# Behaviour Analysis of Beam-Type Timber and Timber-Concrete Composite Panels
## 2 Materials and Methods
### Design Method for Timber-Concrete Composite Structural Members  
A simplified design method based on the transformed section method and the \(\gamma\)-method outlined in Annex B of EN1995-1-1 [25] for mechanically jointed beams was considered for behaviour analysis of the beam-type timber-concrete composite panels [25; 26; 27; 28]. Timber panels were analysed by the \(\gamma\)-method. The determination of the geometric parameters of the section transformed into the timber of CLT layers with the grains oriented parallel to the longitudinal axis of the member was carried out at the first stage of the design process. The widths of all the layers, excluding the mentioned ones, should be multiplied by the reduction factor equal to the relation of the moduli of elasticity of the considered layer to the modulus of elasticity of the timber of the CLT layers parallel to the grain direction. An example of the transformed section obtained for the TCC beam-type panel, considered in the current study, is shown in Figure 2.  
Figure 2: Transformed to the timber of CLT layers with the grains oriented parallel to the longitudinal axis of the member section of the TCC beam-type panel. The effective bending stiffness of the transformed section should be determined by Equation (1) as follows:  
\[\left(EI\right)_{ef}=\sum_{i=1}^{n}\left(E_{i}\times I_{i}+\gamma_{i}\times E_{i }\times A_{i}\times a_{i}^{2}\right) \tag{1}\]  
where \(E_{i}\)--mean value of modulus of elasticity of separate material layer, MPa; \(I_{i}\)--moment of inertia of the separate layer relative to its own main axis, mm4; \(\gamma_{i}\)--reduction factor, which takes into account compliance of the bonds; \(A_{i}\)--area of cross-section of the separate layer, mm2; \(a_{i}\)--distance from the neutral axis of the whole cross-section to the neutral axis of the separate layer, mm. The reduction factor \(\gamma_{i}\) is equal to 1 in the case of an adhesive timber-to-concrete connection. An approach described in Annex B of EN1995-1-1 should be used for the determination of the values of reduction factor \(\gamma_{i}\) in the case of mechanical fasteners being used for timber-to-concrete connections. The maximum normal stresses acting at the edge fibre of the transformed section, should be determined by Equation (2) as follows:  
\[\left(\sigma\right)_{max}=\frac{M_{d}\times E_{i}}{\left(EI\right)_{ef}}\times \left(\gamma_{i}\times a_{i}+0.5\times h_{i}\right) \tag{2}\]  
where \(M_{d}\)--design value of bending moment, kNm, and \(h_{i}\)--the height of the separate layer, mm. Maximum shear stresses should be obtained by Equation (3) as follows:  
\[\tau_{max}=\frac{V_{d}\times\left(ES\right)_{ef}}{\left(EI\right)_{ef}\times b} \tag{3}\]  
where \(V_{d}\)--design value of shear force, kN; \(b\)--the width of the separate layer, where shear stresses are calculated, mm; \(\left(ES\right)_{ef}\)--effective statical moment of the transformed section, which can be determined by Equation (4) as follows:  
\[\left(ES\right)_{ef}=\sum_{i=1}\gamma_{i}\times E_{i}\times A_{i}\times a_{i} \tag{4}\]  
The instantaneous value of the maximum vertical displacements should be determined by Equation (5) for the case of three-point bending.