Deflection Calculation of FRP Reinforced Concrete Beams Based on Modifications to the Existing Branson Equation

Abstract

Fundamental concepts of tension stiffening are used to explain why Branson’s equation for the effective moment of inertia Ie does not predict deflection well for fiber reinforced polymer (FRP) reinforced concrete beams. The tension stiffening component in Branson’s equation is shown to depend on the ratio of gross-to-cracked moment of inertia (Ig∕Icr), and gives too much tension stiffening for beams with an Ig∕Icr ratio greater than 3. FRP beams typically have an Ig∕Icr ratio greater than 5, leading to a much stiffer response and underprediction of computed deflections as observed by others in the past. One common approach to computing deflection of FRP reinforced concrete beams has been to use a modified form of the Branson equation. This paper presents a rational development of appropriate modification factors needed to reduce the tension stiffening component in Branson’s original expression to realistic levels. Computed deflections using this approach give reasonable results with the right modification factor, and compare well with a more general unified approach that incorporates a realistic tension stiffening model. Comparison is made with the existing and past correction factors recommended by ACI 440 for predicting deflection of FRP beams. The method presently used by ACI 440 gives reasonable estimates of deflection for glass and carbon FRP reinforced beams. However, this method underestimates deflection of aramid FRP reinforced beams and is restricted to rectangular sections. A proposal is made for adoption of a simple modification factor that works well for all types of FRP bar and beam cross-sectional shape.