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Moment Distribution Carryover at a Joint

Mediummoment-distributionstiffness
At joint J, two prismatic members have fixed far ends and the joint cannot translate. Member J1 has EI = 2EI₀ and length 4 m; member J2 has EI = EI₀ and length 6 m. The unbalanced moment at J is +24 kN·m (clockwise positive). In moment distribution, find the balancing moment assigned to member J1 at J.
  1. A−16.0 kN·m
  2. B−12.0 kN·m
  3. C+18.0 kN·m
  4. D−18.0 kN·m
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Answer: D. −18.0 kN·m

Stiffness K = 4EI/L: K₁ = 4(2EI₀)/4 = 2EI₀, K₂ = 4EI₀/6 = 0.667EI₀. DF₁ = 2/(2 + 0.667) = 0.75. The balancing moment is the negative of the unbalance: ΔMJ1 = 0.75(−24) = −18.0 kN·m (J2 gets −6; the sum is zero). Wrong: −16 uses EI only (DF = 2/3) and ignores length; −12 splits equally; +18 has the right share but the wrong sign (it adds to the unbalance instead of cancelling it).
kN·m
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