A beam with end A having fixed support, end B having roller support and an internal hinge at C. Its conjugate beam is
- Aend A is free, ends B and C are on rollerCorrect
- Bend A is hinged, end B is fixed, C is on roller
- Cend A is free, end B is fixed and C is hinged
- Dend A is fixed, B is hinged and C is hinged
Solution
Concept
Real beam to conjugate beam supports
Step-by-step solution
1. Fixed end (real) → free end (conjugate). 2. Roller/pin end (real) → roller/pin end (conjugate). 3. Internal hinge (real) → roller (conjugate). 4. A has fixed support → free; B roller → roller; C hinge → roller.
Explanation
Slope and deflection conditions of the real beam become shear and moment conditions of the conjugate beam: fixed ↔ free, internal hinge ↔ roller.
Why the other options are wrong
The other options keep a fixed or hinged support at A, which does not follow from the transformation.
Shortcut
Fixed ↔ free; hinge ↔ roller.
Common mistake
Keeping the same support type.
Correct answer: A) end A is free, ends B and C are on roller