The Power of Math in Structural Engineering
Have you ever stopped to marvel at the incredible engineering feats that surround us every day? From the towering skyscrapers to the bridges we cross, the modern world is filled with engineering marvels that are hiding in plain sight. But have you ever wondered how these feats of engineering are made possible? The answer, of course, lies in mathematics. Whenever we hear terms like calculus or differential equations, we tend to shy away from it because it’s viewed as a complex and useless branch of mathematics that exists simply to burden students. However, the math behind these complex fields provides a fascinating framework that is responsible for almost every structure and system in the world that we take for granted today. These include everything from megastructures to means of transportation.
Let's start with the tallest building in the world, the Burj Khalifa in Dubai. Standing at a height of 828 meters (2,717 feet), the Burj Khalifa is a testament to the power of engineering and mathematics. To support such a massive structure, engineers had to use advanced mathematical concepts like calculus and linear algebra to design the foundation and xframework necessary for the building's stability.
For example, the building's unique shape, which narrows as it ascends, required the use of differential equations to determine the optimal wind load distribution. Differential equations are a branch of calculus that involve the study of how quantities change over time. By using differential equations to model the wind loads on the Burj Khalifa, engineers were able to optimize the building's design to withstand high winds and prevent excessive swaying.
Another example of how mathematics is used in engineering is in the design of bridges. Bridges are essential for connecting communities and enabling transportation, but they also have to be able to withstand extreme weather conditions and loads. The world's longest suspension bridge, the Akashi Kaikyo Bridge in Japan, spans a distance of 1,991 meters (6,532 feet) across the Akashi Strait. The design of the bridge relied heavily on mathematical principles like geometry and differential equations to ensure its stability and safety.
For example, engineers used mathematical models to predict how the bridge would behave under different weather conditions like high winds or earthquakes. They used differential equations to model the vibrations that occur in the bridge when it is subjected to external forces. By analyzing these models, engineers were able to determine the optimal design for the bridge's suspension cables and towers, ensuring its stability and safety.
Even the everyday objects we take for granted are feats of engineering in their own right, and they rely heavily on mathematical principles to function. Let's take a closer look at the design of a car, for example. Cars are complex machines with many moving parts, and their design requires the use of a variety of mathematical concepts.
The engine, for example, uses calculus to determine the optimal timing for combustion. Calculus is a branch of mathematics that deals with the study of rates of change and accumulation, and it is essential for modeling the behavior of dynamic systems like engines. By using calculus to model the behavior of the engine, engineers are able to optimize its performance and fuel efficiency.
The suspension system of a car also relies heavily on mathematical principles like geometry to ensure a smooth ride. The suspension system is responsible for absorbing shocks and vibrations that occur when driving on rough roads or over bumps. It achieves this by using a complex arrangement of springs, dampers, and various other components that work together to absorb shocks and vibrations from the road. By using geometric principles to design the suspension system, engineers are able to ensure that the car remains stable and comfortable even in challenging driving conditions.
Every aspect of our modern world is made possible by the principles of engineering and mathematics. From the tallest skyscrapers to the smallest gadgets, engineers rely on advanced mathematical concepts to design and build the structures and devices that make our lives easier and more enjoyable. The examples provided above demonstrate just a few of the ways in which mathematics is used in engineering, and there are countless other examples out there waiting to be discovered. So the next time you're walking down the street or driving to work, take a moment to appreciate the incredible engineering feats that surround you, and remember that behind every one of them lies the power of mathematics.
Source:
Britannica, The Editors of Encyclopaedia. "Burj Khalifa". Encyclopedia Britannica, 8 Dec. 2022, https://www.britannica.com/topic/Burj-Khalifa. Accessed 24 April 2023.
X-engineer. “Home.” x, 2022, x-engineer.org/modeling-simulation-automotive-suspension/.
