## 7 Example of Using CPM to Determine the Resistance of a Continuous I-Beam
### I-Section Consisting of Two Cold-Formed Channel Sections (2C)
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**L (m)**} & \mul  
Note: for comparison, Table 7 also includes the values of \(q_{cr}\) and \(q_{eff}\) determined according to CPM for the case where the resistance of the beam is decided by the span section. This would be the case, for example, in protection against local buckling of the support segment. Table 8 compares the \"local\" critical resistances (\(M_{cr}^{L}\), \(q_{cr}\)) of beams with box sections [6] and compound I-sections (2C) depending on the wall thickness (t = 5, 4, 3, and 2 mm). Comparison of the values presented in Table 8 shows that for 2C sections, where critical resistance is determined by cantilever walls, \"local\" critical moments \(M_{cr,s}^{L}\) determined according to CPM were lower in relation to corresponding box sections by approx. 24.3% for t = 5 mm, up to 27.3% for t = 2 mm. For \(M_{cr,p}^{L}\), the differences ranged from 25.4% for t = 5 mm to 28.3% for t = 2 mm. For \(M_{cr}^{\rm EC3}\), \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Wall Thickness (mm)** & \(t=\) & **5** & **4** & **3** & **2** \\ \hline Slenderness & \(\lambda\)=b/t= & 24.00 & 30.25 & 40.67 & 61.50 \\ Euler stress (N/mm\({}^{2}\)) & plate \(\sigma_{\rm E,i}\)= & 329.86 & 207.64 & 114.89 & 50.23 \\  & web \(\sigma_{\rm E,i}\)= & 79.13 & 50.23 & 28.03 & 12.36 \\ Buckling coefficient & for \(l_{p}\): k*= & 0.94 & 0.94 & 0.94 & 0.94 \\  & for \(l_{s}\): k*= & 1.11 & 1.11 & 1.11 & 1.11 \\ Critical stress acc. to CPM (N/mm\({}^{2}\)) & for \(l_{p}\): \(\sigma_{\rm C,res}\)= & 310.46 & 195.42 & 108.13 & 47.28 \\ Critical stress acc. to EC3 (N/mm\({}^{2}\)) & for \(l_{s}\): \(\sigma_{\rm C,res}\)= & 366.13 & 230.47 & 127.52 & 55.76 \\ Critical stress acc. to EC3 (N/mm\({}^{2}\)) & \(\sigma_{\rm C,0}\)= & 411.84 & 89.28 & 49.40 & 21.60 \\  & for \(l_{s}\): \(M_{cr}^{L}\)= & 126.49 & 64.13 & 26.80 & 7.86 \\ “Local” critical resistance (kNm) & for \(l_{s}\): \(M_{cr}^{L}\)= & 149.17 & 75.63 & 31.60 & 9.28 \\  & \(M_{cr}^{EC3}\)= & 57.79 & 29.30 & 12.24 & 3.59 \\ Critical load acc. to CPM (kN/m) & for \(l_{s}\): \(\sigma_{\rm C,res}^{L}\)= & 101.49 & 51.45 & 21.50 & 6.31 \\  & for \(l_{s}\): \(\sigma_{\rm C,res}^{L}\)= & 88.57 & 44.91 & 18.76 & 5.51 \\ Critical load acc. to EC3 (kN/m) & \(q_{cr}^{EC3}\)= & 34.31 & 17.40 & 7.27 & 2.13 \\ Percentage increment of resistance (\%) & \(q_{cr}^{CP}/q_{cr}^{EC3}\)= & \multicolumn{4}{c}{158.13} \\  & for \(l_{p}\): \(M_{cr}^{CP}\)= & 122.56 & 89.15 & 59.47 & 34.28 \\ Design ultimate resistance (kNm) & for \(l_{s}\): \(M_{eff}^{CC}\)= & 127.15 & 92.43 & 61.51 & 35.26 \\  & \(M_{c,R}^{EC3}\)= & 103.28 & 75.77 & 51.38 & 30.43 \\ Ultimate load acc. to CPM (kN/m) & for \(l_{s}\): \(q_{eff,p}^{EC3}\)= & 98.33 & 71.52 & 47.72 & 27.50 \\  & for \(l_{s}\): \(q_{eff,p}^{EC3}\)= & 75.50 & 54.88 & 36.52 & 20.94 \\ Ultimate load acc. to EC3 (kN/m) & for \(l_{s}\): \(q_{eff}^{EC3}\)= & 61.32 & 44.99 & 30.51 & 18.07 \\ Percentage increment of resistance (\%) & \(q_{eff}^{CP}/q_{eff}^{EC3}\)= & 23.12 & 21.99 & 19.71 & 15.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of results according to CPM and EC3 for the 2C-250\(\times\)250\(\times\)t section and four wall thickness variants. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**f (mm)** & \(M_{cr,p}^{L}\) & \(M_{cr,s}^{L}\) & \(M_{cr}^{EC3}\) & \(q_{cr}^{CP}\) & \(q_{cr,s}^{EC3}\) & \(q_{cr,s}^{CP}\)/\(q_{cr}^{EC3}\) \\ \hline
**5** & **SK** & 169.45 & 197.05 & 124.23 & 117.00 & 73.76 & 1.59 \\  & **2C** & 126.49 & 149.17 & 57.79 & 88.57 & 34.31 & 2.58 \\  & **\%** & \(-25.35\) & \(-24.29\) & \(-53.48\) & \(-24.29\) & \(-53.48\) & 62.74 \\
**4** & **SK** & 87.09 & 101.27 & 63.85 & 60.13 & 37.91 & 1.59 \\  & **2C** & 64.13 & 75.63 & 29.30 & 44.91 & 17.40 & 2.58 \\  & **\%** & \(-2 the reduction was 53.5% for t = 5 mm to 55.3% for t = 2 mm. The same relationship occurred when comparing the respective critical loads \(q_{cr}\).