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Fixed vs Hinged Far End Carryover

Easymoment-distributioncarry-over
Two separate prismatic members each receive a +12 kN·m balancing moment increment at their near end, with joint translation prevented and clockwise end moments positive. Member 1 has a fixed far end; member 2 has a true hinge at its far end. Find the far-end moment increments for member 1 and member 2, in that order.
  1. A+6.00 kN·m, +6.00 kN·m
  2. B+12.0 kN·m, 0
  3. C+6.00 kN·m, 0
  4. D0, +6.00 kN·m
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Answer: C. +6.00 kN·m, 0

A prismatic member with a fixed far end has carry-over factor ½: 0.5(+12) = +6 kN·m. A hinge cannot carry moment, so the far-end increment of member 2 is 0. Answer: (+6, 0). Wrong: (+6, +6) applies ½ to the hinged end; (+12, 0) uses a carry-over factor of 1 for the fixed end; (0, +6) swaps the two members.
kN·m
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