## 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} \hline \hline
**Span Length (m)** & \(L\) = & **4** & **5** & **6** & **7** \\ \hline Slenderness & \(\lambda\)=b/t= & & & 30.25 & & \\ Euler stress (N/mm\({}^{2}\)) & flange \(\sigma_{\text{E,i}}\) = & & & 207.64 & & \\  & web \(\sigma_{\text{E,i}}\) = & & 50.23 & & \\ Length of ranges (m) & \(l_{p}\)= & 1600 & 2000 & 2400 & 2800 \\  & \(l_{s}\)= & 843 & 1050 & 1263 & 1474 \\ Buckling coefficient & for \(l_{p}\): k\({}^{*}\)= & 0.94 & 0.93 & 0.92 & 0.92 \\  & for \(l_{s}\): k\({}^{*}\)= & 1.11 & 1.08 & 1.05 & 1.04 \\ Critical stress acc. to CPM & for \(l_{p}\): \(\sigma_{\text{cr,s}}\)= & 195.42 & 193.34 & 191.98 & 191.03 \\  (N/mm\({}^{2}\)) & for \(l_{s}\): \(\sigma_{\text{cr,s}}\)= & 230.47 & 223.70 & 218.80 & 215.20 \\ Critical stress acc. to EC3 & \(\sigma_{\text{cr,0}}\)= & & 89.28 & & \\ (N/mm\({}^{2}\)) & for \(l_{p}\): \(M_{cr,p}^{L}\)= & 64.13 & 63.45 & 63.00 & 62.69 \\ “Local” critical resistance (kNm) & for \(l_{s}\): \(M_{cr,s}^{L}\)= & 75.63 & 73.41 & 71.80 & 70.62 \\  & \(M_{cr}^{EC3}\)= & & 29.30 & & \\ Critical load acc. to CPM & for \(l_{p}\): \(q_{cr}^{CP}\)= & 51.45 & 32.58 & 22.47 & 16.42 \\  (kN/m) & for \(l_{s}\): \(q_{cr,s}^{EC3}\)= & 44.91 & 27.90 & 18.95 & 13.69 \\ Critical load acc. to EC3 & \(q_{cr}^{EC3}\)= & 17.40 & 11.13 & 7.73 & 5.68 \\ Percentage increment of & \(q_{cr}^{CP}/q_{cr}^{EC3}\)= & 158.13 & 150.54 & 145.06 & 141.03 \\  & for \(l_{p}\): \(M_{eff}^{CP}\)= & 89.15 & 88.94 & 88.80 & 88.71 \\  & for \(l_{s}\): \(M_{eff}^{CP}\)= & 92.43 & 91.82 & 91.38 & 91.04 \\  & \(M_{<,Rd}^{EC3}\)= & & 75.77 & & \\ Ultimate load acc. to CPM & for \(l_{p}\): \(q_{eff,p}^{CP}\)= & 71.52 & 45.67 & 31.67 & 23.24 \\  (kN/m) & for \(l_{s}\): \(q_{eff,s}^{CC3}\)= & 54.88 & 34.89 & 24.11 & 17.65 \\ Ultimate load acc. to EC3 & for \(l_{s}\): \(q_{eff}^{EC3}\)= & 44.99 & 28.79 & 19.99 & 14.69 \\  & Percentage increase of & \(q_{eff}^{CP}/q_{eff}^{EC3}\)= & 21.99 & 21.19 & 20.60 & 20.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of results according to CPM and EC3 for the 2C-250\(\times\)250\(\times\)4 section and four span-length range variants. 1.74. Of course, this does not change the fact that the critical and ultimate resistance of an internal plate is much higher than that of a cantilever plate with the same geometrical and material parameters. In turn, Table 6 compares the design ultimate resistances (\(M_{eff}^{CP}\), \(q_{eff}^{CP}\)) of the same box section beams [6] and 2C compound I-sections, also depending on the span length. For the 2C sections, the design ultimate resistances \(M_{eff}^{CP}\) determined according to CPM were on average 4-5% lower than the corresponding box sections. The reduction, however, of \(M_{eff}^{EC3}\) was nearly 14%. The same relationship occurred when comparing the respective ultimate loads \(q_{eff}\). In this case, the relation \(q_{eff}^{CP}/q_{eff}^{EC3}\) for the 2C sections in relation to Sk sections increased by 11%. Table 7 presents the results of the analysis of the slenderness effect (\(b_{s}/t\)) of the compressed cantilever wall of 2C section on the value of \"local\" critical moment \(M_{cr}^{L}\) and the design ultimate resistance \(M_{eff}\) determined according to CPM and EC3. The calculations were made for a continuous beam with a span length of \(L=4\) m. With the reduction of section wall thickness, the critical load \(q_{cr}\) decreased, whereby the difference between the results obtained according to CPM and EC3 was about +158% regardless of the slenderness of the critical plate. The reduction in thickness also reduced the design ultimate resistance \(M_{eff}\) and the ultimate load \(q_{eff}\), whereby the difference between the results according to CPM and EC3 was about +23% for t = 5 mm and about +16% for t = 2 mm.