Rational model for calculating deflection of reinforced concrete beams and slabs

Deflection control is an important performance criterion that needs to be satisfied to ensure serviceability of the structure for its intended use. The extent of cracking and amount of reinforcement affects the flexural rigidity, E1, of a reinforced concrete member and both the Canadian concrete design standard (CSA A23.3-04) and ACI Building Code (ACI 318-05) use an effective moment of inertia, I, that was originally proposed by Branson to compute beam deflection. This is an empirically derived equation that works well within a narrow range of limits corresponding to steel-reinforced concrete beams with a reinforcing ratio between 1% and 2%. However, the equation underestimates deflection for steel-reinforced concrete beams and slabs with a reinforcing ratio less than 1% and for most beams reinforced with low-modulus, fibre-reinforced-polymer (FRP) bars. Deflection of slender tilt-up wall panels can also be underestimated with Branson's equation. This paper provides an explanation of why the Branson equation does not always work well in predicting deflection, and presents a rational approach to develop an alternative expression for the effective moment of inertia that works equally well for both steel- and FRP-reinforced concrete at all reinforcing ratios. A rational expression is also introduced for continuous beams that uses an averaged moment of inertia, to calculate beam deflection. Changes are included in a proposed revision to deflection prediction requirements specified in clause 9.8 of CSA A23.3-04.