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You need to calculate the hoop stress for the given pressure. This is the force balance between the walls (F=stress*t*L*2) and the projected area the pressure acts on, not the curved area (F=P*L*2*r).
I think you've quoted the ultimate tensile strength there (1.4 GPa) which would lead to true explosion-style failure. The yield stress would be a better target, you'd be able to ride the frame after that loading. For typical 4130 (Cro-moly) steel that's ~460MPa (ref) and gives a radius-thickness ratio of 15/460, or a wall thickness of ~0.46 mm for a 28.6 mm tube. Not dainty, but not a gas pipe by any stretch.
hamrack-
a wall thickness of ~0.46 mm for a 28.6 mm tube. Not dainty, but not a gas pipe
Thinner than an actual frame tube, in fact. Generally you need something better than 4130 to get away with <0.6mm walls in the main tubes of a frame. You also need to account for the tensile load from the two ends being forced apart by the contained pressure, and of course all the usual frame loads which don't disappear just because your pipes are full of gas. In practice, that probably means that using the frame tube as the pressure vessel is probably no better than using the frame tube as a frame tube and adding a completely separate pressure vessel alongside it, should you be minded to use your bike to transport pressurised gas. If the issue is getting tubeless tyres to seat, you'd probably be better off carrying a gas which is liquid at a relatively low pressure at ambient temperature, as that makes your pressure vessel much lighter. People who run very low pressures on off road 4×4s and knock their tyres off the bead seat as an occupational hazard have been doing it for decades
https://www.youtube.com/watch?v=1QDLx6HSOAw
gbj_tester
Sorry, I was out by a factor of 10 in my calculation, so wall thickness of 2mm would suffice for 20bar.
Yeah, 150Bar would need around a 1.4cm wall thickness. Not sure how that is possible. Paging @mdcc_tester to enlighten us all.