Stress Calculator

[GGaskill]

Since my day job is computer programmer and I wanted to practice writing a dynamic javascript web page, I have created a web page that calculates stress in thin wall and thick wall cylinders using the standard equations for that.  Feel free to use it to check your designs or projects. 

Keep in mind that stress from chamber pressure is just one thing that must be considered in barrel design.  Elimination of stress risers, for example, must also be considered.  Since we don't have good chamber pressure values, I use the 20,000 psi that was published by Matt Switlik in his cannon pressure tests of the 1980's.  Keep in mind that pressure can be increased by unsafe loading practices such as too much powder, wrong granulation of powder, and too heavy a shot load.  Also, be sure to understand the caveat at the bottom of the Calculator page.

[kappullen]

George,

I use the number of Bloody Marys it takes to put up with the inlaws as a stress calculator!   :-D  

Thanks, that could be useful!

Kap

[Dictator]

this is a kinda cool item George. Thanks much......Kap, the holidays are coming & so are the inlaws :gulp:

[Cat Whisperer]

George,

I use the number of Bloody Marys it takes to put up with the inlaws as a stress calculator!   :-D  

Thanks, that could be useful!

Kap

Kap -  the same warnings and precautions apply to this equaion as well.  Any formula misapplied can get one into deep trouble!   :-D

[Double D]

George can you build a calculator that will tell the recommended wall thickness given bore size and and using the 80.000 psi safety factor.

[CU_Cannon]

I see some problems with your analysis.  Though the hoop stress is the highest it is not the only stress present.  There is also a radial stress.



The first equation shows the tangential stress or the hoop stress.  It is in a slightly different form than the one GGaskill gave but the result is the same.  The second is the radial stress.  In both formulas ri is the inside radius, ro is the outside radus, p is the pressure and r is the region at which you want to find the stress.  The stress is the highest at the inside of the tube where r = ri.

For example take a barrel with a 2” bore, a 6” outside diameter and a max pressure of 20,000 psi.

The hoop stress would be 25,000 psi
The radial stress would be -20,000 psi

It may seem weird to have a negative stress but think about stretching a rubber band.  It gets longer in one direction but thinner in the other direction.

Just comparing the highest stress to the yield stress does not tell the whole story.  The last equation is von Mises yield theory where Sy is the yield strength of the material.  

For the above example the yield strength of the material should be greater than 39,000 psi.

A word of caution; there is not going to be one set of equations that can tell if a cannon will fail or not.  The max pressure is present for less than a second where as the above equations are based on a constant pressure.  There are also complex stress concentrations present due to geometry.

[Cat Whisperer]

I see some problems ...

....

Just comparing the highest stress to the yield stress does not tell the whole story.  

....

A word of caution; there is not going to be one set of equations that can tell if a cannon will fail or not.  The max pressure is present for less than a second where as the above equations are based on a constant pressure.  There are also complex stress concentrations present due to geometry.

Thankyou CU for mentioning this.  There are areas wherein it is easy to make assumptions, these formulas give one a rough idea of what's going on.  BUT TO USE THEM FOR DESIGN IS IN ANOTHER LEAGUE!  That is why I recommend for us non-metalurgists/mechanical engineers to use the proven experience of others' successful designs.

<< end of rant and rave >>

[Powder keg]

Waohhh, My brain is hurting.

[Cat Whisperer]

I've occasionally used a formula or two from someone's website for getting rough ideas of stress/strain.  (I think the site was for calculating strength of pipe needed for high pressure application.)

However, it is good here to have some discussion as to applicability to mortars and cannons.

It is certainly a good idea if the simple formula indicates not  enough strength to heed that indication.

This is a good starting point - thanks, George for bringing the formulas to our attention.  We certainly have room for more discussion!


If it makes your head hurt, use the rules of thumb.

[GGaskill]

I fully agree that successful design is quite a bit more than just hoop stress calculations.  However, someone who has no formal engineering background can plug in his values and see how close to material strength his design is.  An interesting exercise is to take an old design (e.g., the Tannenberg gonne, M1861 13" seacoast mortar, etc.) and plug in the dimensions and see what stress is calculated.  Since these were successful designs, you will find that they operated well under the maximum stress the material could withstand.
 
DD--It's easy enough to rearrange the thinwall formula to calculate wall thickness from inside diameter, stress and chamber pressure (the thick wall formula is more difficult to rearrange), but that is going to tell you only the boundary condition. and you really don't want to be close to that.  If you try a few samples, you will find that 3/8" wall tubing hits 80K psi at 3" ID assuming 20K psi chamber pressure.  That's the point where it fails.  At 2" ID, the stress is 53,300 psi.  If you use your "wall thickness equals bore diameter" rule, the stress computes to 25K psi, which gives you lots of cushion.

[Cat Whisperer]

....  However, someone who has no formal engineering background can plug in his values and see how close to material strength his design is.  
....

I hope that folks with no formal background in engineering would NOT make the ASSUMPTION that running a simple stress-strain calculation comes close to ensuring or implying safety.

It is a very common practice in enginering (in the tooling design and several other areas I'm familiar with) to do your best with the math and THEN build the prototype and TEST it to see if / how-well it works.  To assume the design should go right into production is foolhardy.


Edited 22 Oct 05: TRK - George graciously pointed out my omission of one word that changes the meaning!  (Changed it above, thanks.)

He further pointed out, correctly, that depending on a formula was very close to depending on a rule of 3/8" thick 80kpsi liner, for all bore sizes.

The N-SSA does mention the 3/8" thickness of steel at a minimum, but does not go further to recommend thicker liners for bigger bores.

In that respect the use of formulas does give one some basis for comparison.  (Again, all the standard disclaimers apply.)