A physically non-linear GBT-based finite element for steel and steel-concrete beams including shear lag effects

• A physically non-linear GBT-based finite element for steel and steel-concrete beams is presented.
• Concrete non-linear material behaviour, steel plasticity and shear lag effects are included.
• Numerical and analytical solutions are presented.
• The examples demonstrate that the element is computationally very efficient.

This paper introduces an accurate and computationally efficient GBT-based finite element, specifically tailored to capture the materially non-linear behaviour of wide-flange steel and steel-concrete composite beams up to collapse. The element incorporates reinforced concrete cracking/crushing, shear lag effects and steel beam plasticity (including shear deformation of the steel web). A set of numerical examples is presented, showing that the proposed element is capable of capturing all relevant phenomena with a very small computational cost. In addition, analytical solutions for elastic shear lag are derived and the GBT modal decomposition features are employed to extract valuable information concerning the effect of shear lag phenomena up to collapse. For validation and comparison purposes, results obtained with shell/brick finite element models are also presented.