Span-to-depth ratio limits for deflection control of reinforced concrete elements

Abstract

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.