Question

A thin cylinder (closed at its ends) of radius \( r \) and thickness \( t \) (\( r \gg t \)) is subjected to internal pressure \( p \). The maximum shear stress in the wall of the cylinder is

• A. \( \frac{pr}{t} \)
• B. \( \frac{pr}{2t} \)
• C. \( \frac{pr}{4t} \)
• D. \( \frac{3pr}{2t} \)

Hint:

For thin-walled cylinders, the maximum shear stress is \( \frac{pr}{2t} \), where \( p \) is the internal pressure, \( r \) is the radius, and \( t \) is the thickness.

Answer 1

The Correct Option is B

For a thin-walled cylinder subjected to internal pressure, the maximum shear stress \( \tau_{\text{max}} \) in the wall of the cylinder is given by the formula: \[ \tau_{\text{max}} = \frac{pr}{2t}. \] This is derived using the relationship between internal pressure, radius, and wall thickness for thin-walled cylinders.

Step 1: Formula for shear stress.
For thin-walled cylinders, the shear stress is inversely proportional to the thickness of the wall and directly proportional to the internal pressure and radius.

Step 2: Conclusion.
Thus, the correct expression for the maximum shear stress is \( \frac{pr}{2t} \).

Final Answer: \text{(B) \( \frac{pr}{2t} \)}