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# Stress Calculation Small Washer Sitting in Square Hole

## Stress Calculation Small Washer Sitting in Square Hole

(OP)
Hi,

I am trying to prove that a small washer will not yield and bend into a square hole that is close to the same size as the washer.

The washer is 316 stainless steel, 13/16" OD, .405 ID. The square cutout is .563"x.563". The bolt diameter is .375". The max tightening torque is 400 in-lbs, which I converted to 5333 lbs. The washer thickness is .06". It's a carriage bolt with a lock washer and a nut.

Does anyone know how to calculate the stress?

### RE: Stress Calculation Small Washer Sitting in Square Hole

5000 lb on a 1/16" SS washer? It's gonna bend.

For a more exact treatment, possibly a Roarkes would help.

Regards,

Mike

The problem with sloppy work is that the supply FAR EXCEEDS the demand

### RE: Stress Calculation Small Washer Sitting in Square Hole

(OP)
Thanks SntMan. Are you talking about Roark's Stress & Strain book? I don't have it. Do you have any equations from it that would help?

### RE: Stress Calculation Small Washer Sitting in Square Hole

It's quarter-point loading so any "strength of materials" textbook should cover it, even the basic ones.

STF

### RE: Stress Calculation Small Washer Sitting in Square Hole

(OP)
Thanks SparWeb. I found Roark's online, but I can't find a suitable equation. Can someone point me in the right direction?

### RE: Stress Calculation Small Washer Sitting in Square Hole

400 inch pounds on a 3/8" carriage bolt?
What are you trying to break?
I think the facets under the head will spin, before you get that torque on it, too.

My understanding of a carriage bolt installation is the the head's facets must be engaged directly in a square hole that fits snugly with no washer under the bolt head.
The hole in the mating part should be round, to allow engagement of the bolt.
The intended use of Carriage bolts is in very lightly loaded applications, especially where things are placed on the surface of the part that would be scratched by bolt-head hexagons.
Use of a lock washer under the nut restricts turning of the nut but that's not proven to be effective in many cases, but it is the "common" thing that people expect.

For this reason, I do not understand your original question about "a small washer will not yield and bend into a square hole" because the washer should not be in contact with the square hole.
Also for this reason, I cannot understand the torqueing of the carriage bolt, since that will be difficult to accomplish, and hints at an application that is not suitable for these bolts.
Are these bolts even heat treated? I've snapped a few in my time.

STF

### RE: Stress Calculation Small Washer Sitting in Square Hole

While this might not be totally relevant, if you look at the history from whence 'carriage' bolts came (hint: the name) you'll realize that they were originally used to hold together parts made of wood. They were placed in round holes with the idea that upon tightening the nut, the square shank would sink into the wood forming a natural 'lock' preventing the bolt from rotating while the nut was being torqued. This also allowed the mechanic to work with only one wrench at a time since there was no need to hold the head to prevent it's rotation, hence the lack of anything even resembling a conventional 'head' being needed. Besides, the 'mushroom' head gave the finished assembly a very neat and clean appearance.

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

### RE: Stress Calculation Small Washer Sitting in Square Hole

Since there is not enough information to tell what the contact between the washer and the bolt is there is no way to figure this out.

### RE: Stress Calculation Small Washer Sitting in Square Hole

(OP)
What information would be needed for the contact area between the two? The carriage bolt comes in from the backside and a 3/8" nut is tightened down. I'm not actually going to tighten the nut to 400 in-lbs, that's just the maximum I'm told we could apply before it would break.

### RE: Stress Calculation Small Washer Sitting in Square Hole

Bolts, nuts and washers are not made equal.

A few dumb questions... may have missed something...

What is the BOLT specification? Head-style/dimensions, thread-type [coarse/fine/rolled/cut] tension-strength and/or alloy/temper are important.

What is the WASHER specification? The exact alloy/temper of the washer are important.

What is the NUT specification? Washer-flange dimensions, thread-type [coarse/fine], thread-depth and alloy/temper are important.

An aerospace grade tension-bolt 160-KSI steel BOLT MS20006 with an aerospace grade tension NUT [Typ NAS1804-6] can withstand ~400-inch# torque-up... but not advisable [usually 310--330-in#]. Usually this bolt/nut combo is paired with a high strength steel washer such as MS20002-6.

What guide did You use for torque-tension calculations? MIL-HDBK-60? other?

How does the 0.375-dia bolt remain perfectly centered in the 0.563 X 0.563 square hole? What IF the bolt shank slides into a corner, hence the stack is asymmetrical to the Square hole?

Regards, Wil Taylor

o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

### RE: Stress Calculation Small Washer Sitting in Square Hole

For what purpose?

For the cost of your time, build a model (square hole in a flat plate can be done with a broach and a hand press, or a hand drill and a file). Then squish the washer to the force you claim to expect into the square hole. Takes 1/2 hour.

Hint: You're also apparently thinking of a "force" being loaded on the washer by the bolt. But that force (when tightening) comes from a torque on the nut on the (usually very coarse or very smooth or lubricated or rusted or easily turned or jammed nut). Assuming a force by tightening a nut is an assumption with a lot of assumptions behind it.

### RE: Stress Calculation Small Washer Sitting in Square Hole

It's gonna bend :)

Regards,

Mike

The problem with sloppy work is that the supply FAR EXCEEDS the demand

### RE: Stress Calculation Small Washer Sitting in Square Hole

Given the axial preload noted, that 316 cres washer will definitely deform locally around its ID. Local areas of the thin bolt head flange are unsupported by the round washer hole, and will bend enough to deform the washer surface.

### RE: Stress Calculation Small Washer Sitting in Square Hole

I'm pretty sure I walk by a few applications of "carriage bolts" in steel panels a few times a day.
http://thelocksmithers.ca/images/donjo.JPG

I'm less sure the bolt body will end up centered in the round through hole. Then there is the .68" Ø lockwasher, which being centered on the bolt, will give the flat washer a noogie in the unsupported region.
https://uproxx.files.wordpress.com/2015/06/brock-l...

### RE: Stress Calculation Small Washer Sitting in Square Hole

Yes, they are ideal for secure situations where it's desirable that something can't be removed or tampered with using normal hand tools.

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

### RE: Stress Calculation Small Washer Sitting in Square Hole

Am I missing something, or is the head of the carriage bolt too large to fit through the hole? If this is the case, then the washer is simply a spacer, in compression, etc.

### RE: Stress Calculation Small Washer Sitting in Square Hole

(OP)
I guess I'm mostly just trying to figure out how much it will deform and how much the stress will increase in comparison to the 1"OD washer they currently use. If anyone has a formula, that would be much appreciated. Some deformation is acceptable.

### RE: Stress Calculation Small Washer Sitting in Square Hole

Have you grabbed a wrench and tried it yet?

### RE: Stress Calculation Small Washer Sitting in Square Hole

I guess there are two cases ...
1) the diameter of the head of the 3/8" bolt is greater than 0.563" then the head will bear against the square hole and the washer isn't doing much and the issue becomes will the head of the bolt fail (as it has only a partial contact with the clamped flanges), assuming the washer isn't effective at distributing the bolt clamp-up force. or
2) if the head of the bolt fits within the square hole (first bad design, no?) then the washer is the loadpath to the clamped flanges. I can easily see that the thickness of the washer is relevant, the diameter less so (as the washer should lift-off around the hole). You can "easily" model this in FEM and spend a month of sundays analyzing it, or you can go to the shop and torque for bolts, carefully.

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