The document provides an introduction to engineering mechanics (statics) for a class. It discusses what mechanics is, different types of bodies, and units of measurement. It also reviews important concepts like free body diagrams and vector addition methods. Sample problems are presented to demonstrate resolving forces into components and determining the resultant force magnitude and direction. Quizzes are included to test understanding of key topics like scalars, vector addition laws, and resolving vectors.
In Engineering Mechanics the static problems are classified as two types: Concurrent and Non-Concurrent force systems. The presentation discloses a methodology to solve the problems of Concurrent and Non-Concurrent force systems.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
In Engineering Mechanics the static problems are classified as two types: Concurrent and Non-Concurrent force systems. The presentation discloses a methodology to solve the problems of Concurrent and Non-Concurrent force systems.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Solution manual for introduction to finite element analysis and design nam ...Salehkhanovic
Solution Manual for Introduction to Finite Element Analysis and Design
Author(s) : Nam-Ho Kim and Bhavani V. Sankar
This solution manual include all problems (Chapters 0 to 8) of textbook.
The use of Calculus is very important in every aspects of engineering.
The use of Differential equation is very much applied in the concept of Elastic beams.
The force is defined as the action of a body about another body and it is a vector quantity. The vector quantity, the force, has four characteristic: magnitude, direction, sense and point of application.
Kesetimbangan kimia merupakan keadaan reaksi bolak-balik dimana laju reaksi reaktan dan produk sama dan konsentrasi keduanya tetap.
Kesetimbangan kimia hanya terjadi pada reaksi bolak-balik dimana laju terbentuknya reaktan sama dengan laju terbentuknya produk.
Keadaan Kesetimbangan kimia adalah suatu keadaaan dimana konsentrasi seluruh zat tidak lagi mengalami perubahan, sebab zat-zat diruas kanan terbentuk dan terurai kembali dengan kecepatan yang sama.
Keadaan kesetimbangan ini bersifat dinamis, artinya reaksi terus berlangsung dalam dua arah dengan kecepatan yang sama.
Pada keadaan kesetimbangan tidak mengalami perubahan secara mikrokopis (perubahan yang dapat diamati atau diukur)
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Solution manual for introduction to finite element analysis and design nam ...Salehkhanovic
Solution Manual for Introduction to Finite Element Analysis and Design
Author(s) : Nam-Ho Kim and Bhavani V. Sankar
This solution manual include all problems (Chapters 0 to 8) of textbook.
The use of Calculus is very important in every aspects of engineering.
The use of Differential equation is very much applied in the concept of Elastic beams.
The force is defined as the action of a body about another body and it is a vector quantity. The vector quantity, the force, has four characteristic: magnitude, direction, sense and point of application.
Kesetimbangan kimia merupakan keadaan reaksi bolak-balik dimana laju reaksi reaktan dan produk sama dan konsentrasi keduanya tetap.
Kesetimbangan kimia hanya terjadi pada reaksi bolak-balik dimana laju terbentuknya reaktan sama dengan laju terbentuknya produk.
Keadaan Kesetimbangan kimia adalah suatu keadaaan dimana konsentrasi seluruh zat tidak lagi mengalami perubahan, sebab zat-zat diruas kanan terbentuk dan terurai kembali dengan kecepatan yang sama.
Keadaan kesetimbangan ini bersifat dinamis, artinya reaksi terus berlangsung dalam dua arah dengan kecepatan yang sama.
Pada keadaan kesetimbangan tidak mengalami perubahan secara mikrokopis (perubahan yang dapat diamati atau diukur)
Introduction;
Resultant of Two Forces;
Vectors;
Addition of Vectors;
Resultant of Several Concurrent Forces;
Sample Problem ;
Rectangular Components of a Force; Unit Vectors;
Addition of Forces by Summing Components ;
Equilibrium of a Particle;
Free-Body Diagrams;
Rectangular Components in Space;
Sample Problem;
Concept of Particles and Free Body Diagram
Why FBD diagrams are used during the analysis?
It enables us to check the body for equilibrium.
By considering the FBD, we can clearly define the exact system of forces which we must use in the investigation of any constrained body.
It helps to identify the forces and ensures the correct use of equation of equilibrium.
Note:
Reactions on two contacting bodies are equal and opposite on account of Newton's III Law.
The type of reactions produced depends on the nature of contact between the bodies as well as that of the surfaces.
Sometimes it is necessary to consider internal free bodies such that the contacting surfaces lie within the given body. Such a free body needs to be analyzed when the body is deformable.
Physical Meaning of Equilibrium and its essence in Structural Application
The state of rest (in appropriate inertial frame) of a system particles and/or rigid bodies is called equilibrium.
A particle is said to be in equilibrium if it is in rest. A rigid body is said to be in equilibrium if the constituent particles contained on it are in equilibrium.
The rigid body in equilibrium means the body is stable.
Equilibrium means net force and net moment acting on the body is zero.
Essence in Structural Engineering
To find the unknown parameters such as reaction forces and moments induced by the body.
In Structural Engineering, the major problem is to identify the external reactions, internal forces and stresses on the body which are produced during the loading. For the identification of such parameters, we should assume a body in equilibrium. This assumption provides the necessary equations to determine the unknown parameters.
For the equilibrium body, the number of unknown parameters must be equal to number of available parameters provided by static equilibrium condition.
1. KULIAH I
MEKANIKA TEKNIK TI
PENDAHULUAN
OLEH:
ALIEF WIKARTA, ST
JURUSAN TEKNIK MESIN, FTI – ITS
SURABAYA, 2007
2. Apa itu Mekanika?
Cabang ilmu fisika yang berbicara tentang
keadaan diam atau geraknya benda-benda
yang mengalami kerja atau aksi gaya
Mechanics
Rigid Bodies Deformable Bodies
Fluids
(Things that do not change shape) (Things that do change shape)
Statics Dynamics Incompressible Compressible
3. Buku apa yang dipakai?
• R. C. Hibbeler, Engineering Mechanics, 7 th - 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
4. Bagaimana evaluasinya ?
• Tugas-Kuis : 25 %
• UTS : 30 %
• UAS : 45 %
Tidak mentolerir segala bentuk kecurangan
Tapi tetap boleh cross check
5. 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
6. 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
8. 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.
9. Apa perbedaan Partikel dan Benda Tegar ?
Partikel: Benda Tegar:
Mempunyai suatu Kombinasi sejumlah
massa namun partikel yang mana
ukurannya dapat semua partikel
diabaikan, sehingga berada pada suatu
geometri benda tidak jarak tetap terhadap
akan terlibat dalam satu dengan yang lain
analisis masalah
12. 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 ?
13. Apa yang harus dilakukan supaya
Mekanika Teknik menjadi mudah ?
Banyak dan sering menyelesaikan soal-soal
Prosedur mengerjakan soal:
1. Baca soal dengan cermat
2. Buat free body diagram dan tabulasikan data soal
3. Tuliskan prinsip dasar / persamaan yang relevan dengan soal
4. Selesaikan persamaan sepraktis mungkin sehingga didapat
hasil yang signifikan dan jangan lupa disertai sistem satuan
5. Pelajari jawaban dengan akal sehat, masuk akal atau tidak
6. Jika ada waktu, coba pikirkan cara lain untuk menyelesaikan
soal tersebut.
14. 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).
15. 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
16. 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
f2
f1 • Parallelogram Law
17. 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
f1
f1 and f2 are equivalent if their • Principle of Transmissibility
magnitudes are the same and the
object is rigid.
18. 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 ?
19. Addition of Vectors
• Trapezoid rule for vector addition
• Triangle rule for vector addition
• Law of cosines,
C
B R 2 = P 2 + Q 2 − 2 PQ cos B
C R = P+Q
• Law of sines,
sin A sin B sin C
= =
B Q R A
• Vector addition is commutative,
P+Q = Q+ P
• Vector subtraction
20. 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.
21. Sample Problem (cont’)
• Trigonometric solution - Apply the triangle rule.
From the Law of Cosines,
R 2 = P 2 + Q 2 − 2 PQ cos B
= ( 40 N ) 2 + ( 60 N ) 2 − 2( 40 N )( 60 N ) cos155°
R = 97.73N
From the Law of Sines,
sin A sin B
=
Q R
Q
sin A = sin B
R
60 N
= sin 155°
97.73N
A = 15.04°
α = 20° + A
α = 35.04°
22. 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.
24. You can also represent a 2-D vector with a
magnitude and angle.
25. 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.
26. 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
27. 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
y
FR
FR = ((16.82)2 + (3.49)2)1/2 = 17.2 kN
φ = tan-1(3.49/16.82) = 11.7° φ
x
28. 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
Four forces act on bolt A as shown. of the resultant.
Determine the resultant of the force
on the bolt.
29. Sample Problem (cont’)
SOLUTION:
• Resolve each force into rectangular
force mag
components. x − comp y − comp
F1 150 + 129.9 + 75.0
F2 80 − 27.4 + 75.2
F3 110 0 − 110.0
F4 100 + 96.6 − 25.9
R x = +199.1 R y = +14.3
• Determine the components of the resultant by
adding the corresponding force components.
• Calculate the magnitude and direction.
R y 14.3 N
tan α = = α = 4.1° α = 4.1°
Rx 199.1 N
14.3 N
R= = 199.6 N
sin α
30. 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
31. 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
32. 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.
33. ATTENTION QUIZ
7. Resolve F along x and y axes and write it in
vector form. F = { ___________ } N
y
A) 80 cos (30°) i - 80 sin (30°) j x
B) 80 sin (30°) i + 80 cos (30°) j
C) 80 sin (30°) i - 80 cos (30°) j 30°
F = 80 N
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
Editor's Notes
Mainly explain the three steps using the example .