Moment Distribution Method Example 1 Drawing SFD BMD and Support Reactions

Moment Distribution Method Example 1 Drawing Shear Force Diagram , Bending Moment Diagram and Support Reactions

Moment Distribution Method

It is force method of analysis of statically indeterminate structures because all the calculations are done in terms of forces and/or moments. It is a method of successive approximations that may be carried out to any desired level of accuracy. In the beginning all the joints are assumed to be fixed. Then each joint is released (in succession) and the internal moments are distributed. This is done until all the joints have rotated to their final position.

Member Stiffness Factor  (Moment - Rotation)

It is defined as moment developed at an end of a beam segment due to unit rotation as the same end of the beam.  K = 4EI/L

Carry Over Factor

It is defined as fraction of moment carried over from one end of the beam segment to other end of the same beam segment. Its value is always equal to half ( 1/2 , 0.5)

Joint Stiffness Factor ( Total Stiffness of a joint)

If several members are connected at a joint whose far ends are fixed then the total stiffness factor at joint is equal to sum of member stiffness factors of all the members.Walls are assumed to be infinitely rigid. Pinned/Hinged/Roller support have zero stiffness.

Distribution Factor

The fraction of total moment at a joint supported by / distributed to a particular member is called distribution factor.

Relative Stiffness Factor (For the purpose of calculating Distribution Factor )

If E is constant for all the members of structures then we can use relative stiffness factor I/L  instead of full member stiffness factor 4EI/L.

If EI is constant for all the members of structures then we can use relative stiffness factor 1/L  instead of full member stiffness factor 4EI/L.

Steps for Moment Distribution Method

1. Find distribution factors at all the joints.
2. Find fixed end moments for all beam segments.
3. Find net moment at each joint (in succession).
4. Moment with sign opposite to found in Step 3 is the moment to be distributed for the joint.
5. Distribution Step : At each joint distribution moment found in Step 4 is distributed to members connected at the joint in proportion to distribution factors.
6. Carry Over Step : For each beam segment, the distributed moment at one end is carried over to other end with carry over factor of half ( 1/2 , 0.5 )
7. Repeat steps 3 to 6 until distributed moments are small enough to be negligible.
8. Stop the cycle without Carry Over Step.
9. Sum of moments ( Fixed End Moment, Distributed Moments, Carried Over Moments) for each end of beam segment (each column of Moment Distribution Table ) gives end moment for that end.
10. Using these end moments, we can find end shears, Shear Force Diagram, Bending Moment Diagram, Support Reaction etc


This video is uploaded by
Alpha Academy, Udaipur
https://alphaacademyudaipur.com/
Minakshi Porwal (9460189461)