## 6 An Example for the Usage of the Proposed Method  
Example calculation for the ultimate capacity of a perforated plate strengthened with FRP under uniaxial compression, according to the winter equations in (22)-(24), where \(\rho\) is a slenderness reduction factor, \(\lambda\) is the plate slenderness, \(f_{y}\) is the yield stress of the steel, and \(f_{\sigma}\) is the critical stress. \(f_{\sigma}\) can be calculated using this method of this paper. \[\rho\ =\ \frac{\lambda-0.22}{\lambda^{2}}\leq 1 \tag{22}\]  
\[\lambda\ =\ \sqrt{\frac{f_{y}}{f_{\sigma}}} \tag{23}\]  
\[P_{u}\ =\ \rho f_{y}bt_{t} \tag{24}\]  
**The basic parameters of the example (Table 2, No. 7):**\(a=b=240\) mm, \(d/b=0.1\), \(e_{x}/b=0.5\), \(e_{x}/b=0.5\), \(t_{s}=2.61\) mm, \(t_{f0}=0.167\) mm, \(n_{f}=1\), \(E_{s}=2.0\times 10^{5}\) MPa, \(E_{f}=2.6\times 10^{5}\) MPa, \(v_{s}=0.3\), \(v_{f}=0.25\),\(f_{y}=287.8\) MPa, BCs: 4S. **The critical stress \(\boldsymbol{f_{crCal}}\):**  
\(t_{t}=2.61+0.167=2.777\) (mm), \(\alpha=\frac{E_{f}/(1-v_{f}^{2})}{E_{s}/(1-v_{f}^{2})}=1.225\), \(\beta=\frac{t_{f}}{t_{s}}=0.064<0.2\),  
\(D_{0}=C_{0}-B_{0}^{2}/A_{0}=E_{s}t_{s}^{3}/12\big{(}1-v_{s}^{2}\big{)}=3.35 \)E5, \(D_{t}/D_{0}=1+3\alpha\beta=1.24\), \(D_{t}=4.14\)E5, \(e_{x}/b=0.5\), \(\beta=1\), \(d/b=0.1\) from Figure 20, \(K_{u}=3.77\),  
\(\omega=\frac{n_{f}E_{f}t_{f0}}{E_{s}t_{s}}=0.0784\), from Equation (20), \(\alpha_{D}=(1.2d/b+0.7)\omega^{2}-(1.6d/b+0.74)\omega+1=0.947\),  
\(f_{crCal}=\alpha_{D}K_{u}\frac{\pi^{2}}{t_{t}b^{2}}D_{t}=90.13\) (MPa). **The ultimate capacity \(\boldsymbol{P_{uCal}}\):**  
\(f_{y}=287.8 MPa\), \(\lambda=\sqrt{\frac{f_{y}}{f_{cr}}}=1.79\),  
\(\rho=\frac{\lambda-0.22}{\lambda^{2}}=0.491\leq 1\),  
\(P_{uCal}=\rho f_{y}bt_{t}=94.12\) (KN). The experimental values of critical stress\(f_{crExp}\) and ultimate load \(P_{uExp}\) are 92.87 MPa and 96.64 KN, it is obvious that the values of \(f_{crCal}\) and \(P_{uCal}\) are very close to \(f_{crExp}\) and \(P_{uExp}\), respectively. Other plates are also calculated using this method and plotted in Table 2.  
**7. Conclusions and Recommendations**  
In order to study the elastic stability and propose a calculation method of perforated plates strengthened with FRP under uniaxial compression, series of FE models are built and several parameters are considered in the study: material's geometrical and mechanical properties, boundary conditions, plate aspect ratio, hole sizes, and hole position. A calculation method of buckling stress is proposed and modified based on the theory of composite plate and the numerical results. In addition to the detailed discussion and conclusions given in the previous section, some general conclusions and recommendations can be summarized as follows:  
* The theory of composite plate proposed by [PERSON] is available to calculate the flexural rigidity of the pure steel plate and the perfectly bonded layered plate, but it should be modified when calculating the flexural rigidity of the perfectly bonded layered plate due to not considered the orthotropic properties of FRP. * The buckling coefficient \(k\) needs to be modified as \(K_{u}\) which considers the change of plate aspect ratio \(\beta\), hole sizes \(d/b\) and the hole position \(e_{x}\) (or \(e_{y}\)). * For BCs of 4S, when \(e_{x}/b\) is an integer, the buckling mode shapes change as \(d/b\) is enlarged, which cause some discontinuities in \(K_{u}\) vs. \(d/b\) curves (Figure 20). And for BCs of 3 SIF, the buckling mode shapes is unchanged irrespective of \(d/b\). * For BCs of 4S, as \(e_{x}/b\) is enlarged from 0 to 0.5, \(K_{u}\) decreases but gradual slow for \(d/b\) is 0.1, and first increases and then decrease for \(d/b\) is 0.2 and 0.3, and drastically increases for \(d/b\) is enlarged from 0.4 to 0.7. It means that when \(d/b\) is bigger than 0.4 and \(e_{x}/b\) is less than 0.5, the buckling coefficient \(K_{u}\) is very unstable, so it should be avoided to place big hole too close to the loading edge in \(x\)-axis, especially when \(d/b\) is bigger than 0.4.