# Numerical Study on the Bending Resistance of Lightweight Built-Up Steel-Concrete Composite Beams
## 2 Materials and Methods
### Analytical Approaches for the Bending Resistance of Composite Beams
#### 2.1.2 Analytical Bending Resistance of Composite LWT-FLOOR Beams  
It was assumed that the analytical bending resistance of composite LWT-FLOOR beams could be calculated using three different approaches. The first approach calculates the plastic bending resistance. To calculate the characteristic plastic bending resistance, finding the position of the plastic neutral axis is necessary, and can be calculated in accordance with Equation (1):  
\[\mathrm{x_{pl,k}=4\times A_{a}\times f_{yk}/(b_{eff}\times 0.85\times f_{ck})}, \tag{1}\]  
where \(\mathrm{A_{a}}\) is the cross-section area of the CFS C profiles, \(\mathrm{f_{yk}}\) is the characteristic steel yield strength, \(\mathrm{b_{eff}}\) is the width of the reinforced concrete slab, calculated in accordance with Chapter 5.4 of EN 1994-1-1 [9], and \(\mathrm{f_{ck}}\) is the characteristic value of the cylinder compressive strength of concrete at 28 days. In the analyzed LWT-FLOOR cross-section, as shown in Figure 1, the position of the plastic neutral axis (n.a.) is assumed to be in the concrete, and the full degree of shear connection is achieved. Therefore, the whole steel section was placed under tense conditions, which allowed for the utilization of its plastic resistance, although the CFS sections are usually taken as cross-sections of class 3 or 4. Equation (2) enables the calculation of plastic bending resistance in the case of a full shear connection, in accordance with the first analytical approach:  
\[\mathrm{M_{pl,RK}=2\times A_{a}\times f_{yk}\times(h_{a}/2+h_{c}+h_{p}-x_{pl,k} /2)+2\times A_{a}\times f_{yk}\times(h-h_{a}/2+h_{c}+h_{p}-x_{pl,k}/2)} \tag{2}\]  
where \(h_{a}\) is the height of the CFS C section, \(h_{c}\) is the height of the concrete slab, and \(h_{p}\) is the height of the metal sheet rib, which is positioned perpendicular to the direction of the composite beam (see Figure 1). The calculated values for the characteristic plastic bending resistance in the case of a full shear connection for steel beam heights of 400 mm, 500 mm, and 600 mm, are 257.7 kNm, 299.7 kNm and 341.7 kNm, respectively. The second analytical approach, comprising a partial shear connection, may be used when the bolts are arranged in such a way that a full shear connection between steel and concrete parts cannot be achieved. In this case, the bending resistance is calculated by modifying the equation from Eurocode 4 [9]; the plastic bending resistance of the structural steel section \(\mathrm{M_{pl,a,RK}}\) is replaced with the elastic bending resistance of the structural steel section, \(\mathrm{M_{el,a,RK}}\), as shown in Equation (3) [13; 18]. \[\mathrm{M_{RK}=M_{el,a,RK}+(M_{pl,RK}-M_{el,a,RK})\times\eta}, \tag{3}\]  
where \(\mathrm{M_{pl,RK}}\) is the bending resistance of the composite beam in the case of full shear connection; this was calculated in accordance with Equation (2), and \(\eta\) is the degree of shear connection, which may be calculated using Equation (4):  
\[\eta=n/n_{full}. \tag{4}\]  
To calculate the degree of shear connection, it is necessary to understand the number of shear connectors required to achieve a full shear connection, \(n_{full}\). In Equation (4), \(n\) is the number of shear connectors used, and it is limited by the number of metal sheet ribs. Figure 1: Cross section of the analyzed LWT-FLOOR composite beam. In addition, the number of shear connectors can be varied by their position within the ribs; it is possible to use two bolts per rib or one bolt per rib, which are then placed in a staggered arrangement along the length of the beam. These two cases are considered in this paper, with the axial spacing of the metal sheet ribs being 240 mm. The quality of the bolts used as shear connectors is 8.8, which means that the tensile strength of the bolts is 800 N/mm\({}^{2}\). This falls outside the scope of the European standard [9], where the equations for calculating the resistance of headed shear studs are valid for tensile strengths up to 500 N/mm\({}^{2}\).