Some considerations on the long-term partial interaction behaviour of composite steel-concrete beams using displacement based finite elements

Abstract This paper presents some of the modelling techniques available in the literature to describe the long-term behaviour of composite steel-concrete beams with partial shear interaction. In particular, the attention is placed on displacement-based formulations. These consist of the finite difference method, the finite element method, the direct stiffness method and analytical solutions. These are derived by means of the principle of virtual work. The finite element method relies on the weak form of the problem while the remaining ones are derived from its strong form. The time-dependent behaviour of the concrete is modelled by means of the Age-adjusted Effective Modulus Method, while the other materials at the cross-section are assumed to be linear-elastic. The main difference between the modelling technique considered is that, while the finite difference method and the finite element method require discretisations in both spatial and time domains to complete a time analysis, the direct stiffness method and the analytical solutions require only the time discretisation. The ability of the proposed formulations to describe the time-dependent behaviour is then discussed using the solutions in closed form as a benchmark. Two different finite elements have been considered and the occurrence of curvature locking problems has been discussed. The comparisons have been carried out for three structural systems, i.e. for simply supported beams, propped cantilevers and fixed ended beams, subjected to a uniformly distributed load and to time effects. For each case, the minimum spatial discretisations required to keep the error within an acceptable tolerance has been identified