The moment distribution method is a structural analysis method for statically indeterminate beams and frames developed by Hardy Cross in 1930. This method applies for flexural effects and ignores axial and shear effects. The moment distribution method was the most widely practiced method until computers began to be widely used in the design and analysis of structures.
It is very well known that support may settle by unequal amount during the lifetime of the structure. Such support settlements induce fixed end moments in the beams so as to hold the end slopes of the members as zero (see Fig.below)
The equation for moments by superposing the end moments developed due to externally applied loads on beam and displacement θA,θB and Δ (settlements) are
This may be written as,
where KAB=EIAB/LAB is the stiffness factor for the beam AB. The coefficient 4 has been dropped since only relative values are required in calculating distribution factors.
Note That
MSAB is the beam end moments due to support settlement and is negative (clockwise) for positive support settlements (upwards). In the moment-distribution method, the support moments MSAB and MSBA due to uneven support settlements are distributed in a similar manner as the fixed end moments,
It is important to follow consistent sign convention. Here counterclockwise beam end moments are taken as positive and counterclockwise chord rotation (Δ/L) is taken as positive.
