ENGINEERING MECHANICS SESSION-4 EQUILIBRIUM OF COPLANAR FORCES
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.
SESSION PLAN Time in Minutes Topic Blooms Taxonomy Level-1 05 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
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
FBD-Example
FBD-Example
Reactions at Various Types of Supports and Connections 1. Rollers F.B.D. Rc Frictionless Surface Single reaction force at 90 0 to supporting surface
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
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
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
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.
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.
Equilibrium equations: Fx = 0 Fy = 0
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
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.
Solution of relevant text book problems. Problem Set 2.3
Solution of relevant text book problems. Problem Set 2.3
Participative session-1 Quiz
Participative session-1 Quiz
Participative session-1 Quiz
Participative session-1 Quiz
Subtopic-2 Solution of relevant text book problems. Problem Set 2.3
Subtopic-2 Solution of relevant text book problems. Problem Set 2.3
Solution of relevant text book problems. Problem-7 Subtopic-2 Solution of relevant text book problems. Problem-7
Solution of relevant text book problems. Problem-7 Subtopic-2 Solution of relevant text book problems. Problem-7
Solution of relevant text book problems. Problem-7 Subtopic-2 Solution of relevant text book problems. Problem-7
Participative session-2 Practice-FBD Draw the fbd of all cylinders together and individual cylinders
Participative session-2 Practice-FBD
Participative session-2 Practice-FBD Draw the FBD of block & pulley
Participative session-2 Practice-problem-8
CONCLUSION Equilibrium of 2-force body Equilibrium of 3-force body Resultant Equilibrant Space diagram Free body diagram Equilibrium equations