Hi Bob ,

I'm afraid that the complete answer would take many pages but here is some of it :

(1) The strongest boiler possible is spherical and made from constant thickness material .

(2) A reasonable working approximation to (1) is a cylindrical centre section with spherical ends and all made from constant thickness material .

NB : Neither (1) nor (2) need any staying – the steam pressure load is resisted by what is properly called a homogenous tension field in the boiler shell – basically works in same way as a toy balloon .

(3) In practical boilers the ends have to be much flatter , the tension field becomes a minor factor and the end plates now have to resist steam load in bending – basically like putting a weight on a circular disc supported at the edges . Bending strength of a flat plate is very poor compared to the balloon strength of curved plates mentioned above and for the same thickness of plate large deflections can occur .

These large deflections can be controlled either by making end plates significantly thicker or by using auxilliary stays .

(4) In boilers with cylindrical main barrel and flat ends there is a secondary problem in that the stresses and deflections at the joint between the two sections don't match and this can give rise to local stresses wich are significantly higher than elsewhere in the boiler .

This mismatch can be managed by using flat end plates but ones designed with a relatively large radius flange where they join the barrel .

There is much much more to it – please ask any questions you like .

Regards ,

Michael Williams .

PS:

Bit hard to get your head around but any pressure vessel which is not already balloon shaped is always trying to become balloon shaped . If you can visualise how any arbitrary design of boiler would have to distort in order to become balloon shaped it is a very good illustration of how it is resisting the internal pressure forces and also how design could be modified to be more structurally efficient .

There are two alternative principles used in more sophisticated pressure vessel design :

(1) The constant stress principle – all parts of vessel stressed to same level and all 'working' to same extent . This is the most weight efficient design and is used in aeroengines .

Usually has to be an approximation due to many conflicting requirements and constraining geometries .

(2) The variable stress principle – all parts which can be easily analysed are relatively highly stressed and all parts which are difficult to analyse are relatively modestly stressed . Not very weight efficient but very conservative and used for many purposes . This fundamentaly is how model boilers have always been designed historically .

Edited By MICHAEL WILLIAMS on 11/12/2012 15:33:57

Michael Williams,

An elegant explanation of a complex subject.

I particularly appreciated your balloon analogy. I might even have gone up a grade in Strength of Materials if I'd had that proposition before me.

Bob D

Hi Bob, The formula for copper Boiler plate thickness is T= P X D /7. This would give you the plate thickness in Thousands of an inch. The formula would give you a safety factor of 10. T refers to thickness, P is Pressure, D is the plate diameter. Brass is not mentioned often because simply it is not a good thing to construct boilers with.

Andy