Question

To generate the $j^{\text{th}}$ column of the flexibility matrix

• A. A unit force is applied at coordinate $j$ and the displacements are calculated at all coordinates
• B. A unit displacement is applied at co-ordinate $j$ and the forces are calculated at all coordinates
• C. A unit force is applied at coordinate $j$ and the forces are calculated at all coordinates
• D. A unit displacement is applied at co-ordinate $j$ and the displacements are calculated at all co-ordinates

Hint:

Flexibility matrix → apply unit {force}, find {displacements}. Stiffness matrix → apply unit {displacement}, find {forces}.

Answer 1

The Correct Option is A

Step 1: Recall the definition of flexibility coefficients.
Flexibility coefficients represent the displacement at one coordinate due to a unit force applied at another coordinate.
Step 2: Meaning of the $j^{\text{th}}$ column.
The $j^{\text{th}}$ column of the flexibility matrix consists of displacements at all coordinates caused by a unit force applied at coordinate $j$.
Step 3: Analyze the options.
(A) Correct, this exactly matches the definition of flexibility coefficients.
(B) Incorrect, this describes stiffness matrix generation.
(C) Incorrect, flexibility matrix relates forces to displacements, not forces to forces.
(D) Incorrect, again related to stiffness, not flexibility.
Step 4: Conclusion.
Hence, option (A) is correct.