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Indirect deflection control usually applies the limitation of the span-to-depth ratio. The procedures that have developed in the past decades have mostly been derived for predefined values of some of the relevant parameters. Assigning values to parameters simplifies the application of criteria. Predefined values may not be suitable for all design situations and some of the recently published procedures allow direct selection of relevant parameters. This paper offers new expressions for span-to-depth ratio limits for deflection control. Expressions include cross-section size, area, and position of tensile and compressive reinforcement, mechanical and long-term properties of concrete and deflection limit. The load level is represented by the stress in the tensile reinforcement so that the ratio of live and total load can be arbitrary. The dimensionless form of deflection calculation by numerical integration of the mean curvature according to Eurocode 2 is used to formulate the expressions. The proposed procedure is verified with a large number of numerical simulations for different combinations of inputs. Measured long-term deflections, available from the literature, are also used to test the procedure. The expressions are suitable for both deflection control and conceptual design.

Indirect deflection control usually applies the limitation of the span-to-depth ratio. The procedures that have developed in the past decades have mostly been derived for predefined values of some of the relevant parameters. Assigning values to parameters simplifies the application of criteria. Predefined values may not be suitable for all design situations and some of the recently published procedures allow direct selection of relevant parameters. This paper offers new expressions for span-to-depth ratio limits for deflection control. Expressions include cross-section size, area, and position of tensile and compressive reinforcement, mechanical and long-term properties of concrete and deflection limit. The load level is represented by the stress in the tensile reinforcement so that the ratio of live and total load can be arbitrary. The dimensionless form of deflection calculation by numerical integration of the mean curvature according to Eurocode 2 is used to formulate the expressions. The proposed procedure is verified with a large number of numerical simulations for different combinations of inputs. Measured long-term deflections, available from the literature, are also used to test the procedure. The expressions are suitable for both deflection control and conceptual design.

Recycled aggregate concrete (RAC) has emerged as a viable solution for solving some of the environmental problems of concrete production. However, design guidelines for deflection control of reinforced RAC members have not yet been proposed. This study presents a comprehensive analysis of the applicability of the fib Model Code 2010 (MC2010) deflection control model to reinforced RAC beams. Three databases of long-term studies on natural aggregate concrete (NAC) and RAC beams were compiled and meta-analyses of deflection predictions by MC2010 were performed. First, the MC2010 deflection control model was tested against a large database of long-term tests on NAC beams. Second, a database of RAC and companion NAC beams was compiled and initial and long-term deflections were calculated using the MC2010 model. It was shown that deflections of RAC beams are significantly underestimated relative to NAC beams. Previously proposed modifications for MC2010 equations for shrinkage strain and creep coefficient were used, and new modifications for the modulus of elasticity and empirical coefficient β were proposed. The improved MC2010 deflection control model on RAC beams was shown to have equal performance to that on companion NAC beams. The proposals presented in this paper can help engineers to more reliably perform deflection control of reinforced RAC members.

Code provisions for a simplified check of the long-term deflection of concrete structures are generally developed for predefined values of the relevant input parameters. Deflection calculation may be of interest to account for different design situations. EN 1992-1-1 advocates the integration of curvatures calculated using the effective modulus of concrete. This paper presents an efficient procedure for calculation of the long-term deflection due to a sustained load. A nondimensional analysis of the mean curvature is applied to evaluate the deflection. The deflection is calculated using a set of algebraic expressions. The result is close to the value obtained by the numerical integration of curvatures. The values of relevant parameters in the expressions may be selected within the common range for the design of engineering structures. The efficiency of the deflection prediction based on the integration of curvatures is tested on the available experimental data. In the first approach, the measured material properties are used. In the second approach, the required values are derived from EN 1992-1-1 expressions to predict the material properties.

Code provisions for a simplified check of the long-term deflection of concrete structures are generally developed for predefined values of the relevant input parameters. Deflection calculation may be of interest to account for different design situations. EN 1992-1-1 advocates the integration of curvatures calculated using the effective modulus of concrete. This paper presents an efficient procedure for calculation of the long-term deflection due to a sustained load. A nondimensional analysis of the mean curvature is applied to evaluate the deflection. The deflection is calculated using a set of algebraic expressions. The result is close to the value obtained by the numerical integration of curvatures. The values of relevant parameters in the expressions may be selected within the common range for the design of engineering structures. The efficiency of the deflection prediction based on the integration of curvatures is tested on the available experimental data. In the first approach, the measured material properties are used. In the second approach, the required values are derived from EN 1992-1-1 expressions to predict the material properties.