Difficulty: Easy
Correct Answer: Bending moment M(x)
Explanation:
Introduction / Context:
“Uniform strength” beams are shaped so that the extreme-fibre stress remains approximately constant along the span. When depth is held constant, width must be adjusted according to how internal bending moment varies with position.
Given Data / Assumptions:
Concept / Approach:
For a rectangular beam, section modulus Z = b d^2 / 6. Bending stress is σ = M / Z = 6M / (b d^2). To keep σ = σ_allow, the width b must be adjusted so that b ∝ M.
Step-by-Step Solution:
σ_allow = 6M / (b d^2)Rearrange → b = 6M / (σ_allow d^2)Hence, b varies directly with M(x), the bending moment diagram.
Verification / Alternative check:
For a simply supported beam with a central point load, M is triangular from support to midspan, and so is the required b(x) when d is held constant.
Why Other Options Are Wrong:
Common Pitfalls:
Confusing uniform strength with uniform stiffness; the former targets constant stress, the latter targets constant EI.
Final Answer:
Bending moment M(x)
Discussion & Comments