# Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.

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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 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?  Green Very efficient with heating/cooling Uses less materials Withstands 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 inches 12 inches Original Dimensions S1S1 S2S2 New Dimensions (S 1 x S 2 ) Scale Factor (New to Original) 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 ? mm 71 mm 75 mmsm bl sm 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 ? mm sm bl sm 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 ? mm sm Yl sm ht lg ht lg Yl =

Today I learned…  Possible Topics Forces Geometric shapes Similar Figures Solving Proportions Scale Factor Geodesic Dome

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