Question

In thin cylindrical pressure vessels, hoop stress is:

• A. Equal to axial stress
• B. Half of axial stress
• C. Twice the axial stress
• D. One-fourth axial stress

Hint:

In thin pressure vessels, remember: hoop stress is $\frac{p d}{2t}$ and axial stress is $\frac{p d}{4t}$, so hoop stress is always twice the axial stress.

Answer 1

The Correct Option is C

In thin-walled cylindrical pressure vessels subjected to internal pressure, two principal stresses are developed:
- Hoop stress (circumferential stress) $\sigma_h = \frac{p d}{2t}$
- Axial stress (longitudinal stress) $\sigma_a = \frac{p d}{4t}$
Where:
$p$ = internal pressure, $d$ = diameter, $t$ = wall thickness
From the formulas,
\[ \sigma_h = 2 \cdot \sigma_a \]
Thus, hoop stress is twice the axial stress.