Member Force in a Truss from Coordinates
Mediummethod-of-jointsreactions
A pin-jointed truss has joints A (0, 0), B (3, 4) and C (9, 0), coordinates in meters, with members AB, BC and AC. A is a pin and C is a roller with vertical reaction. A 30 kN downward load acts at B. Neglect self-weight. Find the force in member AB, including tension or compression.
- A20.0 kN compression
- B25.0 kN tension
- C18.8 kN compression
- D25.0 kN compression
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Answer: D. 25.0 kN compression
Moments about A: RC(9) = 30(3) → RC = 10 kN, RA = 20 kN (not equal, since B is only 3 m from A). Joint A vertical: 20 + NAB(4/5) = 0 → NAB = −25 kN, i.e. 25.0 kN compression (NAC = +15 kN tension). Wrong: 20 kN is the reaction at A reported as a member force; 25 kN tension has the sign reversed; 18.8 kN assumes equal 15 kN reactions (15/0.8 = 18.75).
kN kN
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