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I have this notion that at the top, the building will be more likely to shake than at the bottom, where it is grounded.

So, how does it work with an earthquake? Who would be more likely to perceive a small earthquake? Someone at the ground floor, or at the 3rd floor? Or 20th floor? Or does it depend on the magnitude of the earthquake?

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  • $\begingroup$ Good question, but you might get better answers on Engineering than here. $\endgroup$
    – gerrit ♦
    Aug 18, 2017 at 9:33
  • $\begingroup$ Hmm, Do you know if I can cross post? $\endgroup$
    – Fernando César S.
    Aug 18, 2017 at 13:27
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    $\begingroup$ Please don't cross-post. I discussed with some of the Engineering folks and they're not sure if it's a good fit there. Perhaps Physics would fit better, but I propose we first wait a couple of days to see if it gets a good answer here. Perhaps some of the earthquake folks know enough about propagation through buildings to answer it here. $\endgroup$
    – gerrit ♦
    Aug 18, 2017 at 13:29
  • $\begingroup$ I don't know the answer, but I think that someone who does should also address the different types of earthquake (direction of the wave relative to the surface) $\endgroup$
    – hugovdberg
    Aug 18, 2017 at 16:08
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    $\begingroup$ Like so many things the answer is: it depends. If you're in a building with base isolators and/or tuned mass damper, you may not even realize there was an earthquake. But if you're in a building solidly attached to the ground, you will probably believe the earthquake was worse than it actually was. My basis for this is from anecdotal reports from the Loma Prieta (q.v.) earthquake, which I experienced first hand. Those in highrises generally thought the earthquake was worse than those on the ground. $\endgroup$
    – BillDOe
    Aug 18, 2017 at 18:02

2 Answers 2

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It would depend more on the frequency more than the magnitude, and whether the building has a damper weight, like the Taipei Tower, which is tuned to swing in the opposite direction if the building resonates, in which case, you would feel it more at the bottom, because the building would flex and absorb the movement, the same as if it was not at resonance. But if it was, and there was no damper, you would feel it more at the top, at least until the building collapsed.☹️ The damper weight works like a ball on a string. When you move your hand at it's resonant frequency, it will swing much wider than your hand movement. If you increase the frequency slightly, it will swing the opposite way. It it is called anti resonance. The force on the steel cables pulls on the building the opposite way to which it is swaying, greatly reducing the sway.

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It varies depending on the elasticity of the building.

If the building is earthquake proofed, it will tend to dampen the effect of the quake, so that the top can shake less than the base.

If the building is stiff masonry, it will crack when the difference between the base and the upper levels exceed 2-3 inches for every floor, and when it's higher than that, there are good chances that the building will collapse.

The violence on different levels depends on the resonance of the building, the swing effect. If the resonance at the top compensates the periodicity of the quake, it will be less violent at the top.

If the resonance amplifies the quake, the top will swing additively, so that the top will have a bigger movement than the base.

That's another reason different buildings have different chances of collapsing based on their resonance.

It's possible that one end shakes a greater distance while another end shakes faster with less amplitude / less range.

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