Question

Maximum shear stress in a thin cylindrical shell subjected to internal pressure \( p \) is

• A. \( \dfrac{pd}{t} \)
• B. \( \dfrac{pd}{2t} \)
• C. \( \dfrac{pd}{4t} \)
• D. \( \dfrac{pd}{8t} \)

Hint:

In thin cylinders, maximum shear stress occurs midway between hoop and longitudinal stresses.

Answer 1

The Correct Option is C

Step 1: Identifying principal stresses.
In a thin cylindrical shell subjected to internal pressure, the two principal stresses are:
Hoop stress: \[ \sigma_h = \frac{pd}{2t} \] Longitudinal stress: \[ \sigma_l = \frac{pd}{4t} \]
Step 2: Formula for maximum shear stress.
Maximum shear stress is given by: \[ \tau_{\max} = \frac{\sigma_h - \sigma_l}{2} \]
Step 3: Substituting values.
\[ \tau_{\max} = \frac{\frac{pd}{2t} - \frac{pd}{4t}}{2} \] \[ \tau_{\max} = \frac{pd}{4t} \]
Step 4: Conclusion.
The maximum shear stress in the cylindrical shell is \( \dfrac{pd}{4t} \).