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Moment Distribution Method ExampleThe method and solved problems
Moment distribution (the Hardy Cross method) finds end moments by successive approximation, without solving a system of equations. All joints are first held fixed and the fixed-end moments are written. The joints are then released in turn: the unbalanced moment is distributed to the members in proportion to their stiffness, and half is carried over to the far end. This continues until the carried-over moments are small enough.
It is widely used for continuous beams and frames without sidesway. Frames with sidesway need an additional correction.
Solution steps
- Compute the fixed-end moments; if pinned ends are released from the start, adjust the moments.
- Find the distribution factors at each joint from the member stiffnesses.
- Distribute the unbalanced moment using the factors.
- Carry half of each distributed moment to the far end, and repeat until the carried-over moments are small enough.
- Sum the columns to get the end moments, find the reactions, and check equilibrium.
Solved problems
- Three-span beam, unequal stiffness Introductory
- Two-span beam, 3EI/L at the pinned ends Introductory
- Support settlement Exam level
- Frame with three members at a joint Exam level
- Frame with an overhang Exam level
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