ch05 - Chapter5: EquilibriumofaRigidBody...

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Engineering Mechanics: Statics Chapter 5:  Equilibrium of a Rigid Body
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Chapter Objectives To develop the equations of equilibrium for a  rigid body. To introduce the concept of the free-body  diagram for a rigid body. To show how to solve rigid-body equilibrium  problems using the equations of equilibrium.
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Chapter Outline Conditions for Rigid Equilibrium Free-Body Diagrams Equations of Equilibrium Two and Three-Force Members Equilibrium in Three Dimensions Equations of Equilibrium Constraints for a Rigid Body
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5.1 Conditions for Rigid-Body  Equilibrium Consider rigid body fixed in the x,  y and z reference and is either at  rest or moves with reference at  constant velocity Two types of forces that act on it,  the resultant internal force and  the resultant external force Resultant internal force  f i  is  caused by interactions with  adjacent particles
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5.1 Conditions for Rigid-Body  Equilibrium Resultant external force  F i   represents the effects of  gravitational, electrical, magnetic,  or contact forces between the i th   particle and adjacent bodies or  particles not included within the  body Particle in equilibrium, apply  Newton’s first law,    F i  +  f i  = 0
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5.1 Conditions for Rigid-Body  Equilibrium When equation of equilibrium is  applied to each of the other particles  of the body, similar equations will  result Adding all these equations  vectorially,    F i  + ∑ f i  = 0 Summation of internal forces = 0  since internal forces between  particles in the body occur in equal  but opposite collinear pairs  (Newton’s third law)
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5.1 Conditions for Rigid-Body  Equilibrium Only sum of external forces will  remain Let ∑ F i  = ∑ F , ∑ F  = 0 Consider moment of the forces  acting on the i th  particle about the  arbitrary point O By the equilibrium equation and  distributive law of vector cross  product, r i  X ( F i  +  f i ) =  r i  X  F i  +  r i  X  f i  = 0
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5.1 Conditions for Rigid-Body  Equilibrium Similar equations can be written for  other particles of the body Adding all these equations  vectorially, ∑r i  X  F i  +  ∑r i  X  f i  = 0 Second term = 0 since internal  forces occur in equal but opposite  collinear pairs Resultant moment of each pair of  forces about point O is zero Using notation  ∑M O  =  ∑r i  X  F i ,   ∑M O  = 0
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5.1 Conditions for Rigid-Body  Equilibrium Equations of Equilibrium for Rigid Body ∑F  = 0 ∑M O  = 0 A rigid body will remain in equilibrium  provided the sum of all the external forces  acting on the body = 0 and sum of moments 
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ch05 - Chapter5: EquilibriumofaRigidBody...

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