Accounting for deviations – minimum factor of safety: If the maximum deviations in the computed load P and the computed strength E are each taken as 25% (i.e., ΔP = 0.25 P and ΔE = 0.25 E), what is the minimum factor of safety recommended to ensure safety under worst credible deviations?

Introduction / Context:Engineering design often addresses uncertainties in both actions (loads) and resistances (strength). A practical way to represent this in an allowable-stress context is to select a factor of safety (FOS) that maintains a margin when both the applied load is higher than computed and the available strength is lower than computed by specified percentages.

Given Data / Assumptions:

• Computed load = P; possible positive deviation ΔP = 0.25 P (applied load may be 1.25 P).
• Computed strength = E; possible negative deviation ΔE = 0.25 E (available strength may be 0.75 E).
• We seek a single minimum factor of safety such that demand ≤ capacity even in this worst case.

Concept / Approach:Define factor of safety F such that allowable load = E / F. Under worst deviations, the demand becomes 1.25 P and the capacity becomes 0.75 E. Safety requires 1.25 P ≤ 0.75 E / F, which implies F ≤ 0.75 E / (1.25 P) = 0.6 * (E / P). To guarantee safety irrespective of E/P in the original computation (i.e., when E/P ≈ F in the base design), Rearrangement shows the minimum F consistent with these deviations is about 1 / 0.6 ≈ 1.67.

Step-by-Step Solution:Worst applied load = 1.25 P.Worst available strength = 0.75 E.Require: 1.25 P ≤ (0.75 E) / F.Solve for F: F ≥ (0.75 E) / (1.25 P) = 0.6 * (E / P).For a base design where E/P ≈ F, we get F ≈ 1 / 0.6 = 1.67 (rounded).

Verification / Alternative check:If F = 1.67, allowable = E / 1.67 ≈ 0.60 E. Under worst deviations, demand = 1.25 P, capacity = 0.75 E / 1.67 ≈ 0.449 E. Ensuring initial E/P comfortably exceeds F provides adequate margin; the 1.67 value is a widely taught minimum in classic problems for ±25% deviations.

Why Other Options Are Wrong:

• 1.00: no margin for uncertainty.
• 0.67: nonsensical for a factor of safety (less than unity).
• 2.67: overly conservative for the stipulated ±25% deviations.

Common Pitfalls:

• Treating deviations as mutually exclusive rather than compounding worst-case simultaneously.
• Confusing partial safety factors (limit-state) with a single global FOS (allowable stress method).

Final Answer:1.67