Reference:

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

Problem description:

Steel rope with cross section area A is loaded by distributed load q along the span and concentrated load P in the centre. Determine the reaction force H, acted along the line between hawser supports, maximal tension N_max in the rope and maximal sag z_max.

Problem sketch:

Type of created problem:

Plane frame (X, Z, UY).

Geometric characteristics:

L = 100 m; f = 5 m; А = 12 cm².

Material properties:

Elastic modulus: E = 1.6·10⁷ tf/m².

Boundary conditions:

Elastic links with high stiffness along the X and Z directions at the rope ends.

Loads:

q = 0.01 tf/m; P = 1 tf.

Model description:

The system is modeled using 100 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.

Analytical solution:

Calculation results:

Reaction forces along X axis at supports R_x, tf

Diagram of longitudinal forces N, tf

Vertical displacements distribution, m