The solution of differential equations governing the static analysis of a helicoidal segment

Curvilinear space bars are occasionally used in building civil and mechanical structures. For safety and/or economical considerations designers of such structures bear the responsbility of ensuring adequate performance under expected functional requirements. Under specified load conditions the appropriate analytical tools which account for all kinematic and equilibrium requirements are presented in this paper for a typical helicoidal segment as one of the more general classes of space bars. The governing differential equations of the static response of a helicoid are derived and methods of solving these equations are discussed. Finally a transport-function-based solution is presented, implemented in an example and compared with a displacement-function-based finite element solution.