TEST CASE 4.2 STEEL ROPE WITH EQUALLY HIGH SUPPORTS
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_{0} 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; А_{0} = 15.96 cm^{2}.
Material properties:
Elastic modulus: E = 1.6·10^{7} tf/m^{2}.
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:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
H, tf |
89.142 |
88.889 |
0.28 |
N_{max}, tf |
120.93 |
120.61 |
0.26 |
z, m |
-38.824 |
-38.785 |
0.10 |
Reaction forces along X axis at supports R_{x}, tf
Diagram of longitudinal forces N, tf
Vertical displacements distribution, m