Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.
-
Upload
ralph-green -
Category
Documents
-
view
217 -
download
0
Transcript of Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.
![Page 1: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/1.jpg)
Strength in Structure
Created by Brian Domroes
Rene’ Ehrhardt, Flickr
![Page 2: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/2.jpg)
What forces are at work here?
Bill Lim, Flickr
Frank Kovalchek, Flickr
![Page 3: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/3.jpg)
Tension and Compression
![Page 4: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/4.jpg)
Tension and Compression
Tension The force that results from things being
pulled apart
Compression The force that results from things being
pushed together
![Page 5: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/5.jpg)
Which is the most stable?
![Page 6: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/6.jpg)
Increasing Stability
![Page 7: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/7.jpg)
More Triangles!
![Page 8: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/8.jpg)
Why is the triangle so strong?
Balance of compression and tension Angles are fixed
Key
Compression (push)
Tension (pull)
![Page 9: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/9.jpg)
Compression/Tension Example
![Page 10: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/10.jpg)
A system of triangles
![Page 11: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/11.jpg)
Geodesic Construction Enough class materials for 10 domes Domes will be assembled in groups of 3
![Page 12: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/12.jpg)
Strut and Connector
Strut
Connector
![Page 13: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/13.jpg)
Geodesic Construction Appoint a leader in each group Leader gives group members roles
![Page 14: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/14.jpg)
Measure Your Isosceles Triangle
Measure in millimeters Measure from the middle of struts
![Page 15: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/15.jpg)
Geodesic Construction Do you notice forces working together? GENTLY press on connectors to check
![Page 16: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/16.jpg)
Do You Remember?
Key
Compression (push)
Tension (pull)
![Page 17: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/17.jpg)
How can you offset tension?
![Page 18: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/18.jpg)
How do we anchor new triangles?
![Page 19: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/19.jpg)
How do you keep these triangles in place?
![Page 20: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/20.jpg)
And so on…
![Page 21: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/21.jpg)
A complete system of triangles
The tension at the base…
is offset by the compression at the joints
![Page 22: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/22.jpg)
Why is there no place like dome?
Only manmade structure that gets proportionally stronger as it increases in size
Martin Ujaki, Flickr
![Page 23: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/23.jpg)
Why is there no place like dome?
Has the biggest enclosed volume to weight ratio for any manmade structure
notfrancois, Flickr
![Page 24: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/24.jpg)
Why is there no place like dome?
GreenVery efficient with heating/coolingUses less materialsWithstands harsh weather
Courtesy of Plantagon
![Page 25: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/25.jpg)
Do you see geometric shapes?
andy_0306uk, Flickr
![Page 26: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/26.jpg)
Geometric Shapes
Equilateral Triangle Isosceles Triangle Acute Triangle Hexagon Regular Pentagon Decagon (base of your dome)
![Page 27: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/27.jpg)
Do you see similar shapes?
andy_0306uk, Flickr
![Page 28: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/28.jpg)
Two shapes are similar if:
One shape is an enlargement of the original
One shape is a shrinkage of the original
![Page 29: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/29.jpg)
Two shapes are similar if:
Both shapes are congruent
![Page 30: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/30.jpg)
Two shapes are similar if:
Corresponding sides are proportional
3
54
6
8 10
![Page 31: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/31.jpg)
Similar Shapes
What is the missing value?
12 feet
4 feet ?
6 feet
![Page 32: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/32.jpg)
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
![Page 33: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/33.jpg)
Challenge
What are the lengths of the two isosceles triangles that you did NOT construct?
?
?
?
?
![Page 34: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/34.jpg)
3 Similar Domes
Smallest dome height is 71 mm
Medium dome height is 115 mm
Large dome height is 184 mm
![Page 35: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/35.jpg)
Rules
You may not share any information with other groups
YOU MUST SHOW ALL WORK
Everyone in your group should be able to explain
![Page 36: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/36.jpg)
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.
![Page 37: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/37.jpg)
Smallest Triangle
Show your work
![Page 38: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/38.jpg)
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
![Page 39: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/39.jpg)
Medium Triangle
Show your work
![Page 40: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/40.jpg)
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=
![Page 41: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/41.jpg)
Largest Triangle
Show your work
![Page 42: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/42.jpg)
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=
![Page 43: Strength in Structure Created by Brian Domroes Rene’ Ehrhardt, Flickr.](https://reader035.fdocuments.in/reader035/viewer/2022062803/56649cd65503460f9499d1a1/html5/thumbnails/43.jpg)
Today I learned…
Possible Topics Forces Geometric shapes Similar Figures Solving Proportions Scale Factor Geodesic Dome