Bending Stress MCQ with answer and solution

Concept

Section modulus of circular cross section

Formula

Z = π × d³ / 32

Step-by-step solution

1. Section modulus Z is defined as the ratio of moment of inertia I to the distance of outer fiber from neutral axis y (Z = I / y). 2. For a solid circular section of diameter d, I = πd⁴ / 64 and y = d / 2. 3. Z = (πd⁴ / 64) / (d / 2) = πd³ / 32. Answer: C

Explanation

Section modulus is defined as the ratio of the area moment of inertia to the distance from the neutral axis to the outermost fiber. For a solid circular section of diameter d, the moment of inertia is πd⁴ divided by 64, and the maximum distance is d divided by 2. Dividing the moment of inertia by this distance yields a section modulus of πd³ divided by 32.

Why the other options are wrong

A) πd²/16 does not have the cubic length dimensions required for section modulus. B) πd³/16 is the polar section modulus for a circular section. D) πd⁴/64 represents the area moment of inertia about the neutral axis.

Shortcut

Section Modulus Z for a solid circular section is Z = I / y = πd³/32.

Common mistake

Confusing section modulus (πd³/32) with moment of inertia (πd⁴/64) or polar section modulus (πd³/16).