## 1 Introduction
Moreover, the current code for the seismic design of electrical installations in China [15] indicates that the scope of the application of this code does not include UHV electrical equipment; in other words, the code is only applicable for electrical facilities in AC transmission and substation projects with voltage levels of 110 kV to 750 kV or in DC transmission and substation projects with voltage levels of \(\pm\)660 kV and below. Therefore, it is necessary to establish a bending stiffness model and equation for cement-bonded joints suitable for connecting the porcelain bushing and flange in UHV electrical equipment. The mechanical behavior of the joints of porcelain pillar UHV electrical equipment has been studied by many researchers. [PERSON] et al. [19] evaluated the seismic performance of a 1100 kV UHV transformer busing under seismic loads through shaking table tests. The test results showed that the joint connecting the porcelain bushing and flange in the UHV electrical equipment was easily damaged during an earthquake. Based on finite element simulations, theoretical analyses, and shaking table tests, [PERSON] et al. [20] evaluated the effects of the flange material and shape on the seismic response of 1100 kV UHV transformer bushings. The results showed that properly designed flanges could improve the seismic performance of UHV transformer bushings. [PERSON] et al. [21] established a dynamic model of porcelain electrical equipment by considering the nonlinear behavior of the joint connecting the porcelain bushing and flange, and the nonlinear seismic response of porcelain pillar electrical equipment was revealed. Based on experiments and the finite element method, [PERSON] et al. [22] improved the code formula. They modified the empirical parameter to vary with the radius of the porcelain bushing to make it suitable for UHV electrical equipment. However, the improved equation still could not express the influence of the material properties of the flange, porcelain bushing, or cement bond on the mechanical properties, nor could it be applied to the material fatigue damage of UHV electrical equipment during long-term use. To solve this problem, [PERSON] et al. [23] established a mechanical model to describe the bending deformation of a porcelain bushing and flange bonded by cement according to the structural composition of the joint. Based on the established model, an equivalent bending stiffness equation was derived. However, the model did not consider the effect of deformation of the porcelain pillar in the flange on the bending system. Based on a previous study [23], the bending deformation of the porcelain column in the flange was calculated in this study using the energy method, and the equation for the equivalent bending stiffness of the cement-bonded joint was improved. The rationality and applicability of the proposed equation for UHV electrical equipment engineering were verified based on experimental results in the literature. Compared with the code equation, the equation established by a mechanical model in this paper does not contain empirical parameters, but material and geometric parameters. It can mechanically reveal the bending mechanism of the joint connecting porcelain bushings and flanges, and provide a basis for the seismic design of the structure of this type of electrical installation.