For a 3 stories building, in terms of seismic vertical instability which one is worse: a higher mass on Level 2 or, higher mass on the roof? Both are compared to L1 mass.
1 Answer
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The one with the higher mass on level three is worse.
Assuming the building as an SDF vibration for simplicity:
The period of the building will moderately increase due to the reduction of K, $$K=P/\delta $$ By moving mas from 2nd floor to 3rd floor we increase deflection by roughly 1.2 hence decreasing the K by 1/5.
Natural frquency $ \ \omega_n=\sqrt\frac{K}{m} \\ \tau= 2\pi/\omega_n \ $ decreases moderately (0.04) which is good but it can not make up for the increase in the additional overturning moment by 150% and extra shear due to triangular sheer distribution.
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$\begingroup$ I see. I was confused because per ASCE: weight irregularity occurs where the effective mass of one story is greater than 150% of that of an ADJACENT story. $\endgroup$– SSanCommented Jan 7, 2021 at 2:42
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$\begingroup$ then why don't you accept my answer so it will be used by others? thanks. $\endgroup$– kamranCommented Jan 7, 2021 at 2:50