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

1. Devil physicsThe baddest class on campusIB PhysicsPre-IB Physics

2. Lsn 9-7: FractureLsn 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)