Members of uniform strength – definition in axial loading If, under axial loading, the stress at every cross-section of a bar is equal to the allowable (working) stress, the bar is referred to as a:

Introduction / Context:
Bars can be shaped so that the maximum permissible stress is fully utilized along the entire length. This is important in weight-critical designs (e.g., ties, columns, connecting rods).

Given Data / Assumptions:

• Axial (tension/compression) loading only.
• Allowable working stress is the same everywhere.
• Bar geometry may vary to achieve uniform stress.

Concept / Approach:
A body of equal (uniform) strength is one in which the cross-sectional area A(x) is adjusted along the length so that σ(x) = P/A(x) equals the allowable stress everywhere. For constant load P, this implies A(x) is constant; for members with self-weight or varying load, A(x) varies to keep σ constant.

Step-by-Step Solution:
Define target: σ_allow = P/A(x) for all x.Solve for area profile: A(x) = P/σ_allow; if P varies with x (e.g., self-weight), A(x) changes accordingly.Name the concept: body of equal (uniform) strength.

Verification / Alternative check:
Design texts show tapered bars under self-weight as classic examples where A increases toward the fixed end to maintain constant stress.

Why Other Options Are Wrong:

• Equal section does not guarantee equal stress unless load is constant and the bar is prismatic.
• “Body of equal (incomplete term)” is not a proper descriptor.
• “Mechanism” is unrelated.

Common Pitfalls:
Confusing equal strength with equal section; the former is a stress condition, the latter is geometric.

Final Answer:
Body of equal strength (uniform strength)