If a cantilever beam is subjected to an upward point load at the free end, the nature of the stresses developed will be:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 05/06/2024 (9 am–11 am)
Detailed Explanation
In bending, the fibres on the concave side of the bent beam shorten and those on the convex side lengthen. The neutral axis separates the two zones. So you only need to picture which way the beam curves.
Why “compressive above the neutral axis and tensile below the neutral axis of the beam cross-section” Is Correct
A downward end load makes a cantilever hog: top in tension, bottom in compression. Reverse the load to upward and the curvature reverses: the beam becomes concave upward, so the fibres above the neutral axis are compressed and those below are in tension — option (d).
Why the Other Options Are Wrong
- A. tensile above as well as below the neutral axis of the beam cross-section: Bending always produces opposite stresses on the two sides of the neutral axis.
- B. compressive below as well as above the neutral axis of the beam cross-section: Same reason — one side must be in tension.
- C. tensile above the neutral axis and compressive below the neutral axis of the beam cross-section: This is the case for a downward load on a cantilever (hogging).
Key Point
Concave side in compression, convex side in tension; reverse the load and the stresses swap.
Key Concepts for Students
- Bending stress σ = My/I is zero at the neutral axis and largest at the extreme fibres.
- Sagging: top compression, bottom tension. Hogging: the reverse.
- In RCC cantilevers, main steel goes on the tension side — the top for normal (downward) loads.
Practice more: this is question 5 in Bending Moment and Shear Force MCQs – Part 1. Try the whole set and check every answer instantly.