Section Modulus Definition at a Beam Section At any point along a beam, the section modulus Z is defined as the moment of inertia I of the cross-section divided by which geometric quantity?

Introduction / Context:
The section modulus Z is a geometric property used to relate bending moment to extreme-fiber stress in flexure: σ_max = M / Z. It depends on the second moment of area and the distance to the most distant fiber.

Given Data / Assumptions:

• Beam bending about a principal centroidal axis.
• Linear elastic stress distribution.

Concept / Approach:
By definition, Z = I / y_max, where y_max is the distance from the neutral axis to the extreme fiber (top or bottom). None of the listed options a–d correctly state “distance to the extreme fiber from the neutral axis.”

Step-by-Step Solution:
Z = I / y_maxy_max is not “depth of the section” (that would be overall depth).y_max is not “depth of the neutral axis.”Z is not computed by dividing by stresses (options c and d).

Verification / Alternative check:
For a rectangle, I = b * d^3 / 12 and y_max = d / 2, hence Z = (b * d^3 / 12) / (d / 2) = b * d^2 / 6, consistent with the definition.

Why Other Options Are Wrong:

• a: overall depth is not the same as y_max.
• b: the neutral axis depth is ambiguous and not the required y_max.
• c and d: stress quantities are results, not geometric divisors.

Common Pitfalls:
Equating y_max to total depth or mixing geometric definitions with stress values yields incorrect formulas.

Final Answer:
None of these