Stress in a Boiler Shell

A special section just for steam engines and boilers, as without these you may as well fit a sail.
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fredrosse
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Stress in a Boiler Shell

Post by fredrosse » Mon Jan 04, 2021 4:10 pm

From Mike: "Fred? Ron? Anyone with some advice on this subject?"

Hoop Stress in a pressurized cylinder, as illustrated in the attached picture.


Pressure Force tends to force the cylinder apart, and is equal to:

Pressure x Area of pressure action = Pressure x Diameter x Length


This Pressure Force is opposed by the metal cylinder wall tensile stress, and this force tending to hold the cylinder together is equal to:

Stress x Area of stress action = Stress x wall thickness x 2 x Length

Setting these two forces equal to one another, and solving for the hoop stress:

Hoop Stress = ( Pressure x Diameter ) / ( t x 2 )


This simple classic equation may be used to approximate the metal stress in a cylindrical pressure vessel, however there are several complications, such as holes in the cylinder wall, thermal distortion, weld seams, welded attachments, end connections, etc., etc. When considering this equation, it is prudent to use very conservative allowable stress values, especially with the potential danger of a steam boiler. For example, the ASME Boiler Code only allows 17,000 PSI hoop stress in the shell of my simple firetube boiler, yet the actual material has a yield stress of over 37,000 PSI, and an ultimate tensile stress of over 70,000 PSI.

Another VERY important requirement for pressure vessels is to use materials that are ductile, so that they can be distorted without potentially producing cracks and brittle fracture when exposed to all the stresses caused by the issues of the previous paragraph. In general, pressure vessel material for our typical launch boilers must be able to withstand a fully closed 180 degree bend, without producing any cracks in the material.
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Re: Stress in a Boiler Shell

Post by barts » Mon Jan 04, 2021 7:42 pm

An additional item to add here is that seams along the length of the drum are more heavily stressed than those around the drum.

Load attempting to remove cap from end of drums is area * pressure = 3.14*r^2 * p.
Area in tension resisting load = 2 * 3.14 * r * t.

Stress in radial direction is (p * r)/ (2 * 3.14 * t), half of that seen in the longitudinal case. Pictures of notable pressure vessel/pipe failures demonstrate this, with typical failures involving longitudinal breaks:
https://en.wikipedia.org/wiki/San_Bruno ... _explosion

This also explains why seamless tubing with welded end caps is the preferred fabrication technique for steam drums. Note that for small sizes, drum/pipe thickness is governed by practical considerations rather than pressure stresses.

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Re: Stress in a Boiler Shell

Post by TahoeSteam » Wed Jan 06, 2021 9:07 pm

What about calculating for webbing strength between tubes?
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Re: Stress in a Boiler Shell

Post by barts » Wed Jan 06, 2021 11:40 pm

TahoeSteam wrote:
Wed Jan 06, 2021 9:07 pm
What about calculating for webbing strength between tubes?
Tubesheet calculations are very complex and depend on design details such as type of tube layout, sizes, material, manner of fastening, etc. On small model steam locomotive boilers I've seen people just use some stays that are sized to take the entire load so that their design is quite conservative; the tubes are ignored. Welded in tubes/flues/furnaces, of course, act as stays.

As always, the ASME boiler code will answer this; I don't have a copy.

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Re: Stress in a Boiler Shell

Post by ccdewitt » Thu Jan 07, 2021 3:24 pm

It is important to distinguish between “ligaments” and “tube sheets”. In the code (ASME) ligaments are the material between tubes through the shell as in a water tube boiler. Tube sheets are typically flat, applied inside a shell as in a firetube boiler.

In so far as the shell is typically self-supporting the only stresses that are examined in a tube sheet, under the code, are those acting to push the tube sheet out the end of the shell which are resisted by the tubes and stays. The total area of the tube sheet in which tubes have been applied is comparatively small compared to the area of the sheet without tubes. Tubes typically support the tube sheet and only the flat area without tubes needs additional staying. It is prudent to flare 10% of the tube ends, for support, in a tube sheet where direct flame impingement isn’t an issue. Otherwise bead all tube ends in a combustion space for mechanically applied tubes. See ASME, Section I, PFT-25.1 and ASME, Section I, PG-46.

Ligaments are a different case. PG-52 discusses the issue for regular openings in a shell and PG-53 discusses irregular openings in a shell. An example of regular openings is the repetitive pattern found in rows of water tubes in a shell. An example of irregular holes in a shell might be pipe fittings, studs for mechanical supports, and such.

For instance, in calculating a locomotive boiler some time ago I calculated a longitudinal line in the first course along the top of the boiler. In that line were the rivet holes for the circumferential joints, studs for the bell bracket and sand dome, and the top mounted boiler check valve. That valve assembly had been added by the railroad and was not original equipment and the opening was not compensated. The opening was sufficiently large that the total material removed in that line reduced strength of that line and the MAWP of the boiler was accordingly reduced. Bad news for the owner.

PG-32 supports these calculations and discusses compensation for the openings if required. The math isn’t difficult just tedious.
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Re: Stress in a Boiler Shell

Post by TahoeSteam » Thu Jan 21, 2021 3:43 pm

Chris,

Thank you for that information. Now off to find a copy of Section 1 of the ASME code.

I have an idea about weldless watertube boilers that is nagging me and I want to pursue it as far as it'll take me.

Hope all is well out your way.

~Wes
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Re: Stress in a Boiler Shell

Post by ccdewitt » Fri Jan 29, 2021 3:02 pm

Wes, If you want you can borrow my ASME section I. I will point you in the correct direction.
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Re: Stress in a Boiler Shell

Post by TahoeSteam » Sat Jan 30, 2021 5:53 am

I appreciate your offer. I actually had a member send me an electronic copy already. Thank you anyway ☺️
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Re: Stress in a Boiler Shell

Post by Kelly Anderson » Sun Jan 31, 2021 9:02 pm

TahoeSteam wrote:
Wed Jan 06, 2021 9:07 pm
What about calculating for webbing strength between tubes?
In the case of a steam drum with a line of tube holes along its side, the full length of the drum is under load per the formula in Fred's post, while only the remaining length of the metal in the drum after the holes are subtracted is available to resist the load. The ratio of the two is known as "efficiency". Say in the case of a Balckstaffe boiler, the steam drum is 16" long, and has six 1/2" holes for the coils drilled in it, leaving 13" of steel left to resist 16" of load from the steam pressure. 13/16 means that the steam drum is 81% efficient. The inverse of 81% is; 1/.81=1.23, so the wall thickness of the steam drum will need to be increased by 23% over what is shown in Fred's formula to compensate for the loss of that 3" of steel.

However, that basic system really only is in effect if the holes are evenly spaced along the length of the drum. When you have two or more holes closer together than the rest, that makes a weaker spot along the length of the drum and the more conservative route is to treat that worst case scenario as the case along the entire length of the shell. For example, if there is a a 3" long section that has three 1/2" diameter holes in it, that leaves 1.5" of steel to support 3" of load, so that area of the shell is only 50% efficient, and so would need to be twice as thick as an undrilled drum.

Accordingly, Yarrow boilers and the like need to have the parts of the drum used for the tube patterns quite thick due to the great loss of supporting steel between the many tubes. In full sized boilers, sometimes those areas were made considerably thicker than the balance of the drum.
It was not easy to convince Allnutt. All his shop training had given him a profound prejudice against inexact work, experimental work, hit-or-miss work.
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Re: Stress in a Boiler Shell

Post by fredrosse » Mon Feb 01, 2021 4:05 am

Kelly's explanation about the a row of tubes in a boiler drum is correct, and Kelly indicates that drum wall thickness would need to increase in these areas. That is one option, if the nominal stress is close to the maximum allowable stress. Many boilers are designed with relatively low stress, and if there is enough extra stress value available, then no extra wall thickness may be required.

A good example is the typical two drum watertube boilers made for steam launches (Lune Valley Type), where each drum has constant wall thickness, but maximum stress values are still within allowable limits. The stresses in the vicinity of the extra holes are higher, but still sufficiently low as to not require increased wall thickness.
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