In the cantilever truss shown (top chord A–B–C, 100 t load at B, vertical BD, members AD, ED, and CD at 30°), the force in member BC is:
Try it first: pick an option, then read the explanation.
Correct answer: C. zero
Asked in SSC JE 04/03/2017 (Evening)
Detailed Explanation
Apply the two-member rule at joint C, the free end of the cantilever truss.
Joint C: \(\Sigma F_y = 0 \Rightarrow F_{CD} = 0\); \(\Sigma F_x = 0 \Rightarrow F_{BC} + F_{CD}\cos30^\circ = 0 \Rightarrow F_{BC} = 0\).
Why “zero” Is Correct
With CD zero, BC has nothing to balance it horizontally, so BC = 0 — option (c).
Why the Other Options Are Wrong
- A. 100 t compressive: 100 t compression is the force in BD.
- B. 100 t tensile: No member at C carries 100 t.
- D. indeterminate: Joint C gives the answer directly.
Key Point
Free-end joint with two non-collinear members and no load → both zero.
Key Concepts for Students
- Adding a load at C would make BC and CD carry force.
- Top chord AB of this cantilever truss is in tension.
- Bottom members at the wall (ED) are in compression for downward loads.
Practice more: this is question 25 in Beams and Trusses MCQs – Part 2. Try the whole set and check every answer instantly.