Force in a Vertical Truss Member
Easyzero-forcejoint-equilibrium
At an ideal truss joint B, two members extend horizontally to the left and right. A third member BD extends vertically upward to D. A 12 kN external load acts downward at B, and no support reaction acts at B. All member forces are axial. Find the force in BD and state whether it is tension or compression.
- A12.0 kN compression
- BZero, by the zero-force joint rule
- C6.00 kN tension
- D12.0 kN tension
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Answer: D. 12.0 kN tension
The horizontal members have no vertical components, so vertical equilibrium at B gives NBD − 12 = 0 with BD assumed in tension (pulling up on B). NBD = +12 kN, tension. Wrong: zero applies only to unloaded joints, and this joint carries a 12 kN load; compression would push B downward and add to the load; 6 kN wrongly splits the load between two members when the horizontal ones cannot carry any vertical force.
kN (T)
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