Kinematic Indeterminacy MCQ with answer and solution

Concept

Degrees of freedom of a pin-jointed truss

Formula

Dk = 2j − r

Step-by-step solution

1. Joints j = 6 (two top, four bottom). 2. Reactions: hinge 2 + roller 1 = 3. 3. Dk = 2 × 6 − 3 = 9.

Explanation

Each joint has two translations; supports remove as many as their reaction components.

Why the other options are wrong

Other values do not equal 2j − r.

Shortcut

Dk = 2j − r.

Common mistake

Counting members instead of joints.