BT204 Engineering Mechanics RGPV 1st year

1st year student engg mechanics

1. Engineering Mechanics BT204 1

2. Engineering Mechanics 2

3. Mechanics The branch of science which deals with the forces and their effects on the bodies on which they act is called mechanics Applied Mechanics Applied mechanics also known as engineering mechanics is the branch of engineering which deals with the laws of mechanics as applied to the solution of engineering problems. Application of applied mechanics Some of the important practical applications of the principals and laws of mechanics are given below: 1. The motion of vehicles such as trains, buses etc. 2. The design of building and forces on columns and walls. 3

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5. Rigid Body A rigid body is an idealized solid body in which the distance between any two points does not change, regardless of the forces applied. In reality, no body is perfectly rigid, but for engineering analysis many solids are assumed rigid to simplify calculations. Examples: A steel rod considered rigid while analyzing the motion of a mechanism. A ladder leaning against a wall in statics problems. Deformable Body (Deformable/Elastic Body) A deformable body is one in which the distance between some points changes when external forces are applied, i.e., it undergoes deformation (change in shape or size). Examples: A spring stretching under load. A rubber band elongated when pulled. A beam bending under applied load. 5

6. 1. Statics:  It is the branch which deals with the forces and their effects on an object or a body at rest. Example: 1. A ladder resting against a wall. The forces of weight, wall reaction, and floor reaction are analyzed to ensure equilibrium. 2. A bridge structure under load. The applied loads and support reactions are studied while the bridge remains stationary. 2. Dynamics: It is the branch which deals with the forces and their effects on the bodies which are in motion. Example: 1. A car accelerating on a road. The applied engine force, friction, and air resistance determine its motion. 2. A projectile fired from a cannon. Its motion is analyzed under the influence of gravity and air resistance. 6

7. Types of Dynamics Dynamics is also divided into two branches and these are: ( i ) Kinetics : (study of motion considering forces.) Kinetics is defined as the branch of dynamics which deals with the bodies that are in motion due to the application of forces . A bullet fired from a gun. Motion is analyzed considering the force of expanding gases. (ii) Kinematics: ( study of motion without considering forces.) It is defined as the branch of dynamics which deals with the bodies that are in motion, without knowing the reference of forces responsible for the motion in the body . A train moving at constant speed of 60 km/h. Only speed, distance, and time are studied. 7

8. SI System of units 8

9. Fundamental units of S.I system 9

10. Principal S.I. units 10

11. S.I. Prefixes 11

12. UNIT CONVERSION 12

13. Concept of Force 13

14. Force A force may be defined as an external agency that tends to change the state of rest or the state of uniform motion of a body on which it acts. In mechanics, a force is treated as a vector quantity because it possesses both magnitude and direction.  It is calculated using  Newton's Second Law of Motion ,  F = ma (Force = mass × acceleration), and measured in the SI unit  Newtons (N). 14

15. Concept of Force 15

16. The necessity of force: To move a stationary object i.e. to move a body which is at rest. To change the direction of the motion of an object To change the magnitude of the velocity (speed) of the motion of an object To change the shape of an object. 16

17. Characteristics of Force It has four characteristics Magnitude Direction Point on which it acts Line of action 17

18. Line of Action of force Th e li n e o f action of a f o r c e f i s a g eom e tr i c representation of how the force is applied. It is the line through the point at which the force is applied in the same direction as the vector f→. 18

19. 19 To completely specify a force, the following characteristics must be stated: Magnitude – The numerical value of the force expressed in suitable units ( newton in SI). Point of Application – The exact point on the body where the force is applied. Direction – The orientation of the force in space, usually defined with respect to a reference axis or plane. Line of Action – The direction of a force is the direction, along a straight line through its point of application in which the force tends to move a body when it is applied. This line is called line of action of force.

20. Force applied with a spanner on a nut Magnitude: 40 N Direction: tangential to spanner end Point of application: at the hand grip of spanner Line of action: tangential line at that point Pulling a cart with a rope Magnitude: 200 N Direction: 30° above horizontal Point of application: handle of cart Line of action: along the rope 20

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22. System of Forces When t w o a r e or mo r e f o r ces acts act o n a body, they are called system of forces. Coplanar Force system – 2D and Non – Coplanar system – 3D Concurrent and Non – Concurrent Force system Collinear and Non- Collinear Force system Parallel – Like and Unlike 22

23. System of Forces 23

24. Classification of Force Systems (A) Coplanar Force System All forces act in a single plane. Collinear : Forces act along the same line. Example: Tug of war, forces in a straight rope. Concurrent : Lines of action of forces meet at one point. Example: Cables pulling a ring at a common joint. Parallel : All forces are parallel but do not meet at a point. Example: Loads on a simply supported beam. CL- Engg. Mechanics, DoCL- SPP, DDU, Nadiad 24 (B) Non-Coplanar Force System Forces act in different planes (3D space). Concurrent : Lines of action meet at one point in space. Example: Strings tied to a single knot pulling in different directions in 3D. Parallel : Forces are parallel but not in the same plane. Example: Multiple vertical loads on different levels of a frame.

25. Coplanar Force System – 2D 25

26. Non- Coplanar Force System – 3D 26

27. Concurrent and Non – Concurrent Force system Concurrent Forces Non- Concurrent Forces 27

28. Collinear and Non- Collinear Force system Collinear Forces Non – Collinear Forces 28

29. Parallel Force system 29

30. 30 Resultant force Resultant force is the single force that has the same effect on an object as all the different forces acting on it body. Eg . Consider three forces acting on a box: 80 N and 100 N to the right, and 30 N to the left. The resultant force  (R)  is: R=80  N+100 N−30 N= 150 N  This means replacing all three forces with a single force of 150 N to the right will have the same effect on the box.

31. 31 METHOD FOR FINDING RESULTANT FORCE 1. Algebraic method (collinear forces): If forces act along the same line, simply add them with sign convention. Example: 20  N right, 15  N left → Resultant = 20−15=5  N to the right. 2. Parallelogram method (two forces at an angle): Draw the two forces as adjacent sides of a parallelogram. The diagonal represents the resultant. 3 . Triangle method (two or more forces): Place forces head-to-tail in sequence. Draw the closing side from start to end → that is the resultant. 4. Polygon method (several forces): Extension of triangle method for many forces. Join forces head-to-tail as vectors. Resultant = line from starting point to end point. 5. Component method (general case, preferred in calculations): Resolve each force into horizontal (x ) and vertical (y ) components .

32. 32 PARALLELOGRAM LAW OF FORCES It states, "If two forces, acting simultaneously on a particle, be represented in magnitude and direction by the two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by the diagonal of the parallelogram, which passes through their point of intersection .” If two concurrent forces  P  and  Q  are acting at an angle  θ, Draw them as adjacent sides of a parallelogram from a common point . At point  O  draw two vectors representing the two forces. OA represents  P. OB represents  Q. Complete the parallelogram by drawing a line through A parallel to OB and a line through B parallel to OA. Their intersection is C. The diagonal OC is the geometrical resultant  R . It represents the single force equal in effect to   P  and   Q  acting together.

33. CL- Engg. Mechanics, DoCL- SPP, DDU, Nadiad 33