Prediction of load–deflection behavior of multi-span FRP and steel reinforced concrete beams

This paper presents a numerical procedure to determine the deflection of concrete members reinforced with fiber reinforced polymer (FRP) or steel bars. This procedure is implemented into the stiffness matrix to allow for general use in the structural analysis. It considers effective flexibilities of members in the cracked state using either the curvature distribution along the member or available effective stiffness models under any loading or support condition. In general, structural concrete members can be considered to have three cracked regions (two at the ends and one at midspan) and two uncracked regions along their length. In this numerical procedure, the contributions of these regions to the member stiffness matrix are computed using a numerical integration technique. Using this procedure, a software program is developed which allows for the load–deflection behavior of a member reinforced with either FRP or steel bars and subjected to any loading or support condition to be rapidly determined. This calculation procedure is evaluated using available experimental data on the load–deflection behavior of simple and two-span beams reinforced with FRP and steel bars. Through comparison of the results, it is observed that the load–deflection behaviors calculated using the proposed approach utilizing the member moment–curvature response are consistent with the experimental data. This approach can provide a useful tool for the general calculation of deflection regardless of reinforcement type and can be used throughout the entire range of member behavior up to flexural failure.