Approximating Formulas for Out-of-Plane Stiffness of Flange Plates in Inner-Outer Flanges

The inner-outer flange(IO flange) is a high-capacity connection for circular hollow section(CHS) tubes, and is mainly implemented in long-span tubular transmission towers for the connection of the high-strength members. The axial tension capacity of IO flanges depends not only on the number and strength of the bolts, but also on the ratio of the tension force of the inner bolt to that of the outer bolt. The out-of-plane stiffness of the flange plate in IO flanges is a crucial parameter in computing this ratio, and has received much attention. However, the analytic solution that is suitable for design is hard to be attained, since many parameters, e.g. the size of the bolt's hole, relationship between the geometrical parameters, and the type of flange, would be involved with regard to the out-of-plane flange stiffness, leading to the complex boundary conditions for the mechanical balance equations. Therefore, it is necessary to perform an in-depth study on the out-of-plane flange stiffness to attain a concise approximating equation for design.
Regarding the inner and the outer flange plates presented in the IO flanges, the mechanical balance equations with the corresponding boundary conditions based on the theory for elastic thin plates were first established in the polar coordinate system. Thereby, the mutual effects of the parameters of the flange plates were analyzed, and the corresponding non-dimensional parameters were derived. In accordance with the ranges of the non-dimensional parameters summarized from practice engineering, a parametric sensitive analysis was performed via 7 144 finite element(FE) models established for outer flange plates and 5 630 FE models for inner outer flange plates. The influences of the non-dimensional parameters on the out-of-plane stiffness of the flange plates were then clarified. Meanwhile the mechanical characteristics of the flange plate was clearly defined. Finally, a concise approximating equation for the out-of-plane stiffness of the flange plate was proposed, which was suitable for the design of IO flanges.
The results show that the out-of-plane stiffness of the flange plate can be characterized by the non-dimensional deflection of the flange plate. It is found that the out-of-plane stiffness of the flange plate increases with the increase of the flange plate thickness, as well as the decrease of the radius of tube. Overall, for common IO flanges, the non-dimensional deflection decreases with the increase of the number of the bolts, as well as the increase of the non-dimensional diameter of the bolts, which means the out-of-plane stiffness of the flanges would increase. In addition, if the ratio of the flange plate's circumferential length to the flange plate's width is relatively big, the flange plate subjected to the bolt force presents a state similar to the cantilever slab, and the loaded flange plate would be similar to the one-way slab if the length to width ratio is sufficiently small. Furthermore, a moderate ratio brings the plate into the triple-side force-bearing state. In terms of the ratio of the FE result to the result obtained via the approximating equation, the statistical results show that the mean value of the ratio is 1.0 and the coefficient of variance is less than 0.7%, which implies that the approximating equation is capable of well estimating the out-of-plane stiffness of the flange plates.