Define the Factor of Safety (FoS) in design.

• A. FoS = Allowable stress / Resistance
• B. FoS = Resistance × Allowable stress
• C. FoS = Resistance − Allowable stress
• D. FoS = Resistance / Allowable stress

Answer: (D)

The factor of safety measures how much stronger the design is than the load it must handle. It is defined as the component’s resistance (its capacity to withstand load, such as yield or ultimate strength) divided by the allowable or actual design stress that must be resisted. This ratio is dimensionless and conveys the margin for uncertainty. For example, if a material can safely carry 200 MPa and the design requires only 100 MPa, the FoS is 2, meaning the capacity is twice the required stress.

This form—resistance divided by allowable stress—is essential because it directly expresses how much extra strength is available. Inverting it would imply the margin is smaller when the capacity is large, which misrepresents safety. Multiplying or subtracting would produce values that don’t quantify how close you are to the limit, so they don’t provide a meaningful safety margin.