Static Indeterminacy MCQ with answer and solution

Concept

Static indeterminacy of beams

Formula

Ds = r − 3 − (number of hinge conditions)

Step-by-step solution

1. Fixed ends: 3 + 3 reactions; two roller supports: 1 + 1 reactions → r = 8. 2. One internal hinge gives 1 extra condition. 3. Ds = 8 − 3 − 1 = 4.

Explanation

Reactions minus the three equilibrium equations minus one equation of condition for the internal hinge.

Why the other options are wrong

3, 5 and 6 do not agree with r − 3 − 1.

Shortcut

Ds = r − 3 − hinges.

Common mistake

Forgetting the hinge.