Covers All 18 Chapters
SOLUTIONS MANUAL
, CONTENTS
Part I BASICS
Chapter 1 INTRODUCTION 1
Chapter 2 MATERIALS 16
Chapter 3 STRESS AND STRAIN 24
Chapter 4 DEFLECTION AND IMPACT 48
Chapter 5 ENERGY METHODS AND STABILITY 68
Part II FAILURE PREVENTION
Chapter 6 STATIC FAILURE CRITERIA AND RELIABILITY 100
Chapter 7 FATIGUE FAILURE CRITERIA 117
Chapter 8 SURFACE FAILURE 135
Part III APPLICATIONS
Chapter 9 SHAFTS AND ASSOCIATED PARTS 145
Chapter 10 BEARINGS AND LUBRICATION 164
Chapter 11 SPUR GEARS 176
Chapter 12 HELICAL, BEVEL, AND WORM GEARS 194
Chapter 13 BELTS, CHAINS, CLUTCHES, AND BRAKES 208
Chapter 14 MECHANICAL SPRINGS 225
Chapter 15 POWER SCREWS, FASTENERS, AND CONNECTIONS 240
Chapter 16 MISCELLANEOUS MACHINE COMPONENTS 261
Chapter 17 FINITE ELEMENT ANALYSIS IN DESIGN 278
Chapter 18 CASE STUDIES IN MACHINE DESIGN 308
vi
, NOTES TO THE INSTRUCTOR
The Solutions Manual to accompany the text MECHANICAL DESIGN of Machine Components
supplements the study of machine design developed in the book. The main objective of the manual is
to provide efficient solutions for problems in design and analysis of variously loaded mechanical
components. In addition, this manual can serve to guide the instructor in the assignment of
problems, in grading these problems, and in preparing lecture materials as well as examination
questions. Every effort has been made to have a solutions manual that cuts through the clutter and is
self –explanatory as possible thus reducing the work on the instructor. It is written and class tested
by the author.
As indicated in its preface, the text is designed for the junior-senior courses in machine or
mechanical design. However, because of the number of optional sections which have been included,
MECHANICAL DESIGN of Machine Components may also be used to teach an upper level course. In
order to accommodate courses of varying emphases, considerably more material has been presented in
the book than can be covered effectively in a single three-credit-hour course. Machine/mechanical
design is one of the student’s first courses in professional engineering, as distinct from basic science
and mathematics.
There is never enough time to discuss all of the required material in details.
To assist the instructor in making up a schedule that will best fit his classes, major topics that
will probably be covered in every machine design course and secondary topics which may be
selected to complement this core to form courses of various emphases are indicated in the following
Sample Assignment Schedule. The major topics should be covered in some depth. The secondary
topics, because of time limitations and/or treatment on other courses, are suggested for brief
coverage. We note that the topics which may be used with more advanced students are marked with
asterisks in the textbook.
The problems in the sample schedule have been listed according to the portions of material
they illustrate. Instructor will easily find additional problems in the text to amplify a particular subject in
discussing a problem assigned for homework. Answers to selected problems are given at the end of the
text. Space limitations preclude our including solutions to open-ended web problems. Since the
integrated approach used in this text differs from that used in other texts, the instructor is advised to
read its preface, where the author has outlined his general philosophy. A brief description of the topics
covered in each chapter throughout the text is given in the following. It is hoped that this material will
help the instructor in organizing his course to best fit the needs of, his students.
Ansel C. Ugural
Holmdel, N.J.
vii
, DESCRIPTION OF THE MATERIAL CONTAINED IN
“MECHANICAL DESIGN of Machine Components”
Chapter 1 attempts to present the basic concepts and an overview of the subject. Sections 1.1
through 1.8 discuss the scope of treatment, machine and mechanical design, problem formulation,
factor of safety, and units. The load analysis is normally the critical step in designing any machine or
structural member (Secs.
1.8 through 1.9). The determination of loads is encountered repeatedly in subsequent chapters. Case
studies provide a number of machine or component projects throughout the book. These show that
the members must function in combination to produce a useful device. Section 1.10 review the work,
energy, and power. The foregoing basic considerations need to be understood in order to appreciate
the loading applied to a member. The last two sections emphasize the fact that stress and strain are
concepts of great importance to a comprehension of design analysis.
Chapter 2 reviews the general properties of materials and some processes to improve the
strength of metals. Sections 2.3 through 2.14 introduce stress-strain relationships, material behavior
under various loads, modulus of resilience and toughness, and hardness, selecting materials. Since
students have previously taken materials courses, little time can be justified in covering this chapter.
Much of the material included in Chapters 3 through 5 is also a review for students. Of particular
significance are the Mohr’s circle representation of state of stress, a clear understanding of the three-
dimensional aspects of stress, influence of impact force on stress and deformation within a
component, applications of Castigliano’s theorem, energy of distortion, and Euler’s formula. Stress
concentration is introduced in here, but little applications made of it until studying fatigue (Chap.7).
The first section of Chapter 6 attempts to provide an overview of the broad subject of
“failure”, against which all machine/mechanical elements must be designed. The discipline of
fracture mechanics is introduced in Secs. 6.2 through 6.4. Yield and fracture criteria for static failure
are discussed in Secs. 6.4 through 6.12. The last 3 sections deal with the method of reliability
prediction in design. Chapter 7 is devoted to the fatigue and behavior of materials under repeated
loadings. The emphasis is on the Goodman failure criterion. Surface failure is discussed in Chapter 8.
Sections 8.1 through 8.3 briefly review the corrosion and friction. Following these the surface wear
is discussed. Sections 8.6 through 8.10 deal with the surfaces contact stresses and the surface
fatigue failure and its prevention. The background provided here is directly applied to representative
common machine elements in later chapters.
Sections 9.1 through 9.4 of Chapter 9 treat the stresses and design of shafts under static
loads. Emphasis is on design of shafts for fluctuating loading (Secs. 9.6 and 9.7). The last 5 sections
introduce common parts associated with shafting. Chapter 10 introduces the lubrication as well as
both journal and roller bearings. As pointed out in Sec. 8.9, rolling element bearings provide
interesting applications of contact stress and fatigue. Much of the material covered in Secs. 11.1
through 11.7 of Chapter 11 introduce nomenclature, tooth systems, and fundamentals of general
gearing. Gear trains and spur gear force analysis are taken up in Secs. 11.6 and 11.7. The remaining
sections concern with gear design, material, and manufacture. Non-spur gearing is considered in
Chapter 12. Spur gears are merely a special case of helical gears (Secs. 12.2 through 12.5) having zero
helix angle. Sections 12.6 through 12.8 deal with bevel gears.
ix
,Worm gears are fundamentally different from other gears, but have much in common with power
screws to be taken up in Chap. 15.
Chapter 13 is devoted to the design of belts, chains, clutches, and brakes. Only a few
different analyses are needed, with surface forms effecting the equations more than the functions of
these devices. Belts, clutches, and brakes are machine elements depending upon friction for their
function. Design of various springs is considered in Chapter 14. The emphasis is on helical coil springs
(Secs. 14.3 through 14.9) that provide good illustrations of the static load analysis and torsional
fatigue loading. Leaf springs (Sec. 14.11) illustrate primarily bending fatigue loading. Chapter 15
attempts to present screws and connections. Of particular importance is the load analysis of power
screws and a clear understanding of the fatigue stresses in threaded fasteners. There are alternatives
to threaded fasteners and riveted or welded joints. Modern adhesives (Secs. 15.17 and 15.18) can
change traditional preferred choices.
It is important to assign at least portions of the analysis and design of miscellaneous
mechanical members treated in Chapter 16. Sections 16.3 through 16.7 concern with thick-walled
cylinders, press or shrink fits, and disk flywheels. The remaining sections concerns with the bending of
curved frames, plate and shells-like machine and structural components, and pressure vessels.
Buckling of thin-walled cylinders and spheres is also briefly discussed. Chapter 17 represents an
addition to the material traditionally covered in “Machine/Mechanical Design” textbooks. It
attempts to provide an introduction to the finite element analysis in design. Some practical case
studies illustrate solutions of problems involving structural assemblies, deflection of beams, and
stress concentration factors in plates. Finally, case studies in preliminary design of the entire crane
with winch and a high-speed cutting machine are introduced in Chapter 18.
ix
,Section I BASICS CHAPTER
1 INTRODUCTION
SOLUTION (1.1)
Free Body: Angle Bracket (Fig. S1.1)
(a) M 0 F ( 0 .5 ) 6 8 ( 0 .2 5 ) 2 8 .8 ( 0 .5 ) 0, F 6 2 .8 k N
B
;
x Bx Bx
(b) F 0: R 2 8 .8 F 0, R 3 4 kN
Fy 0: RBy 6 8 2 1 .6 0, RBy 8 9 .6 k N
Thus
RB ( 3 4 ) (8 9 .6 )
2 2
9 5 .8 k N
and
o
ta n
1 34
8 9 .6
2 0 .8
F A
34 B
0.5 68 kN 21.6 kN
89.6
R Bx B 28,8 kN
C RB
Figure S1.1 R By 0.25 0.25
SOLUTION (1.2)
Free Body: Beam ADE (Fig. S1.2)
M A 0: W (3 .7 5 a ) F (2 a ) 0,
BD
E F BD 1 .8 7 5W
D R Ax 0
Fx 0:
Fy 0: R Ay F BD W 0,
W
R Ay 0 .8 7 5W
A FBD
R Ax
R Ay 2a 1.75a Free-Body: Entire structure (Fig. S1.2)
M 0:
A
RC ( 3 a ) W ( 3 .7 5 a ) 0,
a V 1 .2 5W
A F RC
O Free Body: Part AO (Fig. S1.2)
M”
0.875 kN Figure S1.2 V 0 .8 7 5W
F 0
M 0 .8 7 5 a W
1
,SOLUTION (1.3)
29 kN/m
32 kN R 1 1 .0 2 k N
m M A 0: B
C D A E B Fy 0: RA 4 5 .8 2 k N
0.6 m RA RB
2.4 m 2.4 m
1,2 m
Segment CD
29 kN/m
1 2
M D
( 2 9 )( 0 .6 ) 5 .2 2 k N m
C VD D
M 1 72 .4 k N
0.6 m D V D
Segment CE
3 4.8 k N V
E
0.6 m M E
3 4 .8 (1 .8 ) 4 5 .8 2 (1 .2 ) 7 .6 5 6 k N m
C M E
1.2 m A 1.2 m E VE 1 1 .0 2 k N
45 . 82
SOLUTION (1.4)
B C C
(a) M 0 0.8 R ( 6 ) 0.6 (2 ) 24 ( 4 ) 0
1m : R
8 kN m 2m
10 kN R C
26 .667 kN
C R Cx 1 kN , R Cy 21 .334 kN
3m D B 2m 6
RC
4 R Bx Then
R 2m Fx 0 R Bx 16 kN
By
3 :
A Fy 0 R By 12 .66 kN
:
( b ) Segment CD
8 M 21 (3 ) 12 (1 .5 ) 6 (2 ) 34 kN m
D
.334
4 M F 16 kN
16 D
D
FD V 21 .334 18 3 .334 kN
C 3m D V D
D
21.334
2
,SOLUTION (1.5)
3m
(a)
A M R Cx 3
A 2 RCy
0:
2 2m
3
C
RCx
RCy 4
3
RBy R Cy M 0: 4 0 (5 ) 4 R C y RC y 50 kN
B
0
R Bx B R Cx 40 kN Then R Cx 7 kN
C
5
4m 1 RBy 10 kN , RBx 75 kN
(b)
D
D
F 75 ( 3 ) 50 ( 4 ) 85 kN
FV D
M0.75
D 5 5
D
4 3
1.0 75 V 75 ( ) 50 ( ) 30 kN
C 5
D 5 5
50 4 M D
7 5 (1) 5 0 ( 0 .7 5 ) 3 7 .5 k N m
3
SOLUTION (1.6) Free body entire connection
(a) B
M 0 R A ( 0 .7 ) T 0
P A T 0.15 m C
: T 0 .7 R
( 0 .5 ) ( 0 .1 5 )
2 2
Segment AB FCA B AB 0A.5 2 2 m
RA B
0,5
0.5m 0 18 ( 0 .15 ) R A( 0 .5 ) 0
18 kN A
0.15mm
0.2 M B
m : RA 5 .4 k N
and
T 3 .7 8 k N m
RA
x 0 .5 2 2
AB AB
0 .5
(b) F 0: 18 F 0 F 1 8 .7 2 9 k N
,
SOLUTION (1.7) Free Body: Entire Crankshaft (Fig. S1.7a)
( a ) From symmetry: R R A B
Fz 0 : RA RB 2 kN
120 mm
120 mm M x 0: 4 ( 0 .0 5 ) T 0,
T 0 .2 k N m 200 N m
RA
A y 70 mm
(CONT.)
D T
B
2 k N
z R B 2 k N x
50 mm C
4 kN (a)
3
,1.7 (CONT.)
M y
D ( b ) Cross Section at D (Fig. S1.7b)
Vz V z 2 k N
(b) T 2 0 0 N m
T
Figure S 1.7 M y
2 ( 0 .0 7 ) 0 .1 4 k N m
1 4 0 N m
SOLUTION (1.8)
30 kN
B Free-Body Diagram, Beam AB
4
1.8 m x
7
CD CD
65
7 F 0: F F, 6 0 3 0 0 , 0F R 6 96.14 1.3k kNN
F 0: R
4
C FCD y A CD A
65
A CD A
1.2 m 7
M 0: 6 0 (1 .8 ) 65
F (3 ) M 0,
M A 72 kN m
60 kN
1.8 m
A
M A
RA
SOLUTION (1.9)
B 1.2 m
C Free body entire frame
129.6 kN 1
M A
0 129 .6 ( 0 .9 ) R (1 .2 ) R (3 ) 0
0.9 m 0.9 m 1.2 m : 2 Dy Dy
2 2.4 m
RDy 4 8 .6 k N , R Dx 2 4 .3 k N
A 1
1
D 2
R Dy
R Dy RD
B RBy
C Free body BCD
R B x 1.2 m Fx 0: RBx 2 4 .3 k N
2.4 m Fy 0: RBy 4 8 .6 k N
D 24.3 2 4 .3 4 6 .6
2 2
RB 5 2 .6 k N
48.6
4
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5
SOLUTIONS MANUAL
, CONTENTS
Part I BASICS
Chapter 1 INTRODUCTION 1
Chapter 2 MATERIALS 16
Chapter 3 STRESS AND STRAIN 24
Chapter 4 DEFLECTION AND IMPACT 48
Chapter 5 ENERGY METHODS AND STABILITY 68
Part II FAILURE PREVENTION
Chapter 6 STATIC FAILURE CRITERIA AND RELIABILITY 100
Chapter 7 FATIGUE FAILURE CRITERIA 117
Chapter 8 SURFACE FAILURE 135
Part III APPLICATIONS
Chapter 9 SHAFTS AND ASSOCIATED PARTS 145
Chapter 10 BEARINGS AND LUBRICATION 164
Chapter 11 SPUR GEARS 176
Chapter 12 HELICAL, BEVEL, AND WORM GEARS 194
Chapter 13 BELTS, CHAINS, CLUTCHES, AND BRAKES 208
Chapter 14 MECHANICAL SPRINGS 225
Chapter 15 POWER SCREWS, FASTENERS, AND CONNECTIONS 240
Chapter 16 MISCELLANEOUS MACHINE COMPONENTS 261
Chapter 17 FINITE ELEMENT ANALYSIS IN DESIGN 278
Chapter 18 CASE STUDIES IN MACHINE DESIGN 308
vi
, NOTES TO THE INSTRUCTOR
The Solutions Manual to accompany the text MECHANICAL DESIGN of Machine Components
supplements the study of machine design developed in the book. The main objective of the manual is
to provide efficient solutions for problems in design and analysis of variously loaded mechanical
components. In addition, this manual can serve to guide the instructor in the assignment of
problems, in grading these problems, and in preparing lecture materials as well as examination
questions. Every effort has been made to have a solutions manual that cuts through the clutter and is
self –explanatory as possible thus reducing the work on the instructor. It is written and class tested
by the author.
As indicated in its preface, the text is designed for the junior-senior courses in machine or
mechanical design. However, because of the number of optional sections which have been included,
MECHANICAL DESIGN of Machine Components may also be used to teach an upper level course. In
order to accommodate courses of varying emphases, considerably more material has been presented in
the book than can be covered effectively in a single three-credit-hour course. Machine/mechanical
design is one of the student’s first courses in professional engineering, as distinct from basic science
and mathematics.
There is never enough time to discuss all of the required material in details.
To assist the instructor in making up a schedule that will best fit his classes, major topics that
will probably be covered in every machine design course and secondary topics which may be
selected to complement this core to form courses of various emphases are indicated in the following
Sample Assignment Schedule. The major topics should be covered in some depth. The secondary
topics, because of time limitations and/or treatment on other courses, are suggested for brief
coverage. We note that the topics which may be used with more advanced students are marked with
asterisks in the textbook.
The problems in the sample schedule have been listed according to the portions of material
they illustrate. Instructor will easily find additional problems in the text to amplify a particular subject in
discussing a problem assigned for homework. Answers to selected problems are given at the end of the
text. Space limitations preclude our including solutions to open-ended web problems. Since the
integrated approach used in this text differs from that used in other texts, the instructor is advised to
read its preface, where the author has outlined his general philosophy. A brief description of the topics
covered in each chapter throughout the text is given in the following. It is hoped that this material will
help the instructor in organizing his course to best fit the needs of, his students.
Ansel C. Ugural
Holmdel, N.J.
vii
, DESCRIPTION OF THE MATERIAL CONTAINED IN
“MECHANICAL DESIGN of Machine Components”
Chapter 1 attempts to present the basic concepts and an overview of the subject. Sections 1.1
through 1.8 discuss the scope of treatment, machine and mechanical design, problem formulation,
factor of safety, and units. The load analysis is normally the critical step in designing any machine or
structural member (Secs.
1.8 through 1.9). The determination of loads is encountered repeatedly in subsequent chapters. Case
studies provide a number of machine or component projects throughout the book. These show that
the members must function in combination to produce a useful device. Section 1.10 review the work,
energy, and power. The foregoing basic considerations need to be understood in order to appreciate
the loading applied to a member. The last two sections emphasize the fact that stress and strain are
concepts of great importance to a comprehension of design analysis.
Chapter 2 reviews the general properties of materials and some processes to improve the
strength of metals. Sections 2.3 through 2.14 introduce stress-strain relationships, material behavior
under various loads, modulus of resilience and toughness, and hardness, selecting materials. Since
students have previously taken materials courses, little time can be justified in covering this chapter.
Much of the material included in Chapters 3 through 5 is also a review for students. Of particular
significance are the Mohr’s circle representation of state of stress, a clear understanding of the three-
dimensional aspects of stress, influence of impact force on stress and deformation within a
component, applications of Castigliano’s theorem, energy of distortion, and Euler’s formula. Stress
concentration is introduced in here, but little applications made of it until studying fatigue (Chap.7).
The first section of Chapter 6 attempts to provide an overview of the broad subject of
“failure”, against which all machine/mechanical elements must be designed. The discipline of
fracture mechanics is introduced in Secs. 6.2 through 6.4. Yield and fracture criteria for static failure
are discussed in Secs. 6.4 through 6.12. The last 3 sections deal with the method of reliability
prediction in design. Chapter 7 is devoted to the fatigue and behavior of materials under repeated
loadings. The emphasis is on the Goodman failure criterion. Surface failure is discussed in Chapter 8.
Sections 8.1 through 8.3 briefly review the corrosion and friction. Following these the surface wear
is discussed. Sections 8.6 through 8.10 deal with the surfaces contact stresses and the surface
fatigue failure and its prevention. The background provided here is directly applied to representative
common machine elements in later chapters.
Sections 9.1 through 9.4 of Chapter 9 treat the stresses and design of shafts under static
loads. Emphasis is on design of shafts for fluctuating loading (Secs. 9.6 and 9.7). The last 5 sections
introduce common parts associated with shafting. Chapter 10 introduces the lubrication as well as
both journal and roller bearings. As pointed out in Sec. 8.9, rolling element bearings provide
interesting applications of contact stress and fatigue. Much of the material covered in Secs. 11.1
through 11.7 of Chapter 11 introduce nomenclature, tooth systems, and fundamentals of general
gearing. Gear trains and spur gear force analysis are taken up in Secs. 11.6 and 11.7. The remaining
sections concern with gear design, material, and manufacture. Non-spur gearing is considered in
Chapter 12. Spur gears are merely a special case of helical gears (Secs. 12.2 through 12.5) having zero
helix angle. Sections 12.6 through 12.8 deal with bevel gears.
ix
,Worm gears are fundamentally different from other gears, but have much in common with power
screws to be taken up in Chap. 15.
Chapter 13 is devoted to the design of belts, chains, clutches, and brakes. Only a few
different analyses are needed, with surface forms effecting the equations more than the functions of
these devices. Belts, clutches, and brakes are machine elements depending upon friction for their
function. Design of various springs is considered in Chapter 14. The emphasis is on helical coil springs
(Secs. 14.3 through 14.9) that provide good illustrations of the static load analysis and torsional
fatigue loading. Leaf springs (Sec. 14.11) illustrate primarily bending fatigue loading. Chapter 15
attempts to present screws and connections. Of particular importance is the load analysis of power
screws and a clear understanding of the fatigue stresses in threaded fasteners. There are alternatives
to threaded fasteners and riveted or welded joints. Modern adhesives (Secs. 15.17 and 15.18) can
change traditional preferred choices.
It is important to assign at least portions of the analysis and design of miscellaneous
mechanical members treated in Chapter 16. Sections 16.3 through 16.7 concern with thick-walled
cylinders, press or shrink fits, and disk flywheels. The remaining sections concerns with the bending of
curved frames, plate and shells-like machine and structural components, and pressure vessels.
Buckling of thin-walled cylinders and spheres is also briefly discussed. Chapter 17 represents an
addition to the material traditionally covered in “Machine/Mechanical Design” textbooks. It
attempts to provide an introduction to the finite element analysis in design. Some practical case
studies illustrate solutions of problems involving structural assemblies, deflection of beams, and
stress concentration factors in plates. Finally, case studies in preliminary design of the entire crane
with winch and a high-speed cutting machine are introduced in Chapter 18.
ix
,Section I BASICS CHAPTER
1 INTRODUCTION
SOLUTION (1.1)
Free Body: Angle Bracket (Fig. S1.1)
(a) M 0 F ( 0 .5 ) 6 8 ( 0 .2 5 ) 2 8 .8 ( 0 .5 ) 0, F 6 2 .8 k N
B
;
x Bx Bx
(b) F 0: R 2 8 .8 F 0, R 3 4 kN
Fy 0: RBy 6 8 2 1 .6 0, RBy 8 9 .6 k N
Thus
RB ( 3 4 ) (8 9 .6 )
2 2
9 5 .8 k N
and
o
ta n
1 34
8 9 .6
2 0 .8
F A
34 B
0.5 68 kN 21.6 kN
89.6
R Bx B 28,8 kN
C RB
Figure S1.1 R By 0.25 0.25
SOLUTION (1.2)
Free Body: Beam ADE (Fig. S1.2)
M A 0: W (3 .7 5 a ) F (2 a ) 0,
BD
E F BD 1 .8 7 5W
D R Ax 0
Fx 0:
Fy 0: R Ay F BD W 0,
W
R Ay 0 .8 7 5W
A FBD
R Ax
R Ay 2a 1.75a Free-Body: Entire structure (Fig. S1.2)
M 0:
A
RC ( 3 a ) W ( 3 .7 5 a ) 0,
a V 1 .2 5W
A F RC
O Free Body: Part AO (Fig. S1.2)
M”
0.875 kN Figure S1.2 V 0 .8 7 5W
F 0
M 0 .8 7 5 a W
1
,SOLUTION (1.3)
29 kN/m
32 kN R 1 1 .0 2 k N
m M A 0: B
C D A E B Fy 0: RA 4 5 .8 2 k N
0.6 m RA RB
2.4 m 2.4 m
1,2 m
Segment CD
29 kN/m
1 2
M D
( 2 9 )( 0 .6 ) 5 .2 2 k N m
C VD D
M 1 72 .4 k N
0.6 m D V D
Segment CE
3 4.8 k N V
E
0.6 m M E
3 4 .8 (1 .8 ) 4 5 .8 2 (1 .2 ) 7 .6 5 6 k N m
C M E
1.2 m A 1.2 m E VE 1 1 .0 2 k N
45 . 82
SOLUTION (1.4)
B C C
(a) M 0 0.8 R ( 6 ) 0.6 (2 ) 24 ( 4 ) 0
1m : R
8 kN m 2m
10 kN R C
26 .667 kN
C R Cx 1 kN , R Cy 21 .334 kN
3m D B 2m 6
RC
4 R Bx Then
R 2m Fx 0 R Bx 16 kN
By
3 :
A Fy 0 R By 12 .66 kN
:
( b ) Segment CD
8 M 21 (3 ) 12 (1 .5 ) 6 (2 ) 34 kN m
D
.334
4 M F 16 kN
16 D
D
FD V 21 .334 18 3 .334 kN
C 3m D V D
D
21.334
2
,SOLUTION (1.5)
3m
(a)
A M R Cx 3
A 2 RCy
0:
2 2m
3
C
RCx
RCy 4
3
RBy R Cy M 0: 4 0 (5 ) 4 R C y RC y 50 kN
B
0
R Bx B R Cx 40 kN Then R Cx 7 kN
C
5
4m 1 RBy 10 kN , RBx 75 kN
(b)
D
D
F 75 ( 3 ) 50 ( 4 ) 85 kN
FV D
M0.75
D 5 5
D
4 3
1.0 75 V 75 ( ) 50 ( ) 30 kN
C 5
D 5 5
50 4 M D
7 5 (1) 5 0 ( 0 .7 5 ) 3 7 .5 k N m
3
SOLUTION (1.6) Free body entire connection
(a) B
M 0 R A ( 0 .7 ) T 0
P A T 0.15 m C
: T 0 .7 R
( 0 .5 ) ( 0 .1 5 )
2 2
Segment AB FCA B AB 0A.5 2 2 m
RA B
0,5
0.5m 0 18 ( 0 .15 ) R A( 0 .5 ) 0
18 kN A
0.15mm
0.2 M B
m : RA 5 .4 k N
and
T 3 .7 8 k N m
RA
x 0 .5 2 2
AB AB
0 .5
(b) F 0: 18 F 0 F 1 8 .7 2 9 k N
,
SOLUTION (1.7) Free Body: Entire Crankshaft (Fig. S1.7a)
( a ) From symmetry: R R A B
Fz 0 : RA RB 2 kN
120 mm
120 mm M x 0: 4 ( 0 .0 5 ) T 0,
T 0 .2 k N m 200 N m
RA
A y 70 mm
(CONT.)
D T
B
2 k N
z R B 2 k N x
50 mm C
4 kN (a)
3
,1.7 (CONT.)
M y
D ( b ) Cross Section at D (Fig. S1.7b)
Vz V z 2 k N
(b) T 2 0 0 N m
T
Figure S 1.7 M y
2 ( 0 .0 7 ) 0 .1 4 k N m
1 4 0 N m
SOLUTION (1.8)
30 kN
B Free-Body Diagram, Beam AB
4
1.8 m x
7
CD CD
65
7 F 0: F F, 6 0 3 0 0 , 0F R 6 96.14 1.3k kNN
F 0: R
4
C FCD y A CD A
65
A CD A
1.2 m 7
M 0: 6 0 (1 .8 ) 65
F (3 ) M 0,
M A 72 kN m
60 kN
1.8 m
A
M A
RA
SOLUTION (1.9)
B 1.2 m
C Free body entire frame
129.6 kN 1
M A
0 129 .6 ( 0 .9 ) R (1 .2 ) R (3 ) 0
0.9 m 0.9 m 1.2 m : 2 Dy Dy
2 2.4 m
RDy 4 8 .6 k N , R Dx 2 4 .3 k N
A 1
1
D 2
R Dy
R Dy RD
B RBy
C Free body BCD
R B x 1.2 m Fx 0: RBx 2 4 .3 k N
2.4 m Fy 0: RBy 4 8 .6 k N
D 24.3 2 4 .3 4 6 .6
2 2
RB 5 2 .6 k N
48.6
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