Moment distribution method of structure analysis is the method which was introduced after the slope deflection method by prof. Hardy Cross. This method uses the following properties of the beam for
(1) one end hinged and far end fixed: The moment required to apply to produce the unit slope at hinged end of the beam when the far end is fixed is equal to 4EI/L. It is known as the stiffness of the beam. At the same time half the moment applied at A is carried over to the far fixed end B, known as the carry over moment.
(2) One end hinged and far end also hinged:
When the far end is also hinged, the stiffness of the beam to produce the unit slope at end A by applying the moment at a is 3EI/L. The moment is not carried over to the far end because it is free.
Procedure to follow the Moment distribution analysis:
All the joints are initially fixed so that each span between joints behaves as the independent fixed beams.Calculate the fixed end moments on each span after adding algebraically moments due to the external loading, sinking of the supports. Now release the joints which are not fixed one at one time. There will be some unbalanced moment at joints (where two or more than two spans meet), and the ends with hinged or simple supports. balance the joints by distributing the moment at the joints among the member meeting at the joint proportional to their relative stiffness. The carry over moment to the far ends becomes the unbalanced moment for the next cycle of balancing.
Note: It is brief introduction of the method, you can write in if you need any further support in this method.
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