The principle of superposition is not applicable when 1) the material obeys Hooke’s law 2) the effect of temperature changes are not taken into consideration 3) the yielding of support of structure takes place Which of the above statements is/are correct?
- A2 only
- B1 and 2
- C3 onlyCorrect
- D2 and 3
Solution
Concept
Principle of Superposition
Formula
No
Step-by-step solution
1. Identify the condition for the Principle of Superposition, which requires linear structural behavior and constant boundary conditions. 2. Evaluate statement 3: Yielding or settlement of a support alters boundary conditions and introduces non-linear behavior, making the principle non-applicable. 3. Statements 1 and 2 describe conditions where linear superposition remains valid, so only statement 3 correctly answers the question.
Explanation
The principle of superposition requires a linear structure where loads cause proportional deformations without altering the basic geometry or boundary conditions. When a support yields (moves or settles), it changes the structure's boundary conditions and causes non-linear behavior, making the superposition principle invalid. Statements 1 and 2 describe conditions where the principle actually works, so only statement 3 correctly identifies when it fails.
Shortcut
Remember: Superposition requires a linear & stable structure (Hooke's law applies, constant temperature). Any yielding, support settlement, or non-linear behavior breaks linearity, so superposition FAILS. Therefore, yielding (Statement 3) is the only condition where it is not applicable.
Common mistake
Many students misread the question as asking when the principle of superposition *is* applicable instead of *not* applicable, leading them to select Option B (1 and 2) instead of Option C (3 only).
Correct answer: C) 3 only