A Consideration on the Slackened and Tightened Cables

Abstract

On the exact equilibrium configuration of an elastic cable spanned, the potential of uniform self-weight and the strain energy in stretching are analytically estimated. Those quantities are related to the work done by the chord force into an energy conservation. By the differentiation of the energy relation with respect to the span elongation, the chord force is separated into two components reflecting the sag effect and the elastic elongation. In a numerical analysis, it is shown that a characteristic magnitude of the stretching exists between the slackened and the tightened states.

A Shape-Finding Analysis of Suspended Structures on the Displacement-Method Equilibrium

“…The differential relations of the former (13), (14) and (16) are apparent. Let the element tangent stiffness matrices be collected into S{F…”

“…(11) and 12 in which subscript "Fixed" means a quantity on the temporary joint positions. By continuity relation (14) and 16…”

“…According to Ref. 14), the strain energy U(c) and the self-weight potential Vc) are obtained as follows…”

“…(3) A cable-trussed bridge The cable-trussed bridge shown in Fig. 11 is made with the use of compressive axial members, namely (5), (7), (12) and (14). The girder has area 0.…”

“…218 are for axial member (5) and (12); and E=20600, A=160 and w =1. 232 for (7) and (14). Joint 5 is hinged to the ground at the origin of {x, y}-coordinates, and joint 1 and 9 are kept on y=0 by horizontal rollers.…”