Just FYI - hoop stress as you've quoted it assumes a thin walled cylinder. I haven't worked on the LHC so don't know the dimensions; however, this assumption is

Just FYI - hoop stress as you've quoted it assumes a thin walled cylinder. I haven't worked on the LHC so don't know the dimensions; however, this assumption is really only valid for D/t > 20 or so before solutions diverge at which point the interaction becomes more complex than R/t.