# 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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## Understanding the Strength in Columns

A column is a structural member, usually upright, that supports a weight that pushes down on it. It therefore must have good compressive strength to prevent buckling and then collapsing.

### Activity

Students will take a piece of paper to form different shapes of columns and test the strength of each. In general, a column becomes strong against buckling with the more material away from its central vertical axis. Predict which shape column would buckle the least.

1. Roll a 4 x 11 inch strip of paper and paste to form a circular hollow column.

2. To form a square hollow column, cut a 5 x 11 in. strip and fold it length wise every inch, five times and glue into a square.

3. Fold another to form a triangular hollow column. Cut a strip of paper 4 x 11 in. and fold it vertically every one inch and glue.

4. Fold another to form an I-beam. Cut a two 2 x 11 inch strips. Fold them along two lines ½ in. from the long edges each. Test each folded strip alone for strength. Then glue the middle sections back to back and notice the difference in bending under a compression load. Next glue two one-inch strips of paper, one each on the top and bottom of the "I". Test. Glue two more 1-inch strips on either side of another I-beam. Predict the result before you test again. This last model should be less strong because more material was placed closer to the central axis. The circular column will be the strongest, 20% stronger than a square one of comparable size. Circular columns are not used as much because they are difficult to fasten to beams.

The most important factor that enables a column, unless it is quite short, to resist being deformed is its load bearing capacity, or how much weight it will support. This capacity depends on four factors: (1) on the stiffness of its material, (2) the geometry of its cross-sectional area, (3) its length and (4) if the ends of the column are fixed to something.

Look at the table below of four common structural materials and their modulus of elasticity.

Compare the materials.

- 1. Find the factor by which a concrete column has a greater load bearing capacity than a wooden one of the same size. Round to the nearest tenth.
- 30 / 13 is about 2.3 times
- 2. Approximately what fraction of a steel column's load bearing capacity is that of a concrete column's?
- 30 / 200 is about 1 / 6
- Material Young's Modulus (109 N / m2) Newtons of force/meters
- Wood (Douglas fir tree) 13
- Concrete 30
- Aluminum 70
- Structural steel 200