The degree of static indeterminacy of the beam (as shown below) for general case of loading is:
The degree of static indeterminacy of the beam (as shown below) for general case of loading is:
Show Hint
- One
- Two
- Three
- Zero
The Correct Option is A
Solution and Explanation
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.
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