Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12...
Transcript of Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12...
![Page 1: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/1.jpg)
Chapter 12 Equilibrium and Elasticity
► 12-1 What Is Physics? ► 12-2 Equilibrium ► 12-3 The Requirements of Equilibrium ► 12-4 The Center of Gravity ► 12-5 Some Examples of Static Equilibrium ► 12-6 Indeterminate Structures ► 12-7 Elasticity
![Page 2: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/2.jpg)
12-1 What is Physics?
► Human buildings should be stable in spite of the gravitational force and wind forces on it, and a bridge should be stable in spite of the gravitational force pulling it downward and the repeated jolting it receives from cars and trucks.
► In this chapter we examine the two main aspects of stability: the equilibrium of the forces and torques acting on rigid objects and the elasticity of non-rigid objects, a property that governs how such objects can deform.
![Page 3: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/3.jpg)
12-2 Equilibrium
► Equilibrium: ( Force and torque are zero) ,
► Static equilibrium: ( constant = 0 )
![Page 4: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/4.jpg)
12-3 The Requirements of Equilibrium
► E
► Examples: with zero net External force and zero net external torque
![Page 5: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/5.jpg)
Coplanar problems:
where the location of the axis of the torque equation is arbitrary.
![Page 6: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/6.jpg)
12-4 The Center of Gravity
► Center of mass:
![Page 7: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/7.jpg)
► Center of gravity:
![Page 8: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/8.jpg)
![Page 9: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/9.jpg)
Example:
![Page 10: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/10.jpg)
![Page 11: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/11.jpg)
Example:
![Page 12: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/12.jpg)
![Page 13: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/13.jpg)
Example:
![Page 14: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/14.jpg)
![Page 15: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/15.jpg)
Example:
![Page 16: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/16.jpg)
![Page 17: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/17.jpg)
![Page 18: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/18.jpg)
Example:
![Page 19: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/19.jpg)
![Page 20: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/20.jpg)
Example:
![Page 21: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/21.jpg)
![Page 22: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/22.jpg)
Example:
![Page 23: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/23.jpg)
![Page 24: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/24.jpg)
![Page 25: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/25.jpg)
12-6 Indeterminate Structures
► For the problems of this chapter, we have only three independent equations at our disposal, usually two balance of forces equations and one balance of
torques equation about a given rotation axis. Thus, if a problem has more than three unknowns, we cannot solve it.
![Page 26: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/26.jpg)
► Consider an unsymmetrically loaded car. What are the forces-all different on the four tires?
► We can solve an equilibrium problem for a table with three legs but not for one with four legs. ► Problems like these, in which there are more unknowns
than equations, are called indeterminate.
► To solve such indeterminate equilibrium problems, we must supplement equilibrium equations with some knowledge of elasticity.
![Page 27: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/27.jpg)
12-7 Elasticity
![Page 28: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/28.jpg)
![Page 29: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/29.jpg)
Stress-Strain curve
![Page 30: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/30.jpg)
Elastic modulus
![Page 31: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/31.jpg)
Young’s Modulus: Elasticity in Length (E or Y)
![Page 32: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/32.jpg)
![Page 33: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/33.jpg)
Shear Modulus: Elasticity of Shape
![Page 34: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/34.jpg)
Bulk Modulus: Volume Elasticity
![Page 35: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/35.jpg)
Example:
![Page 36: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/36.jpg)
![Page 37: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/37.jpg)
Example:
![Page 38: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/38.jpg)
![Page 39: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/39.jpg)
![Page 40: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/40.jpg)
![Page 41: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/41.jpg)
Example:
![Page 42: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/42.jpg)
Example:
![Page 43: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/43.jpg)
Example:
![Page 44: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/44.jpg)
Example:
![Page 45: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/45.jpg)
Example:
![Page 46: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/46.jpg)
Example:
![Page 47: Chapter 12 Equilibrium and Elasticity - Sharifsharif.edu/~rahimitabar/pdfs/L12.pdf · Chapter 12 Equilibrium and Elasticity 12-1 What Is Physics? 12-2 Equilibrium 12-3 The Requirements](https://reader033.fdocuments.in/reader033/viewer/2022051011/5b4541e47f8b9a05708b84d1/html5/thumbnails/47.jpg)
Example: