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 bending moment at mid-span is:
Try it first: pick an option, then read the explanation.
Correct answer: A. 30 kN·m
Asked in SSC JE 09/10/2023 (10 am–12 pm)
Detailed Explanation
For a cantilever, work from the free end: the forces between the section and the free end are known, and the fixed-end reactions are not needed.
Section at mid-span C (1 m from the free end). The 20 kN load is exactly at C, so its lever arm is zero.
\[ M_C = 30 \times 1 + 20 \times 0 = 30\ \text{kN·m (hogging)} \]
Why “30 kN·m” Is Correct
Only the 30 kN end load has a lever arm about C, giving 30 kN·m — option (a).
Why the Other Options Are Wrong
- B. 50 kN·m: 50 kN·m treats both loads as acting 1 m from C.
- C. 3000 N·m: 3000 N·m is only 3 kN·m.
- D. 5000 N·m: 5000 N·m is only 5 kN·m.
Key Point
Cantilever: M at a section = Σ(load × distance) for loads between the section and the free end.
Key Concepts for Students
- A load acting at the section itself contributes nothing to the moment there.
- Cantilever moments are hogging under downward loads.
- 1 kN·m = 1000 N·m — watch the unit traps in the options.
Practice more: this is question 12 in Bending Moment and Shear Force MCQs – Part 1. Try the whole set and check every answer instantly.