In the symmetrical truss shown (bottom chord A–C–B, apex D, vertical CD, base angle 30°, 3 t load at D), the force in CD is:
Try it first: pick an option, then read the explanation.
Correct answer: C. zero
Asked in SSC JE 23/01/2018 (Evening)
Detailed Explanation
A useful rule: when three members meet at a joint with no external load, and two of them are collinear, the third member carries zero force.
Joint C: \(\Sigma F_y = 0\): only CD has a vertical component \(\Rightarrow F_{CD} = 0\).
Why “zero” Is Correct
The two collinear members can only balance each other along their line; nothing can balance a force in CD. So CD = 0 — option (c).
Why the Other Options Are Wrong
- A. 3 t compression: The 3 t load acts at D and is carried by the rafters, not CD.
- B. 3 t tension: CD has nothing to balance it at C, so it cannot be in tension.
- D. 1.5 t compression: 1.5 t is a support reaction, not the CD force.
Key Point
Three members at an unloaded joint, two collinear → third is zero.
Key Concepts for Students
- If a load were hung at C, CD would carry it in tension.
- Zero-force members reduce the effective length of other members.
- AC = CB in force (both tension 3√3/2 t here).
Practice more: this is question 17 in Beams and Trusses MCQs – Part 2. Try the whole set and check every answer instantly.