Sign in /
Register
   

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 Nmax in the rope and maximal sag zmax.

 

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:

Target value

Analytical solution

LIRA 10

Deviation, %

H, tf

6.45

6.4577

0.12

Nmax, tf

6.53

6.5339

0.06

zmax, m

5.81

5.8170

0.12

 

Reaction forces along X axis at supports Rx, tf

 

Diagram of longitudinal forces N, tf

 

Vertical displacements distribution, m