## 2 Material and Methods
### Semirigid Connection Frame Theory with Lateral Displacement
#### 2.2.2 Consider the Node Semirigid Crossbar Stiffness Coefficient Correction
The \(\Phi 48.3\times 3.6\) steel pipe with modulus of elasticity \(E=2.06\times 10^{5}\) and \(I=12.71\) cm\({}^{4}\) is used, the crossbar stiffness correction coefficient \(\alpha_{u}\) can be obtained according to Formulas (7) and (9), the end restraint coefficient of the upright can be obtained according to Formulas (2) and (3), the calculated length coefficient \(\mu\) of the upright can be obtained by substituting into Formula (12), and finally the stable load capacity of the upright can be obtained according to the Euler formula F = \(\pi^{2}EI/\mu^{2}l^{2}\). The theoretical value of the load bearing capacity, the erection parameters, and calculation results of the frame are shown in Table 4.  
According to the experimental results of the torsional stiffness performance of the right-angle fastener, when the bending moment of the right-angle fastener is 0.8 kN\(\cdot\)m, the bending moment-rotation curve of each group has an obvious gentle trend, the tangent slope of the curve becomes smaller, and the stiffness value of the joint is obviously reduced. At this time, the torque of the right-angle fastener node is too large, and the deformation of the right-angle fastener is large. Therefore, it is safe to take the slope of the corresponding curve when the bending moment of the right-angle fastener is 0.8 kN\(\cdot\)m as the node stiffness value [30], and calculate when the torsional moment of the right-angle fastener bolt is 40 N\(\cdot\)m. At this time, the fastener angle is 0.04 rad. The calculation process is as follows:  
\(R_{k}=M^{\prime}=-2\times 164.080+24.35=11.27\) kN\(\cdot\)m/rad  
\(R_{k}\)--Torsional stiffness of right-angle fastener  
Therefore, in the calculation, the stiffness value of the joint is substituted into the Formula (10) to obtain the stiffness correction coefficient \(\alpha_{u}\) of the crossbar, then substituted into the Formula (11) to obtain the constraint coefficient \(K\) at the end of the vertical bar, and finally substituted \(\mu\) into the Formula (12). The stability bearing capacity of the vertical rod under different working conditions is calculated by Euler formula F = \(\pi^{2}EI/\mu^{2}l^{2}\), as shown in Tables 5 and 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Pace**} & \multicolumn{3}{c}{**Pole Pitch (m)**} \\  & \(\mathbf{1.2\times 1.2}\) & \(\mathbf{1.0\times 1.0}\) & \(\mathbf{0.9\times 0.9}\) \\ \hline
1.5 & 13.08 & 13.23 & 13.31 \\
1.2 & 16.77 & 16.97 & 17.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Based on the theory of semirigid frame with lateral displacement, the stable bearing capacity of vertical bar is analyzed(kN). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Moment of** \\ **Twisting (N\(\cdot\)m)** \\ \end{tabular} & \begin{tabular}{c} **Joint Initial Rigidity** \\ **(kN\(\cdot\)m/rad)** \\ \end{tabular} & **Extension (m)** & **Lag Spacing (m)** & \
\begin{tabular}{c} **Coefficient for** \\ **Effective Length \(\mu\)** \\ \end{tabular} &
\begin{tabular}{c} **Buckling** \\ **Strength (kN)** \\ \end{tabular} \\ \hline
20 & 10.87 & 1.5 & 1.2 \(\times\) 1.2 & 3.01 & 12.70 \\
30 & 19.25 & 1.5 & 1.2 \(\times\) 1.2 & 2.42 & 19.68 \\
40 & 26.03 & 1.5 & 1.2 \(\times\) 1.2 & 2.18 & 24.18 \\
50 & 33.18 & 1.5 & 1.2 \(\times\) 1.2 & 2.02 & 28.12 \\
60 & 42.40 & 1.5 & 1.2 \(\times\) 1.2 & 1.89 & 32.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Stable bearing capacity of vertical rod under fastener rotational stiffness. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Pace**} & \multicolumn{3}{c}{**Pole Pitch (m)**} \\  & \(\mathbf{1.2\times 1.2}\) & \(\mathbf{1.0\times 1.0}\) & \(\mathbf{0.9\times 0.9}\) \\ \hline
1.5 & 2.96 & 2.95 & 2.94 \\
1.2 & 3.27 & 3.25 & 3.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Effective length coefficient \(\mu\) of vertical bar based on theory of semirigid frame with lateral displacement.