Analytical Models for Load and Warping in Kinematic Bending With Partial Heating of Profiles With Arbitrary Asymmetric Cross Section

Abstract The difference between the position of the load axis and the shear center leads to warping in asymmetric bending of profiles. In a previous study, partial heating during bending was proposed to reduce warping. This work did prove the reduction of warping for an L-shaped cross section using experimental and numerical data and an analytical model for the description of the bending moment and profile warping was created. However, the analytical model was not able to describe the movement of the shear center position and was restricted to the description of L-profiles. The present work generalizes the previous analytical model to describe the movement of the shear center position due to the heating strategy for any cross section. Additionally, descriptions for strain-free fiber, force calculation, and warping have been adjusted to achieve high accuracy when modeling arbitrary profile cross sections. The analysis is carried out on the example of L- and U-shaped profiles consisting of S500MC fine grain steel. Using the adjusted model, the error in the prediction of bending load has been reduced from 30% to 4% and for warping the error changes from 46% to 6%. The reason for the deviation can be attributed to less simplified force and strain-free fiber calculations as well as a simplification approach of bending angle by linearization. A formulation for the shear center movement has been successfully implemented, showing that the shear center moves in the direction of the load axis with the analyzed partial heating strategies.