Design concept: A beam of “uniform strength” is characterised by which of the following conditions along its length under a given bending moment distribution?

Introduction / Context:The idea of a “beam of uniform strength” is used to design lightweight members by varying the cross-section so that allowable stress is reached everywhere, fully utilising material while avoiding overdesign.

Given Data / Assumptions:

• Bending stress formula applies: sigma = M*y / I.
• Material is linearly elastic with allowable stress sigma_allow.
• Geometry can vary along the length (e.g., variable depth or width).

Concept / Approach:Uniform strength means the maximum fibre stress equals the allowable stress at every section. Because bending moment M varies along the span, the section modulus Z = I / y must be varied so that sigma = M / Z = constant (equal to sigma_allow). This yields tapered or cut-out sections that are lighter than prismatic beams.

Step-by-Step Solution:

Verification / Alternative check:For a cantilever with end load, M rises linearly to the fixed end; a triangular (tapered) depth keeping Z proportional to M provides near-uniform stress along the length.

Why Other Options Are Wrong:

• Same cross-section: defines a prismatic beam, not uniform strength under varying moments.
• Same bending moment: depends on loading, not a design property of the section.
• Same shear stress: not the principle behind uniform strength; shear varies differently and usually governs near supports in deep webs.

Common Pitfalls:Ignoring stress concentrations and local buckling when tapering; confusing section modulus with second moment of area alone.

Final Answer:Same bending stress at every section