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Engineering · L4 · Truss free-body diagram: method of joints for a simple truss

Method of joints applied to a simple truss with free-body diagrams at each node.

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Simple Pratt TrussSpan L, Load P at apexReactions:A_y = P/2 (pin)B_y = P/2 (roller)Joint A (pin)ΣFy = 0: AB sin θ + P/2 = 0ΣFx = 0: AC − AB cos θ = 0Joint B (roller)ΣFy = 0: BC sin θ + P/2 = 0ΣFx = 0: BD + BC cos θ = 0Joint C (apex)ΣFy = 0: −P + AB sin θ + BC sin θ = 0AB and BC: compression(push toward joint)AC and BD: tension(pull away from joint)

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