chapter 11 outline equilibrium and elasticity conditions for equilibrium center of gravity and...

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Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and plasticity

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Page 1: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Chapter 11 OutlineEquilibrium and Elasticity

• Conditions for equilibrium

• Center of gravity and stability

• Stress and strain• Elastic moduli

• Elasticity and plasticity

Page 2: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Equilibrium

• If a body is not accelerating, we say that it is in equilibrium.

• If it is at rest, we have static equilibrium.

• Conditions for equilibrium:

• about any point

Page 3: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Equilibrium Example

Page 4: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Center of Gravity and Stability

• If the acceleration due to gravity is constant (good approximation on Earth) the center of gravity is the same as the center of mass.

• If the center of gravity is outside the area bounded by the supports the object will tip.

Page 5: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Stress and Strain

• Real objects are not perfectly rigid.• Forces can deform the objects in a number of ways (stretching,

squeezing, twisting…)

• Stress characterizes the strength of the forces causing the deformation.

• Measured in force per area, or pascals

• Strain describes the resulting deformation.• Generally a ratio of lengths, areas, or volumes (dimensionless)

Page 6: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Elastic Modulus

• For relatively small stress and strain, the two are often directly proportional. (Hooke’s law)

• This proportionality constant is the elastic modulus.

• This relationship is generally only valid over a limited range.

Page 7: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Tension

• When forces pull on an object in opposite directions, it is in tension.

• Young’s modulus, , describes tension.

Page 8: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Tensile Stress Example

Page 9: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Compression

• When forces push on an object in opposite directions, it is in compression.

• Young’s modulus, , also describes compression.

• For many materials, the value is the same.

Page 10: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Bulk Stress and Strain

• When the pressure is uniform, the we use bulk, or volume, stress and strain.

• The Bulk modulus, , describes bulk stress and strain.

Page 11: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Shear Stress and Strain

• When the forces act tangentially to opposite sides, we have shear.

• The shear modulus, , describes shear stress and strain.

Page 12: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Elastic Moduli

Page 13: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Shear Stress Example

Page 14: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Elasticity and Plasticity

• If the stress is too great, Hooke’s law no longer describes the situation well.

• Past the proportional limit, the behavior is no longer elastic.

• Plastic deformation follows.

• Finally, the material fractures.

Page 15: Chapter 11 Outline Equilibrium and Elasticity Conditions for equilibrium Center of gravity and stability Stress and strain Elastic moduli Elasticity and

Chapter 11 OutlineEquilibrium and Elasticity

• Conditions for equilibrium

• about any point

• Center of gravity and stability

• Stress and strain• Stress: Force/area

• Strain: Deformation

• Elastic moduli

• Elasticity and plasticity