How is design stress related to ultimate stress and factor of safety?

The relationship between design stress, ultimate stress, and the factor of safety is fundamental in ensuring the reliability and safety of mechanical components. Design stress is defined as the stress level at which a material is allowed to operate safely without risking failure. The ultimate stress, often referred to as ultimate tensile strength, is the maximum stress that a material can withstand before it fails.

The factor of safety is a critical value used in design to provide a margin of safety against unexpected loads or material defects. It is defined as the ratio of ultimate stress to the design stress. To ensure safety, engineers use this ratio to determine the maximum permissible stress on the material.

By rearranging the definition of factor of safety, you find that design stress can be calculated by dividing the ultimate stress by the factor of safety. This relationship means that the design stress is always lower than the ultimate stress when a safety factor greater than one is applied, which helps to ensure that even if the material is subjected to unexpected conditions, it will not reach failure.

This clear mathematical relationship is essential in mechanical design and provides a systematic approach to ensuring component integrity under varying loads and potential uncertainties. Hence, the statement that design stress equals ultimate stress divided by the factor of safety accurately encapsulates this important principle