Uniform strength concept: A beam is said to be “of uniform strength” if which condition holds along its length under bending?

Introduction / Context:
The design idea of a “beam of uniform strength” aims to utilize material efficiently by tailoring the section so that the extreme-fiber bending stress is constant along the entire span, rather than overdesigning where bending moments are small.

Given Data / Assumptions:

• Elastic bending (σ = M y / I).
• Beam geometry may vary along the span to satisfy a target stress distribution.
• Focus is on bending stress, not necessarily shear or deflection.

Concept / Approach:
In regions of high bending moment, section modulus Z = I / y must be larger to keep σ = M / Z constant. In regions of smaller bending moment, Z can be reduced. The idealized concept results in a beam where maximum fiber stress is uniform along the length.

Step-by-Step Solution:
Target: σ_max(x) = constant = σ_allow.Use σ = M(x) / Z(x) ⇒ choose Z(x) ∝ M(x).Thus, by varying depth/width to achieve Z(x) matching M(x), the beam attains “uniform strength.”

Verification / Alternative check:
Classic tapered beams (e.g., parabolic depth variation under UDL) illustrate this principle where material use aligns with bending moment distribution.

Why Other Options Are Wrong:
Equal bending moment, shear stress, deflection, or constant curvature are not the defining criteria and are rarely true for real loadings.

Common Pitfalls:
Confusing “uniform strength” with “constant section” or with uniform deflection or shear.

Final Answer:
Bending stress is the same at every section along the longitudinal axis.