The steel bent frame structure of single-story factory buildings is actually a spatial structure system. Different bent frame columns are connected with the roof of bent frame structure, making the columns work and bearing the load together. In the steel frame of the factory building with bridge cranes below 20 t, variable-section columns with corbels are used to bear the crane load. In this article, the steel bent frame column of single-story factory buildings was taken as the research object. The bent frame column was simplified as a cantilever variable stepped column bearing a transverse concentrated force at the top. After simplifying the model, the theoretical formula of deflection, rotating angle, and bending moment of the compression rod was put forward. Moreover, bending deformation and stability of variable stepped columns were analyzed in order to obtain the theoretical and practical formula, then the ANSYS software was used to simulate the bent column.

The shield tunnel is a common solution for natural gas pipelines crossing rivers. Consequently, the development of natural gas tunnel filling materials with excellent performance is crucial to the safe operation and maintenance of pipelines. The foam concrete offers a reasonable solution. Nevertheless, since its inherent compressive strength decreases almost proportionally with the decrease in density, obstacles remain concerning obtaining the high density and relatively low strength required for natural gas tunnel filling. Here, a synergistic optimization strategy was proposed involving the orthogonal test, univariate control, and comprehensive balance method. It involves modifying the type and proportion of cementitious matrix, in particular by incorporating fly ash and PVA fibers in the mix design, and synergetic determining the best mix ratio from the aspects of compressive strength, stability, and dry density. The obtained foam concrete has a compressive strength of 4.29 MPa (FC4) and a dry density of 1060.59 kg/m3 (A11), which meets the requirements of pipeline pressure and pipeline anti-floating. This study is applied to the Yangtze River shield crossing project of the Sino-Russian Eastern Gas Pipeline, and ANSYS was used to simulate the stress and deformation of the foam concrete. This work provides an efficient foam concrete optimization mix scheme, and supports the application of foam concrete in the filling of the long-distance cross-river natural gas tunnels.