chapter 11 outline equilibrium and elasticity conditions for equilibrium center of gravity and...
TRANSCRIPT
Chapter 11 OutlineEquilibrium and Elasticity
• Conditions for equilibrium
• Center of gravity and stability
• Stress and strain• Elastic moduli
• Elasticity and plasticity
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
Equilibrium Example
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.
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)
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.
Tension
• When forces pull on an object in opposite directions, it is in tension.
• Young’s modulus, , describes tension.
Tensile Stress Example
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.
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.
Shear Stress and Strain
• When the forces act tangentially to opposite sides, we have shear.
• The shear modulus, , describes shear stress and strain.
Elastic Moduli
Shear Stress Example
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.
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