Reference:

«Designers handbook. Engineering and theoretical», edited by A.A. Umansky, – M.: Stroyizdat, 1960, p. 326.

Problem description:

Steel rope with cross section area A₀ with equally high supports is loaded by distributed load q along the span and by distributed load f at half span. Determine the reaction force at hawser supports H, acted along x-axis, maximal tension N_max in the rope and projection distance between points A and B along z-axis.

Problem sketch:

Type of created problem:

Plane frame (X, Z, UY).

Geometric characteristics:

L = 100 m; fн = 8.94 m; А₀ = 15.96 cm².

Material properties:

Elastic modulus: E = 1.6·10⁷ tf/m².

Boundary conditions:

Points А and В: Z = 0; Elastic links with high stiffness along the X direction at the rope ends.

Loads:

q = 0.5 tf/m; f = 0.42 tf/m.

Model description:

The system is modeled using 106 bar geometrically nonlinear finite elements of the “string” type (FE type is 304) and 2 single-noded elements of elastic link (FE type is 56). Automatic selection of step of loading applying for nonlinear problem solution is used.

Calculation results:

Reaction forces along X axis at supports R_x, tf

Diagram of longitudinal forces N, tf

Vertical displacements distribution, m