# copper tube wall thickness



## firebird (Aug 21, 2008)

Hi

I'm thinking ahead here (a long way ahead) but the way metal prices are rising I'm thinking its worth keeping a look out. A future project I would like to build is a model of a stationary engine something like this.







With a boiler somewhere in the region of 4 to 6 inch diameter what wall thickness of copper pipe should I be looking for?

Cheers

Rich


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## SandyC (Aug 21, 2008)

Hi All,

Rich,

It will depend upon both working pressure and diameter, however it is quite easy to calculate once you know these.

As Follows: -

The tensile strength of copper is generally given as 27,000psi at 20deg C.
However, for model boiler work, where higher temperatures are being used, this must be reduced to take account of the reduction in material strength at higher temperatures and the generally accepted figure of 25,000psi is more generally used.

It is also general practice, for model boiler work, to allow for a high margin of safety of between 6 and 12 to be applied, which further reduces the figure.

For boiler shell/flu calculations the applied safety factor is generally accepted a being 8, which results in an accepted tensile strength of: -

				25,000/8 = 3,125psi

 Hence this will be the figure used for (t) in the remainder of these calculations.

Further reductions to this figure would also be required in the case of a rolled tube having a seam joint being supported by either rivets or an internal/external strap plate, however, assuming the boiler is constructed from Solid Drawn (seamless) tube, these need not concern us.


1. The formula for plate/wall thickness is given as: -

			T = P x D 
	  		&#160;  ______&#160; &#160; &#160; 
                       2t
2. And for Pressure as: -

			P = 2T x t&#160; 
			  ______&#160; &#160; &#160; &#160; &#160; 
                        D
Where D = Exposed dia
	t = Tensile strength 
	T = Thickness 
And 	P = Working pressure


I hope this helps.

Best regards.

Sandy.

BTW how is the small boiler coming along?


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## firebird (Aug 21, 2008)

Hi sandy

Thanks for that. Could you give an example of the formulae with some numbers, that would help. The small boiler is doing fine. I've been away on holiday so haven't had a lot of shop time of late. I'm working on a pump to hydraulic test it at the moment. I should have it done over the coming bank holiday weekend so I will post that when it's done.

Cheers

Rich


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## BobWarfield (Aug 22, 2008)

Geez that's a cool steam engine!

BW

PS Calcs are cool too, but sorry, the steam engine is much more interesting!


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## SandyC (Aug 22, 2008)

;D 

I agree, the engine is much nicer to look at than a load of numbers, however, since you asked!!!

here are a few: -&#160;&#160; 1, 17, 5, 36, 19, 45....... can't give you any big ones, Bog's has used them all up adding at least 4 zero's to the National debt ;D ;D ;D... just kidding John.... good to see you are getting back on track.

Ok, try this for size: -

For boiler shell/flu calculations the applied safety factor is generally accepted a being 8, which results in an accepted tensile strength of: -

				25,000/8 = 3,125psi = Tensile strength (t)

1. The formula for plate/wall thickness is given as: -

			T = P x D / 2t


2. And for Pressure as: -

			P = 2T x t / D

Where D = Exposed dia
	t = Tensile strength 
	T = Thickness 
And 	P = Working pressure


As an example let&#8217;s take the max working pressure for the boiler to be 90psi

Minimum wall thickness required.

Using formula 1. (Above)

NOTE&#8230;. D is expressed as the EXPOSED dia&#8230;.. this means the dia actually exposed directly to the steam pressure.
In the case of an outer barrel, this would normally be the INSIDE DIA.

In the case where the ID is unknown, which is the case when the wall thickness required is an unknown, it is quite satisfactory to use the known OD to make a first order calculation. The resulting value/figure will be slightly higher than actually necessary, however, since the thickness required increases with dia for any given pressure, the small error will be in favour of safety.

This can be verified in a subsequent pressure calculation. 

To return to our calculations: -

Boiler outer shell thickness required.

Given an OD of 4&#8221; this becomes: -

T = 90 x 4&#160; / 2 x 3125&#160; = 360 / 6250&#160; = 0.0576&#8221;&#160;&#160; 
		&#160; &#160; &#160; &#160; 
Which is just a thousandth of an inch or so over 17swg.



To prove the case for the small error described above: -

Correction to D for calculated thickness.

This gives the correct ID for the calculation.

ID = OD &#8211; 2 x calculated thickness&#160; = 4&#8221; &#8211; 2 x 0.0576&#8221;&#160; = 4&#8221; &#8211; 0.1152&#8221; = 3.8848&#8221;

Using formula 2.

P = 2T x t / D&#160; = 2 x 0.0576&#8221; x 3125 / 3.8848&#8221; 

= 0.1152&#8221; x 3125 / 3.8848&#8221; = 92.668psi.

Which, as you can see, is a little higher than required, however, it is, as stated above, on the safety side.


Ok, as calculated, the gauge of material required is just a little over 17swg.

This is not an easy thickness to source; therefore, it would be more usual to select/use a barrel material of 16swg (0.064&#8221 since this would be the more readily available material.
NOTE: - In such cases, always go to a higher, more readily available, thickness. Never go lower. 


Using this thicker gauge will result in the following pressure capability: -

D becomes 4&#8221; &#8211; 2 x 0.064&#8221;&#160; = 4&#8221; &#8211; 0.128&#8221;&#160; = 3.872&#8221;

P = 2T x t / D&#160; = 2 x 0.064&#8221; x 3125 / 3.872&#8221; 

= 0.128 x 3125 / 3.872&#8221;&#160; = 103.3psi.

Which gives an even greater safety margin.


The portable engine design you are contemplating appears to be a 2 cylinder compound type which would probably be operating at around 120psi &#8211; 150psi.

Taking this at its highest level (150psi) and using a barrel dia of 5&#8221; OD, then a first order calculation would yield the following: -

Thickness required (T) 

T = P x D / 2 x tensile strength&#160; = 150 x 5&#8221; / 2 x 3125

= 750 / 6250&#160; = 0.120&#8221;

This lies between 11swg (0.116&#8221 and 10swg(0.128&#8221

So choose 10swg or thicker.


Ok Rich, I think this should be sufficient for you to see how the numbers fit with the formulae, however, if anything is still not clear then just ask.

Best regards to all who are still awake..... ;D ;D ;D ;D ;D ;D ;D

Sandy


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## firebird (Aug 22, 2008)

Hi Sandy

Thanks for the example. I'll print it out and sit and study it. I'm OK at maths but must admit its not my strongest subject. I'm a bit slow but get there in the end.

Cheers

Rich


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## IanN (Aug 24, 2008)

Hi,

There is an unfortunate error in Sandy's calculations for boiler shell thickness. The formulae for the outer shell using the internal diameter of the shell are correct (or at least, they are the ones that I use), but you cannot use the same calculations for a flue or tube subject to external pressure as Sandy suggests:




			
				SandyC  said:
			
		

> NOTE. D is expressed as the EXPOSED dia.. this means the dia actually exposed directly to the steam pressure.
> In the case of an outer barrel, this would normally be the INSIDE DIA.
> 
> For an internal flue tube (e.g. centre flue boiler); then the outer dia would be the correct figure to use.




The outer shell is in tension due to the high internal pressure, but the flue is in compression (as the boiler is on the outside of the flue tubes) and so the strength of the structure is not a direct function of the UTS.

The work done by Martin Evens (published in the book 'Model Locomotive Boilers') and K. N. Harris ('Model Boilers and Boilermaking') and summarised by Tubal Cain (T. D. Walshaw) in 'The model Engineers Handbook' gives a series of recommendations for the thickness of tubes under compression, but there are a number of complicating factors:

1) A tube under compression is an inherently unstable structure - any slight deviation from a circular cross section will significantly weaken the structure and precipitate collapse.

2) Tubes subject to compression can be reinforced by fitting rings to the outside of the tube (like very thick washers).

3) On the positive side, the failure mode of a tube under compression is a collapse rather than a bursting failure and the collapsed tube seldom ruptures unless the end of the tube tears out of the boiler end plate.

Ian.


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## Jasonb (Aug 24, 2008)

SandyC's thickness of 0.120 for a 5" boiler would seem about right based on the size of my Fowler TE. That has a 4 3/4" barrel and 10swg wall thickness. Working pressure is 100psi.

Would like top know what allowance is made for the boiler needing to be tested to twice working pressure, is the allowance for the tensile strength enough to cover this?

It Would be interesting if anyone has the issues of Model Engineer (142-145) that cover the building of W.J.Hughes Marshall portable as this has a boiler of approx 4" and see what that suggests. The Alchin has a 3 3/4x 13swg boiler

JAson


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## ianjkirby (Aug 25, 2008)

Hi Jason,
 If I might put in my 2 bob's worth here, I would suggest that the cold-water hydraulic test to 2 x wp is covered by the pressure-based calculations offered above.
 As an aside, given that Rich's original message showed a portable engine rather than a self-propelled machine, ie a traction engine or "road locomotive", I suggest that no other consideration is necessary. If one were to be building a traction engine however, I would advise that an allowance is included in the Australian Miniature Boiler Safety Code, Part 1 for the boiler being subject to cyclic loading from the cylinder mechanism above, and random loading from the rod shocks below, as the boiler forms the chassis of the vehicle. This allowance obviously increases the thickness of the material used for the barrel and outer throatplate. Given that material is only available in a few commercially available sizes, it usually means using the next thickness up from that prescribed by pressure calculations alone.
 The AMBSC codes are legal documents within Australia and NZ, but have no authority outside those regions.
Regards, Ian.
Chairman, AMBSC.


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## SandyC (Aug 25, 2008)

Hi Guy's,

Well then, who's a silly thicko? :'( :'( ???

Thanks IanN, for pointing out my oversight.

For the record, there is no actual error in the calculations given, or in the formulae.

I do, however, accept that perhaps the wording could have been a little better.

On re-reading through the post, the statement: -

&#147;For an internal flue tube (e.g. centre flue boiler); then the outer dia would be the correct figure to use&#148;.

(statement now deleted from original post)

Could indeed be taken to mean the same formulae applied to flue tubes or any other tube under external pressure.

This is clearly not the case, as has been highlighted by Ian, and I should have made this more clear.

The correct formulae for flue tube thickness would actually be: -

T = (PxD / 2xS + P) + 0.005 x D

And for pressure this would be: -

P = S [2xT &#150;0.01 x D / D - (T - 0.005 x D)]

Where S = Maximum allowable stress value of the design material at design temperature.

For copper @ temperatures below 450deg F it is reasonable/acceptable to use: -

S = Tensile Strength / 3.5. (Above this temperature, then reference to stress tables would be required).

For copper with an 8 times safety factor this would amount to: -

 S = 3125 / 3.5 = 892.857psi.

Also in this case D = Outside dia.

This is in fact a much-simplified version of the formulae, however, for the purposes of designing of model boilers, operating at relatively low pressure and temperatures and which are using silver soldered jointing methods, it is perfectly satisfactory/adequate. 

My apologies if my original statement led to any confusion, this certainly was not my intent.

Jasonb,

The pressure test at twice working pressure is, indead,&#160; well catered for in the calculations, so no worries on that score.

Iankirby,

Yes you are quite correct, an additional factor should/must be added for boilers forming the chassis of a vehicle, such as on a traction engine.

In the UK this is generally accepted as being T + 75% and then taking the next thickest available standard material.
Jasonb's boiler barrel seems to follow this rule with his 10swg material.

How does this tie in with OZ rules?&#160; Generally yours are not too different to ours. 

Best regards,

Embarrassed SandyC&#160; :-[ :-[ :-[


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## IanN (Aug 25, 2008)

Hi Jason,

I have a different opinion to Ian (Oz) and Sandy regarding which "pressure" should be used in the calculations. 

The pressure used in the calculations should be the hydraulic test pressure (i.e. twice the working pressure). The working pressure is taken as the normal operational pressure of the boiler plus 10% (which is the pressure setting for the safety valve(s) in order to comply with the UK boiler tests).

If you do not use the hydraulic test pressure you run into the following problem:

The figure used for the tensile strength of copper in the formula is 1/8 of the ultimate tensile strength for the metal in its annealed state (which it almost certainly will be after the various brazing operations during the construction of the boiler - although it will work-harden due to the pressure cycling as the boiler is used).

The yield strength of annealed copper (again - the annealed material is the worst case) is about 1/5 the UTS - if the boiler experiences this level of tension it will stretch past its elastic limit and be permanently deformed.

Testing at twice the calculated operational pressure (giving a safety margin of 4:1) will take the boiler shell past its elastic limit - this is not considered a good thing to do.

As a further complication you need to do the calculations again for the boiler under steaming conditions. From steam tables, at 100 psi + 10% (gauge) the boiler temp will be 344F (174C) - at this temperature it is recommended to use a UTS for copper of about 80% of the value at room temperature (the temperature of the hydraulic test) - as Sandy points out, it is this figure that he has used in the formula. For most boiler temperatures the reduction in UTS is less than the reduction in pressure and so the cold test remains the most significant, until the pressure gets up to about 210 psi (gauge) - a temperature approaching 400F. 


Some other thoughts:

The EU regulations for commercial systems requires the test to include all of the system under pressure - that includes the piping and the cylinders of the engine, displacement lubricators, feed pumps, injectors, etc, etc. while this does not extend to model boilers (at present) it would seem sensible to do the calculations for these parts of the system too if they are large enough to contain sufficient stored energy to be a danger in the event of catastrophic failure.

If the boiler shell is not made from a tube, but fabricated from a rolled sheet the figure used for tensile strength is multiplied by a "joint efficiency" factor. This is taken as 0.7 for joggled, lap or butt joints and 0.8 for the dovetailled "brazier's joint"

Ian.

P.S. Sandy - I would like to know more about the calcs for tubes in compression - I have data derived from boiler tests but no reliable theory. I am doing the calcs for a boiler design produced in the mid 60s by E.T. Westbury and I will need to have all the evidence to hand before entering into discussions with my local boiler inspector. I would appreciate it if you woul e-mail me at:

[email protected]

Many thanks, Ian


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## firebird (Aug 26, 2008)

Hi

A bit of luck has come my way in the shape of a piece of copper tube 4 inch dia with a wall thickness of .080. How doe's that sound?

Cheers

Rich


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## firebird (Sep 20, 2008)

Hi

I have the piece of tube now. Its a bit dirty but in excellent condition. I'll leave it in the pickle for a couple of days to get it cleaned up.











Cheers

Rich


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## Mcgyver (Sep 20, 2008)

firebird  said:
			
		

> A bit of luck has come my way in the shape of a piece of copper tube 4 inch dia with a wall thickness of .080. How doe's that sound?



sounds like pretty good luck - that stuff iirc was like $100 a foot 10 years ago or some crazy assed big number


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## steamboatmodel (Sep 21, 2008)

For all you want to know about copper tube
http://www.copper.org/publications/pub_list/pdf/copper_tube_handbook.pdf
Regards,
Gerald


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## firebird (Sep 22, 2008)

Hi

Thanks Gerald. Iv'e saved a copy of that for future reference.

Cheers

Rich


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