Calculating Period and WEIRD Buildings.

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.

Harmonic motion. My job would be a lot more fun if we were hanging buildings from springs.

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?

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ASCE’s Live Load Model

Parts of this are older than me.

(Thanks to Dr. Ross Corotis for help in obtaining some of these original papers.)

The live load on a structure consists of the weight of people, pets, furniture, and anything else that has weight and can be moved around. Despite how heavy concrete, steel, and masonry are, it’s often the magnitude of the live load which governs a structure’s capacity.¬†However, unlike other loadings, live loads are extremely difficult to model accurately. They depend on how people decide to live and where they decide to go, and are thus not very amenable to the sort of mathematical modeling building codes like to be rooted in.

But that hasn’t stopped the codes from trying.

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The Origin of Minimum Design Loads

This is what you get if you search “1920s construction”

At the turn of the 20th century, building codes in this country were a disorganized mess. At the time, code adoption and enforcement wasn’t done at the federal or even state level – it was done city-by-city. ¬†This resulted in a mishmash of regulations varying from nonexistant (25% of towns over 5000 people had no code or inspector) to extremely strict, depending on where in the country you were. This led to a number of problems. In areas with overly strict codes, the resulting high construction costs were causing a housing shortage. And in others areas, lack of code or lack of enforcement resulted in shoddy, dangerous buildings.

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Building Code Usability

Building codes face an interesting set of design constraints. First and foremost, they’re legal documents describing minimum requirements for buildings. This means they need to be exhaustive enough to cover what, where, why, and how any given structure gets built. And they need to do it persnickety legalistic language to ensure the requirements are precise and specific, and can’t be avoided through loopholes.

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