# Math in the Beauty and Realization of Architecture

## CONTENTS OF CURRICULUM UNIT 06.04.06

- Introduction to Unit
- Unit Objectives
- The History of Bridges
- Motivation for Unit
- Introduction Discussion with Students
- Bridge Language
- The Types of Bridges
- Interesting Famous Bridges
- How to Choose the Right Bridge for the Job
- Geometric Shapes in Bridge Trusses
- Icebreaker activity
- Bridge of the Day or Week and Daily Bonus Question
- Understanding the Strength in Columns
- Building Stability - Columns
- Building Stability - Beams
- Finding the Forces in a Truss
- Final Project: Designing a Community Friendship/Peace Bridge
- Final Project Rubric
- Bibliography

### Unit Guide

## The Math in the Design and Building of Bridges

Your feedback is important to us!

After viewing our curriculum units, please take a few minutes to help us understand how the units, which were created by public school teachers, may be useful to others.

## Building Stability - Beams

How a beam acts under a load depends on how it is supported and how its ends are attached to the supports. It can be supported on one or both ends (roots). The amount of force applied to the root depends on the load size and the distance from the root. This is called the bending moment.

Make up an equation for this last statement, using variables of your choice and then compare them to the formula that is used:

M = P L

Bending moment (M) = load (P) x distance from root (L)

The bending moment is zero at the end supports and maximum in the middle.

A lower strength material can be used in a beam that is made greater in height.

The strength of a beam, simply supported and loaded in the middle, to resist sagging/bending is a function of its height squared, span, width, and E. Simply said:

- 1. if you the double the height, the strength is quadrupled and the stresses reduced by a factor of 4.
- 2. if you double the length of a span, the strength is cut in half.
- 3. if you double the width, the strength is doubled.
- 4. if the modulus of elasticity is doubled, then the strength is doubled.