Transcript MEKANIKA TEKNIK TI PENDAHULUAN KULIAH I – ITS

KULIAH I
MEKANIKA TEKNIK TI
PENDAHULUAN
OLEH:
ALIEF WIKARTA, ST
JURUSAN TEKNIK MESIN, FTI – ITS
SURABAYA, 2007
Apa itu Mekanika?
Cabang ilmu fisika yang berbicara tentang
keadaan diam atau geraknya benda-benda
yang mengalami kerja atau aksi gaya
Mechanics
Rigid Bodies
(Things that do not change shape)
Statics
Dynamics
Deformable Bodies
(Things that do change shape)
Fluids
Incompressible
Compressible
Buku apa yang dipakai?
• R. C. Hibbeler, Engineering Mechanics, 7th - 10th
Edition, Person Prentice-Hall
• F. P. Beer and E. R. Johnston Jr., Vector
Mechanics for Engineers: Statics, SI Metric
Edition, Mcgraw-hill, 3rd Edition
• R. C. Hibbeler, Mechanics of Material, 3th
Edition, Person Prentice-Hall
• dll
Bagaimana evaluasinya ?
• Tugas-Kuis : 25 %
• UTS
: 30 %
• UAS
: 45 %
Tidak mentolerir segala bentuk kecurangan
Tapi tetap boleh cross check
Penjelasan TUGAS
• Dikerjakan pada kertas A4
• Tulis nama dan NRP di sebelah kanan atas,
serta tanggal dan tugas ke berapa
• Silahkan mengerjakan soal apa saja yang
berkaitan dengan materi yang disampaikan
• Silahkan mengerjakan berapa pun soal yang
sanggup anda selesaikan
• Soal-soal harus dari buku yang disepakati
• Mencantumkan judul buku, pengarang, dan
nomer soal yang dikerjakan, plus halaman buku
Apa saja yang dipelajari?
• Keseimbangan partikel
• Keseimbangan benda tegar
• Diagram gaya normal, diagram gaya
geser, dan diagram momen
• Konsep tegangan
• Momen inersia dan momen polar
• Teori kegagalan statis
Apa pentingnya mekanika (statik) /
keseimbangan ?
Apa perbedaan partikel dan benda tegar?
• Particle: A very small amount of matter which
may be assumed to occupy a single point in
space.
• Rigid body: A combination of a large number
of particles occupying fixed position with
respect to each other.
Apa perbedaan Partikel dan Benda Tegar ?
Partikel:
Mempunyai suatu
massa namun
ukurannya dapat
diabaikan, sehingga
geometri benda tidak
akan terlibat dalam
analisis masalah
Benda Tegar:
Kombinasi sejumlah
partikel yang mana
semua partikel
berada pada suatu
jarak tetap terhadap
satu dengan yang lain
Contoh Partikel
Contoh Benda Tegar
Review Sistem Satuan
• Four fundamental physical quantities. Length, Time, Mass, Force.
• We will work with two unit systems in static’s: SI & US Customary.
Bagaimana konversi dari SI ke US atau sebaliknya ?
Apa yang harus dilakukan supaya
Mekanika Teknik menjadi mudah ?
Banyak dan sering menyelesaikan soal-soal
Prosedur mengerjakan soal:
1. Baca soal dengan cermat
2. Buat free body diagram dan tabulasikan data soal
3. Tuliskan prinsip dasar / persamaan yang relevan dengan
soal
4. Selesaikan persamaan sepraktis mungkin sehingga didapat
hasil yang signifikan dan jangan lupa disertai sistem satuan
5. Pelajari jawaban dengan akal sehat, masuk akal atau tidak
6. Jika ada waktu, coba pikirkan cara lain untuk menyelesaikan
soal tersebut.
THE WHAT, WHY AND HOW OF A
FREE BODY DIAGRAM (FBD)
Free Body Diagrams are one of the most important things for
you to know how to draw and use.
What ? - It is a drawing that shows
all external forces acting on the
particle.
Why ? - It helps you write the
equations of equilibrium used to
solve for the unknowns (usually
forces or angles).
How ?
1. Imagine the particle to be isolated or cut free from its
surroundings.
2. Show all the forces that act on the particle.
Active forces: They want to move the particle.
Reactive forces: They tend to resist the motion.
3. Identify each force and show all known magnitudes
and directions. Show all unknown magnitudes and /
or directions as variables .
A
Note : Engine mass = 250 Kg
FBD at A
Fundamental Principles
• The parallelogram law for the addition of forces: Two
forces acting on a particle can be replaced by a single
force, called resultant, obtained by drawing the diagonal
of the parallelogram which has sides equal to the given
forces
f1+f2
f2
f1
• Parallelogram Law
Fundamental Principles (cont’)
• The principle of transmissibility: A force acting at a point
of a rigid body can be replaced by a force of the the same
magnitude and same direction, but acting on at a different
point on the line of action
f2
f1
f1 and f2 are equivalent if their
magnitudes are the same and the
object is rigid.
• Principle of Transmissibility
APPLICATION OF VECTOR
ADDITION
There are four
concurrent cable forces
acting on the bracket.
How do you determine
the resultant force acting
on the bracket ?
Addition of Vectors
• Trapezoid rule for vector addition
• Triangle rule for vector addition
C
B
C
B
• Law of cosines,
R 2  P 2  Q 2  2 PQ cos B
  
R  PQ
• Law of sines,
sin A sin B sin C


Q
R
A
• Vector addition is commutative,
   
PQ  Q P
• Vector subtraction
Sample Problem
SOLUTION:
• Trigonometric solution - use the triangle
rule for vector addition in conjunction
with the law of cosines and law of sines
to find the resultant.
The two forces act on a bolt at
A. Determine their resultant.
Sample Problem (cont’)
• Trigonometric solution - Apply the triangle rule.
From the Law of Cosines,
R 2  P 2  Q 2  2 PQ cos B
 40N 2  60N 2  240N 60N  cos155
R  97.73N
From the Law of Sines,
sin A sin B

Q
R
sin A  sin B
Q
R
 sin 155
A  15.04
  20  A
  35.04
60N
97.73N
ADDITION OF SEVERAL VECTORS
• Step 1 is to resolve each force
into its components
• Step 2 is to add all the x
components together and add all
the y components together. These
two totals become the resultant
vector.
• Step 3 is to find the magnitude
and angle of the resultant vector.
Example of this
process,
You can also represent a 2-D vector with a
magnitude and angle.
EXAMPLE
Given: Three concurrent forces
acting on a bracket.
Find: The magnitude and
angle of the resultant
force.
Plan:
a) Resolve the forces in their x-y components.
b) Add the respective components to get the resultant vector.
c) Find magnitude and angle from the resultant components.
EXAMPLE (continued)
F1 = { 15 sin 40° i + 15 cos 40° j } kN
= { 9.642 i + 11.49 j } kN
F2 = { -(12/13)26 i + (5/13)26 j } kN
= { -24 i + 10 j } kN
F3 = { 36 cos 30° i – 36 sin 30° j } kN
= { 31.18 i – 18 j } kN
EXAMPLE (continued)
Summing up all the i and j components respectively, we get,
FR = { (9.642 – 24 + 31.18) i + (11.49 + 10 – 18) j } kN
= { 16.82 i + 3.49 j } kN
y
FR
FR = ((16.82)2 + (3.49)2)1/2 = 17.2 kN
 = tan-1(3.49/16.82) = 11.7°

x
Sample Problem
SOLUTION:
• Resolve each force into rectangular
components.
• Determine the components of the
resultant by adding the corresponding
force components.
Four forces act on bolt A as shown.
Determine the resultant of the force
on the bolt.
• Calculate the magnitude and direction
of the resultant.
Sample Problem (cont’)
SOLUTION:
• Resolve each force into rectangular components.
force mag
x  comp
y  comp

 129.9
 75.0
F1 150

 27.4
 75.2
F2
80

 110.0
F3 110
0

 96.6
 25.9
F4 100
Rx  199.1 R y  14.3
• Determine the components of the resultant by
adding the corresponding force components.
• Calculate the magnitude and direction.
Ry 14.3 N
tan  

  4.1   4.1
Rx 199.1 N
14.3 N
R
199.6 N
sin 
READING QUIZ
1. The subject of mechanics deals with what happens to a body
when ______ is / are applied to it.
A) magnetic field
B) heat
D) neutrons
E) lasers
C) forces
2. ________________ still remains the basis of most of today’s
engineering sciences.
A) Newtonian Mechanics
B) Relativistic Mechanics
C) Euclidean Mechanics
C) Greek Mechanics
READING QUIZ
3. Which one of the following is a scalar quantity?
A) Force B) Position C) Mass D) Velocity
4. For vector addition you have to use ______ law.
A) Newton’s Second
B) the arithmetic
C) Pascal’s
D) the parallelogram
CONCEPT QUIZ
5. Can you resolve a 2-D vector along two directions, which
are not at 90° to each other?
A) Yes, but not uniquely.
B) No.
C) Yes, uniquely.
6. Can you resolve a 2-D vector along three directions (say
at 0, 60, and 120°)?
A) Yes, but not uniquely.
B) No.
C) Yes, uniquely.
ATTENTION QUIZ
7. Resolve F along x and y axes and write it in
vector form. F = { ___________ } N
y
A) 80 cos (30°) i - 80 sin (30°) j
x
B) 80 sin (30°) i + 80 cos (30°) j
C) 80 sin (30°) i - 80 cos (30°) j
30°
F = 80 N
D) 80 cos (30°) i + 80 sin (30°) j
8. Determine the magnitude of the resultant (F1 + F2)
force in N when F1 = { 10 i + 20 j } N and F2 =
{ 20 i + 20 j } N .
A) 30 N
B) 40 N
D) 60 N
E) 70 N
C) 50 N