Equilibrium and Elasticity

1
CHAPTER-12

• Equilibrium and Elasticity

2
Ch 12-2 Equilibrium

• A body is said to be in equilibrium if
• i) Translational equilibrium
• Fnetdp/dt 0 pmvconstant vconstant
• ii) Rotational equilibrium
• ?net dl/dt 0 lI?0 ? constant
• Zero and Non-Zero constant values of v and ?
• 1) Static equilibrium
• v ?0 Fnet ?net0
• 2) Dynamical equilibrium
• v ??0 Fnet ?net0

3
Ch 12-3 Requirement of Static Equilibrium

• For static equilibrium of a rigid body
• i) ?Fext0
• ii) ??ext0
• iii) P?pi0

4
Ch 12-2 Center of Gravity

• Center of gravity (cog) of a body is a point
  where gravitational force Fg effectively acts on
  a body.
• For a constant value of g for all elements of
  body com and cog coincides

5
Sample Problem 12-1

• A uniform beam and a block is resting on two
  scales. What do the scales read?
• Draw FBD
• Solve for two conditions of static equilibriums
• 1) ?F0 and ??0
• ?FFlFr-Mg-mg0
• 2) Taking the moment about the point of action of
  Fl
• ??FrxL-mgx(L/2)-Mgx(L/4)0
• Fr-mg/2-Mg/40
• Frmg/2Mg/4
• FlFr-Mg-mg0
• Fl Mgmg- Fr

6
Ch 12-7 Elasticity

• A rigid body is said to be elastic if we can
  change its dimension by pulling, pushing,
  twisting, or compressing them
• Stress deforming force per unit area
• Strain fractional change in dimension
• Tensile stress associated with stretching
• Shearing Stress associated with a force
  surface area
• Hydraulic stress from a fluid on an immersed
  object to shrink its volume by an amount ?V

7
Ch 12-7 Elasticity

• Over linear (elastic range) Stressmodulus x
  strain
• For further increase in stress beyond yield
  strength Sy of the specimen, the specimen becomes
  permanently deformed
• For additional increase in stress beyond yield
  strenth Sy, the specimen eventually rupture at
  ultimate strengthSu

8
Ch 12-7 Elasticity

• Tension and Compression For simple tension or
  compression the stress is force F/area A (?to the
  direction of application of force). The strain is
  fractional change ?L/L in the length of specimen.
• The modulus of for tensile and compressive
  stresses is called the Young modulus E (F/A)/
  (?L/L)
• Shearing , the shearing stress force F/area A
  (to the direction of application of force). The
  strain is fractional change ?x/L in the length of
  specimen.Shear modulus G (F/A)/ (?x/L)
• Hydraulic Stress
• For Hydraulic Stress the stress is fluid pressure
  p (force F/area A ) The strain is fractional
  change in volume ?V/V.
• The modulus of for hydraulic stresses the Bulk
  modulus B p/(?V/V)