July 3, 2025

Jessica A. Dennehy

11th Grade

Williamsville East High School

Introduction

The earliest known evidence of bridge-building dates back to ancient Babylon around 4000 BC, where a massive reservoir system was engineered to control the overflow from the Euphrates River. While the purpose of a bridge may seem straightforward, building one that lasts for any extended period of time is anything but. Constructing a durable structure requires interfield collaboration; from local architects and engineers to material scientists and local government, everyone has to work together to ensure that a bridge is built to be structurally sound. With this in mind, every subcomponent matters in the construction of a bridge: every beam, truss, bolt, nut, and weld plays a role, and mathematics ensures that these individual components are able to withstand the test of time.

Bridges come in many forms, each designed with a specific purpose in mind. Most modern bridges are a combination of many different simple bridges, but for introductory purposes, here’s a quick breakdown of the most common simple bridges and what makes them unique.

Beam Bridges

A traditional beam bridge consists of two abutments, which serve as a means of support, and a level, horizontal deck, which spans the two ends. These are the simplest style of bridge, being the first ever built. However, even with its apparent simplicity, their design is grounded in an understanding of both physics and mathematics. All loads of a beam bridge should be applied to its level surface. Fundamentally, when this occurs, the top of the beam will compress, being squeezed downwards, while the bottom will be under tension, being stretched outwards; depending on the materials used and the intended use of the bridge, these forces must be precisely calculated to ensure safety and stability. To ensure that the deck is able to withstand loads, the weight of the load can not remain entirely on the flat surface; instead, most of it is transferred vertically through the beam and down into the supports, where they are then compressed. With different materials, shapes, and supports, there are a multitude of variables that must be accounted for. Mathematics is used in order to calculate and rely on equations from statics and material science to calculate bending moments, shear forces, and stress distribution. Math is used to model these internal forces, predicting how the beam will bend before the bridge is ever built.