Question

At the centroid of a loaded beam cross section,

• A. bending stress is equal to zero
• B. bending stress is maximum
• C. shear stress is equal to zero
• D. shear stress is minimum

Hint:

Remember the stress distribution across a beam's cross-section:
- Bending Stress ($\sigma$): Zero at the neutral axis (centroid), Maximum at the top and bottom (extreme fibers).
- Shear Stress ($\tau$): Maximum at the neutral axis (centroid), Zero at the top and bottom (extreme fibers).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
At centroid of beam cross-section, what are bending stress and shear stress?

Step 2: Key Formulas (Alternate):
σ=My/I. At NA, y=0 → σ=0. τ=VAȳ/Ib. At NA, first moment Aȳ is maximum → τ=τ_max.

Step 3: Detailed Explanation:
Centroid lies on neutral axis. Bending stress is zero there (y=0). Shear stress is maximum there (Aȳ max for most sections). Options stating bending stress is zero are correct; shear stress is not zero.

Step 4: Final Answer:
Bending stress is zero. Shear stress is maximum (not zero).