KULIAH I MEKANIKA TEKNIK TI PENDAHULUAN

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KULIAH I MEKANIKA TEKNIK TIPENDAHULUAN

• OLEH
• ALIEF WIKARTA, ST
• JURUSAN TEKNIK MESIN, FTI ITS
• SURABAYA, 2007

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Apa itu Mekanika?

• Cabang ilmu fisika yang berbicara tentang
  keadaan diam atau geraknya benda-benda yang
  mengalami kerja atau aksi gaya

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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

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Bagaimana evaluasinya ?

• Tugas-Kuis 25
• UTS 30
• UAS 45
• Tidak mentolerir segala bentuk kecurangan
• Tapi tetap boleh cross check

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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

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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

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Apa pentingnya mekanika (statik) / keseimbangan ?
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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.

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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

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Contoh Partikel
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Contoh Benda Tegar
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Review Sistem Satuan

• Four fundamental physical quantities. Length,
  Time, Mass, Force.
• We will work with two unit systems in statics
  SI US Customary.

Bagaimana konversi dari SI ke US atau sebaliknya ?
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Apa yang harus dilakukan supaya Mekanika Teknik
menjadi mudah ?

• Banyak dan sering menyelesaikan soal-soal

• Prosedur mengerjakan soal
• Baca soal dengan cermat
• Buat free body diagram dan tabulasikan data soal
• Tuliskan prinsip dasar / persamaan yang relevan
  dengan soal
• Selesaikan persamaan sepraktis mungkin sehingga
  didapat hasil yang signifikan dan jangan lupa
  disertai sistem satuan
• Pelajari jawaban dengan akal sehat, masuk akal
  atau tidak
• Jika ada waktu, coba pikirkan cara lain untuk
  menyelesaikan soal tersebut.

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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).
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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
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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

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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

f1 and f2 are equivalent if their magnitudes are
the same and the object is rigid.
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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 ?
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Addition of Vectors

• Law of cosines,

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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.
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Sample Problem (cont)

• Trigonometric solution - Apply the triangle
  rule.From the Law of Cosines,

From the Law of Sines,
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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.

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Example of this process,
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You can also represent a 2-D vector with a
magnitude and angle.
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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.
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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
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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
FR ((16.82)2 (3.49)2)1/2 17.2 kN ?
tan-1(3.49/16.82) 11.7
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Sample Problem

• SOLUTION
• Resolve each force into rectangular components.

• Determine the components of the resultant by
  adding the corresponding force components.

• Calculate the magnitude and direction of the
  resultant.

Four forces act on bolt A as shown. Determine
the resultant of the force on the bolt.
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Sample Problem (cont)

• SOLUTION
• Resolve each force into rectangular components.

• Determine the components of the resultant by
  adding the corresponding force components.

• Calculate the magnitude and direction.

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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 C)
forces D) neutrons E) lasers
2. ________________ still remains the basis of
most of todays engineering sciences. A)
Newtonian Mechanics B) Relativistic Mechanics
C) Euclidean Mechanics C) Greek Mechanics
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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) Newtons Second B) the arithmetic
C) Pascals D) the parallelogram
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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.

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ATTENTION QUIZ
7. Resolve F along x and y axes and write it in
vector form. F ___________ N A) 80 cos
(30) i - 80 sin (30) j B) 80 sin (30)
i 80 cos (30) j C) 80 sin (30) i -
80 cos (30) j 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 C) 50 N D)
60 N E) 70 N
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Terima Kasih