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Civil Engineering QUESTION #2119
Question 1
In the moment distribution method for analyzing indeterminate structures, the distribution factor (DF) for a member at a joint is defined as:
  • The ratio of the member stiffness to the sum of stiffnesses of all members meeting at the joint✔️
  • The ratio of the fixed-end moment in the member to the total applied moment at the joint
  • The carry-over factor multiplied by the member stiffness
  • The ratio of span length to total length of all members at the joint
Correct Answer Explanation
Distribution Factor \(DF = \dfrac{K_{member}}{\sum K_{members\,at\,joint}}\), where \(K = \dfrac{4EI}{L}\) for far-end fixed and \(K = \dfrac{3EI}{L}\) for far-end pinned. The sum of DFs at any joint always equals 1.0 (except at fixed supports where DF = 0). The DF determines what fraction of the unbalanced moment is distributed to each member at a joint.