An overhanging beam CADEBF rests on supports A and B (AB = 4.5 m). The left overhang CA is 1.5 m and a UDL of 9 kN/m acts over 3 m from C to D; a 5 kN point load acts at E, 1.8 m left of B; the right overhang BF is 1.5 m and carries a UDL of 3 kN/m. Ignoring signs, the sum of the bending moments at A and B is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 04/12/2023 (9 am–11 am)
Detailed Explanation
The bending moment at a support of an overhanging beam is most easily found from the overhang side: only the load on the overhang is involved, and no reaction needs to be calculated.
At A, take the part to the left (overhang CA, 1.5 m with 9 kN/m):
\[ |M_A| = \frac{w a^2}{2} = \frac{9 \times 1.5^2}{2} = 10.125\ \text{kN·m} \]
At B, take the part to the right (overhang BF, 1.5 m with 3 kN/m):
\[ |M_B| = \frac{3 \times 1.5^2}{2} = 3.375\ \text{kN·m} \]
\[ |M_A| + |M_B| = 10.125 + 3.375 = 13.5\ \text{kN·m} \]
Why “13.50 kN·m” Is Correct
Both support moments are hogging, caused only by the overhang loads. Their magnitudes add to 13.5 kN·m — option (b). The UDL between A and D and the 5 kN load at E lie on the other side of each section, so they do not enter.
Why the Other Options Are Wrong
- A. 16.78 kN·m: 16.78 kN·m does not follow from the overhang loads.
- C. 10.00 kN·m: 10 kN·m is roughly the moment at A alone (10.125), not the sum.
- D. 12.50 kN·m: 12.5 kN·m misses part of one of the overhang moments.
Key Point
Support moment of an overhang with UDL = wa²/2, taken from the overhang side.
Key Concepts for Students
- Choose the side of the section with fewer forces.
- Overhang moments are hogging (negative).
- Support reactions are needed only for moments inside the span.
Practice more: this is question 6 in Bending Moment and Shear Force MCQs – Part 1. Try the whole set and check every answer instantly.