Engineering mechanics and how to torque.ppt

A very good slideshow about physics

1. Engineering Mechanics Engineering Mechanics
1
FORCES
Batch : UG CE 2024 Section C
Lecture 3
Lecturer Atif Mehmood Khan
BE Civil Engineering - NUST
MS Structural Engineering – NUST
amehmood.nice.nust.edu.pk
0332-2777543
Office 120 SCEE (NICE)

2. 2
Chapter OutlineChapter Outline
Types of Forces
Analysis of Forces
2-Dimensional Force Systems
Equilibrium Conditions for a Rigid Body

3. 3
3.1 Types of Forces3.1 Types of Forces
Terminology:
Line of Action:
The straight line collinear with the force
vector

4. 4
3.1 Types of Forces3.1 Types of Forces
System of Forces:
Coplanar or 2 dimensional-
line of action of the forces lie in a
plane
3 dimensional (Not Included In the
course)!!!!!
Concurrent –
lines of action of the forces
intersect at a point
Parallel – lines of action are parallelParallel
Concurrent

5. 5
3.1 Types of Forces3.1 Types of Forces
External & Internal Forces:
External force – given object is subjected to
a force exerted by a different object
Internal force – one part of a given object is
subjected to a force by another part of the
same object
Requires clear definition of object in
consideration

6. 6
3.1 Types of Forces3.1 Types of Forces
Body & Surface Forces:
Body Force – force acting on the volume of
an object
E.g. gravitational force on an object
Surface Force – force acting on the surface
of an object
Can be exerted on an object by contact
with another object

7. 7
3.1 Types of Forces3.1 Types of Forces
Gravitational Forces:
The force exerted on an object by the earth’s
gravity
Gravitational force, or weight, of
an object can be represented by a vector

8. 8
3.1 Types of Forces3.1 Types of Forces
Gravitational Forces:
Magnitude of an object’s weight is related to
its mass by:
|W| = mg
where g = 9.81 m/s
2
in SI units
(acceleration due to gravity at sea level)

9. 9
3.1 Types of Forces3.1 Types of Forces
Contact Forces:
Forces those result from contacts between
objects
E.g. push on a wall  exert a contact force
Surface of hand exerts a force F on surface
of wall
Wall exerts an equal & opposite force F on
your hand (Newton’s 3
rd
Law)

10. 10
3.1 Types of Forces3.1 Types of Forces
Surfaces:
Consider 2 plane surfaces in contact:
Force exerted on right surface by left
surface F

11. 11
3.1 Types of Forces3.1 Types of Forces
Surfaces:
Resolve F into:
 Normal force N (normal to surface)
 Friction force f (parallel to surface)
Smooth surfaces – friction force
assumed to be negligible
Rough surfaces – friction force cannot
be neglected

12. 12
3.1 Types of Forces3.1 Types of Forces
If the contacting surfaces are curved:
Normal force & friction force are
perpendicular & parallel to the plane tangent
to the surface at their point of contact

13. 13
3.1 Types of Forces3.1 Types of Forces
Ropes & Cables:
Contact force can be exerted on an object
by attaching a rope or cable to the object &
pulling on it

14. 14
3.1 Types of Forces3.1 Types of Forces
Ropes & Cables:
Example:
 Cable exerts a force T on container
 Magnitude of T – tension in cable
 Line of action of T collinear with cable
 Cable exerts an equal & opposite force
T on crane

15. 15
3.1 Types of Forces3.1 Types of Forces
Assumption:
Cable is straight
Tension where cable is connected to
container = tension near crane
Approximately true if weight of cable <<
tension

16. 16
3.1 Types of Forces3.1 Types of Forces
Pulley – wheel with grooved rim that can be
used to change the direction of a rope or
cable

17. 17
3.1 Types of Forces3.1 Types of Forces
Assumption:
Tension is the same on both sides of a
pulley
True when pulley can turn freely & the
rope or cable is either stationary or turns
at a constant rate

18. 18
3.1 Types of Forces3.1 Types of Forces
Springs:
To exert contact forces in mechanical
devices
E.g. suspension of cars

19. 19
3.1 Types of Forces3.1 Types of Forces
Consider a coil spring of
unstretched length: L
o

When stretched: L  L
o
Pulls on the object to
which it is attached with
force F
Object exerts an equal &
opposite force F on spring

When compressed: L  L
o
Compressed too much 
buckle

20. 20
3.1 Types of Forces3.1 Types of Forces
Spring designed to exert a force by being
compressed is often provided with lateral
support to prevent buckling:
E.g. enclosing it in a cylindrical sleeve
Shock absorbers within coils in car
suspensions

21. 21
3.1 Types of Forces3.1 Types of Forces
Coil springs commonly used in mechanical
devices exert a force approximately
proportional to the change in length:
|F| = k|L  L
o|
(3.1)
Force is a linear function of change in
length: linear spring

22. 22
3.1 Types of Forces3.1 Types of Forces
Spring constant k
depends on
material & design
of spring
(units: force/length)
From Eq. (3.1) k = magnitude of the force
required to stretch or compress the spring a
unit of length

23. 23
3.1 Types of Forces3.1 Types of Forces
Example: L
o
= 1 m & k = 3000 N/m, L = 1.2 m
Magnitude of the pull spring exerts:
k|L  L
o| = 3000(1.2  1) = 600 N

24. 24
3.1 Types of Forces3.1 Types of Forces
Springs can be used to
model situations in which
forces depend on displacements
E.g. force necessary to bend
steel beam is a linear function
of displacement  if  is not
too large
|F| = k
 model force-deflection behaviour of
beam with a linear spring

25. 25
3.2 Analysis of Forces3.2 Analysis of Forces
Equilibrium:
Unchanging state – state of balance
Examples:
Objects are at rest (stationary) relative to the
building are in equilibrium
Objects within a train traveling at a constant
speed on a straight track, that are at rest
relative to the train, are in equilibrium
If the train begin increasing or decreasing its
speed, the person standing in the aisle would
no longer be in equilibrium & might lose his
balance

26. 26
3.2 Analysis of Forces3.2 Analysis of Forces
Definition: an object is in equilibrium only if
each point of the object has the same constant
velocity (steady translation)

27. 27
Assumption: objects in steady translation
relative to the earth can be assumed to be in
equilibrium
Vector sum of external forces acting on an
object in equilibrium = 0:
 F = 0 (3.2)
3.2 Analysis of Forces3.2 Analysis of Forces

28. 28
Free-Body Diagrams:
Serves to focus attention on the object of
interest & helps identify the external forces
acting on it
Also used in dynamics to study the motions of
objects
Drawing of an isolated or freed object & the
external forces acting on it
3.2 Analysis of Forces3.2 Analysis of Forces

29. 29
3.2 Analysis of Forces3.2 Analysis of Forces
Drawing a free-body diagram involves 3 steps:
1. Identify the object to isolate – the choice is
often dictated by particular forces you want
to determine
2. Draw a sketch of the object isolated from its
surroundings & show relevant dimensions &
angles
3. Draw & label vectors representing all the
external forces acting on the isolated object
– don’t forget to include the gravitational force

30. 30
3.2 Analysis of Forces3.2 Analysis of Forces
A coordinate system is necessary to express
the forces on the isolated object in terms of
components.

31. 31
3.2 Analysis of Forces3.2 Analysis of Forces
Equilibrium equation:
F = T
ABj – Wj = (T
AB  W)j = 0

Tension in cable AB is T
AB = W

32. 32
3.2 Analysis of Forces3.2 Analysis of Forces
Isolate upper block
External forces: W, T
CD & T
AB
Equilibrium equation:
F = T
CD
j – T
AB
j – Wj
= (T
CD – T
AB  W)j = 0
Since T
AB
= W, T
CD
= 2W

33. 33
3.2 Analysis of Forces3.2 Analysis of Forces
Alternatively, treat the 2
blocks & cable AB as a
single object:
Equilibrium equation:
F = T
CD
j – Wj – Wj
= (T
CD
– 2W)j = 0
Again, T
CD = 2W

34. 34
By orienting a coordinate system so that
external forces acting on an object lie in
the x-y plane:
F = (F
x)i – (F
y)j = 0
where F
x & F
y are the sums of the x & y
components of the forces
A vector is zero only if each of its components is
zero  Scalar equilibrium equations:
F
x
= 0, F
y
= 0 (3.3)
3.3 2-Dimensional Force Systems3.3 2-Dimensional Force Systems

35. 35
Fig. 3.19
Example 3.1 Using Equilibrium to Determine Example 3.1 Using Equilibrium to Determine
Forces on an ObjectForces on an Object
For display at an automobile show, the 1440-kg car
in Fig. 3.19 is held in place on the inclined surface
by the horizontal cable from A to B. Determine the
tension that the cable (& the fixture to which it is
connected at B) must support. The car’s brakes are
not engaged, so the tires exert only normal forces
on the inclined surface.

36. 36
Example 3.1 Using Equilibrium to Determine Example 3.1 Using Equilibrium to Determine
Forces on an ObjectForces on an Object
StrategyStrategy
Since the car is in equilibrium, we can draw its
free-body diagram & use Eqs. (3.3) to determine
the forces exerted on the car by the cable & use
the inclined surface.

37. 37
Example 3.1 Using Equilibrium to Determine Example 3.1 Using Equilibrium to Determine
Forces on an ObjectForces on an Object
SolutionSolution
Draw the Free-Body Diagram:
First, draw a free-body diagram of
the car isolated from its
surroundings.
Complete the free-body diagram
by showing the force exerted by
the car’s weight, the force T
exerted by the cable & the total
normal force N exerted on the
car’s tires by the inclined surface.

38. 38
SolutionSolution
Apply the Equilibrium Equations:
Introduce a coordinate system & resolve the normal
force into x & y components:
Example 3.1 Using Equilibrium to Determine Example 3.1 Using Equilibrium to Determine
Forces on an ObjectForces on an Object
F
x = T  N sin 20° = 0
F
y = N cos 20°  mg = 0

39. 39
Example 3.1 Using Equilibrium to Determine Example 3.1 Using Equilibrium to Determine
Forces on an ObjectForces on an Object
SolutionSolution
Resolve the 2nd equilibrium equation for N:
Then we solve the 1st equilibrium equation for
tension T:
T = N sin 20° = 5140 N
N 000,15
20cos
)sm 81.9)(kg 1440(
20cos
2





mg
N

40. 40
Example 3.1 Using Equilibrium to Determine Example 3.1 Using Equilibrium to Determine
Forces on an ObjectForces on an Object
Critical ThinkingCritical Thinking
How to identify the external forces that act on an
object?
Free-body diagram to isolate the car:

Remove cable AB, which exerts the
horizontal force T on the car at A that keeps
the car in place on the inclined surface

Remove the inclined surface, which exerts
forces on the car’s tires

The example stipulated that the surface
could exert only normal forces on the tires

41. 41
Example 3.1 Using Equilibrium to Determine Example 3.1 Using Equilibrium to Determine
Forces on an ObjectForces on an Object
Critical ThinkingCritical Thinking
Free-body diagram to isolate the car:

Finally remove the earth itself, which exerts
the car’s weight mg
Thinking about what must be eliminated in
order to isolate an object focuses your
attention on those things that may exert
external forces on it

42. 42
Example 3.2 Choosing a Free-Body Example 3.2 Choosing a Free-Body
DiagramDiagram
The automobile engine block in
Fig. 3.20 is suspended by a
system of cables. The mass of
the block is 200 kg. the system
is stationary. What are the
tensions in cables AB & AC?
Fig. 3.20

43. 43
Example 3.2 Choosing a Free-Body Example 3.2 Choosing a Free-Body
DiagramDiagram
StrategyStrategy
We need a free-body diagram that is subjected to
the forces we want to determine. By isolating part
of the cable system near point A where the cables
are joined, we can obtain a free-body diagram that
is subjected to the weight of the block & the
unknown tensions in cables AB & AC.

44. 44
Example 3.2 Choosing a Free-Body Example 3.2 Choosing a Free-Body
DiagramDiagram
SolutionSolution
Draw the Free-Body Diagram:
Isolate part of the cable system near point A:

W = mg = (200 kg)(9.81 m/s
2
) = 1962 N

45. 45
Example 3.2 Choosing a Free-Body Example 3.2 Choosing a Free-Body
DiagramDiagram
SolutionSolution
Apply the Equilibrium Equation:
Select the coordinate system shown.

46. 46
Example 3.2 Choosing a Free-Body Example 3.2 Choosing a Free-Body
DiagramDiagram
SolutionSolution
Apply the Equilibrium Equation:
Resolve cable tensions into x & y
components:
F
x
= T
AC
cos 45°  T
AB
cos 60° = 0
F
y = T
AC sin 45° + T
AB sin 60°  1962 N = 0
Solving these equations,
The tensions in the cables are
T
AB = 1436 N & T
AC = 1016 N.

47. 47
Example 3.2 Choosing a Free-Body Example 3.2 Choosing a Free-Body
DiagramDiagram
Critical ThinkingCritical Thinking
How to choose a free-body diagram that permits
you to determine particular unknown forces?
May be necessary to try several free-body
diagrams before finding one that provides the
information you need
Forces to be determined should appear as
external forces on the free-body diagram
Objective is to obtain a number of equilibrium
equations = number of unknown forces

48. 48
Example 3.3 Applying Equilibrium to a System Example 3.3 Applying Equilibrium to a System
of Pulleysof Pulleys
The mass of each pulley of the
system in Fig. 3.21 is m & the mass
of the suspended object A is m
A
.
Determine the force T necessary
for the system to be in equilibrium.
Fig. 3.21

49. 49
Example 3.3 Applying Equilibrium to a System Example 3.3 Applying Equilibrium to a System
of Pulleysof Pulleys
StrategyStrategy
By drawing free-body diagrams of the individual
pulleys & applying equilibrium, we can relate the
force T to the weights of the pulleys & the object A.
SolutionSolution
Draw a free-body diagram of pulley C to which the
force T is applied.
Notice that we assume the tension in the cable
supported by the pulley to equal on both sides.

50. 50
Example 3.3 Applying Equilibrium to a System Example 3.3 Applying Equilibrium to a System
of Pulleysof Pulleys
SolutionSolution
From equilibrium equation:
T
D
 T  T  mg = 0
The tension in the cable
supported by pulley D:
T
D = 2T + mg

51. 51
Example 3.3 Applying Equilibrium to a System Example 3.3 Applying Equilibrium to a System
of Pulleysof Pulleys
SolutionSolution
Draw the free-body diagram of
pulley B.
Equilibrium equation:
T + T +(2T + mg)  mg  m
A
g = 0
Solving, T = m
Ag/4.

52. 52
Example 3.3 Applying Equilibrium to a System Example 3.3 Applying Equilibrium to a System
of Pulleysof Pulleys
Critical ThinkingCritical Thinking
Notice the objects we isolate in Figs. (a) & (b)
include parts of the cable:
Weight of those parts of cable are external
forces acting on the free-body diagrams 
neglected in comparison to the weights of
pulleys & suspended object A

53. 53
Example 3.3 Applying Equilibrium to a System Example 3.3 Applying Equilibrium to a System
of Pulleysof Pulleys
Critical ThinkingCritical Thinking
Weights of objects are often neglected in
analyzing the forces acting on them:
Valid approximation for a given object if its
weight is small compared to the other forces
acting on it
But in real engineering application, this
assumption must be carefully evaluated