Stress in a Thin Cylindrical Shell

When a thin cylindrical shell is subjected to an internal pressure, it experiences two types of stresses: longitudinal stress and hoop stress.

- Longitudinal stress: It is the stress that is developed in the direction of the axis of the cylinder. It is also known as axial stress or tensile stress.
- Hoop stress: It is the stress that is developed circumferentially around the cylinder. It is also known as radial stress or compressive stress.

Ratio of Longitudinal Stress to Hoop Stress

The ratio of longitudinal stress to hoop stress in a thin cylindrical shell can be calculated using the following formula:

σ_L/σ_H = 0.5

where σ_L is the longitudinal stress and σ_H is the hoop stress.

Explanation

The ratio of longitudinal stress to hoop stress in a thin cylindrical shell is 0.5. This means that the longitudinal stress is half of the hoop stress.

This can be explained as follows:

- When an internal pressure is applied to a thin cylindrical shell, the hoop stress is developed circumferentially around the cylinder. This stress is proportional to the internal pressure and the radius of the cylinder.
- The longitudinal stress, on the other hand, is developed in the direction of the axis of the cylinder. It is proportional to the internal pressure and the length of the cylinder.
- Since the length of the cylinder is twice the radius, the longitudinal stress is half of the hoop stress.

Therefore, the correct answer is option A, which states that the ratio of longitudinal stress to hoop stress in a thin cylindrical shell is 0.5.