Which expression represents the hoop stress in a thin-walled cylinder under internal pressure?

Which expression represents the hoop stress in a thin-walled cylinder under internal pressure?

• A. PR/t
• B. PD/2t
• C. P R^2 / t
• D. P t / R

Answer: (A)

For a thin-walled cylinder under internal pressure, the hoop (circumferential) stress is found from balancing the pressure trying to split the wall around the circumference with the tensile resistance of the wall. The result is sigma_hoop = p r / t, where p is the internal pressure, r is the inner radius, and t is the wall thickness. This is the standard membrane-stress expression for the circumferential direction in thin-walled vessels. If you prefer using diameter, since r = D/2, you get sigma_hoop = p D / (2 t); that form is numerically the same as the radius form when D is indeed the diameter. The other expressions don’t match the correct balance of forces or the dimensional dependencies: they either mix in the wrong factors or yield the wrong relationship between p, r (or D), and t.

For a thin-walled cylinder under internal pressure, the hoop (circumferential) stress is found from balancing the pressure trying to split the wall around the circumference with the tensile resistance of the wall. The result is sigma_hoop = p r / t, where p is the internal pressure, r is the inner radius, and t is the wall thickness. This is the standard membrane-stress expression for the circumferential direction in thin-walled vessels.

If you prefer using diameter, since r = D/2, you get sigma_hoop = p D / (2 t); that form is numerically the same as the radius form when D is indeed the diameter. The other expressions don’t match the correct balance of forces or the dimensional dependencies: they either mix in the wrong factors or yield the wrong relationship between p, r (or D), and t.