A simply supported beam of length L carries two point loads, each P, at one-third of the span from either end. The bending moment at the left end support is:
Try it first: pick an option, then read the explanation.
Correct answer: D. Zero
Asked in SSC JE 15/11/2022 (Shift I)
Detailed Explanation
A simple support (hinge or roller) lets the beam rotate freely. Since it offers no resistance to rotation, it cannot carry a moment. Unless a couple is applied there or an overhang loads it, the bending moment at a simple end support is zero.
Why “Zero” Is Correct
The moment at A is zero — option (d). The moment builds up from zero at A to PL/3 at the first load, stays PL/3 to the second load and falls back to zero at B.
Why the Other Options Are Wrong
- A. 2PL/3: 2PL/3 is not reached anywhere on this beam.
- B. PL: PL would be the fixed-end moment of a cantilever, not a simple support.
- C. PL/3: PL/3 is the moment under the loads and in the middle third, not at the support.
Key Point
Simple end supports (no overhang, no applied couple) always have zero BM.
Key Concepts for Students
- Fixed supports carry moment; hinges and rollers do not.
- An overhang creates a hogging moment over the adjacent support.
- Maximum BM for this loading is PL/3.
Practice more: this is question 21 in Bending Moment and Shear Force MCQs – Part 2. Try the whole set and check every answer instantly.