In the cantilever truss shown (top chord A–B–C attached to a wall at A, vertical BD, members AD, ED and CD, with CD inclined at 30° at C, and 100 t load at B), the force in member BD is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 29/01/2018 (Evening)
Detailed Explanation
Start the method of joints where only two unknowns meet. Joint C has just two members, BC and CD, and no load.
Joint C: \(\Sigma F_y = 0 \Rightarrow F_{CD}\sin30^\circ = 0 \Rightarrow F_{CD} = 0\); then \(\Sigma F_x = 0 \Rightarrow F_{BC} = 0\).
Joint B: AB and BC are horizontal, BD is vertical. \(\Sigma F_y = 0\): \(F_{BD}\) must push up on B with 100 t.
Why “100 t compressive” Is Correct
A member that pushes on the joint is in compression. So BD carries 100 t compression — option (a).
Why the Other Options Are Wrong
- B. 100 t tensile: BD pushes up on joint B, so it is in compression, not tension.
- C. zero: BD is the only member at B that can carry the vertical load.
- D. indeterminate: The truss is determinate; joint C then joint B give the answer directly.
Key Point
Unloaded joint with two non-collinear members → both zero. Then solve the next joint.
Key Concepts for Students
- Zero-force members are still needed for stability and bracing.
- Compression members (struts) push on joints; tension members (ties) pull.
- Start the method of joints at a joint with at most two unknowns.
Practice more: this is question 2 in Beams and Trusses MCQs – Part 1. Try the whole set and check every answer instantly.