## 4 Analysis of Bending Stiffness Calculation Coefficients
The load carried by the cement bond also increases, whereas the elasticity coefficient exhibits a decreasing trend, as indicated in Table 3.  
According to the data in Table 3, the curve of the cement height, \(h_{c}\), and elasticity coefficient, \(\mu\), is fitted. Owing to the limitation of the number of test samples, a more precise functional relationship of the curve still requires further analysis and demonstration. The functional relationship of the fitted curve shown in Figure 7 can be expressed as follows:  
\[\mu\ =\ 70.325\times h_{c}^{-1.093} \tag{28}\]  
or  
\[\mu\ =\ \left\{ \begin{array}{ll}2.817E-05\times h_{c}^{2}-0.011649h_{c}+1.383,\,(h_{c}\leq 206)\\ 0.179,\,(h_{c}>206)\end{array} \right. \tag{29}\] \begin{table}
\begin{tabular}{c c c c} \hline
**Specimen** & **Experiment** & **Equation (3)** & **Elasticity** \\
**(\(\times\)10\({}^{6}\) N\(\cdot\)m\(\cdot\)rad\({}^{-1}\))** & **(\(\times\)10\({}^{6}\) N\(\cdot\)m\(\cdot\)rad\({}^{-1}\))** & **Coefficient, \(\mu\)** \\ \hline
1 & 2.97 & 3.61 & 0.77 \\
2 & 2.84 & 3.20 & 0.86 \\
3 & 3.36 & 4.03 & 0.79 \\
4 & 4.61 & 5.80 & 0.74 \\
5 & 9.16 & 14.19 & 0.55 \\
6 & 20.95 & 31.51 & 0.54 \\
7 & 27.7 & 50.16 & 0.44 \\
8 & 57.6 & 146.64 & 0.22 \\
9 & 133 & 317.03 & 0.19 \\ \hline \end{tabular}
\end{table} 
Table 2: Elasticity coefficient, \(\mu\). \begin{table}
\begin{tabular}{c c c} \hline
**Specimen** & **Cement Height, \(h_{c}\) (mm)** & **Elasticity Coefficient, \(\mu\)** \\ \hline
1 & 60 & 0.77 \\
2 & 55 & 0.86 \\
3 & 60 & 0.79 \\
4 & 65 & 0.74 \\
5 & 85 & 0.55 \\
6 & 100 & 0.54 \\
7 & 110 & 0.44 \\
8 & 170 & 0.22 \\
9 & 230 & 0.19 \\ \hline \end{tabular}
\end{table} 
Table 3: Variation in the elasticity coefficient, \(\mu\), with the cement height. A comparison of the results shows that Equation (29) is highly consistent with the experimental data. Thus, Equation (29) is recommended for calculating the elastic coefficient, \(\mu\), of cement. Once \(\mu\) is obtained, the bending stiffness of the joints connecting the porcelain bushings and flanges can be calculated using Equation (27). To determine the bending stiffness of the above typical UHV electrical equipment, [PERSON] et al. [18,22] modified the coefficient \(\beta\) of the code formula in Equation (1) based on experimental results. They found that the coefficient \(\beta\) varied with the diameter of the porcelain bushing, \(d_{c}\), according to Equation (30), which could improve the calculation accuracy of the bending stiffness of UHV electrical equipment. \[\beta\ =\ \left\{ \begin{array}{l}6.54\times 10^{7},(d_{c}\leq 275\text{mm})\\ (-15.4d_{c}+10.775)\times 10^{7},(275\text{mm}<d_{c}<375\text{mm})\\ 5.00\times 10^{7},(d_{c}\geq 375\text{mm})\end{array} \right. \tag{30}\]  
The values calculated using Equations (1) and (27) were compared with the experimental bending stiffness results, as presented in Table 4 and Figure 8. It can be seen from Table 4 that when the diameter of the porcelain bushing, \(d_{c}\), in a specimen is large, e.g., \(d_{c}=375\) mm, the maximum error of the code formula in Equation (1) with \(\beta=6.54\times 10^{7}\) is 36.72%. When the coefficient \(\beta\) in Equation (1) is modified to \(\beta=5.00\times 10^{7}\), the error is reduced to 4.53%. However, when the modified coefficient \(\beta=5.00\times 107\) is applied to a small specimen with \(d_{c}=160\) mm, the error increases to 26.68%.