Stress Analysis of Lifting Plate With Bail

[Drew Sandlin]

TL;DR

How do you analyze the stresses on the bail on a lifting plate?

I'm designing a custom lifting plate that has two shackles hanging from it and a large slot at the top for hooking into an overhead crane. I have a few stress analysis questions:

1. The plate will be cut on a waterjet table, which means the slot will have sharp edges, and that the hook will contact the inside of the slot on the lifting plate at two points. See the attached pictures. What is the best way to analyze these contact stresses? Case 4 in Table 14.1 in Roark's Formulas for Stress and Strain, page 704? Is this something I should even be concerned about?

2. The bail at the top of the lift plate is approximately a curved beam. Can I analyze an equivalent curved beam that fits within the plate profile, and assume the stresses in the actual plate will be no higher than the stresses in this hypothetical curved beam?

3. For the bending strength of the plate, can I take a similar approach to (2) and analyze a smaller rectangular beam that fits within the plate profile and assume the stresses in the actual plate will be no higher the stresses in this hypothetical beam?

4. I've been reading through ASME BTH-1 and my understanding is it gives safety factors for certain loading scenarios and member designs, but leaves the method of determining stresses up to the analyst. Is that an accurate statement?

5. Does laser cutting this plate versus waterjetting it affect fatigue life for the plate? I couldn't find anything in ASME BTH-1 that discusses this. I could have missed it. Are there any considerations that need to be accounted for in the heat affected zone if components in a lifting device were laser cut?

Maybe what I'm really asking for is, "how would you approach analyzing this lifting plate to show it's compliant with ASME BTH-1?"

 

[jrmichler]

Trying to remember from when I wrote the corporate procedure for lifting calculations from over ten years ago...

I've been reading through ASME BTH-1 and my understanding is it gives safety factors for certain loading scenarios and member designs, but leaves the method of determining stresses up to the analyst. Is that an accurate statement?

Yes

Lifting beams and fittings are normally made from a relatively low strength steel, such as A36. Such steel is ductile. Lifting calculations are made using gross section stresses, not local contact stresses. This was specifically stated in one code, which stated that the code calculations applied to gross section stresses, not local peak stresses from FEA. Because the steel is ductile, local yielding removes stress concentrations from sharp corners. The crane hook will round off the contact surfaces. Also, between the ductility and the low carbon content, there should be no difference between laser cut and waterjet cut plates. This statement is specific to relatively low cycle applications. If the lifting plate will see millions of load cycles, you will need to design for high cycle fatigue. I think that high cycle fatigue is mentioned in BTH-1. If not, look in the structural steel codes.

The steel plate is analyzed in steps. The first step is checking for shear failure as shown in the diagram below. The diagram is from Aircraft Structures, by Peery.

The next step is checking for tensile failure as shown in the diagram below from the same book:

Riveted thin plates used in aircraft have other failure modes that need to be checked. Those modes do not apply to your situation.

The bail at the top of the lift plate is approximately a curved beam. Can I analyze an equivalent curved beam that fits within the plate profile, and assume the stresses in the actual plate will be no higher than the stresses in this hypothetical curved beam?

Such a short beam has fixed ends, so shear must also be calculated. Do not be surprised if the shear and tensile calculations shown above are sufficient to show safety.

For the bending strength of the plate, can I take a similar approach to (2) and analyze a smaller rectangular beam that fits within the plate profile and assume the stresses in the actual plate will be no higher the stresses in this hypothetical beam?

Sure, that works. After the areas around the three points of applied force are strong enough, the rest of the plate is normally good. Unless, of course, you are trying to minimize the overall height of the plate.