What is the basic idea behind the moment distribution method in frame analysis?

• A. It balances moments at joints using stiffness-based distribution factors and carries over moments along members.
• B. It solves by discretizing into linear elements and solving global equilibrium.
• C. It uses dynamic time integration to track story displacements.
• D. It assumes all joints are rigid and uses fixed-end moments.

Answer: (A)

Moment distribution analyzes frames by balancing the moments at each joint using how stiff each connected member is. Each member resists rotation at its ends in proportion to its rotation stiffness, which for a prismatic member is related to EI over its length. At a joint, you determine a distribution factor for every connected member: the stiffness of that member at the joint divided by the sum of stiffnesses of all members tied to that joint. This tells you what portion of any unbalanced moment at the joint goes into each member.

The process starts with fixed-end moments, which are the end moments produced by the applied loads if the ends of every member were fixed (no rotation). Then you look at joints and balance any unbalanced moment by distributing it to the connected members according to the distribution factors. Once you distribute, moments are carried over to the opposite ends of those members—usually by a fixed fraction (often 0.5 for a balanced, prismatic member end). After each distribution and carryover, you re-check the joints and repeat the process until all joints are in equilibrium, meaning the sum of moments at each joint is zero.

This approach directly uses the stiffness of each member to control how rotational effects are shared among members at a joint, and the carryover step ensures continuity of moment effects along the frame.