# Seismic question

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

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.

• 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. – SSan Jan 7 at 2:42
• then why don't you accept my answer so it will be used by others? thanks. – kamran Jan 7 at 2:50