and they've become more deadly as our cities have grown,

with collapsing buildings posing one of the largest risks.

Why do buildings collapse in an earthquake,

and how can it be prevented?

If you've watched a lot of disaster films,

you might have the idea

that building collapse is caused directly by the ground beneath them

shaking violently, or even splitting apart.

But that's not really how it works.

For one thing, most buildings are not located right on a fault line,

and the shifting tectonic plates go much deeper than building foundations.

So what's actually going on?

In fact, the reality of earthquakes and their effect on buildings

is a bit more complicated.

To make sense of it, architects and engineers use models,

like a two-dimensional array of lines representing columns and beams,

or a single line lollipop with circles representing the building's mass.

Even when simplified to this degree, these models can be quite useful,

as predicting a building's response to an earthquake

is primarily a matter of physics.

Most collapses that occur during earthquakes

aren't actually caused by the earthquake itself.

Instead, when the ground moves beneath a building,

it displaces the foundation and lower levels,

sending shock waves through the rest of the structure

and causing it to vibrate back and forth.

The strength of this oscillation depends on two main factors:

the building's mass, which is concentrated at the bottom,

and its stiffness,

which is the force required to cause a certain amount of displacement.

Along with the building's material type and the shape of its columns,

stiffness is largely a matter of height.

Shorter buildings tend to be stiffer and shift less,

while taller buildings are more flexible.

You might think that the solution is to build shorter buildlings

so that they shift as little as possible.

But the 1985 Mexico City earthquake is a good example of why that's not the case.

During the quake,

many buildings between six and fifteen stories tall collapsed.

What's strange is that while shorter buildings nearby did keep standing,

buildings taller than fifteen stories were also less damaged,

and the midsized buildings that collapsed

were observed shaking far more violently than the earthquake itself.

How is that possible?

The answer has to do with something known as natural frequency.

In an oscillating system,

the frequency is how many back and forth movement cycles occur within a second.

This is the inverse of the period,

which is how many seconds it takes to complete one cycle.

And a building's natural frequency, determined by its mass and stiffness,

is the frequency that its vibrations will tend to cluster around.

Increasing a building's mass slows down the rate at which it naturally vibrates,

while increasing stiffness makes it vibrate faster.

So in the equation representing their relationship,

stiffness and natural frequency are proportional to one another,

while mass and natural frequency are inversely proportional.

What happened in Mexico City was an effect called resonance,

where the frequency of the earthquake's seismic waves

happen to match the natural frequency of the midsized buildings.

Like a well-timed push on a swingset,

each additional seismic wave amplified the building's vibration

in its current direction,

causing it to swing even further back, and so on,

eventually reaching a far greater extent than the initial displacement.

Today, engineers work with geologists and seismologists

to predict the frequency of earthquake motions at building sites

in order to prevent resonance-induced collapses,

taking into account factors such as soil type and fault type,

as well as data from previous quakes.

Low frequencies of motion will cause more damage to taller

and more flexible buildings,

while high frequencies of motion pose more threat

to structures that are shorter and stiffer.

Engineers have also devised ways to abosrb shocks

and limit deformation using innovative systems.

Base isolation uses flexible layers

to isolate the foundation's displacement from the rest of the building,

while tuned mass damper systems cancel out resonance

by oscillating out of phase with the natural frequency

to reduce vibrations.

In the end, it's not the sturdiest buildings that will remain standing

but the smartest ones.