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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 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 Nmax 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; = 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:

Target value

Analytical solution

LIRA 10

Deviation, %

H, tf

89.142

88.889

0.28

Nmax, tf

120.93

120.61

0.26

z, m

-38.824

-38.785

0.10

 

Reaction forces along X axis at supports Rx, tf

 

Diagram of longitudinal forces N, tf

 

Vertical displacements distribution, m