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I am just posting about hoop stress today.
That is like the pressure rating calculation of pipe.
If there is interest, and I don't get kicked off Beartooth, I will post other examples of gun strength calculations, like the section modulus of the breech of a break action.

The thin wall hoop stress is directly devirable:
The inside diameter  times the pressure is the force, and the thickness
of two walls are in tension, hence:
Steel stress  = [ID][P]/[[2][wall thickness]]

When the walls are thin, Lame's Formula gives the same answer, but as
the walls get thicker, Lame's
formula gives an increasingly  greater stress.

I got Lame's formula from "Mechanics of Materials"  by Laurson and Cox,
1938 Wiley and Sons.
The derivation was first done the the French mathematician, Lame, 500
years ago. It is a difficult derivation.
If the barrel is thick, read an two inches further down my post to Lame's formula:
 

"Hoop stress for barrels with thick walls and high accuracy we need

Lame's formula for maximum stress in a thick walled cylinder subject to

internal pressure:
 
 

S=P(r2 squared +r1 squared)/(r2 squared - r1 squared)

Where S is the stress in psi of tension

P is the chamber pressure in psi

r1 is radius of the chamber or bore in inches

r2 is radius of the barrel [center to outside] in inches"

How to tell which can handle more pressure: CZ52 or Tokarev:

Measure the OD of the barrel in a CZ52 at the chamber:.590"
Measure the OD of the barrel in a Tokarev at the chamber:.640"
Measure the OD of the barrel in a CZ52 on the barrel:.468"
Measure the OD of the barrel in a Tokarev on the barrel:.494"

The Chamber ID is .390" and the grooves ID is .308" for the 7.62x25mm
Tokarev cartridge.

This makes the walls in the chamber of a CZ52 .1" thick
This makes the walls in the chamber of a Tokarev .125" thick
This makes the walls in the barrel of a CZ52 .08" thick
This makes the walls in the barrel of a Tokarev .093" thick

The formula for thin wall hoop stress is S=[chamber
Pressure][ID]/2[thickness of walls]

Assume 4140 steel heat treated.

If heat commercially treated and quenched 4140 steel has an ultimate
maximum tension yield strength of 180ksi,
http://et.nmsu.edu/~etti/winter99/manufacturing/kollmer/kollmer.html
Then the max chamber pressure for a CZ52 may be calculated:
Pmax[CZ52]ch = S[2][thickness or walls]/[ID]= 180ksi
[2][.1"]/.390"=92,000 psi
Pmax[Tok]ch= 180ksi[2][.125"]/.39"= 115,000 psi

This must be added to the pressure capacity of the brass:
Pbrass = S[2][thickness or walls]/[ID]= 66ksi [2][.035]/[.39
-(2).035]=14kpsi

The CZ52 chamber would then fail at 106,000 psi
The Tokarev chamber would then fail at 129,000 psi

Pmax[CZ52]barrel= S[2][thickness or walls]/[ID]=
180ksi[2][.08"]/.308"=94kpsi
Pmax[Tok]barrel= S[2][thickness or walls]/[ID]= 180ksi[2][.093"]/.308"=
109kpsi

It looks like the barrels are weaker than the chambers.
It looks like the CZ52s are weaker than the Tokarevs.
 

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The Hog Whisperer (Administrator)
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Interesting... say, I found an old Gun Digest in a used book store a while back.  It was from the '60's.  Anyway, there was a article about heat-treating steels for guns.  Although the article may be somewhat dated, it went into detail about how different parts could be heat-treated, depending on how they would be used.

For example... a semi-auto frame, even if made from the same steel as the barrel, undergoes different stresses, so it is heat treated to a different level.  That gives the different parts different yield strengths (ie threshold of failure).

So... I guess my point is, based on the limited amount of information at my disposal, that perhaps it is probably a mistake to assume that all gun steels, or even different parts of the same gun, have the same failure point.

One thing that I'll mention from personal experience is, receivers are one heck of a lot harder than barrels.  This observation from drilling/tapping a few receivers, and crowning a couple of barrels.

Well anyway, like I said, it is interesting, in a theoretical sort of way.
 

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failure other than complete barrel burst

This is good math, but assumes that a complete barrel burst is the criteria of failure. Usually, the first failure (in a bottle neck case) is from case-head seperation. Pressure pushes the bolt face back enough that the case stretches and cracks circumferentially, allowing gas to escape. Hopefully the action is designed to direct hot gas away from the shooter and not too much damage is done. More pressure, that exceeds the yield strength but not the tensile strength, will bulge the chamber or barrel, making the gun relatively useless. I have mostly heard of bulged barrels, confirming the fact that receivers are harder, thicker, and stronger. Of course safety dictates that it is better for a barrel to burst at the far end than for the receiver to blow up in your face!

Which brings up my question: Has anyone tried designing a muzzle loader for use with smokeless powder and modern pressures or is the pressure severely limited by the relatively open ignition system?

Ed
 

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"Which brings up my question: Has anyone tried designing a muzzle loader for use with smokeless powder....."
Savage makes just such a beast- or did recently- a smokeless muzzleloader. Never seen or used one, so I can't comment on pressure limits, etc.
 
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