An open-ended thin cylindrical shell subjected to uniform internal pressure will be subjected to:

Asked in SSC JE 2009

Detailed Explanation

Longitudinal stress in a cylinder comes from the pressure acting on its end caps, which pulls the ends apart. Hoop stress comes from the pressure pushing the curved wall outward.

Why “Hoop stress only” Is Correct

In an open-ended shell (for example a pipe whose ends slide in sealed glands), there are no end caps for the pressure to act on, so the longitudinal stress is zero. The wall still carries the bursting force, so there is hoop stress only — option (a).

Disputed answer: the book's printed key gives (c), but that applies to a closed cylinder. For an open-ended shell, as the question states, (a) is correct.

Stresses in the wall of a thin cylinder (internal pressure p, diameter d, wall thickness t). The hoop (circumferential) stress σ_h = pd/2t acts around the circumference; the longitudinal stress σ_l = pd/4t acts along the axis (only when the ends are closed). So σ_h = 2σ_l.

Why the Other Options Are Wrong

B. Longitudinal stress only: Longitudinal stress needs end caps; the hoop stress is always present.
C. Both hoop stress and longitudinal stress: Printed in the book's key, but that is the closed-cylinder case.
D. None of the above: Hoop stress is definitely present.

Key Point

Open-ended cylinder: σh = pd/2t, σl = 0. Closed: σh = pd/2t, σl = pd/4t.

Key Concepts for Students

Pipes with expansion joints behave approximately as open-ended.
Boilers and gas cylinders are closed shells.
End caps of a closed cylinder carry the force p·πd²/4.

Practice more: this is question 5 in Thin Cylindrical and Spherical Shells MCQs – Part 1. Try the whole set and check every answer instantly.