TAILIEUCHUNG - Ebook Engineering mechanics - Statics and dynamics (12th edition): Part 2

(BQ) Part 2 book "Engineering mechanics - Statics and dynamics" has contents: Kinematics of a particle, force and acceleration, planar kinematics of a rigid body, planar kinetics of a rigid body - Force and acceleration, planar kinetics of a rigid body - Work and energy, planar kinetics of a rigid body - Impulse and momentum, three - Dimensional kinematics of a rigid body,.and other contents. | Virtual Work CHAPTER OBJECTIVES • To introduce the principle of virtual work and show how it applies to finding the equilibrium configuration of a system of pin-connected members. • To establish the potential-energy function and use the potentialenergy method to investigate the type of equilibrium or stability of a rigid body or system of pin-connected members. Definition of Work The principle of virtual work was proposed by the Swiss mathematician Jean Bernoulli in the eighteenth century. It provides an alternative method for solving problems involving the equilibrium of a particle, a rigid body, or a system of connected rigid bodies. Before we discuss this principle, however, we must first define the work produced by a force and by a couple moment. 11 564 CHAPTER 11 VIRTUAL WORK Work of a Force. A force does work when it undergoes a F u displacement in the direction of its line of action. Consider, for example, the force F in Fig. 11–1a that undergoes a differential displacement dr. If u is the angle between the force and the displacement, then the component of F in the direction of the displacement is F cos u. And so the work produced by F is F cos u dr (a) dU = F dr cos u Notice that this expression is also the product of the force F and the component of displacement in the direction of the force, dr cos u, Fig. 11–1b. If we use the definition of the dot product (Eq. 2–14) the work can also be written as F dr cos u u dr dU = F # dr (b) As the above equations indicate, work is a scalar, and like other scalar quantities, it has a magnitude that can either be positive or negative. In the SI system, the unit of work is a joule (J), which is the work produced by a 1-N force that displaces through a distance of 1 m in the direction of the force (1 J = 1 N # m). The unit of work in the FPS system is the foot-pound (ft # lb), which is the work produced by a 1-lb force that displaces through a distance of 1 ft in the direction of the force. The moment of a force .

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