Strength in Structure

Created by Brian Domroes

Rene’ Ehrhardt, Flickr

What forces are at work here?

Bill Lim, Flickr

Frank Kovalchek, Flickr

Tension and Compression

Tension and Compression

Tension The force that results from things being

pulled apart

Compression The force that results from things being

pushed together

Which is the most stable?

Increasing Stability

More Triangles!

Why is the triangle so strong?

Balance of compression and tension Angles are fixed

Key

Compression (push)

Tension (pull)

Compression/Tension Example

A system of triangles

Geodesic Construction Enough class materials for 10 domes Domes will be assembled in groups of 3

Strut and Connector

Strut

Connector

Geodesic Construction Appoint a leader in each group Leader gives group members roles

Measure Your Isosceles Triangle

Measure in millimeters Measure from the middle of struts

Geodesic Construction Do you notice forces working together? GENTLY press on connectors to check

Do You Remember?

Key

Compression (push)

Tension (pull)

How can you offset tension?

How do we anchor new triangles?

How do you keep these triangles in place?

And so on…

A complete system of triangles

The tension at the base…

is offset by the compression at the joints

Why is there no place like dome?

Only manmade structure that gets proportionally stronger as it increases in size

Martin Ujaki, Flickr

Why is there no place like dome?

Has the biggest enclosed volume to weight ratio for any manmade structure

notfrancois, Flickr

Why is there no place like dome?

GreenVery efficient with heating/coolingUses less materialsWithstands harsh weather

Courtesy of Plantagon

Do you see geometric shapes?

andy_0306uk, Flickr  

Geometric Shapes

Equilateral Triangle Isosceles Triangle Acute Triangle Hexagon Regular Pentagon Decagon (base of your dome)

Do you see similar shapes?

andy_0306uk, Flickr  

Two shapes are similar if:

One shape is an enlargement of the original

One shape is a shrinkage of the original

Two shapes are similar if:

Both shapes are congruent

Two shapes are similar if:

Corresponding sides are proportional

3

54

6

8 10

Similar Shapes

What is the missing value?

12 feet

4 feet ?

6 feet

Similar Dimensions

16 inche

s

12 inches

Original Dimensions

S1

S2

New Dimensions

(S1 x S2)Scale Factor

(New to Original)

to

to

to

to

to

Challenge

What are the lengths of the two isosceles triangles that you did NOT construct?

?

?

?

?

3 Similar Domes

Smallest dome height is 71 mm

Medium dome height is 115 mm

Large dome height is 184 mm

Rules

You may not share any information with other groups

YOU MUST SHOW ALL WORK

Everyone in your group should be able to explain

If you finish early…

Please take you dome apart carefully

Read the stickers on the bags so you know how many parts go in each bag.

Smallest Triangle

Show your work

Blue is 47 mm, Yellow is 42 mm

? mm71 mm

75 mmsm blsm ht md ht

md bl=115 mm

Smallest Triangle

115 ÷ 71 ≈ 1.62 = scale factor for medium to small

75 ÷ 1.62 ≈ 46 mm = small blue

Medium Triangle

Show your work

Medium Triangle

Blue is 76 mm, Yellow is 68 mm

115 ÷ 71 ≈ 1.62 = scale factor for medium to small

47 x 1.62 ≈ 76 mm = medium blue

47 mm 71 mm 115 mm

? mmsm blsm ht md ht

md bl=

Largest Triangle

Show your work

Largest Triangle

Blue is 122 mm, Yellow is 108 mm

184 ÷ 71 ≈ 2.59 = scale factor for large to small

42 x 2.59 ≈ 109 mm = large yellow

42 mm 71 mm 184 mm

? mmsm Ylsm ht lg ht

lg Yl=

Today I learned…

Possible Topics Forces Geometric shapes Similar Figures Solving Proportions Scale Factor Geodesic Dome