Consider the following statements regarding the principle of super position : 1. The total displacement of the stress at a point in a structure subjected to several external loadings can be determined by adding together the displacements caused by each of the external loads acting together. 2. The material must behave in a non-linear elastic manner. 3. The geometry of the structure must not undergo significant change when the loads are applied. Which of the above statements is/are correct ?
- A1 and 2
- B2 only
- C3 onlyCorrect
- D1 and 3
Solution
Concept
Principle of superposition
Step-by-step solution
1. The effects of the loads are added when each acts SEPARATELY, not "together" (statement 1 as printed is false). 2. The material must be linearly elastic (statement 2 is false). 3. The geometry must not change significantly under load (statement 3 true).
Explanation
Superposition holds for a linear elastic material with small deformations, so that the response to separate loads can be added.
Why the other options are wrong
Options with statement 1 or 2 are wrong: the loads are applied separately and the behaviour is linear.
Shortcut
Superposition = linear + small deformations + separate loads.
Common mistake
Accepting "non-linear elastic".
Correct answer: C) 3 only