Sling properties#
This section describes the properties of slings as modelled in DAVE.
Length and length definition#
The length of a sling is defined either by its “ultimate length” or its “nominal” length.
Length of slings and grommets is measured by inserting pins in both ends and pulling the item taut (under a low tension).
The length is then the distance between the insides of the eyes or the outside of the pins.
Nominal length#
For nominal length the diameters of the pins are prescribed in the IMCA and EN13414 standard and are copied below for convenience:
Cable diameter [mm] |
Pin diameter [mm] |
|---|---|
60…150 (EN) |
300 |
151…250 |
500 |
251…375 |
750 |
376…500 |
1000 |
Note that these pin sizes are a recommendation only. Supplier/manufacturer and purchaser may decide to deviate from these values.
Ultimate length#
This is hypothetical length of the sling when measured using pins with a diameter of zero.
Note
When performing length variations, for example as required for DNV, DAVE applies the variation on the ultimate length for slings or circumference length for grommets.
Eye length#
The length of the eye of a sling is the distance between the splice and the inside of the eye or outside of the pin.
The eye-length thus depends on the pin diameter and thus on the length definition.
Stiffness#
DAVE assumes that slings are produced from a single rope that is splices back into itself at the ends. This results in the following stiffnesses:
Total stiffness#
The total stiffness \(k = { EA \over L} [kN/m]\) of a sling can be calculated from the individual parts. The main part and the splices are easy:
\(k_{main} = EA / (L_{main})\)
\(k_{splice} = 2EA / (L_{splice})\)
The stiffness of the eyes of the sling in ultimate (flat eyes) configuration can be estimated by
\(k_{eye} \approx 4 EA / (L_{rope,eye})\)
here \(L_{rope,eye}\) is the amount of rope in the eye, roughly two times the length of the eye.
This does not account for the angle that the rope in the eyes makes due to the diameter of the pins and the rope. If the eyes are not flat then the total stiffness becomes non-linear because the geometry changes when the rope stretches.
When linearized the stiffness of an eye becomes:
\( k_{eye, linearized} = 2 * EA * cos^2(\alpha) / (L1 + L2) \)
Linearization is accurate when the stretch of a sling is small. This is usually the case for rigging. In that case the geometry can be calculated assuming that L1 and L2 are the unstretched wire lengths.
Finally the total stiffness can be calculated using:
\(k_{total} = { 1 \over 1/k_{eye,left} + 1/k_{splice,left} + 1/k_{main} + 1/k_{eye,right} + 1/k_{splice,right}}\)
Weight#
The weight distribution follows directly from the rope distribution. This means that the spliced sections have double the weight per length of the main section.
Alternative Models#
DAVE offers three ways to model slings in DAVE.
By default the MEAN model is used. The GUI does not have an option to switch to another model.
Lumped: massless ropes, mass lumped at the ends of the splices
this model is good for dynamics
the lumped mass at the end of the splice prohibits the splice from entering shackles or otherwise contacting anything else.
can be fast because without cable weight the catenary equations can be skipped
Mean: single rope with average stiffness and mass.
fewer degrees of freedom (no lumped masses)
Gives warnings when sling splices or eyes come into contact with the next connection
splices and eyes are not modelled separately so the level of detail is slightly lower. This mainly affects the mass distribution in the sling itself.
can be fast because without the frames or bodies at the splice ends the sling does not add degrees of freedom to the scene (otherwise it adds 12)
Accurate: complete model: rope with mass, frames at the end of the splices.
most complete model
but also the most complex model to solve
Comparing the extension vs tension curves of the three models it appears that the results are such that for rigging applications it should not make any difference in the results as long as the same model-type is used for all slings.
Splice positions#
Where the models really do differ is in the position of the splices for cases where slings are slack or stretch of the sling is not negligible. In the following screenshots the upper sling is calculated using the mean model and the lower is calculated using the accurate model.
