While using three moments equation, a fixed end of a continuous beam is replaced by an additional span of

The three-moment equation is used for the analysis of continuous beams. When one end of a continuous beam is fixed, an imaginary or fictitious span is introduced beyond the fixed end so that the three-moment equation can be applied.

For a fixed end, this additional imaginary span is assumed to have zero length. This allows the fixed-end condition of zero rotation (zero slope) to be incorporated into the three-moment equation.

Option A: Zero length
Correct. A fixed end is represented by an imaginary span of zero length when applying the three-moment equation.

Option B: Infinite length
Incorrect. An infinite-length span is not used to represent a fixed end in the three-moment equation.

Option C: Zero moment of inertia
Incorrect. Zero moment of inertia would imply zero flexural stiffness and does not represent a fixed-end condition.

Option D: None of the above
Incorrect because Option A correctly represents the fixed end.

Hence, Option A — Zero length is the correct answer.