Abstract
In order to overcome the complicated iterative process of the cable length adjustment based on catenary theory and large error of length adjustment for cable with a small sag based on the parabola theory, this paper firstly develops a direct and simply calculation method based on parabola theory, considering the influence of elastic elongation on the cable unstressed length, which can apply for datum strand of the main cable and catwalk bearing rope with a small sag to improve the construction accuracy of the datum strand of suspension bridges. Then, the applicability of the proposed cable length adjustment formula under different conditions of the sag-span ratio is analyzed and compared with other calculation methods based on the theory of catenary or parabola. Finally, numerical examples are presented and discussed to illustrate the accuracy and efficiency of the proposed analytical method.
Highlights
Cable-supported structures such as suspension bridges have been recognized as the most appealing structures due to their aesthetic appearance as well as the structural advantages of the cables [1,2,3,4,5,6]
Designers cannot determine the initial shape arbitrarily when cable structures are considered. e initial shape is determined to satisfy the equilibrium condition between dead loads and internal member forces including cable tensions in the preliminary design stage, because cable members display strongly geometric nonlinear behaviors and the configuration of a cable system cannot be defined in the stress-free state. e process determining the initial state of cable structures is referred to as “shape finding,” “form finding,” or “initial shape or initial configuration’’ [7,8,9,10,11,12,13]
There are two catenary-type analytical elements available which can be used to model the cables with a large sag in suspension bridges: (1) inextensible catenary elements: the cable elements adopted are infinitely stiff in the axial direction and cannot experience any increment of the length; (2) elastic catenary elements: an elastic catenary curve is defined as the curve formed by a perfectly elastic cable, which obeys Hooke’s law and has negligible bending resistance when suspended from its ends and subjected to gravity
Summary
Cable-supported structures such as suspension bridges have been recognized as the most appealing structures due to their aesthetic appearance as well as the structural advantages of the cables [1,2,3,4,5,6]. E calculation formula of cable length adjustment based on quasi-catenary theory (adopt inextensible catenary elements) can represent explicitly by the ratio (c) of applied distribution load to the horizontal component of cable force, but the solution of c need to use a complicated iterative method. E cable length adjustment based on parabola theory is a direct method, but the error of the adjustment amount is large when the sag is small (generally, the sag-span ratio is less than 1/30), since the effect of elastic elongation on the unstressed cable length of the cable strand is not considered. In order to overcome the complicated iterative process of the cable length adjustment based on catenary theory and large error of length adjustment for cable with small sag based on the parabola theory, we aim to find a simple and direct calculation method having both high search efficiency and accuracy. Numerical examples are presented and discussed to illustrate the accuracy and efficiency of the proposed analytical method
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