It seems to me this whole debate is much ado about nothing. The only thing that Smith and Brown actually propose is using the material’s yield point as the limiting stress without (as far as I can see) any stated Factor of Safety on top of that. The Barlow formula (not a name I know it by, but no bother) stands regardless.
We haven’t escaped the much stated problem that determining yield point for annealed copper is a tricky business as demonstrated by the spread of figures presented by S&B and in this forum. This is a physical problem in that we can’t measure the yield stress without yielding the material and if we yield the material, then the yield stress will change due to work hardening. That is why the yield value for annealed copper is a slippery customer that defies catching.
It seems to me that the underlying assumption that “any permanent deformation in a copper boiler shell during a 2WP hydraulic test is not allowable” is fundamentally flawed. It is a constraint that does not in fact exist. As I have previously stated, an FEM analysis by Wim Merks published in ME around 2020 or 21 showed that firebox corners and stays will see plastic deformation in a well proven design. As has been stated by others in this thread, how is anybody going to know exactly what diameter of shell you started with when you have already done your own 2WP hydraulic before getting a boiler tester involved? You will be presenting it in a semi work hardened state by that point. Finally, most telling of all, point to a boiler failure that has not involved poor workmanship in jointing.
Next we have Jason’s and S&B’s figures which show the actual difference in result between the Yield point and UTS based stress calculations is small. Could this be that the UTS criterion is used with basic FOS of 4 (as far as I know from copper boiler calculations) and looking at S&B’s graph on page 27, annealed copper has a UTS around 30000 psi and a YP of 7500 psi – coincidentally a factor of 4. Or predictably depending on your point of view.
The “YP method” seems to have an unstated assumption that a cold hydraulic test will always be the worst case. Depending on working temperature and the associated temperature de-rate in material properties and the number of times hydraulic required by the test authority, this Ain’t necessarily so, as the song goes.
However, the real problem in my view is that the “YP Method” is not a method for designing boilers. It says nothing about allowances for stress in the seam of a shell, it says nothing about concentration factors for penetrations like domes, clack or safety valves. It also is not applicable to the tricky bit where shell meets firebox or smokebox tubeplate, is not applicable to the flat surfaces of inner or outer firebox or flues and tubes. For something that covers all those tricky sums, you need a design code. To attempt to mix the YP method for the shell with the remainder designed to your chosen code is a short cut to getting your sums thrown back at you with “Do it again” scribbled in red. (Memories of school days?).
So we come round to Duncan Webster’s view of a couple of days ago that sticking to an established design code such as the Aussie one is the only way to sensibly proceed. I wish to be associated with the remarks of that gentleman.
Smith and Brown’s article is interesting, but it is not a design method.
Martin
p.s. Just to join in the willy waving as we now seem to be indulging in the sport: B. Tech (1st class) in Mechanical engineering, retired as a C. Eng, F.I. Mech. E. Model engineer since 1969, designed an 18″ shell steel boiler to BS 2790 and obtained approval from a Notified Body for same for my last project, helped with translating the FEM article by Wim Merks.