Discussion
Which of these will lengthen the natural period of an existing building?
Answer: D
Correct answer: Adding mass at the upper floors
Period rises with the square root of mass, so adding mass lengthens it - and adding it high in the building is most effective, since the upper floors have the largest modal displacement.
The other three all add stiffness or reduce height, which shortens the period. Note that the change is rarely worth making deliberately: extra mass attracts extra seismic force in proportion, so the lengthened period is bought at a price the spectrum may not repay.
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