In the cantilever truss shown (top chord A–B–C, 100 t load at B, vertical BD, member DC inclined at 30° to BC), the force in member DC is:
Try it first: pick an option, then read the explanation.
Correct answer: C. zero
Asked in SSC JE 27/01/2018 (Morning)
Detailed Explanation
A quick rule saves a lot of work: if only two members meet at a joint, they are not in a straight line, and no load acts there, both members carry zero force.
At C: \(\Sigma F_y = 0 \Rightarrow F_{DC}\sin 30^\circ = 0 \Rightarrow F_{DC} = 0\).
Why “zero” Is Correct
Only DC has a vertical component at C, and nothing else can balance it. So the force in DC is zero.
Why the Other Options Are Wrong
- A. 100 t compressive: That is the force in BD, not DC.
- B. 100 t tensile: No member at C carries 100 t.
- D. indeterminate: The truss is determinate.
Key Point
Two non-collinear members at an unloaded joint → both zero.
Key Concepts for Students
- Then BC is also zero.
- Zero-force members change if the loading changes (e.g. a load at C).
- Identify zero-force members before detailed analysis.
Practice more: this is question 3 in Beams and Trusses MCQs – Part 1. Try the whole set and check every answer instantly.