In a triangular truss ABC with span AC = 6 m, pin at A, roller at C and a 10 kN downward load at B, find the force in member AB. (Take ∠BAC = 60° and ∠BCA = 30°.)
Try it first: pick an option, then read the explanation.
Asked in SSC JE 30/10/2020 (Evening)
Detailed Explanation
Since ∠A = 60° and ∠C = 30°, the angle at B is 90°. So at joint B the two members are perpendicular, which makes resolving the 10 kN load very simple.
Member AB makes 60° with the horizontal, so it makes 30° with the vertical load; member BC makes 60° with the vertical.
\[ F_{AB} = 10\cos 30^\circ = 10 \times \tfrac{\sqrt3}{2} = 5\sqrt3\ \text{kN} \qquad F_{BC} = 10\cos 60^\circ = 5\ \text{kN} \]
Check by reactions: B is 1.5 m from A horizontally, so \(R_A = 10 \times 4.5/6 = 7.5\) kN. At A: \(F_{AB}\sin 60^\circ = 7.5 \Rightarrow F_{AB} = 8.66 = 5\sqrt3\) kN.
Why “5√3 kN compressive” Is Correct
Both members push up on joint B to hold the downward load, so both are in compression. The force in AB is 5√3 kN (≈ 8.66 kN) compressive — option (b).
Why the Other Options Are Wrong
- A. 2√3 kN tensile: Wrong magnitude, and AB is in compression, not tension.
- C. 3√3 kN tensile: Wrong magnitude and wrong sense.
- D. 2√5 kN compressive: 2√5 kN does not result from these angles.
Key Point
Apex load on a right-angled truss: resolve along the two perpendicular members.
Key Concepts for Students
- Rafters of a roof truss under gravity load are in compression.
- The bottom tie AC is in tension.
- Lami's theorem is another way to solve a joint with three forces.
Practice more: this is question 1 in Beams and Trusses MCQs – Part 1. Try the whole set and check every answer instantly.