It appears that you are fixated on problems that aren't actually there.
No. I'm fixated on problems derived from working with metals in the real world, and limiting myself to discussion of methods that a RW blacksmith of an analagous tech level would have at his disposal. I'm ignoring the use of magic because then you're not just talking about a masterwork weapon, but a construction process dependent on magic, and if you're doing THAT, it is functionally no different than constructing any other magic item- you handwave the difficulties away.
You presume that the sheet of adamantium that makes up the surface of the quarterstaff has to be thick in order to be useful.
No. I'm assuming that you (as you stated) want a staff of adamantium that has the same dimensions and mass as a wooden quarterstaff, which would, perforce, be hollow.
All that is required for a quarterstaff to be effective is a hard striking surface, a consistent density throughout its length and an acceptable degree of rigidity.
Having been struck by hard, light staves, I can assure you that all they do is hurt (sometimes a lot) unless they hit a spot that is inherently fragile- a larynx, an eye, the groin, etc. In game terms, they are subdual weapons at best.
If you want a staff to be a
weapon, something that could break bone or dent armor, you need MASS.
That being said, a thin surface of adamantium with internal bracing for strength is all that is required. This exactly parallels the construction of bracers and greaves which you have conceded is not problematic.
This does not confer a great deal of strength for something so long as a quarterstaff, so it is now required to add internal stiffening and lateral bracing. This is not rocket science.
I beg to differ.
You're talking about internally bracing a 6'-9' long staff of a metal harder than most alloys out there- roughly equivalent to the nickel-iron you'd find at the Gibeon Meteor strike.
Adamantine: Found only in meteorites and the rarest veins in magical areas, this ultrahard metal adds to the quality of a weapon or suit of armor. (PHB p283)
I have some of this stuff- I broke 3 diamond-tipped drills engraving one piece with the Zodiacal symbol for Libra. Its heat resistant, with a crystalline structure- listed as a "high-temperature" alloy. This stuff is tough!
While lateral bracing is indeed a possibility, internally braced metal tubes require special tools that aren't in a blacksmith's toolbox, like acetyline blowtorches.
In fact, doing much more than cutting it, rolling it and riveting it would require things a medieval blacksmith wouldn't have, like a high-temperature forge.
A typical medieval forge was capable of temperatures of 1650-2500 degF.
Working Nickel-Iron requries a
minimum temp of 2600 degF. I don't see how I could let adamantium be forged at a lower temp in my campaign.
100 deg F doesn't sound like much, but it means everything.
Your argument also betrays a lack of imagination.
No, it betrays an understanding of the physics involved in working metals like this.
At no point is it ever required that the construction is limited to a sheet rolled into a tube. There are fighting staff weapons with cross sections that are not circular. An octagonal cross section allows for segmented construction which should be more than doable for a technology base that can manage articulated adamantium armor for sizes ranging from cloud giant to pixie.
While you're correct that you could weld flat sheets, or bundled tubes or rods into a single rod the approximate diameter of a quarterstaff, you still run into the problem of how to weld the stuff.
As pointed out above, you'd have to heat the adamantium to 2600 deg or hotter to do a single metal (adamantium to adamantium) weld.
If you can't do that, you'd have to use welds or bands and caps of lesser metals to bind your rods together...and then you'd lose the effects of having a staff of pure adamantium.
And riveting, as a technology, works better for things like armor than things like tubes of metal.
