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Method of Virtual Work
Contents 10 -  Introduction Work of a Force Work of a Couple Principle of Virtual Work Applications of the Principle of Virtual Work Real Machines.  Mechanical Efficiency Sample Problem 10.1 Sample Problem 10.2 Sample Problem 10.3 Work of a Force During a Finite Displacement Potential Energy Potential Energy and Equilibrium Stability and Equilibrium Sample Problems 10.4
Introduction 10 -  ,[object Object],[object Object],[object Object],[object Object]
Work of a Force 10 -  =  work of the force  corresponding to the displacement
Work of a Force 10 -  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Work of a Couple 10 -  ,[object Object],[object Object],[object Object]
Principle of Virtual Work 10 -  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Applications of the Principle of Virtual Work 10 -  ,[object Object],[object Object],[object Object]
Real Machines.  Mechanical Efficiency 10 -  ,[object Object],[object Object]
Sample Problem 10.1 10 -  Determine the magnitude of the couple  M  required to maintain the equilibrium of the mechanism. ,[object Object],[object Object]
Sample Problem 10.2 10 -  Determine the expressions for     and for the tension in the spring which correspond to the equilibrium position of the spring.  The unstretched length of the spring is  h  and the constant of the spring is k.  Neglect the weight of the mechanism. ,[object Object],[object Object]
Sample Problem 10.3 10 -  A hydraulic lift table consisting of two identical linkages and hydraulic cylinders is used to raise a 1000-kg crate.  Members  EDB  and  CG  are each of length 2 a  and member  AD  is pinned to the midpoint of  EDB .  Determine the force exerted by each cylinder in raising the crate for    = 60 o ,  a  = 0.70 m, and  L  = 3.20 m. ,[object Object],[object Object],[object Object],[object Object]
Sample Problem 10.3 10 -  ,[object Object],[object Object],[object Object],[object Object]
Work of a Force During a Finite Displacement 10 -  ,[object Object],[object Object],[object Object]
Work of a Force During a Finite Displacement 10 -  Work of a weight, Work of a spring,
Potential Energy 10 -  ,[object Object],The work is independent of path and depends only on  potential energy  of the body with respect to the  force of gravity ,[object Object],potential energy  of the body with respect to the  elastic force
Potential Energy 10 -  ,[object Object],[object Object]
Potential Energy and Equilibrium 10 -  ,[object Object],[object Object],[object Object],indicating two positions of equilibrium.
Stability of Equilibrium 10 -  Must examine higher order derivatives.
Sample Problem 10.4 10 -  Knowing that the spring  BC  is unstretched when    = 0, determine the position or positions of equilibrium and state whether the equilibrium is stable, unstable, or neutral. ,[object Object],[object Object],[object Object],[object Object],?
Sample Problem 10.4 10 -  ,[object Object],[object Object],[object Object]
Sample Problem 10.4 10 -  ,[object Object],at   = 0: unstable at   = 51.7 o : stable
Sample Problem 10.4 10 -  ,[object Object],at   = 0: unstable at   = 51.7 o : stable

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Chapter 8 principle of virtual work

  • 2. Contents 10 - Introduction Work of a Force Work of a Couple Principle of Virtual Work Applications of the Principle of Virtual Work Real Machines. Mechanical Efficiency Sample Problem 10.1 Sample Problem 10.2 Sample Problem 10.3 Work of a Force During a Finite Displacement Potential Energy Potential Energy and Equilibrium Stability and Equilibrium Sample Problems 10.4
  • 3.
  • 4. Work of a Force 10 - = work of the force corresponding to the displacement
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15. Work of a Force During a Finite Displacement 10 - Work of a weight, Work of a spring,
  • 16.
  • 17.
  • 18.
  • 19. Stability of Equilibrium 10 - Must examine higher order derivatives.
  • 20.
  • 21.
  • 22.
  • 23.