My handy dandy McMaster-Carr catalog tells me:
5/16" OD Copper tubing Max Pressure 1197 PSI
5/16" OD 304 Stainless Max Pressure 3500 PSI
Unfortunately, the type of steel tubing used on cars isn't listed, but the
type they do list (carbon steel) is about the same strength as 304
Stainless.
In service, I calculate that the peak pressure in a panic stop in the brake
lines of a disk brake car is somewhere in the range of 1200 PSI.
Dick Benjamin