Why Buildings Fall During Earthquakes: Understanding Resonance and Structural Engineering

Earthquakes are terrifying natural disasters, and their impact on densely populated cities can be devastating. One of the most significant dangers is the collapse of buildings. But what causes these structures to fail during an earthquake, and what measures can be taken to prevent such tragedies?

The Physics of Building Collapse

Contrary to what disaster movies might depict, buildings don't usually collapse because of the ground splitting open or shaking violently. The reality is more nuanced. When an earthquake strikes, the ground movement displaces a building's foundation, sending shock waves through the structure. This causes the building to vibrate back and forth. The intensity of this oscillation depends on:

• Mass: Concentrated at the bottom of the building.
• Stiffness: The force needed to cause displacement.

Stiffness is also influenced by the building's material and the shape of its columns, and is largely determined by height. Shorter buildings tend to be stiffer and shift less, while taller buildings are more flexible.

The Mexico City Earthquake: A Lesson in Natural Frequency

The 1985 Mexico City earthquake provides a crucial insight into building behavior during seismic events. Surprisingly, buildings between six and fifteen stories tall suffered the most damage, while shorter and taller buildings fared better. This phenomenon can be explained by understanding natural frequency.

Natural Frequency Explained

In any oscillating system, frequency refers to the number of back-and-forth cycles within a second. A building's natural frequency, determined by its mass and stiffness, is the frequency at which it will naturally vibrate. Increasing a building's mass slows down its natural vibration rate, while increasing stiffness accelerates it.

Resonance: The Amplifying Effect

The Mexico City earthquake highlighted the effect of resonance. Resonance occurs when the frequency of the earthquake's seismic waves matches the natural frequency of a building. This is similar to pushing a swing at just the right moment. Each seismic wave amplifies the building's vibration, causing it to swing further and further, eventually exceeding its structural limits and leading to collapse.

Preventing Earthquake-Induced Collapses

Today, engineers collaborate with geologists and seismologists to predict the frequency of earthquake motions at building sites. This allows them to design structures that avoid resonance-induced collapses. Factors considered include:

• Soil type
• Fault type
• Data from previous earthquakes

Low-frequency motions are more dangerous for taller, more flexible buildings, while high-frequency motions pose a greater threat to shorter, stiffer structures.

Innovative Systems for Shock Absorption

Engineers have developed innovative systems to absorb shocks and limit deformation:

• Base Isolation: Flexible layers isolate the foundation's displacement from the rest of the building.
• Tuned Mass Damper Systems: These systems cancel out resonance by oscillating out of phase with the natural frequency, reducing vibrations.

Ultimately, the buildings that withstand earthquakes are not necessarily the sturdiest, but the smartest ones, designed with a deep understanding of physics and seismic behavior.