In thin-walled cylinders, the ratio of hoop stress to longitudinal stress is:

Asked in SSC JE 27/01/2018 (Morning); SSC JE 2013

Detailed Explanation

Both stresses in a closed thin cylinder come from the same pressure, but over different areas of wall.

\[ \frac{\sigma_h}{\sigma_l} = \frac{pd/2t}{pd/4t} = 2 \]

Why “2” Is Correct

The hoop stress is twice the longitudinal stress. That is why a cylinder under too much pressure splits along its length (the hoop stress breaks it), and why longitudinal seams need to be stronger than circumferential ones.

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. 1/4: 1/4 has no basis in the formulas.
C. 4: 4 is double the true ratio.
D. 1/2: 1/2 is the inverse ratio (longitudinal to hoop).

Key Point

σh : σl = 2 : 1.

Key Concepts for Students

Cylinders burst along a longitudinal line.
Longitudinal joints are designed for the hoop stress.
Circumferential joints carry only the longitudinal stress.

Practice more: this is question 6 in Thin Cylindrical and Spherical Shells MCQs – Part 1. Try the whole set and check every answer instantly.