A simply supported beam of span 6 m carries a UDL of 20 kN/m on the left half of the span. The support reactions are:
Try it first: pick an option, then read the explanation.
Correct answer: C. 45 kN (left), 15 kN (right)
Asked in SSC JE 10/10/2023 (10 am–12 pm)
Detailed Explanation
Replace the UDL by its resultant acting at the centre of the loaded length, then use ΣM = 0 about one support and ΣV = 0.
Resultant \( = 20 \times 3 = 60\ \text{kN} \) at 1.5 m from A.
\[ \Sigma M_A = 0:\; R_B \times 6 = 60 \times 1.5 \Rightarrow R_B = 15\ \text{kN} \]
\[ R_A = 60 - 15 = 45\ \text{kN} \]
Why “45 kN (left), 15 kN (right)” Is Correct
The load is nearer A, so A carries more: 45 kN at the left and 15 kN at the right — option (c).
Why the Other Options Are Wrong
- A. 30 kN (left), 30 kN (right): Equal reactions need a symmetric load.
- B. −20 kN (left), 80 kN (right): A downward load cannot produce a negative (downward) reaction here.
- D. 15 kN (left), 45 kN (right): The values are swapped — the support nearer the load carries more.
Key Point
Reactions: take moments about one support using the resultant of the UDL.
Key Concepts for Students
- A support's reaction is larger when the load is nearer to it.
- Check: R_A + R_B must equal the total load.
- Maximum BM occurs where the shear force is zero.
Practice more: this is question 11 in Bending Moment and Shear Force MCQs – Part 1. Try the whole set and check every answer instantly.