Question

The degree of static indeterminacy of the beam (as shown below) for general case of loading is: 

• A. One
• B. Two
• C. Three
• D. Zero

Hint:

Degree of indeterminacy $D_s = R - E$ (reactions minus equilibrium equations). Internal hinges reduce redundancies.

Answer 1

The Correct Option is A

Step 1: Reaction Count.
- Fixed support (left): 3 reactions (vertical, horizontal, moment).
- Internal hinge: Introduces a compatibility condition; allows moment release.
- Roller support (center): 1 vertical reaction.
- Hinge support (right): 2 reactions (vertical + horizontal).
Total unknown reactions: $3 + 1 + 2 = 6$.

Step 2: Equilibrium Equations.
For a planar structure, there are 3 independent equilibrium equations.

Step 3: Degree of Indeterminacy.
\[D_s = (\text{Reactions}) - (\text{Equations}) = 6 - 5 = 1.\] (Reduction of one due to the internal hinge condition).

Step 4: Conclusion.
The beam's degree of indeterminacy is one.