1. Forces, Moment, Equilibrium and Trusses
Week
Day
Date
Test
Topics 5
Tuesday
08/03/2011
Quiz No.1
Forces and momnet 6
15/03/2011
Quiz No. 2
Equilibrium 7
27/03/2011
Mid-Exam I
Forces, Moment, Equilibrium and Trusses

2. Equilibrium
Of a Rigid Body

3. 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.

4. Part A

5. Conditions for Rigid-Body Equilibrium

6. 2D Supports

7. 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.

11. Rocker

12. Smooth Surface

13. Pinned or Hinged

14. Fixed

15. Modeling

16. Modeling

17. 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.

18. Free Body Diagrams

19. 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.

20. 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.

21. Part B

22. 2D Equilibrium Scalar Equations

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

24. 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.

25. 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.

26. Example 1
Determine the reactions at the supports.

27. Example 2
Determine the reactions at the supports.

28. Example 3
Determine the reactions at the supports.

29. 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

30. 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

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

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