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2009+4-1+EquilibriumofRigidBody

2009+4-1+EquilibriumofRigidBody - Introduction to Solid...

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1 SJTU Introduction to Solid Mechanics -Vm211 Chapter 4 Equilibrium of A Rigid Body Chapter 4 Equilibrium of A Rigid Body SJTU Introduction to Solid Mechanics -Vm211 Objectives To develop the equation of equilibrium for a rigid body Chapter 4 Equilibrium of 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 To develop the concepts of static and kinetic friction with applications to equilibrium problems SJTU Introduction to Solid Mechanics -Vm211 4.1 Conditions for Equilibrium Chapter 4 Equilibrium of A Rigid Body Consider a rigid body, which is at a xyz reference frame and is either at rest or moves with a constant velocity. To develop the necessary and sufficient conditions required for equilibrium of a rigid body SJTU Introduction to Solid Mechanics -Vm211 4.1 Conditions for Equilibrium Establish a free-body diagram of the arbitrary i th particle in the body with a resultant internal force f i and a resultant external force F i from other bodies. Chapter 4 Equilibrium of A Rigid Body 0 x y z i F 1 F 2 F 3 F 4 SJTU Introduction to Solid Mechanics -Vm211 4.1 Conditions for Equilibrium Chapter 4 Equilibrium of A Rigid Body 0 x y z i Applying Newton’s first law F i + f i = 0 F i f i f i the resultant internal force, caused by interactions with adjacent paricles F i the resultant external r i SJTU Introduction to Solid Mechanics -Vm211 4.1 Conditions for Equilibrium Chapter 4 Equilibrium of A Rigid Body 0 x y z i Applying Newton’s first law F i + f i = 0 Σ F i + Σ f i = 0 → Σ F i = 0 → Σ F = 0 F i f i If all these equations are added together vectorially Similarly, about the arbitrary point 0 Σ r i × F i + Σ r i × f i = 0 → Σ r i × F i = 0 → Σ M o = 0 r i
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