strength in structure created by brian domroes rene’ ehrhardt, flickr
Post on 15-Jan-2016
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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 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
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