Understanding Structures Through Geometric Domes

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

2. What forces are at work here? Bill Lim, Flickr Frank Kovalchek, Flickr

3. Tension and Compression

4. Tension and Compression • Tension • The force that results from things being pulled apart • Compression • The force that results from things being pushed together

5. Which is the most stable?

6. Increasing Stability

7. More Triangles!

8. Key Compression (push) Tension (pull) Why is the triangle so strong? • Balance of compression and tension • Angles are fixed

9. Compression/Tension Example

10. A system of triangles

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

12. Strut and Connector • Strut • Connector

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

14. Measure Your Isosceles Triangle • Measure in millimeters • Measure from the middle of struts

15. Geodesic Construction • Do you notice forces working together? • GENTLYpress on connectors to check

16. Key Compression (push) Tension (pull) Do You Remember?

17. How can you offset tension?

18. How do we anchor new triangles?

19. How do you keep these triangles in place?

20. And so on…

21. The tension at the base… is offset by the compressionat the joints A complete system of triangles

22. Why is there no place like dome? • Only manmade structure that gets proportionally stronger as it increases in size Martin Ujaki, Flickr

23. Why is there no place like dome? • Has the biggest enclosed volume to weight ratio for any manmade structure notfrancois, Flickr

24. Courtesy of Plantagon Why is there no place like dome? • Green • Very efficient with heating/cooling • Uses less materials • Withstands harsh weather

25. Do you see geometric shapes? andy_0306uk, Flickr  

26. Geometric Shapes • Equilateral Triangle • Isosceles Triangle • Acute Triangle • Hexagon • Regular Pentagon • Decagon (base of your dome)

27. Do you see similar shapes? andy_0306uk, Flickr  

28. Two shapes are similar if: • One shape is an enlargement of the original • One shape is a shrinkage of the original

29. Two shapes are similar if: • Both shapes are congruent

30. 10 8 4 5 3 6 Two shapes are similar if: • Corresponding sides are proportional

31. ? 4 feet 6 feet 12 feet Similar Shapes • What is the missing value?

32. 16 inches S1 S2 12 inches Original Dimensions Similar Dimensions

33. ? ? ? ? Challenge • What are the lengths of the two isosceles triangles that you did NOT construct?

34. 3 Similar Domes • Smallest dome height is 71 mm • Medium dome height is 115 mm • Large dome height is 184 mm

35. Rules • You may not share any information with other groups • YOU MUST SHOW ALL WORK • Everyone in your group should be able to explain

36. 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.

37. Smallest Triangle • Show your work

38. ? mm sm bl 75 mm md bl = 115 ÷ 71 ≈ 1.62 = scale factor for medium to small md ht 71 mm sm ht 115 mm 75 ÷ 1.62 ≈ 46 mm = small blue Smallest Triangle • Blue is 47 mm, Yellow is 42 mm

39. Medium Triangle • Show your work

40. 115 ÷ 71 ≈ 1.62 = scale factor for medium to small 47mm ? mm sm bl md bl = 71 mm 115 mm mdht sm ht 47 x 1.62 ≈ 76 mm = medium blue Medium Triangle • Blue is 76 mm, Yellow is 68 mm

41. Largest Triangle • Show your work

42. 184 ÷ 71 ≈ 2.59 = scale factor for large to small 42 mm ? mm lg Yl sm Yl = 71 mm lg ht sm ht 184 mm 42 x 2.59 ≈ 109 mm = large yellow Largest Triangle • Blue is 122 mm, Yellow is 108 mm

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