MechanicsHandoutR08_2013_part01

7/27/2019 MechanicsHandoutR08_2013_part01

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Departemen Teknik Mesin

Fakultas Teknik Universitas Indonesia

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INTRODUCTION

CHAPTER 1

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Definition

What is Design?Design is the transformation of concepts and ideasinto useful machinery.

A machine is a combination of mechanism and othercomponent that transforms, transmits, or usesenergy, load, or motion for specific purpose.(hamrock)

Fundamental decisions regarding

loading(=force), kinematics and the choice ofmaterials must be made during the design of amachine.


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Definition

What is Mechanics?Mechanics is the branch of physical science thatdeals with the response of bodies to the action offorces.

Three areas of mechanics:

1> The mechanics of rigid bodies

- statics (equilibrium of bodies)

- dynamics (accelerated motion of bodies)

2> The mechanics of deformable bodies (Mechanicsof Material)

3> The mechanics of fluids



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The Mechanics of Rigid Bodies

What is a rigid-body?

A rigid-body is a solid which does not deform when force areapplied (idealisation).

Statics is concern with bodies that are acted onbalanced force and hence are at rest or haveuniform motions. equilibrium bodies

Dynamics is concern with accelerated motion of

bodies


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Mechanics of deformable bodies

Is the branch of mechanics that deals withinternal force distribution and thedeformations developed in actual engineeringstructure and machine components when theyare subjected to systems of force.

Mechanics of Materials

Strength of Material



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Fluid Mechanics

Fluid mechanics is the branch of mechanicsthat deals with liquids and gases at rest or inmotion.

Fluid- Compressible- Incompressible

Out of this subject


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Example of Application

..



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Review: Force System>>


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Force System

Forces and Their Characteristics

The characteristics of a force are as follows:

Its magnitude

The amount or size of the force

Its direction (orientation)

Orientation of the line segment used to represent the force

Its point of application

The point of contact between the two bodies. A straight line

extending through the point of application in the directionof the force is called its line of action.



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Principle of Transmissibility

The external effect of a force on a rigid body is the same for all

points of application of the force along its line of action.

PUSH PULL

Rigid Ring : Deformable Ring :


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Classification of Forces

With respect to the area over which they act :

2. Concentrated force

1. Distributed force



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Force system

a. Concurrent forces

The action lines of all forcesintersect at common point

b. Coplanar forces

All forces lie in the same plane

F1

F2

F3

Any number of forces treated as a group constitutea force system.

F1

F2

F3


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Force system

c. Parallel forcesThe action lines of the forces are parallel, but theorientation of the forces do not have to be same.

d. Collinear

The forces of a systemhave a common line of

action.

F

F



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Force system

Graphical method

The parallelogram law

F2R

F1O

F2

F1

F2

F1O

RR

The Triangle law


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Force system

Basic of analytical method

The cosine law

c2 = a2 + b2 - 2 ab cos

The sine law

a

b

c

=

=

sin

c

sin

b

sin

a



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Force system

Analytical method

Direction of Resultant

F1

F2

R

Magnitude of Resultant:

++= cosFF2FFR21

2

2

2

1 R

sinFsin

2 =

=

R

sinFsin

21


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Force systemExample :

F1=800 N

F2=500 N

450

300

Determine the magnitude of theresultant R and the angle between the horisontal axis andthe line of action of Resultant

5.1206R

45cos500.800.2500800R

cosFF2FFR

022

21

2

2

2

1

=

++=

++=

0

o121

04.17

5.1206

45sin500sin

R

sinFsin

=

=

=

= 30 + 17.04o = 47.04oF

1=800 N

F2=500 N

450

300

R



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Review: Moment System>>


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Moment System

Moment and their characteristics

The moment of a force about a point or axis is a measureof the tendency of the force to rotate a body about thatpoint or axis.

A moment has both magnitude and a direction vectorquantity

The magnitude of moment M as defined as the product ofthe magnitude of a force and the perpendicular distance dfrom the line of action of the force to the axis.

MO = MO= Fd

Point O = the moment center.



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Principle of Moment :

Varignon's Theorem

The moment M of the resultant R of a system offorce with respect to any axis or point is equalto the vector sum of the moment of theindividual forces of the system with respect tothe same axis or point.

R = F1 + F2 + + Fn

MO = RdR= F1d1 + F2d2+ + Fndn


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Application of Varignon's theorem

MR= R.d= R(h cos)

MA = A.a= A(h cos)

MB= B.b= B(h cos)

R cos= A cos+ B cos

MR= MA + MB

h

AR

B cos A cos

B

b

d

a

Ax

y

O



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Vector Representation of a moment

MO = r x F

MO = r x F = rFsin e

(0 180o)

rd F

d Fr1

23 1

r2

r3

r1sin 1 = r2sin 2 = r3sin 3 = d


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Position vector

rA = xA i + yA j + zA k

rB = xB i + yB j + zB k

rA = rB + rA/B

rA/B = rA - rB

rA/BrA

z

yx

F

rB



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Moment of a force about a point

If force F and r are expressed in Cartesian vector form:

F = Fx i + Fy j + Fz k

r = rx i + ry j + rz k

So the moment Mo about the origin of coordinate O :

MO = r x F

= (rx i + ry j + rz k) x (Fx i + Fy j + Fz k)

= (ry Fz - rz Fy )i + (rz Fx - rx Fz )j + (rx Fy - ry Fx ) k

= Mx i + My j + Mz k


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>>

yr

z

yx

F

MO

x

z

O

The moment Mo about the origin of coordinate O can also be

expressed in determinant form as :

MO = r x F = What is about two-dimensional case ?

zFyFxF

zryrxr

kji

222zMyMxM ++=oM



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Alternatively, Mo can be written as

MO = MO e

Where e = cos x i + cos yj + cos z k

o

xxcos MM=

o

yycos M

M=

ozzcos M

M=


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Moment of a force about a line (axis)

MOJ= M = (MO . en) en= [(r x F) . en] en= MOJ en

zF

yF

xF

zryrxr

kji

J

r

z

yx

F

MO

O

en

MOJ= MO . en = (r x F) . en = . en



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Moment of a force about a line (axis)

Or alternatively as :

MOJ= MO . en = (r x F) . en =

zFyFxF

zryrxr

nzenyenxe

J

r

z

yx

F

MO

O

en


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COUPLES

A couple is a system force whose resultant force iszero but whose resultant moment about a point isnot zero

MA = F1d = F2d

MA = rA/B x F1= F1d en

The characteristics of couples1. The magnitude

2. The sense (direction of rotation)3. The orientation (axis about which rotation isinduced)

en

rA

z

yx

F1F2

n

d



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COUPLES

Several

transformation of acouple can be madewithout changingany of external effectof the couple on thebody

dF

F

d

F F

2d0.5F 0.5F

d

F F

M = Fd


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COUPLES

Resolution of a force into a force and a couple

F

O

p

rd

F

FF O

p

F

O

p

M = Fd



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Moment systemExample :

A parcel is lifted by a fork lift truck. Determine themoment of the weight with respect to the point A atthe two border positions!

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MechanicsHandoutR08_2013_part01