1. Equilibrium of a Rigid Body 5 Engineering Mechanics: Statics in SI Units, 12e Copyright © 2010 Pearson Education South Asia Pte Ltd

2. Chapter Outline Conditions for Rigid Equilibrium Equilibrium in two dimensions 1.Free-Body Diagrams 2.Equations of Equilibrium 3.Two and Three-Force Members Equilibrium in three dimensions 1.Free Body Diagrams 2.Equations of Equilibrium 3.Constraints and Statical Determinacy

3. Copyright © 2010 Pearson Education South Asia Pte Ltd 5.1 Conditions for Rigid-Body Equilibrium The equilibrium of a body is expressed as Consider summing moments about some other point, such as point A, we require

4. EQUILIBRIUM IN TWO DIMENSIONS Copyright © 2010 Pearson Education South Asia Pte Ltd

5. 5.2 Free Body Diagrams Procedure for Drawing a FBD 1. Draw Outlined Shape 2. Show All Forces and Couple Moments 3. Identify Each Loading and Give Dimensions

6. Copyright © 2010 Pearson Education South Asia Pte Ltd Example 5.1 Draw the free-body diagram of the uniform beam. The beam has a mass of 100kg.

7. Copyright © 2010 Pearson Education South Asia Pte Ltd 5.2 Free Body Diagrams Support Reactions If a support prevents the translation of a body in a given direction, then a force is developed on the body in that direction. If rotation is prevented, a couple moment is exerted on the body.

8. Copyright © 2010 Pearson Education South Asia Pte Ltd 5.2 Free Body Diagrams

9. Copyright © 2010 Pearson Education South Asia Pte Ltd 5.2 Free Body Diagrams

10. Copyright © 2010 Pearson Education South Asia Pte Ltd 5.2 Free Body Diagrams

11. Copyright © 2010 Pearson Education South Asia Pte Ltd 5.2 Free Body Diagrams Forces External and internal forces can act on a rigid body For FBD, internal forces act between particles which are contained within the boundary of the FBD, are not represented Particles outside this boundary exert external forces on the system

12. Copyright © 2010 Pearson Education South Asia Pte Ltd 5.2 Free Body Diagrams Weight and Center of Gravity Each particle has a specified weight System can be represented by a single resultant force, known as weight W of the body Location of the force application is known as the center of gravity

13. Example 5.4 Draw the free-body diagram of the unloaded platform that is suspended off the edge of the oil rig. The platform has a mass of 200 Kg. Copyright © 2010 Pearson Education South Asia Pte Ltd

14. 5.3 Equations of Equilibrium For equilibrium of a rigid body in 2D, ∑F x = 0; ∑F y = 0; ∑M O = 0 ∑F x and ∑F y represent sums of x and y components of all the forces ∑M O represents the sum of the couple moments and moments of the force components

15. Copyright © 2010 Pearson Education South Asia Pte Ltd Example 5.5 Determine the horizontal and vertical components of reaction on the beam caused by the pin at B and the rocker at A. Neglect the weight of the beam in the calculations.

16. Copyright © 2010 Pearson Education South Asia Pte Ltd Example 5.7 The member shown in the figure is pin-connected at A and rests against a smooth support at B. Determine the horizontal and vertical components of reaction at the pin A.

17. Copyright © 2010 Pearson Education South Asia Pte Ltd Example 5.9 Determine the horizontal and vertical components of reaction on the member at the pin A, and the normal reaction at the roller B in the figure.

18. Copyright © 2010 Pearson Education South Asia Pte Ltd Example 5.12 Determine the support reactions on the member in the figure. The collar at A is fixed to the member and can slide vertically along the vertical shaft.

19. Copyright © 2010 Pearson Education South Asia Pte Ltd 5.4 Two- and Three-Force Members Two-Force Members When forces are applied at only two points on a member, the member is called a two-force member Only force magnitude must be determined

20. Copyright © 2010 Pearson Education South Asia Pte Ltd 5.4 Two- and Three-Force Members Three-Force Members When subjected to three forces, the forces are concurrent or parallel

21. Copyright © 2010 Pearson Education South Asia Pte Ltd Example 5.13 The lever ABC is pin-supported at A and connected to a short link BD. If the weight of the members are negligible, determine the force of the pin on the lever at A.