GBT-based finite element to assess the buckling behaviour of steel–concrete composite beams

• A GBT-based finite element for the buckling analysis of steel-concrete beams is proposed.
• Shear lag, concrete cracking, distortion and web local deformation effects are considered.
• Discrete changes of the cross-section can be considered.
• The GBT modal solution provides an in-depth insight into the buckling behaviour of composite beams.

In this paper, an accurate and computationally efficient Generalised Beam Theory (GBT) finite element is proposed, which makes it possible to calculate buckling (bifurcation) loads of steel–concrete composite beams subjected to negative (hogging) bending. Two types of buckling modes are considered, namely (i) local (plate-like) buckling of the web, possibly involving a torsional rotation of the lower flange, and (ii) distortional buckling, combining a lateral displacement/rotation of the lower flange with cross-section transverse bending. The determination of the buckling loads is performed in two stages: (i) a geometrically linear pre-buckling analysis is first carried out, accounting for shear lag and concrete cracking effects, and (ii) an eigenvalue buckling analysis is subsequently performed, using the calculated pre-buckling stresses and allowing for cross-section in-plane and out-of-plane (warping) deformation. The intrinsic versatility of the GBT approach, allowing the incorporation of a relatively wide range of assumptions, is used to obtain a finite element with a reasonably small number of DOFs and, in particular, able to comply with the principles of the “inverted U-frame” model prescribed in Eurocode 4 [1]. Several numerical examples are presented, to illustrate the application of the proposed GBT-based finite element and provide clear evidence of its capabilities and potential.