Buildings Resonating With Earthquakes
Most recent answer: 10/22/2007
Q:
What happens if the natural frequency of a building matched the frequency of an earthquake?
- Krystal (age 15)
South Carolina
- Krystal (age 15)
South Carolina
A:
Hi Krystal,
That's a very important, practical question, and as such, has a lot of detail that's important to the answer.
The answer, as it happens for so many other questions, is "it depends". If the earthquake is "small" or at least far away so that the amplitude of the shaking is small, not much of anything will happen to the building. You can get away with building structures that are not particularly safe in an earthquake, so long as no earthquake hits them. I’m not sure there’s really anyplace on the planet that’s totally immune from earthquakes. I live in Illinois, and the flat landscape testifies to the lack of geological activity here. Nonetheless, there was a magnitude 4.0 quake in the northern part of the state just last summer. And there’s a substantial fault system in the southern bit of the state and in neighboring Missouri and Kentucky.
So, given that oscillators amplify vibrations with frequencies close to their natural frequency much more than at other frequencies, how can people design buildings which are not so sensitive to earth movement? One thing to do is to stiffen the building so that the resonant frequency is much higher than the typical frequency component of an earthquake. I’m not sure this is always a good idea, as stiff objects are often more brittle and can crack easily. Building stiffeners (steel beams and supports) are often added to buildings to prevent specific kinds of failure in the buildings. A typical kind of failure for buildings that are only a couple of stories tall (like a typical house) is that the whole building slides off of its foundation by a little bit. Stiffeners may be added to anchor the building to its foundation, but may increase the violence of shaking upstairs during the quake. At least it won’t grind away the bottom floor as the building slides off.
Another kind of stiffener is designed to keep the floor supports where they are held up by vertical supports from buckling. A serious building failure during earthquakes is floors coming loose from their supports and crashing on lower floors, a phenomenon colorfully called "pancaking".
Small buildings typically have resonant frequencies much higher than that of the ground motion and thus just plain structural strength is more important than resonant oscillations.
Tall buildings are another story entirely. Skyscrapers in seismically active zones have to be designed with special care. Many include damping mechanisms to dissipate the energy of the oscillating building. There, you want your structure to be able to flex without breaking, but also to be able to get rid of the shaking energy so it doesn’t build up beyond some part of the building’s breaking point.
I worked on a high-energy physics experiment at the Stanford Linear Accelerator Center, which is just a few hundred yards away from the San Andreas fault in California. We designed oil dampers on the support beams for our big particle detector, called SLD, which performed well during the 1989 Loma Prieta earthquake, although we did have to clean some oil off of our electronics. Big buildings also have large, damped counterweights on top, which are there mostly to suppress building sway when the wind blows. They probably play an important role in the earthquake preparedness plans of these buildings too.
So the answer to your question is that if a building resonates at a frequency which is close to a principal frequency of the ground motion of an earthquake, it will produce more shaking in the building than if the frequencies were more different. But just how much shaking and how much damage is caused depends on the strength, flexibility, geometry, masses, and damping of the components of the building, and the particulars of the earthquake. In some the motion is side-to-side, others it’s a kind of push-pull motion, and others there
That's a very important, practical question, and as such, has a lot of detail that's important to the answer.
The answer, as it happens for so many other questions, is "it depends". If the earthquake is "small" or at least far away so that the amplitude of the shaking is small, not much of anything will happen to the building. You can get away with building structures that are not particularly safe in an earthquake, so long as no earthquake hits them. I’m not sure there’s really anyplace on the planet that’s totally immune from earthquakes. I live in Illinois, and the flat landscape testifies to the lack of geological activity here. Nonetheless, there was a magnitude 4.0 quake in the northern part of the state just last summer. And there’s a substantial fault system in the southern bit of the state and in neighboring Missouri and Kentucky.
So, given that oscillators amplify vibrations with frequencies close to their natural frequency much more than at other frequencies, how can people design buildings which are not so sensitive to earth movement? One thing to do is to stiffen the building so that the resonant frequency is much higher than the typical frequency component of an earthquake. I’m not sure this is always a good idea, as stiff objects are often more brittle and can crack easily. Building stiffeners (steel beams and supports) are often added to buildings to prevent specific kinds of failure in the buildings. A typical kind of failure for buildings that are only a couple of stories tall (like a typical house) is that the whole building slides off of its foundation by a little bit. Stiffeners may be added to anchor the building to its foundation, but may increase the violence of shaking upstairs during the quake. At least it won’t grind away the bottom floor as the building slides off.
Another kind of stiffener is designed to keep the floor supports where they are held up by vertical supports from buckling. A serious building failure during earthquakes is floors coming loose from their supports and crashing on lower floors, a phenomenon colorfully called "pancaking".
Small buildings typically have resonant frequencies much higher than that of the ground motion and thus just plain structural strength is more important than resonant oscillations.
Tall buildings are another story entirely. Skyscrapers in seismically active zones have to be designed with special care. Many include damping mechanisms to dissipate the energy of the oscillating building. There, you want your structure to be able to flex without breaking, but also to be able to get rid of the shaking energy so it doesn’t build up beyond some part of the building’s breaking point.
I worked on a high-energy physics experiment at the Stanford Linear Accelerator Center, which is just a few hundred yards away from the San Andreas fault in California. We designed oil dampers on the support beams for our big particle detector, called SLD, which performed well during the 1989 Loma Prieta earthquake, although we did have to clean some oil off of our electronics. Big buildings also have large, damped counterweights on top, which are there mostly to suppress building sway when the wind blows. They probably play an important role in the earthquake preparedness plans of these buildings too.
So the answer to your question is that if a building resonates at a frequency which is close to a principal frequency of the ground motion of an earthquake, it will produce more shaking in the building than if the frequencies were more different. But just how much shaking and how much damage is caused depends on the strength, flexibility, geometry, masses, and damping of the components of the building, and the particulars of the earthquake. In some the motion is side-to-side, others it’s a kind of push-pull motion, and others there
(published on 10/22/2007)