Moment Distribution Method MCQ with answer and solution

Concept

Sum of distribution factors at a joint

Formula

NONE

Step-by-step solution

1. The distribution factor (DF) of a member at a joint is the ratio of its stiffness to the total stiffness of all members meeting at that joint. 2. Since DF_i = K_i / Sum(K_i), summing the distribution factors across all members meeting at the joint yields Sum(DF_i) = 1. 3. Therefore, the sum of distribution factors for all members meeting at a joint is always equal to one. Answer: B

Explanation

The distribution factor measures the relative proportion of an applied moment that an individual member absorbs based on its stiffness relative to the total stiffness at the joint. Since the sum of individual stiffness contributions equals the total joint stiffness, the sum of all distribution factors at any joint must equal one.

Why the other options are wrong

A) The sum of distribution factors must equal unity to distribute 100% of the unbalanced moment. C) A sum greater than one would over-distribute the unbalanced moment at the joint. D) A sum less than one would leave a portion of the unbalanced moment unassigned.

Shortcut

Sum of distribution factors (DF) for all members meeting at a joint is always equal to 1.

Common mistake

Confusing the sum of distribution factors at a joint (which must equal 1) with carry-over factors or member stiffness values.