## 7 Example of Using CPM to Determine the Resistance of a Continuous I-Beam
### I-Section Consisting of Two Cold-Formed Channel Sections (2C)
In this case, the relation \(q_{cr}^{CP}/q_{cr}^{EC3}\) for 2C sections in relation to Sk box sections increased by 62.7%. In turn, Table 9 compares the design ultimate resistances (\(M_{eff}^{CP}\), \(q_{eff}^{CP}\)) of the same beams with box sections Sk according to Reference [6] and compound I-sections (2C), also depending on the wall thickness. For 2C sections, the design ultimate resistances \(M_{eff,s}^{CP}\) determined according to CPM, in relation to the corresponding box sections Sk, were reduced by 3.1% for t = 5 mm to 5% for t = 2 mm. For \(M_{eff,p}^{CP}\) the differences ranged from 3.8% for t = 5 mm to 5.1% for t = 2 mm. In contrast, the reduction in \(M_{eff}^{EC3}\) ranged from 13.6% for t = 5 mm to 11% for t = 2 mm. The same relationship occurred when comparing the respective ultimate loads \(q_{eff}\). In this case, the relation \(q_{cr}^{CP}/q_{cr}^{EC3}\) for 2C sections in relation to Sk box sections increased from 6.9% for t = 2 mm to 12.2% for t = 5 mm  
Figure 11 shows the relation between the \"local\" critical moment \(M_{cr,s}\) (Figure 11a) and the design ultimate resistance \(M_{eff}\) (Figure 11b) as a function of slenderness \(\lambda_{CP}=b_{s}/t\) of the critical cantilever plate of a compound I-section (2C). Comparison of the graphs shown in Figure 11a showed that the \"local\" critical resistance and the design ultimate resistance decreased non-linearly with increasing slenderness of the cross-section wall. The difference between the value \(M_{cr,s}\) determined by the CPM method and the standard approach according to EC3 was constant in each case of wall thickness and was +158.1%. In contrast, the decrease of \(M_{eff}\) (Figure 11b) was mildly non-linear. The percentage increase of the ultimate resistance according to CPM in relation to EC3 was basically directly proportional to the increase of the cross-section wall thickness from about 16% for t = 2 mm (\(\lambda_{CP}=61.5\)) to about 23% for t = 5 mm (\(\lambda_{CP}=24\)). The relation between the critical load \(q_{cr}\) (Figure 12a) and the ultimate load \(q_{eff}\) (Figure 12b) as a function of the span length is shown in Figure 12. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{\(t\) (mm)} & \multicolumn{2}{c}{\(M_{eff,p}^{CP}\)} & \(M_{eff,s}^{CP}\) & \(M_{eff,s}^{EC3}\) & \(q_{eff,s}^{CP}\) & \(q_{eff,s}^{EC3}\) & \(q_{eff,s}^{CP}/q_{eff}^{EC3}\) \\ \hline \multirow{2}{*}{5} & SK & 127.41 & 131.27 & 119.58 & 77.94 & 71.00 & 1.10 \\  & 2C & 122.56 & 127.15 & 103.28 & 75.50 & 61.32 & 1.23 \\  & \% & –3.80 & –3.14 & –13.64 & –3.14 & –13.64 & 12.16 \\  & SK & 93.62 & 96.59 & 87.79 & 57.35 & 52.12 & 1.10 \\  & 2C & 89.15 & 92.43 & 75.77 & 54.88 & 44.99 & 1.22 \\  & \% & –4.78 & –4.31 & –13.69 & –4.31 & –13.69 & 10.87 \\  & SK & 62.80 & 64.75 & 59.05 & 38.45 & 35.06 & 1.10 \\  & 2C & 59.47 & 61.51 & 51.38 & 36.52 & 30.51 & 1.20 \\  & \% & –5.29 & –5.01 & –12.98 & –5.01 & –12.98 & 9.16 \\  & SK & 36.12 & 37.11 & 34.24 & 22.04 & 20.33 & 1.08 \\  & 2C & 34.28 & 35.26 & 30.43 & 20.94 & 18.07 & 1.16 \\  & \% & –5.10 & –4.99 & –11.12 & –4.99 & –11.13 & 6.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of design ultimate resistances of box sections (Sk) and I-sections (2C) depending on wall thickness. Comparison of the graphs shown in Figure 12 showed that an increase in the span length caused a non-linear decrease both in \(q_{cr,s}\) and \(q_{eff}\). Moreover, it can be stated that the shorter the span, the greater the percentage increase of the critical resistance determined according to CPM in relation to EC3 (from 158% for short beams \(L\) = 4 m, to 141% for long beams \(L\) = 7 m). For ultimate resistance (Figure 12b), the differences in results ranged from 22% for \(L\) = 4 m to about 20% for \(L\) = 7 m, respectively). Figure 12: _Cont._