Question

A thin-walled circular pressure vessel has an internal pressure ‘\( p \)’, radius ‘\( r \)’, and wall thickness ‘\( t \)’. What is the hoop stress?

• A. \( \frac{pr}{t} \)
• B. \( \frac{2pr}{t} \)
• C. \( \frac{pt}{r} \)
• D. \( \frac{pr}{2t} \)

Hint:

For thin-walled pressure vessels, hoop stress is always higher than longitudinal stress and is critical in design: \[ \text{Hoop stress } \sigma_h = \frac{pr}{t}, \quad \text{Longitudinal stress } \sigma_l = \frac{pr}{2t} \]

Answer 1

The Correct Option is A

Step 1: Concept of Hoop Stress in Thin-Walled Pressure Vessels
For a thin-walled cylindrical pressure vessel under internal pressure, the hoop stress (also known as circumferential stress) is given by the formula: \[ \sigma_h = \frac{p r}{t} \] Where:
- \( \sigma_h \) = Hoop stress
- \( p \) = Internal pressure
- \( r \) = Radius of the cylinder
- \( t \) = Wall thickness (assumed \( t \ll r \))
Step 2: Substituting the variables from the question: \[ \sigma_h = \frac{pr}{t} \] Step 3: Final Answer Hence, the hoop stress is: \[ \boxed{\frac{pr}{t}} \]