1. Equilibrium of a Rigid Body Examples

2. Example Problem
Draw the free-body diagram of the plate.

3. Example Problem Rx1 Ry1 Rx2 Ry2 Rx3 Ry3
Does this free-body diagram help?
Rx1
Ry1
Rx2
Ry2
Rx3
Ry3

4. Example Problem
You have to consider one reaction force from the gusset plate. The components of this force are Rx and Ry. Rx Ry

5. Example Problem
Draw the free-body diagram of the weight. B A

6. Example Problem TB TA Determine the force in each supporting wire.
TA and TB are the forces inside the cables and equal to reaction forces at A and B.
W=50lb

7. Example Problem

8. Example Problem
Spanner wrench F

9. Example Problem
Set up the following problem: Length A= 5 ft, and length B =10 ft and angle α= 30o. Determine the angle β of the smooth incline in order to maintain equilibrium.

10. Example Problem
Use line-of-action to solve the problem

11. Example Problem

12. Class Problem
Set up the problem and how would you solve for the resisting force at pin A to maintain equilibrium.

13. Class Problem
Set up the problem and how would you solve for the resisting force at pin A to maintain equilibrium.

14. Class Problem

15. Example - Equilibrium
The tension force in AC is 28 kN, determine the the required values of tension in AB and AD so that the resultant force of the three forces applied at A is vertical. Determine the resultant force.

16. FBD - Example Free-body diagram: (Anything missing?)
Add the dimensions! RA
TAC
TAD
TAB

17. Example-Equilibrium
The vector AB is

18. Example-Equilibrium The unit vector in the AB direction is
The tension vector TAB is

19. Example-Equilibrium
The vector AD is

20. Example-Equilibrium The unit vector in the AD direction is
The tension vector TAD is

21. Example-Equilibrium
The vector AC is

22. Example-Equilibrium The unit vector in the AC direction is
The tension vector TAC is

23. Example-Equilibrium
The tension vector TAC= 28 kN is
The reaction at A

24. Example-Equilibrium Apply the equilibrium condition.
Combine the vectors

25. Example-Equilibrium Break the components of the forces:
Use (3) to solve for TAB

26. Example-Equilibrium
Plug into (1), solve for magnitude of TAD

27. Example-Equilibrium
Use the values to solve for RA