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 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 ?
- A1 and 3
- B2 and 3
- C1 and 2Correct
- D1 only
Solution
Concept
Conjugate beam: stability and determinacy
Step-by-step solution
1. A stable, determinate real beam has a stable, determinate conjugate beam (true). 2. An unstable real beam has a statically indeterminate conjugate beam, so an indeterminate conjugate beam shows the real beam is unstable (true). 3. A statically indeterminate real beam has an UNSTABLE conjugate beam (the conjugate loads must then maintain equilibrium) (statement as printed says stable, so it is false).
Explanation
Statements 1 and 2 correctly describe the correspondence between real and conjugate beams.
Why the other options are wrong
Statement 3 says "stable", which contradicts the correspondence (an indeterminate real beam gives an unstable conjugate).
Shortcut
Indeterminate real ↔ unstable conjugate; unstable real ↔ indeterminate conjugate.
Common mistake
Accepting statement 3.
Correct answer: C) 1 and 2