Chapter 8 principle 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

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