Optimal design of the cable metro with unified intermediate supports

In article was formulated and solved the problem of conditional nonlinear technical and economic optimization of the distance between intermediate supports, uniform in height, during the design of the cable metro lines in highly urbanized city environment. 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. Analysis was done of the influence of the step unification and minimum size of intermediate supports on their optimum step, the cost of intermediate supports, the cost of 1 km cable metro line for different values of the angle of the longitudinal slope of the surface relief along the cable metro line. With the increase of the step unify the discreteness increases: the width of the range of angles of the longitudinal slope of the surface relief within which the height of the supports remains constant, increases. The graph of step installation of unified supports along the cable metro line from the angle of the longitudinal slope of the surface relief also has discrete-step type. The transition to a larger height unified intermediate supports determines the need for installation of supports with a large pitch. Its value then begins to decrease monotonically with further increase of the angle of the longitudinal slope of the surface relief until it needs to transition to the new size of supports. Synchronous change in the optimal values of the height and step of the installation of intermediate supports, depending on the angle of the longitudinal slope of the surface relief leads to the fact that the optimal cost characteristics of the cable metro lines are smooth functions. It has an extreme character with a minimum at angles of inclination of the surface elevation ~5 degrees, which is associated with the form of sagging of the load-bearing ropes. Even for a sufficiently large step of the unification the largest difference in optimal value is almost insignificant: it lies in the range of 2...3%, increasing with increasing the angle of the longitudinal slope of the surface relief and unit cost of the intermediate support. Unification of intermediate supports according to the height and their step practically does not affect the optimal value for horizontal tension on the load-bearing ropes. It determined mainly by the angle of the longitudinal slope of the surface relief.