1. Devil physics The baddest class on campus IB Physics Pre-IB Physics

2. Lsn 9-7: Fracture Lsn 9-8: Spanning A space: Arches and Domes

3. Objectives
Know the meaning of the terms ultimate tensile strength, ultimate compressive strength, and ultimate shear strength.
Apply given safety factors to determine a not to exceed force per unit area.
Explain how reinforced concrete and prestressed concrete are made.

4. Objectives
For a given situation, determine the unit area required to support a maximum allowable force with a given safety factor.
Describe how a post-and-lintel opening is made.
Explain why an arched opening can support more weight than a post-and-lintel opening.
Describe the relationship between an arch and a dome.

5. Ultimate Strength (F/A)
Ultimate strength is the maximum force per cross-sectional area that a material can withstand before breaking
Table 9-2
[Maximum] Tensile Strength
[Maximum] Compressive Strength
[Maximum] Shear Strength
Different values for each type of stress

6. Ultimate Strength (F/A)
Ultimate strength is F/A

7. Ultimate Strength (F/A)
Ultimate strength is F/A

8. Safety Factor
If the ultimate strength is the maximum a material can withstand, you want to design a structure so that the maximum anticipated load is something less than the maximum
We do this by applying a safety factor

9. Safety Factor
We do this by dividing the ultimate strength by the safety factor
This allows us to find maximum force for a given cross-sectional area
Or minimum area for a given force

10. Making Concrete Stronger
Concrete is extremely strong in compression, but weak in tension
Reinforced concrete – embedding iron rods to increase tensile and shear strength
Pre-stressed concrete – applying a tensile stress to iron rods or mesh when the concrete is poured around them giving the concrete a pre-set tensile load which allows them to withstand a higher compressive load

11. Arches and Domes
In a post and lintel entryway, all of the structure’s weight above the entryway is supported by sheer stress in the lintel and compressive stress in the posts.

12. Arches and Domes
Because an arch is at an angle to the weight, the normal force counteracting the weight will have x- and y-components FN

13. Arches and Domes
The x-component of the normal force is transmitted to the walls next to the archway.
The shear stress in both x- and y- directions are distributed over a wider cross-sectional area FN

14. Arches and Domes
Therefore, an arch can support a great deal more weight than a post and lintel made of the same material and same cross-sectional area. FN

15. Arches and Domes
Also, the greater the height-to-width ratio, the greater the supporting capacity because more weight is transferred to the walls and greater cross-sectional are to handle the shear stress.

16. Arches and Domes
A dome is an arch that is rotated 360º and provides the same support properties as an arch
Do the reading activity to gain better understanding and to appreciate the historical and architectural significance of arches and domes

17. Let’s do some homework problems

18. Objectives
Know the meaning of the terms ultimate tensile strength, ultimate compressive strength, and ultimate shear strength.
Apply given safety factors to determine a not to exceed force per unit area.
Explain how reinforced concrete and prestressed concrete are made.

19. Objectives
For a given situation, determine the unit area required to support a maximum allowable force with a given safety factor.
Describe how a post-and-lintel opening is made.
Explain why an arched opening can support more weight than a post-and-lintel opening.
Describe the relationship between an arch and a dome.

20. Questions?

21. Homework
#55-62 (#63 is for brilliant students only)