Rigging - Single Hook 4-Point Lift

[FlounderUM]

I am lifting a rectangular structure, all lift points on the same elevation. However, the 4 lift points are not evenly distributed around the CoG AND we have an intended 10 degree tilt on the structure being lifted to facilitate installation. I have attached a spreadsheet/dwg in PDF

This leads to 4 different length slings to the single lift point. In order to determine the lengths of these slings we have drawn a line in the direction of gravity up to our intended hook height and connected the hook point to the 4 lifting points.

My question specifically is: How do I know the ratio of the load that each sling carries?

Please let me be clear that I understand how the angle of the sling to horizontal effects the tension in the sling. It does not, in my understanding, effect the percentage of the load of the structure being lifted that sling carries.

In order to calculate the amount of the structure weight each sling carries we find the distances between the lifting points and the CoG (L) along the plane of the structure being lifted. We take the inverse of those distances (1/L) and sum them (sum(L)). The load taken by each sling in our theory in terms of the weight (W) of the structure is:

load in individual sling (W*) = W x (1/L*)/sum(L)

In this case the load in the sling is an inverse function of its distance away from the CoG, that is, the closer the sling is to the CoG in plan, the higher percentage of the total weight of the structure being lifted it takes.

Does anyone know if this is an appropriate method?

After that is determined I am able to apply dynamics and other amplifications including angle of sling to horizontal to determine max tension in each sling.

 

[AlephZero]

The simple answer is, there is no way to know what the sling loads will be for this rigging arrangement. They will depend strongly on any small errors in the length of the slings compared with the nominal lengths, and also on the flexibilitiy of the different slings and of the structure you are lifting.

Start with a simpler situation. Imagine a rigid square plate lifted with 4 equal length slings. The vertical load at each corner is only 1/4 of the weight if everything is geometrically perfect. If one sling is slightly too long, you have the same situation as a 4-legged table with unequal length legs. Most likely, all the weiight will be taken two diagonally opposite slings, and the other two will be slack except for a small force to stop the plate spinning around that diagonal into the vertical plane, if its CG is not exactly at its mid point.

So, the simplest (and conservative) estimate is to assume each sling may take ALL the vertical weight, and then apply the amplifications for the angle to the horizontal.

If you need more accurate calculations of the sling tensions, you will have to change the rigging so the structure is statically determinate. For example you could take 2 slings from the crane hook, and then "split" each one into two slings going to the lift points. That would allow the structure to move around a bit to "take up the slack" and compensate for any inaccuracies in the lengths of the slings. You could then calculate the sling tensions the same way as for a statically determinate frame structure, by resolving the forces at the "joints" in the rigging and taking moments. Start at the crane hook and work downwards, since you know the tension in the crane cable is the total weight you are lifting.