A cantilever 2 m long, fixed at the left end, carries 20 kN at 1 m from the fixed end and 30 kN at the free end. The shear force and bending moment at the support are:
Try it first: pick an option, then read the explanation.
Correct answer: B. SF = 50000 N, BM = 80 kN·m
Asked in SSC JE 09/10/2023 (10 am–12 pm)
Detailed Explanation
At the fixed end of a cantilever, the shear equals the total load and the moment equals the sum of each load times its distance from the support.
\[ V_A = 20 + 30 = 50\ \text{kN} = 50\,000\ \text{N} \]
\[ M_A = 30 \times 2 + 20 \times 1 = 80\ \text{kN·m} \]
Why “SF = 50000 N, BM = 80 kN·m” Is Correct
Option (b) gives exactly these values: 50 000 N (= 50 kN) and 80 kN·m.
Why the Other Options Are Wrong
- A. SF = 50 kN, BM = 50 kN·m: BM is wrong: 50 kN·m ignores that the 30 kN load is 2 m away.
- C. SF = 10 kN, BM = 80 kN·m: SF is wrong: 10 kN is the difference of the loads, not their sum.
- D. SF = 50 kN, BM = 8000 N·m: BM is wrong: 8000 N·m = 8 kN·m, not 80 kN·m.
Key Point
Fixed end of cantilever: V = ΣW, M = ΣW·x.
Key Concepts for Students
- Options often mix N and kN — convert before comparing.
- Shear at the fixed end equals the vertical reaction there.
- The fixed-end moment is the largest moment in a cantilever with downward loads.
Practice more: this is question 13 in Bending Moment and Shear Force MCQs – Part 1. Try the whole set and check every answer instantly.