A cantilever beam AB of length l carries a downward load P at its free end and an upward load P at a distance x from the free end. The shear force will be:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 06/06/2024 (9 am–11 am)
Detailed Explanation
The shear force at a section equals the algebraic sum of the vertical forces on one side of the section. For a cantilever, the free-end side is the easy side: no reactions need to be found.
Section between the loads (distance < x from B): only the downward P at B is to its right, so \( V = P \).
Section between A and the upward load: forces to the right are \( +P \) (down) and \( -P \) (up), so \( V = P - P = 0 \).
Why “equal to P, between the two point loads” Is Correct
The shear force is P over the length x between the two loads and zero over the rest of the beam. That is option (d). The fixed end gets no vertical reaction at all, only a moment Px.
Why the Other Options Are Wrong
- A. equal to 2P, between the two point loads: 2P would need both loads to act in the same direction.
- B. equal to P/2, only at the free end: Nothing in the loading halves P.
- C. equal to 2P, only at the free end: At the free end the shear is P, not 2P, and it stays P up to the second load.
Key Point
Shear = sum of vertical forces on one side; equal and opposite loads give shear only between them.
Key Concepts for Students
- Two equal, opposite, parallel forces form a couple of moment P·x.
- A cantilever's fixed end supplies both a vertical reaction and a moment.
- Shear force is constant on any unloaded segment.
Practice more: this is question 3 in Bending Moment and Shear Force MCQs – Part 1. Try the whole set and check every answer instantly.