Optimized non-linear solution for bending wide flange steel beams about their strong axis

Abstract

Cold bending is commonly used for inducing cambers in wide flange steel beams. In this process, the girder is bent about its strong axis using single or dual symmetrically applied concentrated loads and the desired camber develops based on the induced permanent mid-span deformation. In the absence of set criteria, the accuracy of the method relies exclusively on trial and error. This paper derives a non-linear solution that can accurately predict the magnitude of the loads and induced deformations for double-ram systems,which allows optimizing themand increasing their efficiency. Closed form solutions are derived based on idealized elasto-plastic stress-strain curves as a function of the steel girder shape and geometry. Loads are calculated from inelastic stress distributions and equilibrium of moments. Induced deformations are determined from integration of curvatures. Sensitivity analyses are then conducted to identify appropriate values of loads and deformations and their impact on alternative cambering set-ups for dual-load systems. The analysis shows that these systems can develop the required camber profile at small loads without overstraining the steel section. The best results are obtained if the spacing between the loads is kept within one-third to one-quarter of the span. Limits on loads and residual strains that prevent localized damage are finally proposed to ensure they are within acceptable norms.