Force,moment of a force and couple

Definition of force,types of forces,law of forces,system of forces, moment of a force, couple,moment of a couple,types of moments,features of couple and principle of moments.

1. theory of structures Rajesh P V Carmel Polytechnic college

2. Forces & moments Rajesh P V Carmel Polytechnic college

3. Forces & moments Rajesh P V Carmel Polytechnic college, Alappuzha , Kerala, India, [email protected] [phone]

4. Ts i - 3013- contents... SPECIFIC OUTCOME MODULE – I 1.1.0 Understand Moment of a force 1.1.1 Identify the various types of forces 1.1.2 State the principle of moments CONTENT DETAILS MODULE – I Forces and Moments Definition of force –types of forces, Moment of force – types of moments – principle of moments (proof not required)

5. FORCE MATTER - The substance of which all the things are composed. BODY - A limited quantity of matter occupying a certain portion of the space. MASS - The quantity of matter contained in a body.

6. FORCE... Force is anything which changes or tends to change the state of rest or of uniform motion along a straight line. Force is the action of one body on any other body. Force is the product of mass (m) and acceleration (a) F = m x a Force is a vector quantity. Unit-Newton (N) , kN , kg m/s2, dyne( cgs unit), pound force etc. (PVC)

7. FORCE... Some examples of force are: Gravitational force, Electric force, Magnetic force, Nuclear force, Frictional force etc.

8. Types of forces... Contact force Non contact force

9. TYPEs OF FORCEs . CONTACT FORCES. Force which represent the result of physical contact between two objects that is one of the object exerts force on the other is called contact forces. Forces which act on a body either directly or through a medium are called contact forces. Eg : Stretching of a spring balance, kicking of football, etc.

10. Types of forces... NON CONTACT FORCE Forces which act through spaces without making direct contact with the body are called non-contact forces.

11. Elements ( specifications) of FORCE Magnitude. Direction. Point of application . (PVC)

12. PRINCIPLE OF TRANSMISSIBILITY External effect of a force is independent of its point of application. Or External effect of a force on a rigid body is the same for all points of application along its line of action.

13. RESOLUTION OF FORCE The process of splitting up the given force into a number of components , without changing its effect on the body is called resolution of a force. A force is, generally, resolved along two mutually perpendicular directions. Horizontal component , Fx =F cos θ Vertical component,Fy =F sin θ (PVC)

14. RESOLUTION OF FORCE RECTANGULAR COMPONENTS Horizontal component Fx = F cos θ Vertical component Fy = Fsin θ

15. RESULTANT of forces Resultant - It is a single force which has the same action or effect as a given system of forces.

16. RESULTANT

17. EQUILIBRANT Equilibrant- It is a single force which is equal in magnitude but opposite in direction to the resultant of a system of forces.

18. system of forces Parallel forces Non parallel forces Like parallel forces Unlike parallel forces Concurrent forces Non concurrent forces Collinear forces Non collinear forces Coplanar forces Non coplanar forces Coplanar concurrent forces Coplanar non concurrent forces Coplanar like parallel forces Coplanar unlike parallel forces Non coplanar concurrent forces Non coplanar non concurrent forces, etc.

19. Law of forces Triangle law of forces Parallelogram law of forces Polygon law of forces

20. Triangle law of forces If two forces are represented both in magnitude and direction by the adjacent sides of a triangle taken in order, then their resultant is represented by the third side of the triangle taken in the reverse order.

21. Parallelogram law of forces If two forces are represented both in magnitude and direction as the adjacent sides of a parallelogram drawn from a point, then the resultant is represented by the diagonal of the parallelogram drawn from the same point .

22. polygon law of forces If any number of forces, acting on a particle , be represented ,in magnitude and direction by the sides of a polygon ,taken in order, then the forces will be in equilibrium.

23. Moment of a force Moment of a force about a given point is the turning effect of the force about the point and is measured as the the product of that force and the perpendicular distance between the point and the line of action of the force. Moment of a force =force x the perpendicular distance between the point and the line of action of the force. = F x d Unit -Newton metre (Nm) . (PVC)

24. Moment of a force

25. TYPES OF MOMENTS Clockwise moment Anticlockwise moment      

26. TYPES OF MOMENTS CLOCKWISE MOMENT If force acting on a body has the tendency to rotate the body in clockwise direction the moment produced is known as clockwise moment these are taken as negative (-)      

27. TYPES OF MOMENTS ANTICLOCKWISE MOMENT If a force acting on a body has the tendency to rotate the body in anticlockwise direction, then the moment as produced is called anticlockwise moment its taken as positive  (+)         

28. principle of moments ( varignon’s theorem) The Moment of a force about any point is equal to the algebraic sum of the moments of its components about the same point. Or The algebraic sum of the moments of a system of unequal forces about any point in their plane is equal to the moment of their resultant about that point. (PVC)

29. couple Two equal and unlike parallel forces whose line of action are different constitute a couple. Unit - Newton metre (Nm), kNm , kNmm , etc. Effect of couple is to produce turning moment or rotation.

30. moment of a couple The product of one of the two forces forming the couple and the arm of the couple . The arm of the couple is the perpendicular distance between the lines of action of the forces. Unit - Newton metre (Nm), kNm , kNmm , etc (PVC)

31. moment of a couple Arm of the couple = LM Moment of the couple = Force x Arm of the couple = F x LM (PVC)

32. Torque Moment of the couple is called torque Unit -Newton metre (Nm), kNm , kNmm , etc (PVC)

33. Torque

34. MAIN CHARACTERISTICS OF COUPLE The algebraic sum of the forces, having the couple, is zero. The algebraic sum of moment of the forces, constituting couple, about any point is the same, and equal to the moment of couple itself. A couple can't be balanced by a single force, but can be balanced only by a couple, however of opposite sense. Any number of coplanar couples can be reduced to single couple, whose magnitude will be equal to algebraic sum of moments of all the couples.  

35. previous questions .. Define force What are the different types of forces? What are the system of forces? Define moment of a force? What are the different types of moments? Define couple? Define moment of a couple. State Varignon’s theorem ( State the principle of moments) What is the arm of the couple?

36. Additional questions .. Write the unit of 1.)force, 2.)moment of a force, 3.)couple 5.)moment of a couple and 6.)torque. State principle of transmissibility. What are the elements (specifications) of force? State the triangle law of forces. State the parallelogram law of forces. State the polygon law of forces. What is resolution of forces? Differentiate between resultant and equilibrant. Define couple? State Varignon’s theorem ( State the principle of moments) List the characteristics of couple?

37. References.. 1. R.S.Khurmi : Applied Mechanics & Strength of Materials; S. Chand Publishing 2. M.Chakrabroti : Strength of materials ; S.K Kataria &sons. 3. R.K.Rajput : Strength of Materials ; S. Chand Publishing 4. S.S.Bhavikatti : Strength of Materials ; Vikas Publishing House Pvt Ltd, 5.K.N.A.G.K. Manikanta : Theory of structures –I; Radiant Publishing House

38. Thank you