## 2 Materials and Methods
### Models' Assumptions  
Only the main description and equations were presented in the paper. The material properties for wood were taken from the PN-EN 14080 standard [28] and for CFRP tapes as the producer declared [29]. Structural wood used in Poland is usually coniferous (Pine or Spruce) and called \"softwood\". Both the species have similar mechanical properties. The one used in the calculations was GL24h glue laminated timber class. This means that the modulus of elasticity was equal to \(E_{0,mean}=11.5\) GPa, shear modulus \(G_{mean}=0.65\) GPa and bending strength \(f_{m,k}=24\) MPa.  
Glue laminated timber beams without strengthening were noted as BSH and beams made of wood-CFRP composite as BSH-CFRP. Only one reinforcing technique was considered--CFRP tape glued above the bottom wooden lamella (Figure 4)--which was identified as the most effective. The properties of BSH beams may be calculated as for a simple rectangular cross-section, as shown in Figure 5. The cross-sectional area (\(A\)) and moment of inertia (\(J\)) should be calculated from Equation (1), consecutively.  
\[A=bmh_{L},\ J=\frac{b(mh_{L})^{3}}{12} \tag{1}\]  
For BSH-CFRP-beams, the equivalent area method should be used (Figure 6).  
Figure 5: Denotations for BSH beams: \(m\)—number of wooden lamellas (as marked), \(h_{L}\)—height of a single lamella, \(E_{0,mean}\)—modulus of elasticity of wood in bending, \(h\)—entire height of the cross-section, \(b\)—width of the cross-section, \(y_{0}\)—distance of the bottom from the centre of gravity of the cross-section.  
The equations to calculate the cross-sectional properties of BSH-CFRP-beams are Equations (2)-(6). The denotations used in the formulas are: \(S_{x}\)--cross-sectional static moment, \(A\)--cross-sectional area and \(J\)--total moment of inertia.  
\[n=0.85\frac{E_{CFRP}}{E_{0,mean}},\ S_{x}=S_{x,I}+S_{x,II}+S_{x,III},J=J_{I}+J_{ II}+J_{III},\ y_{0}=\frac{S_{x}}{A} \tag{2}\]  
\[A=b[h_{L}(m+1)+nt_{CFRP}],\ S_{x,I}=bmh_{L}\bigg{(}h_{L}+t_{CFRP}+\frac{1}{2} mh_{L}\bigg{)} \tag{3}\]  
\[S_{x,II}=nbt_{CFRP}\bigg{(}h_{L}+\frac{1}{2}t_{CFRP}\bigg{)},\ S_{x,III}=\frac{1 }{2}bh_{L}{}^{2} \tag{4}\]  
\[J_{I}=\frac{b(mh_{L})^{3}}{12}+bmh_{L}\bigg{(}h_{L}+t_{CFRP}+\frac{1}{2}mh_{L }-y_{0}\bigg{)}^{2} \tag{5}\]  
\[J_{II}=\frac{nbt_{CFRP}}{12}+nbt_{CFRP}\bigg{(}y_{0}-h_{L}-\frac{1}{2}t_{CFRP }\bigg{)}^{2},\ J_{III}=\frac{bh_{L}}{12}^{3}+bh_{L}\bigg{(}y_{0}-\frac{h_{L}} {2}\bigg{)}^{2} \tag{6}\]  
An estimation of the load capacity (\(P_{max}\)) for both presented types of the beams in four-point bending, where \(L\) is the length of the beam and \(f_{m,k}\) is wood bending strength according to standard wood class [28], may be completed using Equation (7):  
\[P_{\max}=\frac{6 lf_{m,k}}{Ly_{0}} \tag{7}\]  
Deflection in the middle of the beam (\(w_{max}\)) when the maximal force (\(P_{max}\)) is reached may be calculated from Equation (8). The main material's properties are: \(E_{0,mean}\)--modulus of elasticity of wood in bending and \(G_{mann}\)--shear modulus of wood.  
\[w_{\max}=\frac{23}{1296}\frac{P_{\max}L^{3}}{E_{0,mean}}+\frac{1}{5}\frac{P_{ \max}L}{G_{mean}A} \tag{8}\]  
The results are planned to be presented as a comparison between reinforced and unreinforced beams. Because of that, only one static scheme is representative. The stiffness of the beam (\(K\)) may be defined as Equation (9):  
\[K=\frac{P_{\max}}{w_{\max}} \tag{9}\]  
Figure 6: Denotations for BSH-CFRP beams: \(m\)—number of wooden lamellas (as marked), \(h_{L}\)—height of a single lamella, \(E_{0,mean}\)—modulus of elasticity of wood in bending, \(h\)—entire height of the cross-section, \(b\)—width of the cross-section, \(y_{0}\)—distance of the bottom from the centre of gravity of the cross-section, \(t_{CFRP}\)—CFRP tape thickness, \(E_{CFRP}\)—modulus of elasticity of CFRP tape, \(n\)—coefficient modifying the width of CFRP tape.