Modified Branson’s Formula for Deflection of FRP Strengthened Concrete Beams

This paper will discuss how the use of externally bonded FRP plates and sheets has been established as an effective mean to strengthen concrete beams in flexure and shear. Several investigators have shown that the direct use of Branson equation does not yield conservative deflection results especially after steel yielding. The authors have developed an analytical solution that generates closed form expressions for deflection in simple beams. These expressions were shown to reproduce results that compared well with experiments. These expressions were dependent on the loading condition while Branson equation is not load specific. Branson equation is modified by replacing the cracked section moment of inertia with an effective moment of inertia at steel yielding to evaluate deflections at the service load levels. This revised formula could be easily implemented in the ACI 440.2R format. The predictions are compared against Branson equation and experimental evidence. Furthermore, another new modification to Branson equation is proposed for the region covering response from steel yielding and up to ultimate capacity.