Problem calculating stress from torsion in mounting bolts - PLEASE help.

[patrickv]

Hello all, I need some desperate help. I have a product that is mounted on four corners with 1/4-28 bolts with a shank diameter of .25. The product is mounted to a vibe table and shaken at 20g in each of the three axis. I am currently analyzing the stresses induced in the fasteners in order to prove that a .1875 diameter shank will suffice.

My problem is this:
I am fairly confident I've calculated the tensile and shearing stresses caused by the three different loads (20g in each direction, one at a time) on each fastener.

However when I calculate the torsion in each screw and then the subsequent shearing stresses caused by that moment [tau=(moment)(radius)/(.5)(pi)(r^4)], the stresses are so large, they can't be right. Please help, the attached pdf shows a diagram of the part, numbers and my calcs. I believe I'm approaching this wrong, but I can't tell where. Thank you in advance!

 

[FredGarvin]

Yeah. Those stresses for a 56 Lbf load are way too high. Try calculating the shear due to a moment about the center of the bolt hole pattern, not about specific bolts. I have attached an excerpt from an old article that should help you out.

 

[Mech_Engineer]

The bolts themselves shouldn't have any torsional stresses other than what's caused due to applied torque for proper preload. The moments caused by the bulk forces at the center of mass should be balanced across the bolt pattern as tensile and compressive forces. Those distributed loads will give you an extra tensile/compressive load on each bolt, which you will in turn will add to your bolt stress (but shouldn't be a problem).

Your general goal should be to find the maximum tensile force each bolt will see, and make sure the bolt's preload is greater than that number. Additionally, if your bolts are subject to shear forces it means the joint is sliding (which would be considered a failure), so you want your frictional force in the joint to be greater than those shear forces. Ideally, once your bolts are torqued down with their engineer-specified preload, they will not see any forces other than the preload you have specified, since all tensile forces will be less than the preload, and all shear forces will be less than the preload times a conservative coefficient of friction.

With respect to vibration- you will probably want to use some locking washers as well, to make sure your bolts don't loosen themselves.

 

[patrickv]

Thank you for the input, however I am not concerned in the thread or it's engagement into the mounting surface. I know the 1/4-28 holds fine (based on previous shake tests to a similar product). The issue is that the mounting fastener needed the diameter of the shank above the thread reduced and in lieu of re-testing (expensive), I need to prove the reduced shank will still hold what the .25 dia did.

Where I'm approaching it wrong is that maybe I don't need to calculate the stresses induced by the bending moment of the load on each fastener?

Let me ask this, in this example, when qualifying that the reduced diameter shank will hold the load, do I only analyze the tensile and shearing stresses caused by the load as I did in the first part of the paper I attached? (also is it right?) Do I calculate any other stresses based on this load or is that it?

Isn't there a stress induced from where the load is applied, causing a "twist" in each bolt? The only reason I keep thinking this, is that I thought there would be two sets of stresses to calculate for each. The tensile and shear components of the load on each bolt, which I did, as well as the stress induced by the component of the force acting perpendicular to the point (a moment).

If I'm wrong, and I should only be doing the strict tensile/shear as I did, then I guess that would be it. I want to make sure I'm not leaving anything out while analyzing this. Thank you again.

minger: I calculated the pound-force load by F=ma where m=W/g, W=2.8lb and a=20g so the load P of 20g's in the x-direction would be (20)(2.8) = 56lbf.

 

[Mech_Engineer]

Where I'm approaching it wrong is that maybe I don't need to calculate the stresses induced by the bending moment of the load on each fastener?

Right. The bulk bending moment is taken up by the bolt pattern as tension/compression in the fasteners surrounding the load. A properly torqued bolt pattern should not show any bending moments in any of the fasteners, because this would mean the joint was separating.

Let me ask this, in this example, when qualifying that the reduced diameter shank will hold the load, do I only analyze the tensile and shearing stresses caused by the load as I did in the first part of the paper I attached?

As a point of fact, you really only look at the tensile forces, since a shear force in the fasteners would indicate the joint is sliding (and therefore failed). You can convert the shear force at the joint to a required tensile force in the bolt by taking into account the coefficient of friction in the joint. It's likely the joint's resistance to shearing will be your limiting factor since it will probably take 5-10 times the preload a pure tensile force would.

(also is it right?) Do I calculate any other stresses based on this load or is that it?

You calculated the raw tensile force and stress correctly, but you'll need to take another look at the joint's shear resistance and the loads spread across the bolt pattern due to bulk moments on the box.

Just guessing, I would guess that the force requirements on the bolts will be rated from highest to lowest as such:

1. Shear resistance (friction in joint)
2. Bolt pattern forces (bulk moments, which cause both tension in the fasteners, and shear in the joint)
3. Pure tensile forces (which you've calculated)

Isn't there a stress induced from where the load is applied, causing a "twist" in each bolt? The only reason I keep thinking this, is that I thought there would be two sets of stresses to calculate for each. The tensile and shear components of the load on each bolt, which I did, as well as the stress induced by the component of the force acting perpendicular to the point (a moment).

The only torsional stresses that should occur in the bolts will be when you torque it down. Once the bolt pattern is torqued, an applied moment on that bolt pattern should be absorbed by the friction in the joint. Even if the joint slid in a joint failure, it would apply a tangential shear force to the bolt pattern, not torsion on the bolts.

If I'm wrong, and I should only be doing the strict tensile/shear as I did, then I guess that would be it. I want to make sure I'm not leaving anything out while analyzing this. Thank you again.

You've got the lowest answer, but now you need to calculate required frictional force in the joint and bolt pattern loads. I'm pretty sure the frictional load will be your deciding factor as to whether you can make the smaller bolts work.

 

[patrickv]

Mech. Engineer: Thank you so much! It's been a while since I've had to run numbers like this and everything you said clicked into place, aided by the great example Garvin supplied. Completely makes sense now where I was thinking about it wrong and how to go about solving it. The equivalent force/moment coordination system at the bolts' center was the key. Thank you!

One thing I am not familiar with (even in dusty old memories) is the calculation of the shear resistance in the joint. I notice Garvin's example had the numbers in the summary sheet, but not how they were derived. What would be the units of the shear resistance?

Thank you both, this information has been invaluable in getting familiar with this stuff again.

 

[Mech_Engineer]

One thing I am not familiar with (even in dusty old memories) is the calculation of the shear resistance in the joint. I notice Garvin's example had the numbers in the summary sheet, but not how they were derived. What would be the units of the shear resistance?

It's just a friction calculation. Add up the prload force of all of your bolts, and multiply the sum by your estimated coefficient of friction between the plates. This result is the estimated maximum amount of force the joint will take before sliding (units of force, same as the preload in the bolts).

Don't forget to define what safety factors you want!

 

[wtejada]

Yeah. Those stresses for a 56 Lbf load are way too high. Try calculating the shear due to a moment about the center of the bolt hole pattern, not about specific bolts. I have attached an excerpt from an old article that should help you out.

Hi,

Will the formulas in the attachment of the post that I'm quoting work for a cabinet that I'm designing. The cabinet is made of cold rolled steel and will weigh between 60 and 70lbs when it's fully loaded. It will be wall-mounted using a rectangular bolt pattern. Also, how is shear resistance calculated on page 5 of the attachment?

Thanks.