Outside of California, few places in the country are known for having earthquakes. But because the possibility for one exists nearly everywhere, earthquake loads nearly always need to be considered in the design of a structure. During an earthquake, a building will vibrate back and forth, much like a weight attached to a spring. How fast it vibrates dictates how much force the building experiences – this quantity is known as a building’s period, and determining is an important part of calculating the seismic load on a building.
ASCE 7 allows the use of several possible formulas for calculating period, depending on the exact sort of building being designed. These equations are very simple, and don’t seem to resemble the equations of simple harmonic motion, the concept that seismic load calculations are based on. So where do they come from?