A New Method for Calculating Deflection of FRP Reinforced Concrete Beams Using the Tension Stiffening Concept

Accurate calculation of the deflection of reinforced concrete members has been a challenge since the inception of modern reinforced concrete. Many formulas and methods have been developed, over the years. However, most of them are empirical in nature and do not predict accurately the flexural deflection of reinforced concrete members over the entire loading range. Deflection calculation has important impact on the satisfactory performance of structures, especially in performance based design and in the design of fiber reinforced polymers (FRP) reinforced concrete members, where deflection limits may govern the design. This highlights the need for more accurate deflection calculation methods. This research proposes a method, based on first principles, to more accurately calculate, compared to ACI Committee 440 and CSA S806-12 methods, the deflection of FRP reinforced beams. The method has two key features: (1) It accounts, via a tension-stiffening model, for the contribution of the concrete teeth between flexural cracks to the stiffness of the beam; (2) the method is developed by dividing the beam cross-section at selected points along its span into several layers. The contribution of each layer to the flexural rigidity is computed by finding its elastic modulus (secant modulus) as function of the type and magnitude of the longitudinal stress (strain) at the level of the centroid of that layer. The layers flexural rigidities are summed over each cross-section and used in conjunction with the second moment-area theorem to compute the beam deflection. This method is based on first principles and no empirical factors are involved besides the adopted tension-stiffening model. The validity of the proposed method is demonstrated by comparing its results with corresponding experimental data. It is shown that it can estimates the deflection at the serviceability load levels quite accurately. Also it is reliable in estimating deflection under load levels beyond serviceability, which is a limitation to of both the ACI Committee 440 and CSA S806-12 methods. The proposed method was applied on steel reinforced beam and compared with experimental and ACI Committee 318 results. The proposed method gave reliable results, but further investigation for the case of steel reinforced beams is required.