A beam CAB carries a 20 kN downward load at its free end C. It is pinned at A, 100 mm from C, and rests on a roller at B, a further 100 mm from A. The reaction at support A is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2011
Detailed Explanation
The load hangs on an overhang beyond A. Support A acts as a fulcrum and must push up hard; support B, at the far end, is pulled down (it must hold the beam from lifting).
Note on the answer: the book's key gives (a) 40 kN downward, but its own moment equation gives R_A = 40 kN acting upward at the support next to the load. The correct answer is (b) 40 kN upward.
Take moments about B (lever arms: load 200 mm, A 100 mm):
\[ R_A \times 100 = 20 \times 200 \Rightarrow R_A = 40\ \text{kN}\ (\uparrow) \]
\[ R_A + R_B = 20 \Rightarrow R_B = -20\ \text{kN, i.e. } 20\ \text{kN}\ (\downarrow) \]
Why “40 kN upward” Is Correct
Support A carries 40 kN upward — option (b). It is larger than the load itself because A also balances the downward pull at B. If A had been the far support instead, its reaction would be 20 kN downward (option d), but in this arrangement A is next to the load.
Why the Other Options Are Wrong
- A. 40 kN downward: Correct magnitude, wrong direction — this is the book's key, but the support next to the load must push up.
- C. 20 kN upward: 20 kN upward ignores the lever action of the overhang.
- D. 20 kN downward: 20 kN downward is the reaction at B (the far support), not at A.
Key Point
Overhang load: the near support carries more than the load (upward); the far support is pulled down.
Key Concepts for Students
- Always check ΣV: 40 − 20 = 20 kN = applied load.
- A negative reaction means the support must hold the beam down (anchorage).
- Rollers that may see uplift need hold-down details.
Practice more: this is question 39 in Bending Moment and Shear Force MCQs – Part 3. Try the whole set and check every answer instantly.