Required cross-sectional area at working stress For a prismatic tension member carrying a given load P, if the computed stress equals the specified working (allowable) stress, what can be said about the required cross-sectional area?

Introduction / Context:
Allowable stress design sizes members so that actual stress does not exceed a prescribed limit. This question asks you to connect that concept to the required area for a given load.

Given Data / Assumptions:

• Axially loaded prismatic member.
• Working (allowable) stress = sigma_allow.
• Applied load = P (constant).

Concept / Approach:
Stress is defined by sigma = P / A. To ensure sigma ≤ sigma_allow, the area must satisfy A ≥ P / sigma_allow. The minimum area that just satisfies the limit (and is therefore most economical in terms of area) is A_min = P / sigma_allow.

Step-by-Step Solution:

Verification / Alternative check:
Using any smaller area violates the allowable stress; using any larger area is safe but not minimal for area economy.

Why Other Options Are Wrong:

• Zero or infinite area are physically meaningless for a finite load.
• Maximum area is not required; larger area is conservative but uneconomical.
• Poisson’s ratio is irrelevant for uniaxial allowable-stress sizing.

Common Pitfalls:
Confusing working stress with ultimate or yield stress; forgetting that design often seeks minimum adequate size, not maximum.

Final Answer:
Minimum that satisfies the allowable stress