Zero-Force Member at a Three-Member Joint
Easyzero-forcejoint-equilibrium
At joint J of an ideal planar pin-jointed truss, exactly three members meet. Members JA and JB lie on one straight line; member JC is not on that line. No external load or support reaction acts at J, and all member forces are axial. What is the axial force in JC?
- AZero; JA and JB must also be zero
- BNonzero; JC balances the difference between JA and JB
- CZero (FJC = 0), while JA and JB can still carry force
- DIndeterminate unless the angle of JC is known
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Answer: C. Zero (FJC = 0), while JA and JB can still carry force
Resolve equilibrium perpendicular to the line JA–JB. JA and JB have no perpendicular components, there is no external load, so FJC sinθ = 0. Since sinθ ≠ 0, FJC = 0. JA and JB still balance each other along their common line and can be nonzero. Wrong: declaring all three members zero over-applies the rule; JA and JB are collinear, so any difference between them is balanced along their own line, not by JC; the angle drops out so the result is not indeterminate.
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