Discussion
Assertion (A): Modal superposition may be used for a yielding structure.
Reason (R): Superposition requires the system to be linear.
Select the correct option.
Answer: A
Correct answer: A is false but R is true
The reason is correct and it is exactly what defeats the assertion. Modal superposition rests on decomposing the response into independent modal contributions and adding them, which requires linearity.
A yielding structure has a stiffness that depends on its displacement history, so the modes are not constant and the contributions cannot be superposed. Nonlinear time-history analysis or pushover analysis must be used instead. A true reason refuting rather than supporting the assertion - each must be judged separately.
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