In a rigid joint plane frame structure, introduction of pins to all members at a joint produces additional equations equal to

Concept:

In a rigid joint plane frame structure, the introduction of pins to all members at a joint produces additional equations equal to the number of members meeting at that joint minus one. This is because the introduction of a pin joint restricts the movement and rotation of the connected members, and it introduces equilibrium equations at that joint.

Additional equations = Number of members at the joint - 1

If D becomes a pin joint;

Equilibrium equations = 3 (M_DA = 0, MDB = 0, and MDC = 0.)

Additional equations = 3 - 1 = 2

Hence option (3) is correct.