Bending Stress MCQ with answer and solution

Concept

For the same area, the section with larger section modulus Z resists more moment and is more economical.

Formula

Z_square = a³/6, Z_circle = πd³/32

Step-by-step solution

1. Let the square have side a, so area = a². 2. Equal area for the circle: πd²/4 = a², so d = 1.128a. 3. Z_square = a³/6 = 0.1667a³. 4. Z_circle = π(1.128a)³/32 = 0.1410a³. 5. Z_square > Z_circle (ratio about 1.18). 6. So the square beam is stronger and more economical.

Explanation

With the same area, the square section has a larger section modulus than the circular section. So for the same bending moment, the square beam has lower stress. This makes the square beam more economical.

Why the other options are wrong

A: The circular beam has a smaller Z, so it is less economical. C and D: Their Z values are different, so they are not equally strong or equally economical.

Shortcut

For equal area, Z_square/Z_circle ≈ 1.18, so the square is better.

Common mistake

Thinking the circle is better because it is a 'compact' shape. In bending, more material away from the neutral axis is better.