An efficient assessment of the vibration behaviour of cracked steel–concrete composite beams using GBT

In this paper, a previously developed GBT-based finite element (Henriques et al., 2020) is extended to allow calculating, very efficiently, natural frequencies and vibration mode shapes of steel–concrete composite beams, accounting for cross-section deformation (including shear lag effects) and concrete cracking. This new finite element enables a straightforward characterisation of the vibration modes, due to the unique modal decomposition features of GBT. The element aims at helping structural designers assess, very easily, the vibration behaviour of such beams at the serviceability limit state. A physically non-linear analysis is first carried out, accounting for cracking and cross-section deformation. Then, the natural frequencies and vibration mode shapes are calculated from the associated eigenvalue problem, with a very small computational cost. To illustrate the accuracy and potential of the proposed approach, two numerical examples are presented and discussed. For validation and comparison purposes, shell finite element model results are provided, showing that the proposed element leads to very accurate results with much less DOFs.