Analysis of air-inflated, heavy, membrane tube supported at two points on an incline

• Analytic solutions in closed form are derived.
• Novel general solutions are implemented to solve the two-point anchoring problem.
• The cross-sectional area is analytically evaluated.
• The solutions can cover both the one- and at two-point anchoring problems.

In this study, the cross section of an air-inflated heavy membrane structure anchored at two points on an inclined foundation is examined. Novel general solutions obtained in a previous study for air-inflated membrane structures are used to solve the problem in this work. By imposing boundary conditions on the general solutions, unknown values are formulated as solutions to algebraic equations. The shape and characteristic values are mathematically expressed in closed form. The cross-sectional area is also evaluated analytically. Some results for the characteristic values and shapes are ultimately presented.