Numerical approach for bending stress ascertainment in beam theory considering effects of elastic shear lag

Abstract

In beam theory, normal stresses due to bending moments are usually determined with regard to Bernoullis hypothesis of the cross section staying in a plane state for reasons of simplicity. As a result of this fundamental assumption, the influence of shear on the distribution of normal stresses is not taken into account. However, for cross sections showing wide flanges, as they are commonly applied in bridge engineering for instance, the effect can usually not be disregarded. For the sake of capturing, stiffness oriented numerical approaches allowing the determination of the shear deformation behaviour of cross sections are applied and the shear influence is introduced into the normal stress calculation. This is being exemplarily shown for normal stresses due to bending moments M y.

Keywords

• beam theory
• cross sections
• shear deformations
• shear lag
• bending stresses
• finite elements