Abstract
According to actual working condition, the catenary equations of elastic track tope for setting-up is proposed based on the cableway erection requirement, such as the erection angle of end, the initial cable length and midpoint position of cable. The mechanics equilibrium equations, the loads span equations and the consistent equations are presented by analysis of track rope stress state under loads. The nonlinear equations are constructed for elastic track tope with multiple loads and the initial values of newton iteration method are obtained to solve the nonlinear equations. The results of this method are compared with the testing results and numerical results in other literatures and the contrast verifies the reliability of this method. The method is more concise and has smaller amount of calculations with a unified form. It can provide effective means to design the cargo cableway and to check the engineering safety during the erection stage and running stage of cableway.
Highlights
Catenary equation of elastic cable without centralized loadThe following assumptions are introduced in basic theory for design and calculation of the cableway track rope:
According to actual working condition, the catenary equations of elastic track tope for setting-up is proposed based on the cableway erection requirement, such as the erection angle of end, the initial cable length and midpoint position of cable
In this paper studies the calculation method of track rope under multiple centralized loads is established to provide practicable theory instruction on calculation and selection of the cargo cableway track rope based on catenary equation of the elastic cable
Summary
The following assumptions are introduced in basic theory for design and calculation of the cableway track rope:. (3) The dead load of the track rope is distributed evenly along the arc. The track rope section shown as figure 1 only bears dead weight load of the rope without elasticity elongation. Assume the initial section area of the track rope is A0, the section area is changed to A with elasticity elongation, intensity of the dead weight distributed along the arc becomes q. Shown as figure 1, the micro-section length of the elastic track rope is ds, the initial arc length is ds0. Set E as elastic module of the track rope material, the following equation is obtained from Hooke’s law: ds=[1+T/(EA0)]ds0. According to the mass conservation of the track rope micro-section after and before deformation: q0ds0=qds. V is vertical component of tangential tension at any point. s0 is initial rope length, s is length of the rope after elastic elongation
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