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: Count reactions.
- Fixed end (left): provides 3 reactions (vertical, horizontal, moment).
- Internal hinge: introduces a compatibility condition but allows moment release.
- Roller support (middle): provides 1 vertical reaction.
- Hinge support (right): provides 2 reactions (vertical + horizontal).
Total unknown reactions = $3 + 1 + 2 = 6$.

Step 2: Equilibrium equations.
For a plane structure, number of independent equilibrium equations = 3.

Step 3: Degree of indeterminacy.
\[ D_s = (\text{Reactions}) - (\text{Equations}) = 6 - 5 = 1. \] (One reduction because of internal hinge condition).

Step 4: Conclusion.
Hence, the beam is indeterminate to degree one.