1 Sistem Gaya
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Transcript of 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