Building Resonance: Why some buildings fall in earthquakes and others don't

A period is the amount of time that it takes one wave cycle to pass the given point. A frequency of one cycle per second has a one-second period. If the frequency doubles to two cycles per second, the period is only half of a second. Resonance is a tendency of a system to oscillate with greater amplitude at some frequencies than at others. The resonant frequency of any given system is a frequency at which the maximum amplitude oscillation occurs. For example, the resonant frequency of the one-meter-long pendulum is one-half of a hertz. If the string were one-quarter of the length, it would vibrate at twice the frequency. Small amplitudes can be approximated by this equation using length and the gravity constant. 

Resonance systems can be used to generate vibrations of a specific frequency to create music. Strings under Titan, such as with this cello, have resonant frequencies directly related to the material of the string as well as a mass length-tension of the string. The mass of the slow C string resonates at 264 hertz, whereas the thinner a string of a different material resonates at 440 hertz. Now, we use a simplified analogy of boats and sea. Series of waves, particularly when they hit broadside, can initiate rolling behavior. The smaller boat is affected by short-period low-amplitude waves that slap against the ocean liner with no effect. 

Small boats, on the other hand, will ride up and over long period high amplitude waves as a larger boat, begin a long, slow rock. Now, let's look at how buildings are affected by earthquake-induced seismic waves. All buildings have a natural period, a resonance, which is a number of seconds it takes for the building to naturally vibrate back and forth. The ground also has specific resonant frequency. Hard bedrock has higher frequencies than softer sediments. If the period of ground motion matches a natural resonance of a building, it will undergo the largest oscillations possible and suffer the greatest damage. 

Small buildings of one or two stories resonate naturally at much less than one second period. As one second period will affect buildings of about ten stories. For example, a 30 story building resonates at a period of three seconds, and a 50 story building resonates at a period of 5 seconds. During the 1985 Mexico City earthquake, the ground beneath the city resonated with the two second period for over a minute, thus medium height buildings with similar natural periods suffered the most damage, while short old weak stone buildings and skyscrapers were relatively undamaged. That proved to be what is called a resinous disaster, which is how engineers describe the destruction of a building by seismic vibrations that a system's resonant frequency. 

It is because of prolonged energy input that the system swings more and more strongly until the structural low limit is exceeded. A key point here is that small buildings on hard rock and large buildings on soft sediments may suffer more damage and ground motion effects from an earthquake than small buildings on a soft sediments and large buildings on hard rock. Resinous is one factor that contributes to earthquake damage. Of equal or greater importance are building design and the quality of construction materials. By determining the resonant frequency of the ground beneath the building site, the building design can be modified so that a resonance disaster does not occur. 

The following demonstration shows how model resonance in the classroom. The idea of the boss model is that different height buildings will respond to different frequencies of horizontal ground motion. A tall building will respond to very slow or low frequency oscillations of the ground. So if I move the base slowly back and forth, I can get the tall building to oscillate, where the intermediate and short buildings are not moving. If I move it more briskly, I can dial in the rate of horizontal oscillation so that I move the center building, the intermediate height building, and the short and the tall winds are barely moving. 

To get the short building to oscillate, you need to move the base very briskly back and forth. And dial in to the natural frequency of the short building, and we can see that the intermediate and tall buildings are barely moving. I was built on a weak foundation. When I stand on the floor