Massachusetts 2nd Class Fireman's Practice Exam

What is the relationship between longitudinal stress and circumferential stress?

1. They are the same

2. Longitudinal stress is twice circumferential stress

3. Circumferential stress is twice longitudinal stress

4. There is no fixed relationship between the two

The correct answer is: Longitudinal stress is twice circumferential stress

In the context of pressure vessels, the relationship between longitudinal stress and circumferential stress is crucial for understanding how these stresses are distributed within the structure. Longitudinal stress, which acts along the length of the vessel, typically arises when the vessel is subjected to internal pressure, while circumferential stress, which acts around the circumference of the vessel, is also a result of that internal pressure. In a thin-walled pressure vessel, the circumferential stress is greater than the longitudinal stress due to the geometric distribution of forces. Specifically, the internal pressure exerts a more significant influence on the circumference because it acts to expand the vessel outwards, thus creating higher stresses around the circular cross-section. As a result, the relationship can be expressed quantitatively, with circumferential stress being twice that of longitudinal stress. This relationship is derived from the fundamental mechanics of materials and is crucial for the design and safety assessments of pressure vessels. Understanding this relationship helps engineers ensure that vessels can withstand the pressures they will encounter in service, preventing structural failures.