Question

When a thin cylindrical shell is subjected to internal fluid pressure, the stresses developed in its wall are

• A. Circumferential and longitudinal
• B. Diagonal and bending
• C. Vertical and bending
• D. Irregular and bending

Hint:

For a thin cylindrical pressure vessel, \[ \boxed{ \sigma_h=\frac{pd}{2t}, \qquad \sigma_l=\frac{pd}{4t} } \] where the hoop stress is twice the longitudinal stress.

Answer 1

The Correct Option is A

Step 1: Think about how the internal pressure pushes on the wall.
Internal fluid pressure pushes outward in every direction on the curved wall of a thin cylinder, and this outward push has to be balanced by tension developing within the wall material itself, not by any bending action.
Step 2: Identify the two directions this tension acts in.
Going around the circumference, the wall resists being split open, giving the circumferential or hoop stress. Along the length of the cylinder, the pressure also pushes on the end caps, and this pull is carried along the axis of the shell, giving the longitudinal stress.
Step 3: Conclude.
Since a thin shell has no significant bending stiffness across its thickness, these two tensile stresses are the only ones that matter.
\[ \boxed{\text{Circumferential and longitudinal}} \]