For a given shear force across a symmetrical I-section, the intensity of shear stress is maximum at the:
Try it first: pick an option, then read the explanation.
Correct answer: B. centroid of the section
Asked in SSC JE 2012
Detailed Explanation
In an I-section, τ is small in the wide flanges, jumps up where the width drops to the web thickness, and then continues to rise inside the web as more area lies above the level.
Why “centroid of the section” Is Correct
The first moment Aȳ keeps growing until the neutral axis, while the width stays equal to the web thickness. So the peak is at the centroid of the section (neutral axis), in the web. The value just inside the web at the junction is high, but still below the peak.
Why the Other Options Are Wrong
- A. extreme fibres: Shear stress is zero at the extreme fibres.
- C. junction of the flange and the web, but on the web: The jump at the junction is large, but the stress keeps rising towards the N.A.
- D. junction of the flange and the web, but on the flange: On the flange side of the junction the stress is low, because the flange is wide.
Key Point
I-section: τmax at the neutral axis (centroid), in the web; a jump occurs at each flange–web junction.
Key Concepts for Students
- The web carries about 90–95 % of the shear in an I-beam.
- Average web shear V/(d t_w) is used in steel design.
- The flanges carry most of the bending moment.
Practice more: this is question 46 in Bending and Shear Stress MCQs – Part 4. Try the whole set and check every answer instantly.