Self-equilibrating moments in FRP-reinforced continuous structures

In continuous steel or concrete structures with surface-mounted fibre reinforced polymer (FRP) plates as flexural reinforcement, self-equilibrating moments can influence the loads at first yield and at failure, the latter due to potential buckling of the FRP plate or to end-peel both on account of offsets between points of contraflexure and the nearby FRP curtailments. In this paper, expressions are derived for the total (including self-equilibrating) moments along 2-span continuous structures with differential settlement. The expressions show how moments depend on support-to-member stiffness ratios and on distributions of section stiffness for service and ultimate limit states. Thus, the analysis is generic, applicable to FRP-reinforced steel and concrete structures. This analysis is verified via test data (including observation of end-peel in FRP compression curtailment zones offset from nearby contraflexure) and is used to construct 3D plots that facilitate identification of stiffness ratios which lead to significant self-equilibrating moments and contraflexure offset effects. Use of the plots to assess influences of differential settlement on laboratory test specimens is discussed. The analysis is shown to lead to an unprecedented result, namely that a unique point of load application exists for which changes to the stiffness layout have no impact on the moment distribution.