Basic definitions: The factor of safety (FoS) in traditional working-stress design is defined as the ratio of ________ to the working (allowable) stress.

Introduction / Context:Factor of safety is a foundational concept that links material strength to the stress permitted in service. In working-stress design, FoS is applied to yield (or ultimate) strength to derive an allowable stress that ensures elastic behaviour and sufficient margin against failure under uncertainties.

Given Data / Assumptions:

• Traditional working-stress methodology.
• Allowable (working) stress = reference strength / FoS.
• For ductile metals like structural steel, reference strength commonly taken as yield stress.

Concept / Approach:

For structural steel under service loading, the working stress is typically derived from yield stress divided by a chosen factor of safety. Hence, FoS = yield stress / working stress. While limit-state design uses partial factors on loads and resistances, the underlying safety philosophy still aims for comparable reliability.

Step-by-Step Solution:

Verification / Alternative check:

Standard textbooks define working stress = yield stress / FoS for steel; for brittle materials, ultimate strength may be used instead, but the exam convention for steel is yield-based.

Why Other Options Are Wrong:

• Options b, c, d use actual service stresses, which are not the numerator in FoS definition.
• Option e is a mismatched ratio not generally used.

Common Pitfalls:

• Confusing FoS with load factors from limit-state design.
• Using ultimate instead of yield for ductile steel in working-stress contexts without noting the convention.

Final Answer:

Yield stress.