Basic definitions of terms in moment distribution method of structural analysis
Fixed end moments
Fixed end moments are the moments produced at member ends by when the joints are fixed. Table 1 provides equations for fixed end moment computations. Table 1: Fixed end moment equationsFlexural stiffness
The flexural stiffness (EI/L) of a member is represented as the product of the modulus of elasticity (E) and the second moment of area (I) divided by the length (L) of the member. Additionally, what is needed in the moment distribution method is not the exact value but the ratio of flexural stiffness of all members.Distribution factors
Distribution factors can be defined as the proportions of the unbalanced moments carried by each of the members.Carryover factors
Unbalanced moments are carried over to the other end of the member when the joint is released. Added to that, the ratio of the carriedover moment at the other end to the fixedend moment of the initial end is the carryover factor. Lastly, For prismatic members, the carryover moment in each span has the same sign as the distribution end moment, but is onehalf as large.Sign convention
Any moment acting clockwise is considered to be positive. This differs from the usual engineer's sign convention, which employs a Cartesian coordinate system with positive xaxis to the right and positive yaxis up, resulting in positive moment about the zaxis being counterclockwise.Framed structures
Framed structures with or without sides way can be analysed using the moment distribution method.Moment distribution analysis procedure for beams
1. Restrain all possible displacements. 2. Then, calculate Distribution Factors: The distribution factor DFi of a member connected to any joint J isMe: external moment applied to the joint (if any)
Mo: total out of balance moment at the joint
FEMi: fixedend moment
Mi: moment distributed to any member
DFi: distribution factor of member i
7. Calculation of the carry over moment at the far end of each member.
The procedure is stopped when, at all joints, the out of balance moment is a negligible value. In this case, the joints should be balanced and no carryover moments are calculated.
8. Finally, calculate the final moment at either end of each member.
This is the sum of all moments (including FEM) computed during the distribution cycles.
Analyzing statically indeterminate beam using moment distribution method
 Members AB, BC, CD have the same length
.  Flexural rigidities are EI, 2EI, EI respectively.
 Concentrated load of magnitude
acts at a distance from the support A.  Uniform load of intensity
acts on BC.  Member CD is loaded at its midspan with a concentrated load of magnitude
.
Fixedend moments
In the following calculations, counterclockwise moments are positive:Distribution factors
Carryover factors
The carryover factors areDetails of calculations
Table 2: details of moment distribution calculationsJoints 
A 
B 
C 
D 

Distribution factors  0  1  0.2727  0.7273  0.6667  0.3333  0  0 
Fixedend moments  14.700  6.300  8.333  8.333  12.500  12.500  
Step 1  14.700  7.350  
Step 2  1.450  3.867  1.934  
Step 3  2.034  4.067  2.034  1.017  
Step 4  0.555  1.479  0.739  
Step 5  0.246  0.493  0.246  0.123  
Step 6  0.067  0.179  0.090  
Step 7  0.030  0.060  0.030  0.015  
Step 8  0.008  0.022  0.011  
Step 9  0.004  0.007  0.004  0.002  
Step 10  0.001  0.003  
Sum of moments  0  11.569  11.569  10.186  10.186  13.657 
Results
Moments at joints determined by the moment distribution methodShear force and bending moment diagram
Table 3 provides shear and moment diagram for the analyzed beam. Note that the moment distribution method only determines the moments at the joints. Moreover, developing complete bending moment diagrams require additional calculations using the determined joint moments and internal section equilibrium. Table 3: shear force and moment diagram for the analyzed indeterminate beamShear force diagram

Bending moment diagram
