Design stress and factor of safety: The factor of safety represents the margin between the design (allowable) stress and which other stress level used in service?

Introduction / Context:
Mechanical design codes define allowable (design) stress levels that components must not exceed in operation. The factor of safety (FOS) provides a quantitative margin between material strength (yield/ultimate or other limit states) and the stresses expected during service. Understanding what the FOS protects against clarifies how “design stress” relates to “working stress.”

Given Data / Assumptions:

• Design stress (allowable) is set below damaging levels.
• Working (service) stress is the actual stress expected under normal loading.
• FOS expresses how conservative the design is relative to material limits.

Concept / Approach:
In many formulations, FOS = (limiting stress) / (working stress). The allowable (design) stress is then set as (limiting stress) / FOS. Thus, the “margin” implied by the FOS is between what you allow in design and what the part will actually see in service, i.e., working stress. Keeping working stress below allowable ensures that uncertainties in loads, material properties, and degradation do not push the component into damaging stress regimes.

Step-by-Step Reasoning:

Verification / Alternative check:
Pressure vessel and piping codes compute allowable stresses from material properties and multipliers; compliance is checked by comparing calculated working stresses with these allowables.

Why Other Options Are Wrong:

• (b) “Damaging stress” corresponds to a limit state; FOS is defined using it but the day-to-day margin of concern is vs. working stress.
• (c) Trivial restatement; allowable equals design stress.
• (d) Incorrect; the concept is well-defined.
• (e) Thermal stress can contribute to working stress but is not the singular comparator.

Common Pitfalls:
Confusing FOS based on yield vs. ultimate; ignoring cyclic fatigue where endurance limits change the relevant “damaging” criterion.

Final Answer:
Working (service) stress