1. ENGINEERING MECHANICS SESSION-4
EQUILIBRIUM OF COPLANAR FORCES

2. SESSION OUTCOMES
At the end of this session, Students will be able to :
Understand concept of equilibrium. 
Equilibrant
Space diagram
Free body diagram
Equilibrium equations
Solve relevant problems.

3. SESSION PLAN  Time in Minutes Topic Blooms Taxonomy Level-105
Introduction:
Recap of resultant of forces by different methods. 25
Sub-topic-1 (Lecture)
Introduction, equilibrant, Concept of equilibrium of coplanar concurrent two-force, three force & multi force system. (Analytical & Graphical):, theorem of three forces, lami’s theorem, equations of equilibrium (animation assisted). Solution of relevant text book problems.  15
Participative session
Quiz
Sub-topic-2 (Lecture)
Triangle law& polygon law of forces for condition of equilibrium. Free Body Diagram with Examples. (animation assisted). Solution of relevant text book problems. 20
Students will practice the procedure to use theorem of three forces.(animation assisted).
Conclusion
Session will be concluded by discussing equilibrium and importance of free body diagram.
95 Minutes Total Contact Session + 5 Minutes for Attendance and Transition activities = 100 minutes

4. Free body diagram
Free body diagram is the diagram obtained by removing all supports and replacing them by reactions. It consists of real forces and reactions

5. FBD-Example

6. FBD-Example

7. Reactions at Various Types of Supports and Connections
1. Rollers
 F.B.D.  Rc 
Frictionless
Surface
Single reaction force at to
supporting surface

8. 2. Cable & Short Link F.B.D.  T  Short Rope/ Short Link Cable
Single force following
direction of rope or link
 F.B.D. 
Short Rope/
Cable
Short Link

9. 3. Sliders Or Slot F.B.D. 90o   R Slider on Frictionless Pin in
Single force at 90o to the guide (direction assumed) R 
Slider on
Frictionless Rod
Frictionless Pin in
Slot

10. 4. Hinged Joints F.B.D. or  Fx  R Fy  Rough surface
Two components resolved
into x and y axis or
a single reaction of
unknown direction
Frictionless pin
or hinged joint
Rough surface 

11. EQUILIBRIUM
When two or more forces acting on a body in such a way that the body remains in a state of rest or of uniform motion (no acceleration) then the body is said to be in equilibrium.

12. A body is in equilibrium when the resultant of all forces acting on it is zero
A body is in equilibrium when the force polygon closes
A body is in equilibrium when the algebraic sum of forces in any two rectangular directions vanishes separately i.e., ∑Fx=0 and ∑Fy=0.

13. Equilibrium equations:
Fx = 0
Fy = 0

14. Equilibrium of A Two Force Body
Equilibrium of collinear forces:
Equilibrium law: Two forces can be in equilibrium only if they are equal in magnitude, opposite in direction and collinear in action. P

15. Equilibrium of three force body
Lami’s theorem
If three concurrent forces are acting on a body kept in an equilibrium, then each force is proportional to the sine of angle between the other two forces and the constant of proportionality is same.

16. Solution of relevant text book problems. Problem Set 2.3

17. Solution of relevant text book problems. Problem Set 2.3

18. Participative session-1 Quiz

19. Participative session-1 Quiz

20. Participative session-1 Quiz

21. Participative session-1 Quiz

22. Subtopic-2 Solution of relevant text book problems. Problem Set 2.3

23. Subtopic-2 Solution of relevant text book problems. Problem Set 2.3

24. Solution of relevant text book problems. Problem-7
Subtopic-2
Solution of relevant text book problems. Problem-7

25. Solution of relevant text book problems. Problem-7
Subtopic-2
Solution of relevant text book problems. Problem-7

26. Solution of relevant text book problems. Problem-7
Subtopic-2
Solution of relevant text book problems. Problem-7

27. Participative session-2 Practice-FBD
Draw the fbd of all cylinders together and individual cylinders

28. Participative session-2 Practice-FBD

29. Participative session-2 Practice-FBD
Draw the FBD of block & pulley

30. Participative session-2 Practice-problem-8

31. CONCLUSION Equilibrium of 2-force body Equilibrium of 3-force body
Resultant
Equilibrant
Space diagram
Free body diagram
Equilibrium equations