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Mastering Equilibrium of Rigid Bodies

This lecture focuses on the equilibrium of rigid bodies, covering equilibrium equations, free body diagrams, and different supports for rigid objects. Learn about special cases like two- and three-force members and the importance of drawing accurate free body diagrams. Practice problems include MatLab group exercises and chapter problems, preparing you for the upcoming quiz. Enhance your understanding of Newton’s second law in relation to rigid body motion and the concept of equilibrium. Dive into examples demonstrating equilibrium of rigid bodies in various scenarios.

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Mastering Equilibrium of Rigid Bodies

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  1. ME 221 StaticsLecture #11Sections 5.1 – 5.5 Lecture 11

  2. Homework #4 • Due Today Lecture 11

  3. Homework #5 • Chapter 9 problem: • 43 • Chapter 5 problems • 11, 20, 56 & 69 • Due Monday, June 21 • MatLab Group Problems • 5.22, 5.37 & 5.58 • Due Monday, June 21 Lecture 11

  4. Quiz #5 Wednesday, June 16 Lecture 11

  5. Chapter 5Equilibrium of Rigid Bodies Lecture 11

  6. Equilibrium of Rigid Bodies • Equilibrium equations • Free body diagrams • Modeling supports Lecture 11

  7. Equilibrium of Rigid Bodies • Newton’s second law states that if there is a net force acting on a body, then this will cause motion of the rigid body. • If there is no motion, then the object is said to be in equilibrium. Lecture 11

  8. Equilibrium Equations When the force system is replaced by a resultant force and moment that are zero, the rigid body is in equilibrium. The moment equation is new and differentiates particle from rigid body equilibrium. Lecture 11

  9. Supports for Rigid Bodies If a rigid object is subjected to some set of forces but does not move, then its motion could be restrained by a normal force exerted by the ground, a wall or from fixing the object with some support. Examples of supports: • rollers • smooth surfaces • rockers • cables • links • fixed • clamps • slots • collars Lecture 11

  10. Support Reactions • If the support prevents translation in a given direction, then a force is developed on the member in that direction. Likewise, if a rotation is prevented, then a couple moment is exerted on the member. • See Figures 5.3, 5.9 and 5.10 (supports for rigid bodies subjected to 2-D and 3-D force systems) Lecture 11

  11. Free Body Diagram • Draw the body separate from all other bodies (including ground). • Draw the magnitudes and directions of all external forces acting on the body. • Include: applied loads, reactions due to supports, and the weight of the object. • No need to scale arrow size • Include necessary dimensions of the body • Dimensions are needed for summing moments • Draw the positive sense of the coordinate system used to write out equilibrium equations Lecture 11

  12. Importance of FBD • The FBD is at least half of an equilibrium problem. Lecture 11

  13. Special Cases • Equilibrium of Rigid Bodies • - 2D & 3D • Two- and Three-Force Members • Special Supports Lecture 11

  14. F2 F3 F1 A B F6 Let: FA and F4 F5 A B FB Two- and Three-Force Members Two-Force Members When the member is not subjected to a couple and the forces are applied only at two points, the member is said to be two-force member. These forces will maintain equilibrium if: (FA and FB must be collinear) Lecture 11

  15. F2 F3 F2 O F3 F1 F1 Two- and Three-Force Members Three-Force Members If the member is subjected to three coplanar forces, then it is necessary that the forces are either concurrent or parallel if the member is to be in equilibrium.  Lecture 11

  16. Note: • It should be noted that single bearing, single pin and single hinge supports can support both forces and couples. Most often, however, these supports are used in conjunction with other bearings, pins or hinges to hold the body in equilibrium. In this case, the force reaction at the support may be adequate. Lecture 11

  17. Chapter 5 Equilibrium Examples Lecture 11

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