# Numerical Study on the Bending Resistance of Lightweight Built-Up Steel-Concrete Composite Beams
## 2 Materials and Methods
### Parametric Numerical Analyses  
The numerical model was created using ABAQUS/CAE software [34]. The model is based on a calibrated numerical model of a corrugated web beam (CWB) [35]. Figure 3 shows a comparison of experimentally and numerically obtained results for different magnitudes of initial geometric imperfection (i.e., L/500, L/1000, and L/1500, where L is a CWB beam span). The system's load is set as a vertical displacement of 100 mm in the middle of the span. The load is transferred using two constraints (MPC Beams) that are connected with a MPC Pin, which has a defined reference point (RP) where the load is assigned. Four loading points are used for transferring the load and are defined as kinematic couplings, as shown in Figure 4a. The model is formed as a simply supported beam whose ends are defined as coupling constraints, as shown in Figure 4b. The span of the LWT-FLOOR composite CFS-concrete beam is 6 m. The loading points are located 750 mm from the ends and are 1500 mm apart. The numerical modelling process consists of two steps. First, the initial imperfections are modelled using a static analysis; this produces an imperfect shape with an initial geometric imperfection of L/1500. Next, an explicit dynamic analysis is performed. The analyzed model consists of four CFS C-profiles which are connected to the CW and shear plates to form a unit of a steel beam. The concrete slab on a metal sheet is placed  
Figure 2: Simplified relationship between M and N\({}_{\rm c}\): (**a**) steel beam height of 400 mm; (**b**) steel beam height of 500 mm; (**c**) steel beam height of 600 mm. on the steel beam to form a composite beam. The total height of the concrete slab with ribs is 120 mm. The mesh size of the concrete slab is 30 mm and the assigned element type is C3D8R (an 8-node linear brick with reduced integration). The mesh size of the C-profiles is 15 mm, and the mesh size of the shear plates and CW is 10 mm. The assigned element type for the aforementioned steel elements is S4R (a 4-node doubly curved thin or thick shell). The mesh size of the shear connectors is 8.4 mm, and the assigned element type is B31 (a 2-node linear beam in space). The used concrete class is C25/30, in accordance with [36]. To define concrete damage behavior, different concrete damage plasticity (CDP) models can be found in the literature [37; 38; 39; 40; 41; 42]. The CDP model (shown in Figure 5a), in accordance with [13; 37; 38], is used to model concrete. The used material for all steel elements is S350 GD (Figure 5b), and the bolt quality is 8.8 (Figure 5c). General contact between all FE model parts occurred using the following parameters: normal direction-hard contact, transverse direction-friction contact with a friction coefficient of 0.1, and the free separation of elements to allow contact was permitted. To ensure the joint behavior of steel parts, the connection between them is secured in two ways: tie connection and spot welds. In cases where a tie connection is used, the touching surfaces are connected using a tie constraint. When spot welds are used for connecting C-sections, two and three spot welds are used, in accordance with [43]. The spot welds are secured with attachment points using Point-Based Fasteners with assigned properties investigated in [44; 45]. Each spot weld has defined elasticity, plasticity, damage and failure parameters. The connection section of the spot welds is secured using a bushing connector element that provides a connection between two nodes; this allows independent  
Figure 4: Numerical model of the analyzed composite beam: (**a**) Load introduction; (**b**) Support conditions. Figure 3: Comparison of experimentally and numerically obtained results: (**a**) CWB SW-1; (**b**) CWB SW-2, in accordance with [35]. behavior to occur in three local Cartesian directions, following the system in both nodes, and it allows for different behaviors to occur in two flexural rotations and one torsional rotation.