HSC Engineering Studies Practice Questions

Model answer. Reactions. The truss and load are symmetrical, so R_A = R_B = 24 ÷ 2 = 12 kN upward (check: ΣM_A gives R_B × 8 = 24 × 4, so R_B = 12 kN). There is no horizontal load, so the pin carries no horizontal reaction.

Geometry. Each rafter runs 4 m horizontally and 3 m vertically, so it is 5 m long (3–4–5 triangle): sin θ = 3/5 and cos θ = 4/5.

Joint A. Assume all members are in tension (arrows away from the joint). ΣF_y = 0: 12 + F_AC sin θ = 0, so F_AC = −12 ÷ 0.6 = −20 kN. The negative sign means the assumption was wrong: AC = 20 kN compression. ΣF_x = 0: F_AB + F_AC cos θ = 0, so F_AB = −(−20 × 0.8) = +16 kN: AB = 16 kN tension.

Check. A rafter of a loaded roof truss pushes on its supports, so compression makes sense, and the tie stops the feet spreading, so tension makes sense.

Marking guidance (5 marks). 1 mark for correct reactions; 1 mark for correct geometry or angle; 1 mark for each correct force with magnitude AND nature (2 marks); 1 mark for clear, set-out working with a free-body diagram of the joint. If the nature is stated without being justified, the force mark is not awarded.