1 sistem gaya

MEKANIKA TEKNIK JURUSAN TEKNIK INDUSTRI - FTI

Universitas Islam Sultan Agung

Pengajar : A. Syakhroni, ST, M.Eng

Apa itu Mekanika?Cabang ilmu fisika yang berbicara tentangkeadaan diam atau geraknya benda-bendayang mengalami kerja atau aksi gaya

Mechanics

Rigid Bodies(Things that do not change shape)

Deformable Bodies(Things that do change shape) Fluids

Statics Dynamics Incompressible Compressible

Apa saja yang dipelajari?• Sistem Gaya• Momen dan Kopel• Keseimbangan partikel• Keseimbangan benda tegar• Diagram gaya normal, diagram gaya geser, dandiagram momen

• Konsep tegangan• Momen inersia dan momen polar• Teori kegagalan statis

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 ?

SISTEM GAYA

Proses Manufaktur ‐ A.SNI 1

SISTEM GAYA SPACE (3D)

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

f1+f2

• 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

f1

f2

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

B

B

C

C

QPR

BPQQPR

cos2222

• Law of cosines,

• Law of sines,

A

C

R

B

Q

A sinsinsin

• Vector addition is commutative,

PQQP

• Vector subtraction

Sample Problem

The two forces act on a bolt at

A. Determine their resultant.

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.

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

( ) ( ) ( )( ) °−+=−+=

155cosN60N402N60N40cos222

222 BPQQPR

N73.97=R

From the Law of Sines,

AA

RQBA

RB

QA

+°=°=

°=

=

=

2004.15

N73.97N60155sin

sinsin

sinsin

α °= 04.35α

ADDITION OF SEVERAL VECTORS

• Step 3 is to find the magnitude

and angle of the resultant vector.

• 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.

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

x

y

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

= tan-1(3.49/16.82) = 11.7°

Sample Problem

Four forces act on bolt A as shown.

Determine the resultant of the force

on the bolt.

SOLUTION:

• Resolve each force into rectangular

components.

• Calculate the magnitude and direction

of the resultant.

• Determine the components of the

resultant by adding the corresponding

force components.

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

Sample Problem (cont’)

1.199+=xR 3.14+=yR

9.256.96100

0.1100110

2.754.2780

0.759.129150

4

3

2

1

−+

−

+−

++

−−

F

F

F

F

compycompxmagforce

r

r

r

r

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

• Calculate the magnitude and direction.

°=== 1.4N1199N314tan αα

..

RR

x

y°= 1.4α

N6.199sin

N3.14==R

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 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

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

30°

x

y

F = 80 N

TERIMA KASIH!

Proses Manufaktur - A.SNI 1