Performance of umbelliform tensegrity cable structurebased on energy principles

The simplified model for umbelliform tensegrity cable structure was established in this paper. The total potential energy of both parallel and wheel-shaped tensile structures were calculated under live load and wind load based on energy principles. According to the principle of stationary potential energy, the energy of structure was calculated and the equation was simplified. Then the displacement formula was put forward. After designing proper iteration method, the displacement of overall midspan, cable midspan and final cable force can be calculated. Through different examples, the error between calculation results of the finite element method and the displacement of overall midspan and cable midspan are proved to be very small. The research shows that under different live load levels, the displacement of overall midspan and cable midspan are in linear relationship with load. Under the same wind load, cable midspan is in linear relationship with prestress level but in nonlinear relationship with overall midspan. The formulas are concise and of clear mechanical concept. The formulas are accurate and reliable under the condition that the rise-to-span ratio and sag-to-span ratio are smaller than 1/8. The formulas can be the reference for preliminary design.