[Occasionally6]

Apologies for using SI units. That is what I have formulas for and am comfortable using - the result should be easily converted or the formulas work with imperial units:

If the ratio of radius to thickness is greater than 5, a rotating cylinder (= drum) can be treated as thin wall, and the stress as ~uniform through the wall thickness:

r = 0.19m

t = ? but let's call it 20mm = 20x10^-3m

r/t = 0.19/(20x10^-3) = 9.5; which is >5 so treat as thin wall.

Hoop stress:

fh = rho x v^2; Hoop stress (Pa) = material density (kg/m^3) x linear velocity of rim squared (m/s)^2

Need the linear velocity of the rim:

v = (r x pi x N)/30; velocity (m/s) = radius (m) x (pi x rpm)/30 (s^-1)

v = 0.19 x (pi x 3450)/30 (m/s)

v = 68.64 (m/s)

Plug that into the hoop stress formula, using a density for cast iron of 7200 (kg/m^3):

fh = 7200 x (68.64^2) (Pa)

fh = 33.9 (MPa)

I have the Ultimate Tensile Stress of grey cast iron as 170 (MPa) and, being brittle, that's the stress at which it will fail, so it should be OK.

There will be some margin in the design of the drum because the brake shoes will be pushing out against the drum wall, in addition to the stress due to the rotation of it's own mass.

Depending on what it is you will be centrifuging you might want to add that in (simplistically and conservatively, increase the density by assuming the extra mass is acting within the same volume as the cast iron drum wall) because that will add to the force causing the stress but not act to resist it. It's unlikely to be a problem though.