1.Mektek pendahuluan

MEKANIKA TEKNIKMEKANIKA TEKNIK PENDAHULUAN

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Apa itu Mekanika?Apa itu Mekanika?

C b il fi ik b biCabang ilmu fisika yang berbicara tentang keadaan diam atau geraknya benda-benda g yyang mengalami kerja atau aksi gaya

Mechanics

Rigid Bodies Deformable Bodies Fluidsg(Things that do not change shape) (Things that do change shape) Fluids

Statics Dynamics Incompressible Compressible2SUTRIMO

Buku apa yang dipakai?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 MetricMechanics for Engineers: Statics, SI Metric Edition, Mcgraw-hill, 3rd Edition

• R. C. Hibbeler, Mechanics of Material, 3th

Edition, Person Prentice-HallEdition, Person Prentice Hall • dll

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Bagaimana evaluasinya ?Bagaimana evaluasinya ?

• Tugas-Kuis : 30 %• UTS : 35 %• UTS : 35 %• UAS : 35 %

Tidak mentolerir segala bentuk kecuranganTidak mentolerir segala bentuk kecuranganTapi tetap boleh cross checkp p

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Apa saja yang dipelajari?Apa saja yang dipelajari?

• Keseimbangan partikel • Keseimbangan benda tegarKeseimbangan benda tegar• Diagram gaya normal, diagram gaya

d digeser, dan diagram momen• Konsep tegangano sep tega ga• 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?Apa perbedaan partikel dan benda tegar?

• Particle: A very small amount of matter which may be assumed to occupy a single point in y py g pspace.

• Rigid body: A combination of a large number• 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 ?Apa perbedaan Partikel dan Benda Tegar ?

Partikel: Mempunyai suatu

Benda Tegar:Kombinasi sejumlah p y

massa namun ukurannya dapat

jpartikel yang mana semua partikel y

diabaikan, sehingga geometri benda tidak

berada pada suatu jarak tetap terhadap

akan terlibat dalam analisis masalah

satu dengan yang lain

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Contoh PartikelContoh Partikel

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Contoh Benda TegarContoh Benda Tegar

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Review Sistem SatuanReview Sistem Satuan• Four fundamental physical quantities. Length, Time, Mass, Force.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 ? 11SUTRIMO

Apa yang harus dilakukan supaya Mekanika Teknik menjadi mudah ?

B k d i l ik l lBanyak dan sering menyelesaikan soal-soal

Prosedur mengerjakan soal:Prosedur mengerjakan soal:1. Baca soal dengan cermat2 B t f b d di d t b l ik d t l2. Buat free body diagram dan tabulasikan data soal3. Tuliskan prinsip dasar/persamaan yang relevan dengan soal

S4. Selesaikan persamaan sepraktis mungkin sehingga didapat hasil yang signifikan dan jangan lupa disertai sistem satuansatuan

5. Pelajari jawaban dengan akal sehat, masuk akal atau tidak6 Jika ada waktu coba pikirkan cara lain untuk menyelesaikan6. Jika ada waktu, coba pikirkan cara lain untuk menyelesaikan

soal tersebut. 12SUTRIMO

THE WHAT, WHY AND HOW OF A FREE BODY DIAGRAM (FBD)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 ll l f i hall 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 ?How ?1. Imagine the particle to be isolated or cut free from its

surroundings.g

2. Show all the forces that act on the particle.Active forces: They want to move the particleActive forces: They want to move the particle. Reactive forces: They tend to resist the motion.

3 Identify each force and show all known magnitudes3. Identify each force and show all known magnitudes and directions. Show all unknown magnitudes and / or directions as variables .

AA

FBD at A Note : Engine mass = 250 Kg14SUTRIMO

F d t l P i i lFundamental 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 diagonalforce, called resultant, obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces

f1+f2

f2

f1

f2

f1 • Parallelogram Law15SUTRIMO

F d l P i i l ( ’)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

f1f1

f1 and f2 are equivalent if their it d th d th • Principle of Transmissibilitymagnitudes are the same and the

object is rigid. Principle of Transmissibility

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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

h b k ?on the bracket ?

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Addition of Vectors• Trapezoid rule for vector addition

• Triangle rule for vector addition

L f iB

C

C

QPRBPQQPR

cos2222

• Law of cosines,

C QPR

• Law of sines,CBA sinsinsin

B AC

RB

QA sinsinsin

• Vector addition is commutative• Vector addition is commutative,

PQQP

• Vector subtraction18SUTRIMO

Sample ProblemSample Problem

SOLUTIONSOLUTION:

• Trigonometric solution - use the triangle rule for vector addition in conjunctionrule 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’)Sample Problem (cont )• Trigonometric solution - Apply the triangle rule.

From the Law of Cosines,

155N60N402N60N40cos222

222 BPQQPR 155cosN60N402N60N40 22

N73.97R

BA

sinsinFrom the Law of Sines,

RQBA

RQ

sinsin

A

04.15N73.97

N60155sin

A 20 04.35

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ADDITION OF SEVERAL VECTORS

• Step 1 is to resolve each force S ep s o eso ve e c o ceinto its components

• Step 2 is to add all the x• Step 2 is to add all the x components together and add all the y components together. Thesethe y components together. These two totals become the resultant vector.

• Step 3 is to find the magnitude and angle of the resultant vector.g

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Example of thisExample 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 gforce.

Plan:

a) Resolve the forces in their x-y components.

b) Add the respective components to get the resultant vector.) p p g

c) Find magnitude and angle from the resultant components.

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EXAMPLE (continued)

F { 15 i 40° i 15 40° j } kNF1 = { 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= { -24 i + 10 j } kNF3 = { 36 cos 30° i – 36 sin 30° j } kN

= { 31.18 i – 18 j } kN25SUTRIMO

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= { 16.82 i + 3.49 j } kN

yFRFR = ((16.82)2 + (3.49)2)1/2 = 17.2 kN

x = tan-1(3.49/16.82) = 11.7°

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Sample ProblemSample Problem

SOLUTION:

R l h f i t t l• Resolve each force into rectangular components.

• Determine the components of the• 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

• Calculate the magnitude and direction of the resultant.

Determine the resultant of the force on the bolt.

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Sample Problem (cont’)p ( )SOLUTION:• Resolve each force into rectangular components.

275427800.759.1291501

FF

compycompxmagforce

9.256.961000.11001102.754.2780

4

3

2

FFF

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

1.199xR 3.14yR9.56.96004

14N314tan .Ry

• Calculate the magnitude and direction.

14

adding the corresponding force components.

1.4N1199

tan .Rx

N6.199i

N3.14

R

1.4

sin28

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