Reevaluation of deflection prediction for concrete beams reinforced with steel and fiber reinforced polymer bars

This paper provides a critical evaluation of equations commonly used to compute short-term deflection for steel and fiber reinforced polymer (FRP) reinforced concrete beams. Numerous proposals have been made for FRP in particular, and the different approaches are linked together by comparing the tension-stiffening component of each method. Tension stiffening reflects the participation of concrete between cracks in stiffening the member response. The Branson equation used in North America and other parts of the world is based on an empirically derived effective moment of inertia to calculate deflection. The tension-stiffening component with this method is highly dependent on the applied level of loading relative to the cracking load as well as the ratio of uncracked-to-cracked transformed moment of inertia (I-g/I-cr) for the beam section. Tension stiffening is overestimated for the high I-g/I-cr ratios typical with FRP concrete, leading to a much stiffer response and underprediction of member deflection. Deflection of steel reinforced concrete with reinforcing ratios less than 1% is also likely to be underestimated because of higher I-g/I-cr ratios at these lower reinforcement levels, but not to the same extent. In both cases, service loads are less than twice the cracking load where tension stiffening is most significant. Modifications to Branson's equation for deflection prediction of FRP concrete soften the member response by reducing the tension-stiffening component, mostly by introducing empirical factors that effectively decrease the I-g/I-cr ratio. An alternative expression for calculating beam deflection is developed with a rational approach that incorporates a tension-stiffening model adopted in Europe. The proposed equation gives an effective moment of inertia that is independent of I-g/I-cr and works equally well for either steel or FRP reinforced concrete.