Contents

Slings

Slings are modelled as a combination of cable and rigid-body nodes. Cables are used for the eyes and the mid-section of the sling. Rigid-body nodes are used to model the spliced section. The mass of the sling is included in the rigidbody nodes.

The length of a sling is defined by the “ultimate” length. That is the length between the insides of the eyes when the sling pulled tight over pins with a diameter of zero.

image

from DAVE import *
from DAVE.jupyter import *

s = Scene()

# code for Frame
s.new_frame(name='Frame',
           position=(5.0,
                     0.0,
                     0.0),
           rotation=(0.0,
                     0.0,
                     0.0),
           fixed =(False, True, True, True, True, True) )
# code for Point
s.new_point(name='Left',
          parent=None,
          position=(0.0,
                    0.0,
                    0.0))
# code for Point_1
s.new_point(name='Right',
          parent='Frame',
          position=(0.0,
                    0.0,
                    0.0))
# code for Circle
s.new_circle(name='Circle',
            parent='Left',
            axis=(0.0, 1.0, 0.0),
            radius=0.0 )
# code for Circle_1
s.new_circle(name='Circle_1',
            parent='Right',
            axis=(0.0, 1.0, 0.0),
            radius=0.0 )
# Exporting sling
# Create sling
sling = s.new_sling("sling", length = 10.0,
            LeyeA = 2,
            LeyeB = 2,
            LspliceA = 1,
            LspliceB = 1,
            diameter = 0.1,
            EA = 100000000.0,
            mass = 0.0,
            endA = "Circle",
            endB = "Circle_1",
            sheaves = None)

s.new_force('small_load', parent = 'Right', force = (1,0,0))

s.solve_statics()

show(s, camera_pos = (5, -10, 0),
     lookat = (5,0,0),
     painters = 'Visual',
     width=800,
     height=300,
     zoom_fit = False)
Equilibrium-core version = 2.1
default resource folders:
c:\python\miniconda3\envs\book\lib\site-packages\DAVE\resources
C:\Users\beneden\DAVE_models
C:\data\Dave\Book\DAVE-book\DAVE-notebooks
Blender found at: C:\Program Files\Blender Foundation\Blender 2.93\blender.exe
embedWindow(verbose=True): could not load ipyvtk_simple try:
> pip install -U git+https://github.com/Kitware/ipyvtk-simple.git
Solved to 2.715e-04 kN
../_images/sling_length_1_3.png

The distance between the insides of the loops is defined to be 10m.

This length is distributed over the following items:

Item

Length [m]

left eye

2

left splice

1

main part

4

right splice

1

right eye

2

The amount of wire in the eyes is such that is accounts for the two legs as well as the length of the bend around a zero diameter pin.

\(L_{wire} = 2 * L_{eye} + \pi * d/2\)

In this case the diamter of the wire is 0.1m which makes the length in the eye 2 * 2 + 3.141 * 0.1 * 0.5 = 4.157m

for n in s.nodes_of_type(Cable):
    report(n, ['length'])
Properties of sling>>>_main_part (Cable)
PropertyValueUnitRemarksExplained
length4.000mLength of the cable when in rest

Properties of sling>>>_eyeA (Cable)
PropertyValueUnitRemarksExplained
length4.157mLength of the cable when in rest

Properties of sling>>>_eyeB (Cable)
PropertyValueUnitRemarksExplained
length4.157mLength of the cable when in rest

To double-check the length the sling is pulled tight by a small force. The distance between the two zero-diameter pins should be just over 10m

  • The left end of the sling is located at 0,0,0.

  • the unstretched length of the sling is 10m

  • The right pin should be at x=10m

print(f'Right at {s["Right"].global_position[0]:.3f}m')
Right at 10.000m

Stiffness

The stiffness of the wire of the sling is defined by EA of the wire. The wire (Cable) in the eyes of the sling has this EA.

image

In reality the splices of the sling should have a stiffness of 2 * EA. In the model however they are modelled using a body with infinite stiffness. The EA of the main-part is therefore adjusted to correct for that.

In practice it can be more practical to define the stiffness of the sling by its total stiffness (k).

\( k = { EA_{effective} \over L_{ultimate}} [kN/m]\)

\( k_{main} = EA / (L_{main}) \)

\( k_{splice} = 2EA / (L_{splice}) \)

\( k_{eye} = 4 EA / (L_{wire,eye}) \)

\( k_{total} = { 1 \over 1/k_{eye,left} + 1/k_{splice,left} + 1/k_{main} + 1/k_{eye,right} + 1/k_{splice,right}} \)

sling.EA = 1000 # kN/m
k = sling.k_total
print(sling.k_total)
141.2720738946259

Apply 141.27 kN of force, and check that the sling extends 1m.

  • The left end of the sling is located at 0,0,0.

  • the unstretched length of the sling is 10m

  • The stretch is 1m

so the right end should be at x=11m

s['small_load'].force = (k,0,0)
s.solve_statics()

print(f'Right at {s["Right"].global_position[0]:.3f}m')
Solved to 5.403e-07 kN
Right at 11.000m

The total stiffness can also be set:

sling.k_total = 1000
print(f'Total stiffness set to {sling.k_total:.2f} [kN/m]')
print(f'Resulting EA: {sling.EA:.2f} [kN]')
Total stiffness set to 1000.00 [kN/m]
Resulting EA: 7078.54 [kN]

And check the extension for 1000 kN force:

s['small_load'].force = (1000,0,0)
s.solve_statics()

print(f'Right at {s["Right"].global_position[0]:.3f}m')
Solved to 1.066e-06 kN
Right at 11.000m

When changing the length of a sling, the EA stays the same. This means the k changes:

sling.length = 20

print(f'Total stiffness: {sling.k_total:.2f} [kN/m]')
print(f'Resulting EA: {sling.EA:.2f} [kN]')
Total stiffness: 414.47 [kN/m]
Resulting EA: 7078.54 [kN]