TEST CASE 4.1 STEEL ROPE WITH GIVEN SAG
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 cm^{2}.
Material properties:
Elastic modulus: E = 1.6·10^{7} tf/m^{2}.
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:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
H, tf |
6.45 |
6.4577 |
0.12 |
N_{max}, tf |
6.53 |
6.5339 |
0.06 |
z_{max}, m |
5.81 |
5.8170 |
0.12 |
Reaction forces along X axis at supports R_{x}, tf
Diagram of longitudinal forces N, tf
Vertical displacements distribution, m