In the moment distribution method, how is the distribution factor (DF) for a structural member at a joint determined?

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RRB JE CE 22 Apr 2025 Shift 2 CBT 2 Official Paper

By multiplying the stiffness of the considered member at a joint with the total stiffness of all the members meeting at that joint
By dividing the total stiffness of all the members meeting at a joint by the stiffness of the considered member
By adding the stiffness of the considered member at a joint by the total stiffness of all the members meeting at that joint
By dividing the stiffness of the considered member at a joint by the total stiffness of all the members meeting at that joint

Answer 1

Explanation:

In the Moment Distribution Method, the Distribution Factor (DF) for a member is a measure of how the joint's moment is distributed among the various connected members.
It helps in determining the proportion of the joint's moment that will be distributed to each member.

The formula to calculate the Distribution Factor (DF) for a member is:

$DF = \frac{K_i}{\sum K} $

Where:

Additional Information

The Moment Distribution Method is an approximate iterative technique used to analyze indeterminate structures, especially continuous beams and frames, that cannot be solved easily using simple static equilibrium equations.
It was developed by Dr. Hardy Cross in the early 20th century.
The method works by redistributing the bending moments in a structure in such a way that equilibrium is gradually achieved through an iterative process.

Key Concepts in the Moment Distribution Method:

Fixed-End Moment (FEM):
The moment at the ends of a beam or frame when both ends are assumed to be fixed, considering external loads applied to the structure. It is an initial moment, calculated without considering the flexibility of the joints.
Distribution Factor (DF):
The factor used to distribute the moment at a joint to the connected members, based on the stiffness of the members. It represents the proportion of the joint's moment each member will take.
Carry-Over Factor:
After distributing the moment, the unbalanced moment at the joint is "carried over" to the connected members in the next iteration. The carry-over factor is typically $0.5$ for beams with simple supports.
Convergence:
The iterative process continues until the moment values at the joints do not change significantly between iterations. This indicates that the structure is in equilibrium, and the final moment distribution is achieved.