or bidimensional elements (bar and shell elements, respectively). Less recurrent in these structural models is the use of solid elements, which may be ascribed to the difficulties arising when dimensioning the structure for the complete stress field with six stress components (σx, σy, σz, τxy, τxz, τyz) derived from the analyses. In the present work, the design method for three‐dimensional stress fields combining linear analysis and limit design is revisited, with the description of the resisting mechanism in which the applied stresses are balanced with stresses in the concrete and in the reinforcement. Expressions for the verification of concrete crushing and the evaluation of the required reinforcement are deduced analytically and interpreted physically. The design process is organized into four design cases, according to the internal stresses mobilized in concrete. The proposed equations are presented in a framework for direct application to engineering practice, as demonstrated in noted design examples for selected stress states.

Reinforced concrete shell elements are relevant in several civil and industrial structures. It is important to know the methods for designing and verifying such elements. In this context, the present paper aims at describing the iterative three-layer method proposed by Colombo et al. This method is based on the Model Code/1990, and it can be applied in the design of shell elements. An additional method for verifying reinforced concrete shell elements is also proposed and discussed. This one is based on the multilayer method proposed by Kollegger et al. Formulations as well as numerical examples are presented for both methods. The design proposed by Colombo et al. is verified by using the methodology based on the multilayer method. Although both methods lead to the equilibrium between applied and resistance loads using approximately the same amount of reinforcement, especially for small neutral axes in relation to the element thickness, one may conclude that the three-layer design method has limitations due to not considering strain compatibility along the thickness of the element and due to the impossibility to calculate the compression reinforcement. Although the multilayer method overcomes such limitations, it is a verification method, and more studies about its use in the design of reinforced concrete shell elements are necessary.

This paper presents a method to design membrane elements of concrete with orthogonal mesh of reinforcement which are subject to compressive stress. Design methods, in general, define how to quantify the reinforcement necessary to support the tension stress and verify if the compression in concrete is within the strength limit. In case the compression in membrane is excessive, it is possible to use reinforcements subject to compression. However, there is not much information in the literature about how to design reinforcement for these cases. For that, this paper presents a procedure which uses the model based on Baumann's [1] criteria. The strength limits used herein are those recommended by CEB [3], however, a model is proposed in which this limit varies according to the tensile strain which occur perpendicular to compression. This resistance model is based on concepts proposed by Vecchio e Collins [2].

Since the beginning of twentieth century, along with academic publications of Ritter and Mörsch, several studies have been done in order to understand shear strength in reinforced concrete elements. Approximately 1,200 laboratory tests results of reinforced concrete beams under shear stresses were used in a comparative analysis among values from prediction models of codes and laboratory tests results, enabling classification of the codes according to their applicability in several tests intervals. Although the Brazilian Code NBR 6118 (2007) showed good results in usual ranges of parameters, it presented unsatisfactory results on the following cases: low and medium shear transverse reinforcement rate.Keywords: shear design, shear strength, standards comparison, standards applicability.Desde o início do século XX, com as publicações de Ritter e Mörsch, diversos modelos de cálculo foram desenvolvidos para tentar avaliar o valor da força cortante resistente em elementos em concreto armado. Com um banco de dados de cerca de 1.200 resultados de ensaios de laboratório de vigas de concreto armado, solicitadas por esforços de cisalhamento, efetuou-se a análise comparativa entre os valores de predição das principais normas e os resultados de ensaios, permitindo qualificar o modelo de predição das normas quanto sua aplicabilidade em diversos intervalos de ensaios. O modelo de predição da norma brasileira NBR 6118 (2007) [1] apresentou resultados satisfatórios nos intervalos usuais dos parâmetros, porém pouco satisfatórios para elementos com média e baixa taxa de estribos.Palavras-chave: dimensionamento ao cisalhamento; resistência ao cisalhamento; comparação entre normas; aplicabilidade das normas.

RESUMO:  Concretos de alta resistência (CAR) estão inseridos no grupo II de resistência e possuem fck superior a 50 MPa. Eles possuem curvas tensão-deformação com limites distintos daqueles convencionados como concretos de resistência normal. Por isso, o uso da rigidez secante adimensional apresentada pela norma brasileira de concreto armado – NBR6118 (ABNT, 2014) – necessita de validação para CAR. Para essa validação da expressão que consta na norma brasileira para CAR, foram analisadas disposições de armadura consideradas mais desfavoráveis para a resistência (altos valores de d’/h), com várias taxas mecânicas de armadura. Foram comparados os momentos máximos de 1ª ordem que poderiam ser aplicados na seção caso se considerasse a rigidez kappa a partir do diagrama momento-curvatura, com aqueles momentos obtidos considerando a rigidez kappa aproximada por expressão normativa. Em apenas 4,26% dos 5.840 casos analisados, o valor aproximado resultou maior que o valor real. A maior diferença entre os valores de máximos momentos de primeira ordem obtidos por meio da rigidez adimensional real e aproximada foi de 7,27%, o que pode ser considerado aceitável. Dessa forma a expressão aproximada da rigidez kappa prescrita pela NBR6118 (ABNT, 2014) também é válida para CAR.ABSTRACT: High strength concretes (HSC) are presented in group II of resistance and have compression strength greater than 50 MPa at 28 days. They have stress-strain curves with different limits from those referred as normal resistance concretes. Therefore, the use of the non-dimensional secant stiffness presented by the Brazilian Code of Reinforced Concrete - NBR6118 (ABNT, 2014) - needs validation for HSC. Unfavorable dispositions of steel bar reinforcement (high values of d '/ h), with a several mechanical rates of reinforcement, were analyzed for validation of the expression that appears in the Brazilian Code for HSC. It was compared the maximum moment of 1st order that could be applied in the section if the kappa stiffness was considered from the moment-curvature diagram, with those moments obtained with the normative expression for kappa stiffness. The approximate value was greater than the   real value in only 4.26% of the 5840 cases analyzed. The greatest difference between the values of maximum first-order moments obtained by the real and the approximate non-dimensional stiffness was 7.27%, which can be considered acceptable. Thus the approximate expression of the kappa stiffness prescribed by NBR6118 (ABNT,  2014) is also valid for HSC.