## 3 Results
### Verification of Engineering Example
#### 3.3.3 Stability Checking of Fastener Steel Pipe Support  
It is known that the rotation radius of the vertical rod section is i = 1.60 cm, the net cross-section area is A = 3.974 cm\({}^{2}\), the net cross-section resistance moment is W = 4.25 cm\({}^{3}\), and the compressive strength of the steel pipe is designed. The maximum support reaction force of the horizontal bar is N\({}_{1}\) = 6.072 kN (including the combination coefficient); the top vertical rod section N = 6.072 + 0.271 = 6.343 kN and the non-top vertical rod section N = 6.072 + 1.014 = 7.086 kN. The stability coefficient in the specification [11] and the stability coefficient given in this paper are used to calculate the fastener-type steel pipe support of the project. Taking the wind load as an example, the calculation results are as follows:  
When considering the wind load, according to the standard [12] calculation of the maximum axial pressure of the pole N:  
Top upright:  
\[\text{N}=6.072+1.350\times 0.201+0.9\times 0.980\times 0.016/0.600=6.366\text{ kN} \tag{6}\]  
Non-top upright:  
\[\text{N}=6.072+1.350\times 0.751+0.9\times 0.980\times 0.016/0.600=7.109\text{ kN} \tag{7}\]  
The bending moment of the vertical bar section generated by the wind load design value is calculated according to the formula in the specification [13; 14]:  
\[\text{M}_{\text{W}}=0.9\times 1.4\omega_{\text{k}}\text{l}_{\text{a}}\frac{ \text{h}^{2}}{10} \tag{8}\]  
\[\text{w}_{\text{k}}=\text{u}_{\text{z}}\times\text{u}_{\text{s}}\times w_{0}= 0.250\times 1.000\times 0.185=0.046\text{ kN}/\text{m}^{2} \tag{9}\]  
In the formula:  
\(\text{W}_{\text{k}}\)--characteristic value of wind load (\(\text{kN}/\text{m}^{2}\));  
H--Pole step distance, h = 1.5 m;  
\(\text{l}_{\text{a}}\)--The spacing of the windward side of the pole, \(\text{l}_{\text{a}}\) = 1.2 m.  
Therefore, the bending moment generated by wind load is  
\[\text{M}_{\text{W}}=0.9\times 1.4\text{w}_{\text{k}}\text{l}_{\text{a}}\text{h}^{ 2}/10=0.9\times 1.4\times 0.046\times 1.200\times 1.500\times 1.500/10=0.016 \text{ kN}/\text{m} \tag{10}\]  
For the top vertical bar section: when the vertical rod extension length a = 0.2 m, check the specification Schedule C-2 to get \(\text{l}_{\text{i}}\) = 1.649, the calculated length \(\text{l}_{0}\) = 3.619 m, and the slenderness ratio is allowed (when k takes 1):  
\(\lambda_{0}\) = 225.888/1.155 = 195.574 \(<\) 210. The slenderness ratio calculation meets the requirements. \(\Phi\) = 0.144 (standard value) and \(\varphi^{\prime}\) = 0.0998 (recommended value). Calculated according to the specification \(\varphi\) value:  
\[\sigma=\frac{\mathrm{N}}{\mathrm{A}}+\frac{\mathrm{M_{W}}}{\mathrm{W}}=\frac{6366 6}{0.144\times 397.4}+\frac{16000}{4248}=115.040\ \mathrm{N/mm^{2}} \tag{11}\]  
Calculated as recommended value \(\varphi^{\prime}\):  
\[\sigma=\frac{\mathrm{N}}{\mathrm{A}}+\frac{\mathrm{M_{W}}}{\mathrm{W}}=\frac{63 66}{0.998\times 397.4}+\frac{16000}{4248}=164.279\ \mathrm{N/mm^{2}} \tag{12}\]  
When \(\sigma=115.040\ \mathrm{N/mm^{2}}\), \(\sigma^{\prime}=164.279\ \mathrm{N/mm^{2}}\), the stability check of the pole is \(\sigma\), \(\sigma^{\prime}=[\mathrm{f}]\), which meets the requirements. Stability comparison:  
\[\frac{164.279-115.040}{115.040}\times 100\%=42.8\% \tag{13}\]  
For the non-top vertical bar section: check the specification Schedule C-4 to get the effective length coefficient \(\mu_{2}=1.951\), the effective length \(l_{0}=3.380\ \mathrm{m}\), and then the slenderness ratio:  
\[\lambda=\frac{l_{0}}{i}=\frac{3380}{16.0}=210.993 \tag{14}\]  
Permissible slenderness ratio (when k takes 1):  
\[\lambda_{0}=\frac{210.993}{1.155}=182.678<210 \tag{15}\]  
The slenderness ratio calculation meets the requirements. \(\varphi=0.164\) (standard value) and \(\varphi^{\prime}=0.1132\) (recommended value).