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Question
Consider the following statements regarding the end conditions and internal conditions of a conjugate beam:
1. A stable and statically determinate real beam will have a conjugate beam which is also stable and statically determinate. 
2. An unstable real beam will have statically indeterminate conjugate beam. Hence if a conjugate beam is found to be statically indeterminate, it is concluded that the real beam is unstable and further analysis is not appropriate. 
3. A statically indeterminate. real beam will have stable conjugate beam. Hence its conjugate load must be such that it maintains equilibrium. 
Which of the above statements is/are correct? 
A.
1 and 3
B.
2 and 3
C.
1 and 2
D.
1 only
Answer ( Option C)

1 and 2

Solution

Conjugate beam method:
In this method, the real beam is converted into a conjugate beam where the bending moment in the real beam is represented as the shear force in the conjugate beam, and the slope of the real beam is represented as the bending moment in the conjugate beam. This method helps in determining deflections and rotations in the real beam by analyzing the corresponding conjugate beam, which must be stable and statically determinate for accurate analysis. 

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