Violent Ground Motion During Earthquakes
The seismic waves travel for great distances before finally losing most of their energy. At some time after their generation, these seismic waves will reach the earth’s surface, and set it in motion, which we surprisingly refer to as earthquake ground motion. When this earthquake ground motion occurs beneath a building and when it is strong enough, it sets the building in motion, starting with the buildings foundation, and transfers the motion throughout the rest of building in a very complex way. These motions in turn induce forces which can produce damage.
Real earthquake ground motion at a particular building site is vastly more complicated than the simple wave form. Here it’s useful to compare the surface of ground under an earthquake to the surface of a small body of water, like a pond. You can set the surface of a pond in motion – by throwing stones into it. The first few stones create a series of circular waves, which soon being to collide with one another. After a while, the collisions, which we term interference patterns, are being to predominate over the pattern of circular waves. Soon the entire surface of water is covered by ripples, and you can no longer make out the original wave forms. During an earthquake, the ground vibrates in a similar manner, as waves of different frequencies and amplitude interact with one another.
Building Frequency and Period
The characteristics of earthquake ground motions which have the greatest importance for buildings are the duration, amplitude (of displacement, velocity and acceleration) and frequency of ground motion.
Frequency is defined as the number of complete cycles of vibration made by the wave per second.
Here we can consider a complete vibration to be the same as the distance between one crest of the wave and the next, in other words one full wavelength. Surface ground motion at the building site, then, is actually a complex superposition of vibration of different frequencies. We should also mention that at any given site some frequencies usually predominate.
The response of building to the ground motion is as complex as the ground motion itself, yet typically quite different. It also begins to vibrate in a complex manner, and because it is now a vibratory system, it also posses a frequency content. However, the buildings vibrations tend to center around one particular frequency, which is known as its natural or fundamental frequency. In general…
The shorter a building is, the higher its natural frequency. The taller the building is, the lower its natural frequency
The natural period is the time it takes for the building to make one complete vibration.
The relationship between frequency F and period T is thus given as
T = 1 / F
This means that a short building with a high natural frequency also has a short natural period. Conversely, a very tall building with a low frequency has a long period.