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Civil Engineering Practice • Structural Engineering

Truss Deflection by Virtual Work

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Worked: a king-post truss

A triangular truss spanning 24 ft, pinned at A on the left and on a roller at C on the right, with its apex D 9 ft above the midpoint B of the bottom chord. Members are rafters AD and CD, bottom chord members AB and BC, and a vertical king post BD. A 30 kip load acts downward at the apex D. Every member has A = 4 in² and E = 29,000 ksi.

Reactions are 15 kips each. Each rafter is 15 ft long with slope 9:12, so at A its vertical component balances the reaction: N_AD = 15 × 15/9 = 25 kips compression, and the bottom chord carries 25 × 12/15 = 20 kips tension. The king post BD is a zero-force member: B is unloaded and AB, BC are collinear. A unit load at D gives the same forces divided by 30.

MemberN (k)nL (in)nNL (k-in)
AD, CD (each)−25−0.8331803,750
AB, BC (each)+20+0.6671441,920
BD001080

Σ = 2 × 3,750 + 2 × 1,920 = 11,340 k-in. Δ = 11,340/(4 × 29,000) = 0.098 in downward at the apex.

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