U-Bolt Stress Analysis

[lodgera]

Hi All,
I need some advice/feedback on how to properly analyze a U-bolt. The particular scenario under which this bolt is used is simple enough: It hangs over a pin and then the threads protrude through a restrained plate. The way I'm looking at this, tightening the nuts will develop a tensile preload in the threaded sections. Given the support condition at the inner radius of the U portion where it contacts the pin, the tensile loads on the threaded sections should develop a shear load and a moment at the U center plane. However, we've calculate the resulting bending stresses at that location using initially curved beam equations and the stresses seem unreasonably high. I attached a sketch showing the setup and FBD. This seems so simple, but we're getting equivalent stresses that are higher than the yield strength of the material, even when applying the rated load in the analysis.

 

[dhengr]

Lodgera:
This design question has been asked and discussed before, do a search and see what you can find in the Mech., Structural or Welding and Fastening forums. That is most likely where the pertinent threads would show up. If you have reasonably good fit btwn. the U-bolt and the pin, that is, pin o.d. and U-bolt i.d., you should really not have much bending as you show in your FBD. “F” is just a tensile stress/force along the axis of the U-bolt, and this is reacted by radial forces, and friction, around the contact half of the pin and U-bolt. There is probably some frictional/gripping advantage to having some ground flat surface on the bearing area of the U-bolt. The plate under the nuts on the U-bolt will have a bending moment which is FL/2 and you just make this thick enough, stiff enough to tolerate this loading from the nuts.

 

[chicopee]

I would get a mechanical engineering handbook and check out the section where you have contact stress between two curved surfaces of similar and dissimilar diameters.

 

[lodgera]

I've looked through these forums at length and still cant really find a detailed answer to this question, only other statements that there shouldn't be much bending. I understand in reality the reaction at the U bolt ID will be distributed and radial . . . are you suggesting that these reactions will, if the bolt is sectioned at the apex of the U as shown in my sketch, result in a zero sum on the moment equation such that there is no moment acting on the cross section? How would you draw the FBD? Can you show this result analytically?

 

[SwinnyGG]

The source of your error is using the wrong tool. Winkler-Back (assuming that's the solver you are using for curved beams) assumes just that- a curved beam.

The situation you are describing is not a fixed, curved beam. Because you have cylindrical surfaces in contact, this becomes a hertzian stress problem. Start there.

 

[MJCronin]

I believe that you are using the wrong approach ....Lab test results trumps analysis

Maximum loads on U-bolts has been extensively investigated empirically by the nuclear power industry evaluating pipe supports in the 1980s....

Suggest that you contact some of the major pipe support vendors (ANCHOR, Power piping etc) and discuss this topic.

As I recall, the variety of end conditions (nuts attaching the u-bolt to the structural member) can have a significant affect.

Some fun reading when you cannot sleep some night .......

http://www.nrc.gov/docs/ML0732/ML073230518.pdf

MJCronin
Sr. Process Engineer