Bending Stress MCQ with answer and solution

Concept

Section modulus formula for a circular section

Formula

Z = I / y = π × d³ / 32

Step-by-step solution

1. The moment of inertia for a circular section of diameter d about its neutral axis is I = πd⁴ / 64. 2. The distance from the neutral axis to the outermost fiber is y = d / 2. 3. Section modulus Z is calculated as Z = I / y = (πd⁴ / 64) / (d / 2) = πd³ / 32. Answer: B

Explanation

Section modulus is calculated as the moment of inertia divided by the distance from the neutral axis to the outermost fiber. For a solid circular section of diameter d, the moment of inertia is π times d to the power of 4 divided by 64, and the maximum distance is d/2. Dividing these two values yields a section modulus equal to π times d to the power of 3 divided by 32.

Why the other options are wrong

A) πd²/16 is dimensionally incorrect for section modulus, which requires cubic length units. C) πd³/16 is the polar section modulus for a solid circular section. D) πd⁴/64 is the second moment of area of a circular section.

Shortcut

Section modulus of a circle: Z = I / y = (πd⁴/64) / (d/2) = πd³/32.

Common mistake

Confusing section modulus with moment of inertia or polar section modulus for circular sections.