Bending Stress MCQ with answer and solution

Concept

Plastic Modulus of a Rectangular Section

Formula

Zp = (b × d²) / 4

Step-by-step solution

1. Calculate the area of half the rectangular section: A/2 = (b \* d) / 2. 2. Find the distance between the centroids of the two halves: y1 + y2 = d/4 + d/4 = d/2. 3. Multiply the half-area by the centroidal distance: Zp = (b \* d / 2) \* (d / 2) = bd² / 4.

Explanation

The plastic modulus (Zp) is calculated as the area of half the section multiplied by the distance between the centroids of the two halves. For a rectangular beam of width b and depth d, each half has an area of (b × d / 2) and its centroid is at a distance of d / 4 from the neutral axis. The distance between the centroids of both halves is d / 2. Multiplying the half-area by this distance gives Zp = (b × d / 2) × (d / 2) = bd² / 4.

Common mistake

Students often confuse the plastic section modulus (bd²/4) with the elastic section modulus (bd²/6) and incorrectly select Option B.