Question

The maximum bending stress induced in a beam of rectangular section is 160 N/mm$^2$. If the depth of beam is increased by two times, keeping all the parameters same, the maximum bending stress induced in the beam is

• A. 20 N/mm$^2$
• B. 40 N/mm$^2$
• C. 80 N/mm$^2$
• D. 160 N/mm$^2$

Hint:

For rectangular beams, the section modulus $Z$ is proportional to $d^2$.
Since bending stress $\sigma = M/Z$, the stress is inversely proportional to $d^2$.
This means doubling the depth makes the beam four times stronger in bending.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Rectangular beam depth doubled. Initial stress 160 N/mm². Find new stress.

Step 2: Key Relationship (Alternate):
σ=6M/(bd²). So σ ∝ 1/d². Doubling depth → stress becomes 1/4.

Step 3: Detailed Explanation:
σ₂/σ₁ = (d₁/d₂)² = (1/2)² = 1/4. σ₂ = 160/4 = 40 N/mm².

Step 4: Final Answer:
New maximum bending stress is 40 N/mm².