1. Equilibrium
Of a Rigid Body

2. 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.

3. Part A

4. Conditions for Rigid-Body Equilibrium

5. 2D Supports

6. Support Reactions
General Rule: If a support prevents the translation of a body in a given direction, then a force is developed on the body in that direction. Likewise, if rotation is prevented a couple moment is exerted on the body.

10. Rocker

11. Smooth Surface

12. Pinned or Hinged

13. Fixed

17. Modeling

18. Modeling

19. Procedure for Drawing a Free-Body Diagram
Select co-ordinate axes.
Draw outlined shape isolated or cut “free” from its constraints and connections.
Show all forces and moments acting on the body. Include applied loadings and reactions.
Identify each loading and give dimensions. Label forces and moments with proper magnitudes and directions. Label unknowns.

20. Free Body Diagrams

21. Important Points
No equilibrium problem should be solved without first drawing the appropriate F.B.D.
If a support prevents translation in a direction, then it exerts a force on the body in that direction.
If a support prevents rotation of the body then it exerts a moment on the body.

22. Important Points
Couple moments are free vectors and can be placed anywhere on the body.
Forces can be placed anywhere along their line of action. They are sliding vectors.

23. Part B

24. 2D Equilibrium Scalar Equations

25. Procedure for Analysis
Free-Body Diagrams
Equations of Equilibrium

26. Equations of Equilibrium
Apply the moment equilibrium equation,  MO= 0. Take the point O to be the intersection of the lines of action of two unknown forces. This allows the direct solution for the third force.
Orient the x and y axes along lines that will provide the simplest resolution of the forces into their x and y components.

27. Direction of Forces
If results are a negative scalar for the magnitude the force acts in the opposite sense that you selected on the Free-Body Diagram.

28. Example 1
Determine the reactions at the supports.

29. Example 2
Determine the reactions at the supports.

30. Example 3
Determine the reactions at the supports.

31. Example 4
Three loads are applied to a beam as shown. Determine the reactions at A and B when P = 70kN.
27kN P
0.9m
1.8m
0.6m

32. Example 5
Three loads are applied to a beam as shown. Determine the reactions at A and B.
100 N
200 N
300 N
900 mm d
300 mm

33. Example 6
Distributed load applied to AB beam. Determine the support reactions.
250 kn/m
6 m
4 m
6 m

34. Example 7
A beam supports a distributed load as shown. Determine the equivalent concentrated load and the reactions at the supports

35. Example 8
Determine the horizontal and vertical components of reaction at the pin A and the tension developed in cable BC used to support the steel frame.

36. Example 9
A frame is subjected to two concentrated loads and non-uniformly distributed load as shown below Determine the reactions at supports A and D.

37. Example 10
For the beam shown below, determine the tension in cables AD and BD also find the reactions forces at pin C. Neglect the friction of the pulley at point D,

38. Example 11
Water dam subjected to the water pressure and soil pressure as shown below . Determine the total forces moments on the dam gate about hinge O.