Which of the following statements regarding thin and thick cylinders, subjected to internal pressure only, is/are correct?

1. A cylinder is considered thin when the ratio of its inner diameter to the wall thickness is less than 15.

2. In thick cylinders, tangential stress has highest magnitude at the inner surface of the cylinder and gradually decreases towards the outer surface

Concept:

Thin Cylinder: A cylinder is considered to be ‘thin’ if the ratio of the inner diameter to the thickness of the walls is greater than 20.

\(\frac{d}{t} > 20\)

Thick Cylinder: A cylinder is considered to be ‘thick’ if the ratio of the inner diameter to the thickness of the walls is less than 20.

\(\frac{d}{t} < 20\)

Hence statement 1 is wrong.

In case of thin cylinders, the hoop stress is determined by assuming it to be uniform across the thickness of the cylinder.

But in thick cylinders, the hoop stress (tangential stress) is not uniform across the thickness, it varies from a maximum value at the inner circumference to a minimum value at the outer circumference.

For a thick cylinder hoop stress (tangential stress) is given by,

For a thick cylinder Radial stress is given by,

ri ≤ x ≤ ro

Where, ri and ro are inner and outer radius, respectively