Strength in Structure
Rene’ Ehrhardt, Flickr
Created by Brian Domroes
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?

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
10
8
4
5
3
6
Similar Shapes

What is the missing value?
4 feet
12 feet
?
6 feet
Similar Dimensions
New Dimensions
Scale Factor
(New to Original)
(S1 x S2)
to
16
inches
to
S1
S2
12 inches
Original
Dimensions
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
Smallest Triangle
115 ÷ 71 ≈ 1.62 = scale factor for medium to small
75 ÷ 1.62 ≈ 46 mm = small blue
? mm
sm bl
71 mm sm ht

=
75 mm md bl
115 mm md ht
Blue is 47 mm, Yellow is 42 mm
Medium Triangle

Show your work
Medium Triangle
115 ÷ 71 ≈ 1.62 = scale factor for medium to small
47 x 1.62 ≈ 76 mm = medium blue
47 mm
71 mm

sm bl
sm ht
=
? mm md bl
115 mm md ht
Blue is 76 mm, Yellow is 68 mm
Largest Triangle

Show your work
Largest Triangle
184 ÷ 71 ≈ 2.59 = scale factor for large to small
42 x 2.59 ≈ 109 mm = large yellow
42 mm sm Yl
71 mm sm ht

=
? mm lg Yl
184 mm lg ht
Blue is 122 mm, Yellow is 108 mm
Today I learned…

Possible Topics

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Forces
Geometric shapes
Similar Figures
Solving Proportions
Scale Factor
Geodesic Dome