In the two-bay truss shown (bottom chord A–C–B with pin at A and roller at B; top chord D–E–F; 4 t horizontal load at D and 5 t vertical load at E), the force in member BC is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 25/01/2018 (Evening)
Detailed Explanation
Look at joint B. The members meeting there are BC (horizontal) and BF (vertical). The roller support at B gives only a vertical reaction.
Joint B: \(\Sigma F_x = 0 \Rightarrow F_{BC} = 0\) (no other horizontal force acts at B).
The 4 t horizontal load is carried to the pin at A through the other members.
Why “None of these” Is Correct
Since nothing else at B can balance a horizontal force, the force in BC must be zero. Zero is not among (a)–(c), so the answer is (d) None of these.
Why the Other Options Are Wrong
- A. 4 t tension: BC carries no force, so 4 t tension is wrong.
- B. 4 t compression: BC carries no force, so 4 t compression is wrong.
- C. 5 t tension: The 5 t load is vertical; it does not reach BC.
Key Point
At a roller joint where only one member is horizontal, that member carries zero force (no horizontal load there).
Key Concepts for Students
- The whole horizontal load goes to the pin support at A.
- Roller: one reaction normal to the surface.
- Check joints at supports early — they often give quick answers.
Practice more: this is question 11 in Beams and Trusses MCQs – Part 1. Try the whole set and check every answer instantly.