SHAPE DETERMINING OF A LOADED CABLE VIA TOTAL DISPLACEMENTS

Abstract

Cable structures are very efficient (in economic aspect) when applied to cover large spans. The cable structure consists of a single cable or a network of cables. The cable attractive feature is the highest ratio of strength to weight amongst other carrying structural elements, usually applied in engineering practice. But a cable is a specific structural element able to response only one type of deforming ‐ tension (flexural rigidity actually vanishes). Therefore, when loaded a cable shapes the form to resist tension only. This adaptation is followed by large nonlinear displacements. Thus, the nature of geometrical nonlinear cable behavior is quitie a different from that of rigid structural elements. Both elements response via small deformations when loaded, but large displacements of a cable are conditioned by its adaptation to loading, and those of rigid structural elements ‐ by actual deformations. One can also note that deformations of a cable are significantly less than those of rigid structural elements, but at the same time actual cable displacements are significantly larger. Thus, the main disadvantage of a cable structure is its response to loading by large displacements caused by asymmetric loading component (usually met in engineering practice, e.g. the design of suspension bridges, coverings of stadium, etc). Therefore stiffness conditions predominate in the actual codified cable design. Having identified governing factors conditioning displacement magnitudes one can introduce the constructional means/solutions assigned to reduce them if required. Therefore the evaluation of cable displacements by a reliable and sufficiently exact method compatible with the calculation of actual engineering structures is under current necessity. When analyzing total displacements the principle of superposition is employed in a special sequence. Total displacement is split into two components: kinematic and elastic. The first component represents cable form shaping the loading, the second one is conditioned by elastic deformations. Any point displacement of an asymmetrically loaded cable can be expressed via its middle span. The developed analytical expressions to evaluate middle span displacements are presented. They enable to identify maximal displacements and their locations. The developed analytical method for total displacements evaluation is tested numerically. The comparative analysis in respect of the influence of various parameters conditioning displacement magnitudes is performed. The displacement evaluation errors, their causality conditioned by the application of approximate‐ widely applied engineering methods, are discussed.