The effect of topography on the choice of optimal step intermediate supports along the line of the cable metro

In article was formulated and solved the problem of conditional nonlinear optimization of the distance between intermediate supports during the design of the cable metro lines in highly urbanized environment, taking into account not the horizontal surface of the terrain. The optimization problem involves a single-criterion objective function that expresses the cost of construction of the cable metro line (total cost of intermediate supports and their foundations, traction and carrying steel cables and technical equipment). The specified objective function subject to minimization by finding the optimal combination of the distance between intermediate supports and tension carrying ropes with accounting constructive, modal, structural and planning constraints in the form of nonlinear inequalities. When constructing the objective function were considered three possible forms sagging of carrying ropes, which can be implemented for various values of the efforts of their tension. Analysis was done of the influence of the angle of the longitudinal slope of the surface relief along the line of the cable metro on the value of the optimal distance between intermediate supports depending on the design and cost of intermediate supports and at the cost of 1 km line of the cable metro. Quantitative calculations showed that with the increase of the longitudinal slope of the surface construction cost also increases with nonlinear increasing rate. The dependence of the cost of 1 km of line underground cable metro from the parameters of the relief is of extreme character with a pronounced minimum at small angles of inclination of the terrain surface about 3…60 degrees. The position of the minimum is quite stable and only slightly changes when enough significant change in the cost of intermediate supports and installed on them technological equipment. The most effective conditions for the construction of the cable metro is the terrain with considerable differences in altitude along the length of the route of transport: only if the surface inclination of more than 50…60 degrees cost of 1 km line starts to exceed the cost of 1 km line laid along a strictly horizontal surface. At small angles of inclination of the surface (less than 6…8 degrees) to minimize the cost of construction of the cable metro line requires more frequent installation of intermediate supports. However, despite the possibility of building a lower and cheaper supports, the observed increased values of the cost of 1 km of optimum option of the line. At large angles of inclination of the surface a need for a more rare setup higher intermediate supports. Within the tilt angle 10…60 degrees the range of variation of the optimal step is small enough, amounting to no more than ±10 % from the value of the step at an angle of inclination of the surface 10 degree.