Effect of section modulus on bending stress\n\nIf the section modulus Z of a beam is increased while bending moment M remains the same, how will the maximum bending stress change?

Introduction / Context:
Beam design frequently leverages the relationship σ = M / Z. Increasing section modulus by changing cross-section shape or size is a primary strategy to cut bending stress for a given moment.

Given Data / Assumptions:

• Bending moment M is fixed by loading and span.
• Section modulus Z is altered via geometry (e.g., larger depth, flanges).
• Linear elastic bending; plane sections remain plane.

Concept / Approach:
Maximum bending stress in elastic range is σ_max = M / Z. This is an inverse proportionality: higher Z means lower σ for the same M.

Step-by-Step Solution:
Start with σ = M / Z.Increase Z → denominator increases.Therefore σ decreases proportionally.No sign change occurs; stress nature (tension/compression) is set by loading, not Z.

Verification / Alternative check:
Example: if Z doubles, σ halves. This is why I-sections (large Z for given area) are efficient for bending resistance.

Why Other Options Are Wrong:
Not change: contradicts σ = M / Z. Increase: opposite of the formula. Become zero or reverse sign: impossible without changing M or load sense.

Common Pitfalls:
Confusing section modulus Z with second moment I; Z = I / c, so increasing depth c while adjusting I is key to stress reduction.

Final Answer:
decrease