Principle of superposition is applicable when (i). Deflections are linear functions of applied forces (ii). Material obeys Hooke’s law (iii). The action of applied forces will be affected by small deformations of the structure
- AOnly (i)
- B(i) and (ii)Correct
- C(ii) and (iii)
- D(i), (ii) and (iii)
Solution
Concept
The principle of superposition is valid only for linearly elastic structures with small deformations.
Step-by-step solution
1. Check statement (i): For superposition to hold, total deflection must be the sum of deflections from individual loads. This requires deflections to be linear functions of loads. So, statement (i) is correct. 2. Check statement (ii): Hooke's law states that stress is directly proportional to strain. This ensures material linearity. So, statement (ii) is correct. 3. Check statement (iii): The principle assumes small deformations. This means deformations do not change the line of action or geometry of applied loads. Statement (iii) says applied forces 'will be affected', which describes non-linear behavior (P-Delta effects). Therefore, statement (iii) is incorrect. 4. Hence, only statements (i) and (ii) are correct. Answer: (B) (i) and (ii)
Explanation
Superposition requires both material linearity and geometric linearity. Material linearity means the material obeys Hooke's law. Geometric linearity means deformations are so small that they do not affect the action of the applied loads.
Why the other options are wrong
A: It is incomplete because statement (ii) is also a necessary condition. C: Statement (iii) is incorrect because deformations must NOT affect the action of forces. D: It incorrectly includes statement (iii).
Shortcut
Superposition requires linear behavior and unaffected load geometry (small deflection theory).
Common mistake
Students often misread statement (iii) and assume it correctly describes small deformation theory, missing the word 'affected' instead of 'not affected'.
Correct answer: B) (i) and (ii)