Shear and normal interaction stresses via strain–moment plots

The present paper focuses on prediction of FRP-to-steel longitudinal shear stresses in yield zones of loaded steel beams with bonded fibre reinforced polymer (FRP) strips. Application of multi-variable differential calculus reveals that two physically meaningful quantities permit considerable insight into the longitudinal variations of these shear stresses. One of these quantities—the rate of change of FRP strain with total section moment—is a characteristic of the FRP-steel hybrid section, and is of course readily obtained from the plot of FRP strain versus section moment. The other quantity, the shear force, represents the effect of the applied load along the member. The merits of this approach to longitudinal shear prediction are compared with those of an alternative method developed previously. Illustrative numerical examples are provided. It is then shown that the accompanying FRP-to-steel normal stress is here influenced mainly by the rate of change along the member of the longitudinal shear stress. This fact in turn leads to striking differences between normal stresses obtained from rigid bond analyses and those obtained via bond-slip analyses. Hence it is shown that while rigid bond analysis may be preferred for reduced complexity and greater time efficiency, such analysis may lead to erroneous conclusions on proximity to bond failure in yield zones. Finally, an efficient method for establishing the maximum height of tension yield in the steel web near the FRP strip is presented, and the importance of this height to buckling-restraint of the web is discussed.