Moment Distribution Method MCQ with answer and solution

Concept

Carry-over factor to fixed beam far end

Formula

COF = +1/2 = 0.5

Step-by-step solution

1. In Hardy Cross moment distribution, when moment M is applied at a hinged end A, rotation θ_A occurs. 2. For a prismatic beam with far end B fixed, the induced moment at the fixed end is M_B = M / 2. 3. The carry-over factor (COF) is the ratio of induced moment to applied moment: COF = M_B / M = 0.5. 4. Therefore, the carry-over factor to a fixed far end is 0.5. Answer: C

Explanation

In the Moment Distribution Method for a prismatic beam with uniform flexural rigidity, applying a moment at a near hinged end induces a moment of half the magnitude and the same sign at the far fixed end. Thus, the carry-over factor is 0.5.

Why the other options are wrong

A) 0 is the carry-over factor when the far end is pinned or hinged. B) 1 is the distribution factor sum at a single joint. D) 2 is the inverse of the carry-over factor.

Shortcut

Prismatic far-end fixed = 0.5; far-end hinged = 0.

Common mistake

Selecting 1 or 0 by confusing carry-over factor with distribution factor or a hinged far end.