Verification of deflection according to Eurocode 2

Abstract

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.

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

“…The span-to-depth ratio (l/d) limits derive from the dimensionless procedure described in Peci c et al 17 Total deflections under quasi-permanent load are used as reference values for calibration of the proposed method. Deflections were calculated by numerical integration of the mean curvature 1,2 :…”

“…The reduced concrete tensile strength f ct,red is used to account for the tension induced by internal and external restraints and/or the occurrence of short-term loads that are bigger than quasi-permanent load. It has been shown 17 that the average tensile strength of concrete (f ct ¼ f ctm ) provides satisfactory prediction of deflection, while the use of flexural tensile strength of concrete (f ct,fl ) underestimates the deflection.…”

“…A negative value of Δ indicates that a particular result from expression (17) or (18) is conservative (on the safe side).…”

“…The estimated representative values are: φ eff ¼ 1:8 and ε sh ¼ 0:30 Â 10 À3 for humid (outside) conditions (RH ¼ 80%) and φ eff ¼ 2:5 and ε sh ¼ 0:50 Â 10 À3 for dry (inside) conditions (RH ¼ 50%). With these values, for N ¼ 250 and k s ¼ 0, Equations (17) and ( 18) become:…”