# 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

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## Building Stability - Columns

There are many activities to show how engineers know how to choose the structural material and shape, solid or hollow of a column or beam. We will next calculate one example to spark your interest in this fascinating store of knowledge. To demonstrate how doubling the thickness of a column affects (this is amazing) its load bearing capacity, draw the cross section of two columns. One is a 2x4, and the other is a 4x4(in.) wooden column.

Using the formula above for finding I, compare the moment of inertia of each.

I = (4)(2)3 / 12 which equals 2.67 in. 4

I = (4)(4)3 / 12 which equals 21.3 in.4

Therefore, we see that the 4x4 is _____ times stiffer than the 2x4. (8 times! 21.3 / 2.67 = 7.977…)

You can demonstrate further how a hollow 4x4 will support three times the weight of a solid 2x2.

More activities can be found on such internet sites as http:/polymorph.net/engineer.htm