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.


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.

  • $\begingroup$ 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. $\endgroup$
    – SSan
    Jan 7 '21 at 2:42
  • $\begingroup$ then why don't you accept my answer so it will be used by others? thanks. $\endgroup$
    – kamran
    Jan 7 '21 at 2:50

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