A Nonlinear Finite Element Model for Steel-concrete Composite Beam using a Higher-order Beam Theory

Abstract

Steel-concrete composite beams are commonly used in bridges, buildings and other civil engineering infrastructure for their superior structural performances. This is achieved by exploiting the typical configuration of this structural system where the concrete slab is primarily utilised to resist compressive stresses whereas the steel girder is used to sustain tensile stresses. The composite action is realised by connecting the concrete slab with the steel girder by steel shear studs. The interfacial shear slip is always observed due to the deformation of shear studs having a finite stiffness in reality which is commonly known as partial shear interaction. This is an important feature which should be considered in the analysis of these composite beams to get satisfactory results. It is observed that most of the existing models for simulating composite beams are based on Euler-Bernoulli’s beam theory (EBT) which does not consider the effect of shear deformation of the beam layers. In recent past, the incorporation of this effect is becoming popular and some attempts have already been made where Timoshenko’s beam theory (TBT) is typically used. In this beam theory (TBT), the true parabolic variation of shear stress over the beam depth is replaced by a uniform shear stress distribution over the beam depth to simplify the problem. In order to address this issue, a higher-order beam theory (HBT) has recently been developed at the University of Adelaide. However, the model is so far applied to the linear analysis of these beams. In the present study, a comprehensive nonlinear finite element model is developed based on HBT for an accurate prediction of the bending response of steel-concrete composite beams with partial shear interaction. This is achieved by taking a third order variation of longitudinal displacement over the beam depth for the steel and the concrete layers separately. The deformable shear studs used for connecting the concrete slab with the steel girder are modelled as distributed shear springs along the interface between these material layers. The effects of nonlinearities produced by large deformations and inelastic material behaviours are incorporated in the formulation of the proposed one-dimensional finite element model. The Green-Lagrange strain vector is used to capture the effect of geometric nonlinearity due to large deformations. The von Mises yield criterion with an isotropic-hardening rule is used for modelling the inelastic behaviour of steel girders, reinforcements and steel shear studs. This modelling approach is also applied to the region of concrete slab subjected to compressive stress for simplicity. A damage mechanics model is adopted to simulate the cracking behaviour of the concrete under tensile stress. The nonlinear governing equations are solved by an incremental-iterative technique following the Newton-Raphson method. A robust arc-length method is employed to capture the post peak response successfully where the energy dissipation played an important role. To assess the performance of the proposed model, the results predicted by the model are compared with existing experimental results as well as numerical results produced by using a detailed two dimensional finite element modelling of the composite beams.