Download - 1 Sistem Gaya
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MEKANIKA TEKNIK JURUSAN TEKNIK INDUSTRI - FTI
Universitas Islam Sultan Agung
Pengajar : A. Syakhroni, ST, M.Eng
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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
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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
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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 ?
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SISTEM GAYA
Proses Manufaktur ‐ A.SNI 1
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SISTEM GAYA SPACE (3D)
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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
f1
f2
f1+f2
• Parallelogram Law
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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
f2
f1 and f2 are equivalent if their magnitudes 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
on the bracket ?
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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
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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.
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• 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
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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.
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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
x
y
FR 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
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.
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Sample Problem (cont’)SOLUTION:• Resolve each force into rectangular components.
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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
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• 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
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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 today’s
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) Newton’s Second
B) the arithmetic
C) Pascal’s
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
30°
x
y
F = 80 N
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TERIMA KASIH!
Proses Manufaktur - A.SNI 1