Juvinall, Marshek Fundamentals of Machine Component Design SOLUTIONS

Esta é uma pré-visualização de arquivo. Entre para ver o arquivo original

Experience
Waste
Products
Human
resources
Production
system
Work experience and knowledge feedback
New products
Material
resources
JUVINALL: Machine Design
Fig. 1-1a W-1
JUVINALL: Machine Design
Fig. 1-2 W-2
JUVINALL: Machine Design
Fig. 1-3a W-3
JUVINALL: Machine Design
Fig. 1-3b W-3
JUVINALL: Machine Design
Fig. 1-3c W-3
JUVINALL: Machine Design
Fig. 1-4 W-4
R
F
To
rq
ue
 (
N
 • 
m
m
)
Cam rotation (rad)
(b)(a)
0.10
10
0
Fo
rc
e 
(N
)
Follower
displacement (mm)
(c)
10
1
0
JUVINALL: Machine Design
Fig. 1-5 W-5
JUVINALL: Machine Design
Fig. 1-6 W-6
n = 1000 rpm
T = 10 N • mm
�
3
C
ra
nk
 t
or
qu
e 
(k
N
 • 
m
)
Crank angle (rad)
0
Actual torque
requirement
� 2�
0
2
4
6
8
10
JUVINALL: Machine Design
Fig. 1-7 W-7
2�
C
ra
nk
 t
or
qu
e 
(k
N
 • 
m
)
Crank angle (rad)
Uniform torque
supplying equal
energy
Average torque
Actual torque
requirement
0 �
0
2
4
6
8
10
JUVINALL: Machine Design
Fig. 1-8 W-8
�
3
JUVINALL: Machine Design
Fig. 1-9 W-9
0.2d
Rim
Arm
Hub
0.8d d
Ve
hi
cl
e 
ro
ad
 lo
ad
 p
ow
er
 (
hp
)
Vehicle speed (mph)
0 20 40 60 80 100 120
0
40
80
120
160
JUVINALL: Machine Design
Fig. 1-10 W-11
E
ng
in
e 
ou
tp
ut
 p
ow
er
 (
hp
)
Engine speed (rpm)
0 1000 2000 3000 4000 5000
0
40
80
120
160
JUVINALL: Machine Design
Fig. 1-11 W-12
S
pe
ci
fi
c 
fu
el
 c
on
su
m
pt
io
n 
of
 e
ng
in
e 
(l
b/
hp
 • 
h)
Engine output power (hp)
20 40 60
1000 rpm
1500 rpm
2000 rpm
2500 rpm
3000 rpm
3500 rpm
4000 rpm
80 100 120 140 160 180
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
JUVINALL: Machine Design
Fig. 1-12 W-13
JUVINALL: Machine Design
Fig. 1-13 W-14
g = 9.81 m/s2
5 mm
30
mm
1 N
m
JUVINALL: Machine Design
Fig. P1.18 W-15
JUVINALL: Machine Design
Fig. P1-23 W-16
a = 5 ft/s2
g = 32.2 ft/s2F
Pulley
JUVINALL: Machine Design
Fig. P1-26 W-17
V = 5 ft /s
m = 5 lb
R = 3 in.
JUVINALL: Machine Design
Fig. P1-29 W-18
I = 10 A
Output
shaft
t = 2 hr
n = 1000 rpm
T = 9.5 N • m
V = 110 V +–
0
T max
0.5
Crankshaft rotation, revolutions
C
ra
nk
sh
af
t 
to
rq
ue
1.51.0 2.0
Curve A (linear variation)
Curve B (half-wave rectified sinusoid)
JUVINALL: Machine Design
Fig. P1-42 W-18A
JUVINALL: Machine Design
Fig. P1-49 W-19
55 mph
2.64 axle ratio
JUVINALL: Machine Design
Fig. 2-1 W-20
100 in.
V = 60 mph
50 in.
CP
3000 lb
25 in.
Fd
Ft
Wr Wf
20 in.CG
JUVINALL: Machine Design
Fig. 2-2 W-21
Engine power, 96 hp
W = 3000 lb
Fd = 100 lb
Ft = 567.5 lb
Wr = 1618.5 lb Wf = 1381.5 lb
Fi = 467.5 lb
JUVINALL: Machine Design
Fig. 2-3 W-22
A
X
X
RT
RT
RT
RT – T
RT – T
T
T
RT
A
RT
A
2 in.
3 in.
2 in.
5 in.
3000 lb.in.
T = 3000 lb.in.
(input)RT – T = 5333 lb.in.
Transmission
in low gear
R = 2.778RT = 8333 lb.in.
(output)
5333 lb.in.
8333 lb.in.
(b)
(a)
(d)
(c)
1087 lb
2864 lb
1087 lb
1087 lb
II
IV
1087 lb
4444 lb
4444 lb
2864 lb
2864 lb
2667 lb
2667 lb
III
III
IV
I
I
II
B
D
A
C
JUVINALL: Machine Design
Fig. 2-4 W-23
JUVINALL: Machine Design
Fig. 2-5 W-24
A
A
F F
(a) (b)
a
F
F
Fa
Section
AA plane
Fixed
support
(bending moment)
JUVINALL: Machine Design
Fig. 2-6 W-25
(a)
Fa
b
F
a
(b)
F
Fb (torque) 
F (shear force) 
JUVINALL: Machine Design
Fig. 2-7 W-26
F32 = 40 lb
H12
F42
V12
30°
1
1
in.
1
2
2
1 in.
JUVINALL: Machine Design
Fig. 2-8 W-27
F32 = 40 lb
F42
F42
F12
F32 = 40 lb
0
F12
1
Force polygon for link 2
2
Ft = 60 lb
Fb = 55 lb
Fb (bone
compression force)
0.5 in.
0
Ft (tendon
force)
10 lb
pinch
10 lb
3 in.
JUVINALL: Machine Design
Fig. 2-9 W-28
Force polygon for finger
b2
2L
wb2
2L
b2
4L
Fa
L
Fb
L
Fb
L
–
+
Fa
L
–
a
L
b
F
V
MM
V
JUVINALL: Machine Design
Fig. 2-10 W-29
M
a +
 VV
R2R1
+
+
Positive shear force
Positive bending
moment
wb (a + b/2 )
L
w
wb (a + b/2 )
L
+wb2/2L
wb 2
2L
a
L
b
R2R1
Fab
L
+
M
(b)(a)
Distributed loadSingle concentrated load
JUVINALL: Machine Design
Fig. 2-11 W-29A
2667 lb
2 in.
2864 lb
4444 lb
–2864 lb
–5728 in..lb
Torque
Moment
Shear
Loads
5000 lb.in.
2174 in..lb
2667 lb
IV
III
2 in.5 in.
+ 1580 lb
– 1087 lb
1087 lb
Critical section
C
V
M
T
B
1087 lb
4444 lb
2864 lb
III
IV
B
C
IV
JUVINALL: Machine Design
Fig. 2-12 W-30
2864 lb
4444 lb
T = 5000 lb.in.
V = 1580 lb
C
M = 5728 lb.in.*
* Actually slightly less, depending
upon the width of gear C
d
F
FF
F
JUVINALL: Machine Design
Fig. 2-13 W-31
m
2b
b
b
d
a
1
 2 
3
44
3
2
1
1
4'
4'
6
4'
5
5
3
2
2
2 1
PinFork Blade
F
F
F
F
4'
2
2
3
 7 
JUVINALL: Machine Design
Fig. 2-15 W-33
JUVINALL: Machine Design
Fig. 2-16 W-34
w lb/ft
Spring in tension
k1 = 10 lb/in.
Spring in
compression
k2 = 40 lb/in.
JUVINALL: Machine Design
Fig. 2-17 W-35
100 lb
100 lb
10�
40�
(a)
(b)
JUVINALL: Machine Design
Fig. 2-18 W-36
 3 
1
strap
Top
strap
Right
plate
Bottom
strap
1 
pi
tc
h
1 
pi
tc
h
JUVINALL: Machine Design
Fig. 2-19 W-37
Inner rowMiddle row
Outer row Inner row
Outer row
Area
Plate
Inner row
Top
strap
Bottom
strap
Left
plate
Outer row
(a)
(b)
(d)
(e)
( f )
(c)
Strap
Straps
Inner path
M
iddle path
O
uter path Bearing with plate
Shear
Bearing with straps
Plate
2 straps
Bearing with strap
Bearing with plate
Shear
Plate
Strap
 1 2 
 8 
 9 
 6 
 7 
 5 
 4 
 s
 bp 
 bs
JUVINALL: Machine Design
Fig. P2.2 W-38
gWall channel, C
2 in.
A
B
Density = �
Density = �
r =
1.25 in.
r =
1.25 in.
JUVINALL: Machine Design
Fig. P2.3 W-40
1500 N 1500 N
1000 mm
45°
45° 45°
45°
B
D
C
A
JUVINALL: Machine Design
Fig. P2.4 W-39
A
B
125 N
1000 N
JUVINALL: Machine Design
Fig. P2.6 W-41
10 in.
Motor
1 hp
1800 rpm
Gear box
Direction
of rotation
Blower
6000 rpm
JUVINALL: Machine Design
Fig. P2.7 W-42
50 mm
50 mm
Clockwise
rotation
Forward
air velocity
A
B
A'
Pump
450 rpm
Connecting
tube
Direction
of rotation
4:1 ratio
gear reducer
C'
B
A
B'
Motor 1.5 kW
1800 rpm
These units
are attached to
a fixed support.
JUVINALL: Machine Design
Fig. P2.8 W-43
C
JUVINALL: Machine Design
Fig. P2.9 W-44
Engine
is attached
to aircraft structure here.
Engine
Reduction gear,
ratio = 1.5
Propeller
Rotation
Vertical
drive
shaft
Mounting
flange
Propeller
rotation
Y
X
Y
Z
Z
X
JUVINALL: Machine Design
Fig. P2.10 W-45
2:1 ratio bevel
gears are inside
this housing
Suggested notation
for moments applied
to mounting flange
500 mm
Foward
direction of
boat travel
Mx My
Mz
150 mm
600400
330 R330 R
40 R
100 R
800 N
160
JUVINALL: Machine Design
Fig. P2-11 W-46 
Bevel gear
reducer
Attaches
to motor
Attaches
to load
600 rpm
1800 rpm
JUVINALL: Machine Design
Fig. P2-12 W-47
100 mm
100 mm
A
BC
D
8 in.
4 in.
6 in.
Output
Output shaft
Mountings
6 in. dia. gear
2 in. dia. pinion
Front bearings
Front bearings
Rear
bearings
Motor input torque
100 lb.ft
100 lb.ft
Reducer assembly
Housing and
gear-shaft assembly
details
JUVINALL: Machine Design
Fig. P2-13 W-48
JUVINALL: Machine Design
Fig. P2-14 W-51
X
Y
Y
X
B
D
A
C
12 in.
24 in.
Transmission
2.0 ratio
Rear drive shaft–1200 rpm
Rear axle
(not part of
free body)
Front drive shaft–1200 rpm
Left-front
wheel axle
shaft–400 rpm
Engine
2400 rpm
100 lb.ft torque
Right-front wheel axle
shaft–400 rpm
Mixing paddle
g
JUVINALL: Machine Design
Fig. P2-15 W-49
Motor
Radial
flow
Direction
of rotation
Mass of mixer
system = 50 kg
200 mm
A B
g
JUVINALL: Machine Design
Fig. P2.16 W-50
B
Mounting
width = 75 mm
to 150 mm
Fan
Radial
air flow
Mass of blower
system = 15 kg
A
Motor
Direction of
rotation
JUVINALL: Machine Design
Fig. P2-17 W-52
Y
FC
FA
Z
D
B
A
C
X
45 mm
30 mm
20 mm
Shaft
Gear 2
24-mm dia.
Gear 1
50-mm dia.
20°
20°
300200
JUVINALL: Machine Design
Fig. P2-18 W-53
100 N
A B
300
50 N140
200
100 N
A B
12-in.
pulley radius
JUVINALL: Machine Design
Fig. P2-19 W-54
Cable
Cable
100 lb
100 lb
48 in. 12 in.
27 in.
Motor
attaches
to this end
of shaft
6040
50
JUVINALL: Machine Design
Fig. P2-20 W-55
Fa = 1000 N
Ft = 2000 N
Fr = 600 N
A B
JUVINALL: Machine Design
Fig. P2-21 W-56
Pump shaft is
coupled to this
end of shaft
15050
100
Fa = 100 N
Ft = 1000 N
Fr = 200 N
A B
8020
40
20
30
JUVINALL: Machine Design
Fig. P2-22 W-57
Fa = 200 N
200 N
Fr = 400 N
A B
Ft = 1000 N
JUVINALL: Machine Design
Fig. P2.23 W-58
Fa = 150 N
Ft = 1500 N
Fr = 500 N
150
120
A B
250 N
100 N
200 300 140
L
Section on A-A
Key
JUVINALL: Machine Design
Fig. P2.24 W-59
Rb
r
A
A
F
t
t/2
d
D
F
JUVINALL: Machine Design
Fig. P2-25 W-60
t
d
Total gas force = F
JUVINALL: Machine Design
Fig. P2-26 W-61
a2aa
R
A B
L
F
L
A
L
ttf
JUVINALL: Machine Design
Fig. P2-27 W-62
P P
d D
d D
JUVINALL: Machine Design
Fig. P2-28 W-63
E
A
B
C
D
JUVINALL: Machine Design
Fig. P2-29 W-64
k
k
kk
a
100 N
a
F F
JUVINALL: Machine Design
Fig. P2-31 W-65
P
t '
t '
Rivet diameter = 10 mm
t
S
tr
es
s 
�
 (
ks
i)
Strain � (arbitary nonlinear scale)
Slope = modulus of elasticity, E
F (Fracture)
Sy = 39
Su = 66
Se = 36
C
A
B
0.2% offset
0
20
40
60
JUVINALL: Machine Design
Fig. 3-1 W-66
S
tr
es
s 
�
 (
ks
i)
Strain � (%)
0 10 20 30 40 50 60 70 80 90 100 110
Hot-rolled 1020 steel
Su = 66 ksi
Sy = 39 ksi
Se = 36 ksi
G
A
B
D
C
F
H
120 130 140 150 160
Area ratio R
Area reduction Ar
0 1.1
0.1 0.2 0.3 0.4 0.5 0.6
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
0
20
40
60
JUVINALL: Machine Design
Fig. 3-2 W-67
Tr
ue
 s
tr
es
s 
�
T 
(k
si
 (
lo
g)
)
True strain �T (% (log))
3 4 5 6 7 8 0.1 32 4 5 6 7 8 1.0 32 4 5 6 7 8 10 32 4 5 6 7 8100
10
20
30
40
60
80
100
200
Elastic
region
Transition
region
JUVINALL: Machine Design
Fig. 3-3 W-68
Plastic strain-strengthening region
� T
 =
 E�
T 
(E
 =
 3
0 
× 
10
3 k
si)
�T = Sy = 39 ksi
F
115
�Tf = 0.92
�T = 
�0 �T
 (�0 =
 115 k
si, m =
 0.22)
m
Tr
ue
 s
tr
es
s 
�
T 
(l
og
)
True strain �T (log)
Elastic line (�T = E�T)
Curve II
Curve I (�T = Se ≈ Sy)
Plastic line (�T = �0�T )
m
"Ideal" material
Se3
Se1
Se2
JUVINALL: Machine Design
Fig. 3-4 W-69
Se �f
E
JUVINALL: Machine Design
Fig. 3-5 W-70
S
tr
es
s 
�
0
Strain �
Se
Sy
Su
F
d
D
K
B,
 r
at
io
 S
u
/H
B
m, strain hardening exponent
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
300
400
500
600
700
800
900
1000
JUVINALL: Machine Design
Fig. 3-6 W-71
Steel
d = indentation dia.
D = ball dia.
0.
2
0.
3
0.
4
0.
5
0.
6
D
ia
m
on
d 
py
ra
m
id
 h
ar
dn
es
s 
(V
ic
ke
rs
)
B
ri
ne
ll 
ha
rd
ne
ss
U
lt
im
at
e 
te
ns
ile
 s
tr
en
gt
h 
(k
si
)
Rockwell C hardness
Shore hardness
Rockwell B hardness
(0)
72 80 90 100 (110)
(10) 20 30 40 50 60 70
950
900
760
740
720
700
680
660
640
620
600
580
560
540
520
500
480
460
440
420
400
380
360
340
320
300
280
260
240
220
200
180
160
140
120
100
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
95
90807060504030
85756555464238343228262422
850
800
750
700
650
600
550
500
450
400
350
300
250
200
150
100
JUVINALL: Machine Design
Fig. 3-7 W-72
JUVINALL: Machine Design
Fig. 3-8 W-73
Distance from
quenched end
(b)
(a)
R
oc
kw
el
l C
 h
ar
dn
es
s
Yo
un
gs
 M
od
ul
us
, 
E 
(G
P
a)
Strength S (MPa)
0.1 1 10 100 1000 10,000
0.01
0.1
= 10–3
Woods
Polymers
foams
Ash
Lead
W
WC
Si C
Cermets
Boron
Al203Beryllium
Cast irons
Oak
Pine
PMMA
Porous
ceramics
1.0
10
100
1000
JUVINALL: Machine Design
Fig. 3-11 W-74
Engineering
alloys
S
E
= CS
E
= CS
3/2
E
= 10–4S
E
= 10–2S
E
Min. energy
storage per
unit volume
Yield before
buckling
Max energy
storage per
unit volume
Buckling
before yield
Cork
Pu
Silicone
Hard
butyl
Soft
butyl
= CS
2
E
Elastomers
PP
II to
grain
Mel
LDPE
PTFE
Pine
⊥ to
grain
Balsa
HDPE
Ash
Oak
Engineering
polymers
PVC = 0.1S
E
Balsa
Wood
products
Epoxies
PS
Nylons
Polyester
Design
guide
lines
CFRP
CFRP
uniply
GFRP
Laminates
GFRP
Glasses
Sn
Concrete
+
Al alloys
Common
rocks
Brick etc
Zn alloys
Cu alloys Ti alloys
Mo alloys
Steels
Ni alloys
Diamond
Si3N3
Mg0
Be0
Ge
Silicon
Zr 02
Engineering
ceramics
Engineering
composites
Mg alloys
Cement
S1/2
�
S
tr
en
gt
h 
S 
(M
P
a)
Density � (Mg/m3)
0.1 0.3 1
= CS2/3
�
= C
3 10 30
0.1
1
10
Polymers
foams
100
1000
10,000
JUVINALL: Machine
Design
Fig. 3-12 W-74a
Guide lines
for minimum
weight design
S
�
= C
Cork
Balsa
Balsa
Woods
Soft
butyl Elastomers
Engineering
polymers
Porous
ceramics
Engineering
composites
Engineering
ceramics
Engineering
alloys 
KFRP
CFRP
Mg0
Diamond
Sialons
Si3N4
Al203
Ge
GFRP
Uniply
KFRP
CFRP
Glasses
Ash
Oak
Pine
Pine
Fir
 Parallel
to grain
Ash
Perpendicular
to grain
Fir
Wood
products
LDPE
PU
PTFE
Mel
PVC
Epoxies
Polyesters
Nylons
PMMA
PS
Silicone
PP
Oak
HDPE
Lead
alloys
Engineering
alloys
W alloys
Mo alloys
Ni alloys
Steels
Cast
irons
Zn
alloys
Al alloys
Ti
alloys
Stone,
rock
Cu alloysMg
alloys
Pottery
Si C
B
Si
GFRP
Laminates
Be
Cement
concrete
Cermets
Zr02
S
tr
en
gt
h 
at
 t
em
pe
ra
tu
re
 S
 (
T)
 (
M
P
a)
Temperature T (C)
0
Elastomers
T-Independent
Yield strength
Upper limit on
 strength at
 temperature
Engineering
composites
Woods
100 200 300 400 600 800 1000 1400
0.1
1
10
100
1000
10,000
JUVINALL: Machine Design
Fig. 3-13 W-74b
Engineering
alloys
Porous
ceramics
Engineering
ceramics
Range typical
of alloy series
Polymer
foams
SiliconesButylsIce
LDPE
II to
grain
Engineering
polymers
Polyesters
HDPE
PP
PC
PVC
PF
Mg alloys
Nylons
⊥ to
grain
⊥ to
grain
PTFE
Epoxies
PMMA
Polymides
Laminates
GFRP
CFRP
Uniply
KFRP
GFRP
CFRP
Zn alloys
Al alloys
Ti-
alloys
Glasses
Brick
etc.
Ni alloys
Steels
SiC
Al203
Si3N4
Compression
Mullites
Mg0
Zr02
H
ar
dn
es
s 
(R
oc
kw
el
l C
)
Distance from quenched end (mm)
0 10 20 30 40 50
10
20
30
40
50
60
70
JUVINALL: Machine Design
Fig. P3-14 W-75
P
JUVINALL: Machine Design
Fig. 4-1 W-76
(c)
�
�
�
�
(a)
Isometric view of tensile link
loaded through a pin at one
end and a nut at the other.
(b)
(d)
� = 
Equilibrium of left half showing uniform stress distribution at cutting plane
(e)
View showing "lines of force" through the link
Nut
P
E
E
E
Direct view of element EEnlarged view of element E
+
+
D
P
A
�D2A =
4
P
2
P
2
JUVINALL: Machine Design
Fig. 4-2 W-77
3
1
5
(b)(a) P
P
4
3
1
2
5
6
3
1
3
P
P
JUVINALL: Machine Design
Fig. 4-3 W-78
2
PP
JUVINALL: Machine Design
Fig. 4-4 W-79
JUVINALL: Machine Design
Fig. 4-5 W-80
(a)
T
T
Isometric view
(b)
E
E
E E
Enlarged view of
element
(c)
Direct view of
element E
(d)
Positive shear
Positive shear
Negative
shear
Negative
shear
Shear sign
convention
(a)
T
(b)
2
Torque axis
Zero shear stress exists
along all edges.
Maximum shear stress exists
along this line.
Enlarged view of
element 2
JUVINALL: Machine Design
Fig. 4-6 W-81
a
T
b
Line "A"
3
21
Top
Side Fro
nt
(a)
�max
(b) (c)
Partial beam in equilibrium
Entire beam in equilibrium
Neutral
surface
Transverse
cutting plane
Neutral
bending
axis and
centroidal
axis Typical cross sections
M M
JUVINALL: Machine Design
Fig. 4-7 W-82
M
c
c y
Neutral (bending) surface
(a)
�max
(b) (c)
Partial beam in equilibrium
Entire beam in equilibrium
Neutral
surface
CG
CG CG CG
Typical cross sections
Neutral bending axis
and centroidal axis
M M
JUVINALL: Machine Design
Fig. 4-8 W-83
M
c
y
Neutral (bending) surface
(a)
Initially straight beam segment
(b)
(c)
Initially curved beam segment
CG
Hyperbolic stress distribution with
increased stress at inner surface
M
e
Typical cross section
Center of
initial curvature
Neutral surface
JUVINALL: Machine Design
Fig. 4-9 W-84
M
Centroidal surface
Neutral surface
displaced distance
"e " toward inner
surface
co
ci
Centroidal surface
d�
�
b
ci
a d'
c'
c
e
e
y
d
M M
Neutral surface
Neutral axis
CG
Center of initial curvature
Centroidal axis
JUVINALL: Machine Design
Fig. 4-10 W-85
c
c
ro
co y
r
rnri
�
r
rn
M
c I
Va
lu
es
 o
f 
K
 in
 E
q.
 4
.1
1
: 
�
 =
 K
Ratio r /c
1 2 3 4
Round, elliptical or trapezoidal
Values of Ko for outside fiber as at B
U or T
I or hollow rectangular
5 6 7 8 9 10
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
JUVINALL: Machine Design
Fig. 4-11 W-86
Values of Ki for inside fiber as at A
I or hollow rectangular
Trapezoidal
b
B
B A B
B A
A
B A
b
bA
8
b
2
b
3b
6
A
AB
B b
b
c
c
c
c
4
Round or elliptical
U or T
r
r
JUVINALL: Machine Design
Fig. 4-12 W-87
M
M M
M
h
b
h
h
2
Centroidal axis
CG
r = h
c =
dA = b d�
�
b
JUVINALL: Machine Design
Fig. 4-13 W-88
(b)(a)
Loaded "curved beam"Unloaded "curved beam"
JUVINALL: Machine Design
Fig. 4-14 W-89
M
N.A.
�
�
M
M + dM
Enlarged view of beam segment
V
V
dA dA
y
My/I (M + dM)y/I
dA
b
y0
y c
x dx
Neutral axis
JUVINALL: Machine Design
Fig. 4-15 W-90
(a)
Marked and unloaded
(b)
Loaded as a beam
4
3
N.A.
�av = V/A
�max = V/A
JUVINALL: Machine Design
Fig. 4-16 W-91
3
2
�av = V/A
�max = V/A
N.A.
JUVINALL: Machine Design
Fig. 4-17 W-92
M
V
M
V
JUVINALL: Machine Design
Fig. 4-18 W-93
M
V
X X
100
80
60
100
+40,000 N
–40,000 N
40,000 N
80,000 N
40,000 N
60
40
JUVINALL: Machine Design
Fig. 4-19 W-94
(c)
b = 20
dA = 20dy
dA = 60dy
dx
�
40
(b)
b = 20
dA = 60dy
dx
�
10+
(a)
dA = 60dy
dx
10–
b = 60
�
� = 7.61 MPa0
� = 22.83 MPa
� = 32.61 MPa
JUVINALL: Machine Design
Fig. 4-20 W-95
Oblique viewDirect view
�x
(a)
Marked eraser
(b)
(c)
Enlarged view of element
Oblique viewDirect view
(e)
Element subjected to �max
Loaded eraser
(d)
+�
+�
�max
x
S'
y0
S
Mohr's circle
JUVINALL: Machine Design
Fig. 4-21 W-96
x
y
y
y
x x
S'
S'S
S
S'
S
yx
yx
(a)
Marked eraser (for twisting)
(b)
Enlarged element
(c)
+�
+�
�1�2
#1#2
x
y
Mohr's circle
JUVINALL: Machine Design
Fig. 4-22 W-97
(d)
y
y
y
x
x
TT
x
#2 #1
0
2000 lb
JUVINALL: Machine Design
Fig. 4-23 W-98
2 in.
1 in.
3 in. rad.
JUVINALL: Machine Design
Fig. 4-24 W-99
"B" is at bottom of shaft, opposite "A"
Top of shaft
B
2 in.
A
JUVINALL: Machine Design
Fig. 4-25 W-100
B
V = 2000 lb
2000 lb
M = 4000 in.lb
2000 lb
4000 in.lb
Load diag.
2000 lb
Shear diag.
Moment diag.
2000 lb
4000 lb
V
M
T = 6000 lb in. 
A
y
y
x
y
x
x
y
A A x
JUVINALL: Machine Design
Fig. 4-26 W-102
2 in.
(a)
Isometric view
(b)
Enlarged isometric view
(c)
Direct view
Calculated values: � = 40.8 ksi
 � = 30.6 ksi
(d)
Isometric view
A
�yx
�yx
�yx
�yx
�xy
�x�x
�x
�x
�xy
�xy
�xy
A
x y
�yx�xy
y
y
x A x
JUVINALL: Machine Design
Fig. 4-27 W-103
�yx = 30.6 ksi
�yx
�xy
�x = 40.8 ksi
Direct view of
element A
y (0, +30.6)
x (40.8, –30.6)
�max = 37 ksi
�2 = –17 ksi
+�
+�
�xy
34°
56°
0
�1 = 57 ksi
y
y
x
A
�1 = 57 ksi
�2 = –17 ksi
28°
x
JUVINALL: Machine Design
Fig. 4-28 W-104
y
y
x
A
� = 20 ksi
� = +37 ksi
� = –37 ksi
� = 20 ksi
17°
x
JUVINALL: Machine Design
Fig. 4-29 W-105
–�
JUVINALL: Machine Design
Fig. 4-30 W-106
(�2, 0) (�1, 0)
(�y, �yx)
(�x, �xy)
�x + �y
2
�x – �y
2
0
2
+�
–�
+�
2�
1
�xy
2 +
2
2
�x – �y
�1 + �2
2
�1 – �2
2
cos 2�
�1 – �2
2
sin 2�
0
2
JUVINALL: Machine Design
Fig. 4-31 W-107
+�
+�
�2
�1
2�
1
JUVINALL: Machine Design
Fig. 4-32 W-108
z
x
y
A A
(2) (= z)
(a)
Original element
(c)
1-2 plane
(b)
Principal element
(3)
(1) (2)
(1)
(d)
1-3 plane
(3)
(1)
(e)
2-3 plane
(3)
(2)A
JUVINALL: Machine Design
Fig. 4-33 W-109
+�
�max = 37
Principal circle
123
(57, 0)(0, 0)(–17, 0)
+�
JUVINALL: Machine Design
Fig. 4-34 W-110
A
A �1 (tangential)
�2 (axial)
�3 = 0 (radial)
+�
0 +��2 �1�3
Correct value of �max
Erroneous value of �max obtained if �3 is neglected
r/d
0 0.1 0.2 0.3
1.0
1.2
1.4
1.6
1.8
2.0Kt (a)
2.2
2.4
2.6
2.8
3.0
JUVINALL: Machine Design
Fig. 4-35 W-111
D d
r
M M
Mc
I
32M
�d3
�nom = =
D/d = 6
3
1.5
1.1
1.03
1.01
r/d
0 0.1 0.2 0.3
1.0
1.2
1.4
1.6
1.8
2.0
Kt
(b)
2.2
2.4
2.6
D d
r
PP
P
A
4P
�d2
�nom = =
D/d = 2
1.5
1.2
1.05
1.01
r/d
0 0.1 0.2 0.3
1.0
1.2
1.4
1.6
1.8
2.0
Kt
(c)
2.2
2.4
2.6
D d
r
T T
Tc
J
16T
�d3
�nom = =
D/d = 2
1.2
1.09
r/d
0 0.1 0.2 0.3
1.0
1.2
1.4
1.6
1.8
2.0Kt (a)
2.2
2.4
2.6
2.8
3.0
JUVINALL: Machine Design
Fig. 4-36 W-112
M M
Mc
I
32M
�d3
�nom = =
D/d ≥ 2
1.1
1.03
1.01
0 0.1 0.2 0.3
1.0
1.2
1.4
1.6
1.8
2.0
Kt
(c)
2.2
2.4
2.6
D/d ≥ 2
1.1
1.01
r/d
r/d
0 0.1 0.2 0.3
1.0
1.2
1.4
1.6
1.8
2.0Kt (b)
2.2
2.4
2.6
2.8
3.0
D/d ≥ 2
1.1
1.03
1.01
PP
P
A
4P
�d2
�nom = =
T T
D d
D d
D d
Tc
J
16T
�d3
�nom = =
r
r
r
d/D
0 0.1 0.2 0.3
1.0
1.2
1.4
1.6
1.8
2.0
Kt
2.2
2.4
2.6
2.8
3.0
MM TT
PP
D
d
Axial load:
Bending (in this plane):
�nom = ≈
P
A
P
(�D2/4) – Dd
�nom = ≈
Mc
I
M
(�D3/32) – (dD2/6)
Torsion:
�nom = ≈
Tc
J
T
(�D3/16) – (dD2/6)
JUVINALL: Machine Design
Fig. 4-37 W-113
r/h
(a)
0 0.05 0.10 0.15 0.20 0.25 0.30
1.0
1.2
1.4
1.6
1.8
2.0Kt
2.2
2.4
2.6
2.8
3.0
JUVINALL: Machine Design
Fig. 4-38 W-113A
H/h = 6
2
1.2
1.05
1.01
M
r b
M
Mc
I
6M
bh2
�nom = =
r/h
(b)
0 0.05 0.10 0.15 0.20 0.25 0.30
1.0
1.2
1.4
1.6
1.8
2.0Kt
2.2
2.4
2.6
2.8
3.0
H/h = 3
1.5
2
1.15
1.05
1.01
P
A bh
P�nom = =
PP
hH
r b
hH
r/h
(a)
0 0.05 0.10 0.15 0.20 0.25 0.30
1.0
1.2
1.4
1.6
1.8
2.0Kt
2.2
2.4
2.6
2.8
3.0
JUVINALL: Machine Design
Fig. 4-39 W-114
H/h = ∞
1.5
1.15
1.05
1.01
M
r b
h MH
Mc
A
6M
bh2
�nom = =
r/h
(b)
0 0.05 0.10 0.15 0.20 0.25 0.30
1.0
1.2
1.4
1.6
1.8
2.0Kt
2.2
2.4
2.6
2.8
3.0
H/h = ∞
1.5
1.15
1.05
1.01
r
b
h H
P
A bh
P�nom = =
PP
JUVINALL: Machine Design
Fig. 4-40 W-114A
d/b
(a)
0 0.1 0.2 0.3 0.4 0.5 0.6
d/b
(b)
0 0.1 0.2 0.3 0.4 0.5 0.6
1.0
7
6
5
4
3
2
1
1.2
1.4
1.6
1.8
2.0Kt
Kt
2.2
2.4
2.6
2.8
3.0
d/h = 0
0.25
0.5
M
M
PP
d bh
d bh
Mc
I
6M
(b-d)h2
�nom = =
P
A (b-d)h
P�nom = =
2.0
1.0
Pin
loaded
hole
Unloaded
hole
W/w
1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
1
2
3
4
5
6
7
8
9Kt
10
11
12
13
14
15
16
17
18
JUVINALL: Machine Design
Fig. 4-41 W-115
t
h
w
P
r
W
P
A
�nom = =
P
wt
r/w = 0.050
r/w = 0.10
r/w = 0.20
h/w = 0.5
0.5
0.75
0.5
0.75
1.0
0.75
1.0
1.0
3.0
3.0
3.0
F F
�
�
Sy
Su
JUVINALL: Machine Design
Fig. 4-42 W-116
F F
(a) Unnotched
Stress
F = ASy
(c)
(e)
� = Sy
Stress
�max = Sy
�av = Sy /2
Stress con. factor = K = 2Same cross-section area = K
F =
ASy
2
(d)
Stress
� = Sy
F
( f )
a
b
c
d
(b) Notched
JUVINALL: Machine Design
Fig. 4-43 W-117
0
(a) Load causes no yielding
+ Sy
0
(b) Load causes partial yielding
+ Sy
0
(c) Load causes partial yielding
+ Sy
0
(d) Load causes total yielding
Load stress + =
+
+
+
+
+
=
=
=
=
Sy –2Sy –Sy
–Sy – 0
– 0
– 0
– 0
– 0 +
– 0 +
– 0 +
– 0 +
Load removal
stress change
Residual stress
JUVINALL: Machine Design
Fig. 4-44 W-118
F1
F2
M1 M1
F2
F110 mm
10 mm
50 mm
0
–300 MPa
300 mPa
25 mm
Z = bh
2
6
Z =
Z = 1.042 × 10–5 m3
(0.025)(0.050)2
6
0 300 396 –396
–238
–96
62
Load stress
+
+
=
=
(a) Given information (see text)
(b)
––
0
Load removal stress change
––
0
Residual stress
––
0–96
62
62
62
–104
–62
–200
Residual stress
+
+
=
=(c)
––
0
Load stress
––
0
Total stress (straight beam)
––
0–96 300
Residual stress
+
+
=
=(d)
––
0 396
238
Load stress
––
0
Total stress (ready to yield)
––
0–96 –204
–122
–300
–60
Residual stress
+
+
=
=(e)
––
0
Load stress
––
0
Total stress (ready to yield)
––
JUVINALL: Machine Design
Fig. 4-45 W-119
10.000 in.
T = 80°F
P = 0 lb P = 0 lb
10.008 in.
T = 480°F
P = 60,000 lb P = 60,000 lb
JUVINALL: Machine Design
Fig. 4-61 W-142
60 mm
10 mm dia.
20 mm
P = 400 kN
P
JUVINALL: Machine Design
Fig. P4-2 W-120
FEDCBA
JUVINALL: Machine Design
Fig. P4-10 W-121
di = 20 mm
do = 24 mm
�max = 100 mm
T
JUVINALL: Machine Design
Fig. P4-11 W-122
b
2rT
T
T
T
JUVINALL: Machine Design
Fig. P4-18 W-123
M M
h
r
b
JUVINALL: Machine Design
Fig. P4-19 W-124
4 in.
200 lb
200
lb
1-in.-dia round rod
3 in.
JUVINALL: Machine Design
Fig. P4-21 W-125
A
P Q
A
60
70,000 N
40 80
120
JUVINALL: Machine Design
Fig. P4-23 W-126
h
X
b
a
c
F
JUVINALL: Machine Design
Fig. P4-24 W-127
2 in.
13
in.16
3
in.16
3 in.
4
3
in.16
1 in.
JUVINALL: Machine Design
Fig. P4-25 W-128
A
A
12,000 N
30 mm
24 mm
8 mm
5 mm
5 mm
Section AA
30 mm
400 N
120-mm-dia.
sheave
Free end
of shaft 
100
2000 N
JUVINALL: Machine Design
Fig. P4-27 W-131
B
Connected to
flexible coupling
and clutch
20-mm-
dia. shaft
A
S
T
100
JUVINALL: Machine Design
Fig. P4-29 W-129
8 in.
in.3
in.
in.
1
2
1
2
in.12
3
8
JUVINALL: Machine Design
Fig. P4-30 W-130
5
5 5
5 50
40
12 kN
L
2
Cement L
2
JUVINALL: Machine Design
Fig. P4-34 W-132
100 mm
250 mm
200 mm
25-mm-dia. round
rod bent into crank
1000 N
1 in.
6-in. dia.
1-in. dia.
shaft
Motor
1000-lb
belt tension
3000-lb
belt tension
JUVINALL: Machine Design
Fig. P4-36 W-133
50-mm dia.
100-mm dia.
30-mm dia.
JUVINALL: Machine Design
Fig. P4-40 W-134
50 mm
100 mm
50 mm
4000 lb
F
B
A
500 lb
JUVINALL: Machine Design
Fig. P4-38 W-134a
3 in.
4 in.
3 in.
2 in.
1000 lb
4 in.
1-in.-dia. shaft
A
B
A
JUVINALL: Machine Design
Fig. P4-41 W-135
JUVINALL: Machine Design
Fig. P4-46 W-136
y x
18 45
30
JUVINALL: Machine Design
Fig. P4-49 W-139
Free surface, �3 = 0
20 ksi
30 ksi
JUVINALL: Machine Design
Fig. P4-52 W-140
100
350
75
JUVINALL: Machine Design
Fig. P4-52 W-141
5000 N5000 N 30 mm 200 mm
15 mm
25 mm
500 mm 250 mm
JUVINALL: Machine Design
Fig. P4-54 W-137
d = 40 mm d = 40 mm
r = 5 mm
A
RA
B
RB
1000 N
D = 80 mm
JUVINALL: Machine Design
Fig. P4-55 W-138
5000 N 5000 N50 mm 100 mm
15 mm
25 mm
C
al
cu
la
te
d 
el
as
ti
c
st
re
ss
 (
M
P
a)
Time
0 1 2 3 4 5 6 7 8 9 10 11 12
–200
0
200
400
JUVINALL: Machine Design
Fig. P4-65 W-143
JUVINALL: Machine Design
Fig. 5-1 W-144
(a) (d) (e)(b) (c)
Z
Y
X
x
y
z
dy (neg.)
dz (neg.)
dx
x → 0
�x = lim
dx
x
y → 0
�y = lim
dy
y
z → 0
�z = lim
dz
z
Unloaded element
Element loaded in uniaxial
tension in X direction (with
deflections shown exaggerated)
JUVINALL: Machine Design
Fig. 5-2 W-145
JUVINALL: Machine Design
Fig. 5-3 W-146
�
dx
�yx
�xy
�xy (shown counterclockwise, hence negative)
�yx (shown clockwise, hence positive)
y
x
Z X
Y
y → 0
absolute value = lim = tan � ≈ �dxy
JUVINALL: Machine Design
Fig. 5-4 W-147
+�/2
x
y
0
+�
�2
�y
�x
�xy
�1
JUVINALL: Machine Design
Fig. 5-5 W-148
(a)
Single-element gages oriented
to sense horizontal strain
(b)
Two-element rosettes oriented
to measure horizontal and
vertical strain
(c)
Three-element equiangular
rosettes
(d)
Three-element rectangular
rosettes
JUVINALL: Machine Design
Fig. 5-6 W-149
�2
�1
�240
�120
�0
+�
+�
120°
240°
�2
�1
�120 �240
�0
+�
+�
�2
�1
�240 �120
�0
+�
+�
(a) (b) (c)
JUVINALL: Machine Design
Fig. 5-7 W-150
17°
240° gage
(� = +0.00185)
120° gage (� = +0.0004)
0° gage (� = –0.00075)
�1 = +0.0020
�2 = –0.0010
JUVINALL: Machine Design
Fig. 5-8 W-151
+� /2
120°
240°
0°
34°
+0.00185–0.00075
+0.0004
�2 = –0.001 �1 = +0.0020
+�
JUVINALL: Machine Design
Fig. 5-9 W-152
90°
�2
�1
�0
�90
(a)
45°
+�
+�
�2
�1
�90
�0
�45�45
(b)
+�
+�
�90
�2
�1
�0
�45
(c)
+�
+�
JUVINALL: Machine Design
Fig. 5-10 W-153
+2600 �m/m
+450 �m/m
–200 �m/m
(a)
(b)
�0 = +2600
�90 = +450
�45 = –200
�0 = +2600
�90 = +450
�2 = –510
�1 = +3560
�45 = –200
JUVINALL: Machine Design
Fig. 5-11 W-154
29°
119°
JUVINALL: Machine Design
Fig. 5-12 W-155
+� /2
0°
45°
90°
2600
–510 3560
+�
–200
4500
58°
+�
0
+�
JUVINALL: Machine Design
Fig. 5-13 W-156
�2 = –24
�3 = 0
�1 = 134 �1 = 0.002
(a)
+� /2
+�
�2 = –0.001 �3 = –0.0005
(b)
0
0
–0.04
–1.2
–0.8
–0.4
0
–0.8
–0.4
0
0.4
0.8
0.4
0.8
1.2
, 
(1
0
–6
/m
m
)
M
, 
be
nd
in
g 
m
om
en
t 
(k
N
•m
m
)
V,
 s
he
ar
 f
or
ce
 (
kN
)
0
4
8
12
0
200
400
–2
–1
0
1
2
–0.08
–0.12
D
ef
le
ct
io
n 
(m
m
)
R
el
at
iv
e 
sl
op
e 
(m
ill
ir
ad
ia
ns
)
JUVINALL: Machine Design
Fig. 5-14 W-159
0.093
–0.677
–0.220
0.270
0.835
0.838
0.022
0.007
0.115
0.126
Tangent point
Parallel to true line
of zero deflection
True line of
zero deflectionL
oc
at
io
n 
of
 z
er
o
ab
so
lu
te
 s
lo
pe
In
it
ia
lly
 a
ss
um
ed
lo
ca
ti
on
 o
f 
ze
ro
 s
lo
pe
0.119
+0.001
–1.109
–1.096
A =
0.093 mm
A = 0.011
A = 13 × 10–6
A = 11,000
A = 36,000
M EI
A = 3 × 10–6
A =
0.457 × 10–3 A =
0.270 × 10–3
A = 0.565 × 10–30.220 × 10–3
0.419
× 10–3
A = 0.120 mm
A
bs
ol
ut
e 
sl
op
e 
(m
ra
d)
0.85
2.67
8.46
220 255
325 360
1822
9.80
5.12 5.67
0.69
1.94 2.47 0.28
Area = 58,000 kN•mm2
2.2
0.7
Area =
220 kN•mm
Area = 140 kN•mm
Area = 360 kN•mm
–1.8
d = 30
2.2 kN 1.8 kN
10
d = 40
1050 50
100 200 200
d = 40
1.5 kN 2.5 kN
d = 50d = 60
0 ∆
Deflection
Area = U'
Area = U
Area = dU
dQ
JUVINALL: Machine Design
Fig. 5-15 W-160
QLoad
Area = dU'
JUVINALL: Machine Design
Fig. 5-16 W-161
L/2 P/2P/2
x dx
L
P
b
h
JUVINALL: Machine Design
Fig. 5-17 W-162
200 mm 2500 N2500 N L = 400 mm
P = 5000 N
b = 25 mm
h = 50 mm
JUVINALL: Machine Design
Fig. 5-18 W-163
L
P
h
b
x
c
a
y
Q
JUVINALL: Machine Design
Fig. 5-19 W-164
F
h
b
V
F
F
P M
F
R
R
�
2R
�
�
R – R cos �
(a) (b)
si
n 
�
–1.0
–0.5
0
sin � d� = 1;
(From this, average value = can be determined)
�/2
0
0.5
1.0
2
�
2
�
2
�
4
�
2
�
Avg value =
co
s 
�
–1.0
–0.5
0
0.5
1.0
2
�Avg value =
si
n 
�
 c
os
 �
� (radians)
0 �/2 � 3�/2 2�
–0.5
0
0.5
(0.707)(0.707) = 0.5
2
�Avg value = 0.5 =
1
� = (Half of avg value shown in sin � plot)
co
s2
 �
0
0.5
1.0
Avg value = 0.5
si
n2
 �
0
0.5
1.0
Avg value = 0.5
∫ sin � d� = 02�0∫sin � d� = 2;�0∫
cos � d� = 1;
�/2
0∫ cos � d� = 02�0∫cos � d� = 0;�0∫
sin2 � d� = (0.5) = ;
�/2
0∫ sin2 � d� = �(0.5) =�0∫
sin2 � d� = �
2�
0∫
2
�
4
�
2
�
cos2 � d� = (0.5) = ;
�/2
0∫ cos2 � d� = �(0.5) =�0∫
cos2 � d� = �
2�
0∫
2�
�1
2
1
sin � cos � d� = = ;
�/2
0∫ sin � cos � d� = 0�0∫
sin � cos � d� = 0
2�
0∫
JUVINALL: Machine Design
Fig. 5-20 W-165
JUVINALL: Machine Design
Fig. 5-21a W-166
F
h = 0.3 in.
b = 0.2 in.
E = 18 × 106 psi
G = 7 × 106 psi
F
R =
 2.0
 in.
�
2R = 4 in.
(a)
Copper
Cast iron
Steel
0.2 0.3
Width, h (in.)
(b)
D
ef
le
ct
io
n,
 �
 (
in
.)
0.4 0.5
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
JUVINALL: Machine Design
Fig. 5-21b W-167
D
ef
le
ct
io
n,
 �
 (i
n.
)
Radius, R (in.)
1.0 1.5 2.0 2.5 3.0
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
JUVINALL: Machine Design
Fig. 5-21c W-168
Copper
Cast iron
Steel
0.06
0.05
0.04
0.03
D
ef
le
ct
io
n,
 �
 (
in
.)
0.02
0.01
0.5
0.4
Thic
kne
ss, b
 (in.
)
0.3
0.2
0.3
Width, h (in.)
0.2
0.1
JUVINALL: Machine Design
Fig. 5-21d W-169
F
JUVINALL: Machine Design
Fig. 5-22 W-170
3 m
10 m
y
a
Point of zero
deflection
1.2 m
500 kg mass
P/2
JUVINALL: Machine Design
Fig. 5-23 W-171
a x
y
b
2
a
3'
2'
1
2
3
b
2
Pa/2
M0
P/2
P
P/2
P/2
M0
M0
Pa/2
M0
P/2
M0
P/2
M0
(a)
(b)
P
JUVINALL: Machine Design
Fig. 5-24 W-172
e
L or Le
P
P
P
P
x x
y
y
(b)
Column cross section
(a)
Two views of column
Axis of least I and � becomes
neutral bending axis when
buckling occurs. With column
formulas, always use I and �
with respect to this axis.
Slenderness ration Le /�
10 100
0.0001
0.001
0.010
Scr
E
0.100
JUVINALL: Machine Design
Fig. 5-25 W-173
Slenderness ratio Le /�
20 40 60 80 100 120 140 1600
20
40
60
80
A
B
C
D
100
120
140
160
180
JUVINALL: Machine Design
Fig. 5-26 W-174
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
C
ri
ti
ca
l u
ni
t 
lo
ad
 S
cr
 (
ks
i)
C
ri
ti
ca
l u
ni
t 
lo
ad
 S
cr
 (
M
P
a)
Sy = 689 MPa
Arbitrary values
for illustration
Sy = 496 MPa
Euler, E = 203 GPa (steel)
E
F
Euler, E = 71 GPa (alum)
JUVINALL: Machine Design
Fig. 5-27 W-175
L
Le
(b)
L Le
(c)
Le = L
(a)
(Buckled
shape shown
dotted)
L Le
(d)
L
Le
2
(e)
Le = 0.707L Le = 0.5LLe = L Le = L Le = 2LTheoretical
Le = 0.80L Le = 0.65LLe = L Le = 1.2L Le = 2.1L
Minimum
AISC
Recommend
Source: From Manual of Steel Construction, 7th ed., American Institute of Steel Construction, Inc., New York, 1970, pp. 5–138.
Slenderness ratio Le /�
20 40 60 80 100 120 140 1600
20
40
60
80
A
B
C
D
100
120
140
160
180
JUVINALL: Machine Design
Fig. 5-28 W-176
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
C
ri
ti
ca
l u
ni
t 
lo
ad
 S
cr
 (
ks
i)
C
ri
ti
ca
l u
ni
t 
lo
ad
 S
cr
 (
M
P
a)
Sy = 689 MPa
Johnson,
E = 71 GPa,
Sy = 496 MPa
Johnson, E = 203 GPa, Sy = 689 MPa
Euler, E = 203 GPaTangent
points
Euler, E = 71 GPa
E
F
Sy = 496 MPa
JUVINALL: Machine Design
Fig. 5-29 W-177
80,000 N 80,000 N
D
1 m
SF = 2.5
Sy = 689 MPa
E = 203 GPa (steel)
JUVINALL: Machine Design
Fig. 5-30 W-178
80,000 N 80,000 N
D
200 m
SF = 2.5
Sy = 496 MPa
E = 71 GPa (aluminum)
C
ri
ti
ca
l u
ni
t 
lo
ad
 S
cr
 
(M
P
a)
C
ri
ti
ca
l u
ni
t 
lo
ad
 S
cr
 (
ks
i)
Slenderness ratio Le/�
20 40 60 80 100 120 140 160 180 2000
100
50
150
200
250
300
350
400
450
500
550
600
10
0
20
30
40
50
60
70
80
JUVINALL: Machine Design
Fig. 5-31 W-179
ec/�2 = 1.0
ec/�2 = 0
0.6
0.3
0.1
Euler curve
0.05
JUVINALL: Machine Design
Fig. 5-32 W-180
(a)
Wrinkling, or "accordian
buckling" of thin-wall tube
(b)
Typical local buckling of
an externally pressurized
thin-wall tube
(c)
Wrinkling of thin, unsupported
flanges of a channel section
JUVINALL: Machine Design
Fig. 5-33 W-180A
Beam
Triangle
Quadrilateral
Tetrahedron
Pentahedron
Hexahedron
JUVINALL: Machine Design
Fig. 5-34 W-180B
(1)
(3)
(6)
(7) (9)
(2) 31
2
5 7
W
4
6
(5) (10)
(4)
(8)
(11)
JUVINALL: Machine Design
Fig. 5-35 W-180C
�3x
�3x
3'
3
F (7)3y F (7)3x
6'
6
F (7)
L 6y
F (7)6x �6x
�6x
JUVINALL: Machine Design
Fig. 5-36 W-180D
�
3 3'
F (7)3x
�3x
F (7)
A, E
L
3y
F3
6
�
2 m
2
2' (Constant A, E)
3 N
2 N
3.464 m
4 m
�2x
�2y
�3x
(3)
(2)
3 3'
1
JUVINALL: Machine Design
Fig. 5-37 W-180E
F (1)2y F
(2)
2y
F (1)2x
F (1)1y
F (3)1y
F (3)1x
F (1)1x
F (2)3y
F (2)3x
F (2)2x
(1)
(2)
(3)
4 m
1
1
3
F (3)3y
F (3)3x
3
2 2
2 m
3.464 m
JUVINALL: Machine Design
Fig. 5-38 W-180F
JUVINALL: Machine Design
Table 5-1 W-157
L
P
�
� = PLAE
1. Tension or compression
Cross-section area = A
L
T
�
�
�
2. Torsion
For solid round bar and
deflection in degrees,
K'a = section property. For solid
round section, K' = J = �d4/32.
3. Bending (angular deflection)
I = moment of inertia about
neutral bending axis
M
M
L
4. Bending (linear deflection)
I = moment of inertia about
neutral bending axis
L
�
5. Cantilever beam loaded at end
I = moment of inertia about
neutral bending axis
L
P
� = TLK'G
� = MLEI
� = ML
2
2EI
� = PL
3
3EI
k = =P
�
AE
L
K = =T
�
K'G
L
K = =M
�
EI
L
k = =M
�
2EI
L2
k = =P
�
3EI
L3
�° =
584TL
d4G
(d4 – d4)
JUVINALL: Machine Design
Table 5-2 W-158
d
do
2b
2a
a
a
b
a
K' = J = �d
4
32
di K' = J = o i
�
32
– 3.36 1 –K' = ab
3
16
b4
12a4
16
3
b
a
d
t
K' = �dt
4
32
K' =
K' = 0.0216a4
K' = 2.69a4
�a3b3
a2 + b2
a
a
K' = 0.1406a4 
JUVINALL: Machine Design
Fig. P5-4 W-181
�120 = +625
�240 = +300
�0 = +950
JUVINALL: Machine Design
Fig. P5-9 W-183
�0 = –300
�135 = –380
�270 = –200
�90 = –300
�45 = –380
�0 = –200
Gage readings Equivalent rosettes
JUVINALL: Machine Design
Fig. P5-14 W-182
k = 5 N/mm
A
B
C
100 mm
100 mm
100 mm
F
F
F
JUVINALL: Machine Design
Fig. P5-15 W-184
200 mm
25 mm-dia. steel
1000 N
100 mm
A
JUVINALL: Machine Design
Fig. P5-16 W-185
d = 30 d = 50 d = 40
4 kN
2 kN
100 200 150
JUVINALL: Machine Design
Fig. P5-17 W-186
a
Z
b
YX
F (used in Problem 5.17)
T (used in Problem 5.18)
Solid round rod of
properties E, G, A,
I, and J.
JUVINALL: Machine Design
Fig. P5-19 W-186a
w = 200 lb/in.
d
5 in. 15 in. 5 in.
0.75d 0.75d
JUVINALL: Machine Design
Fig. P5-20 W-187
a
a F
F
b
JUVINALL: Machine Design
Fig. P5-21 W-188
P
R
JUVINALL: Machine Design
Fig. P5-22 W-189
F
b
h
2
b
2
L
JUVINALL: Machine Design
Fig. P05-23 W-190
5 kN
S
500 mm
300 mm
JUVINALL: Machine Design
Fig. P5-27 W-191
2
1 1
2
1 m
0.7 m
1 m
0.7 m
Boom
12 mm-dia. tie-rod
6 kN
JUVINALL: Machine Design
Fig. P5-29 W-192
JUVINALL: Machine Design
Fig. 6-2 W-194
2w
2c
t
P
P
(a) Center crack
w
t
P
P
(b) Edge crack
c
JUVINALL: Machine Design
Fig. 6-3 W-195
2w
 = 6 in.
2c = 1 in.
t = 0.06 in.
7075–T651 Aluminum,
Su = 78 ksi, Sy = 70 ksi,
Kic = 60 ksi
P
P
in.
JUVINALL: Machine Design
Fig. 6-4 W-196
P
P
a
2c
2w
t
JUVINALL: Machine Design
Fig. 6-5 W-197
P
P
a
2c
2w
 = 6 in.
t = 1 in.
�g = 0.73 Sy
a/2c = 0.25
Ti – 6Al – 4V (annealed)
titanium plate
JUVINALL: Machine Design
Fig. 6-6 W-198
+�
�2 = 40 ksi
(�max = 60)
�1 = 80 ksi
(a) Proposed application involving
�1 = 80, �2 = –40, �3 = 0
+�
+�
(�max = 50)
�2 = �3 = 0�3 = 0
�1 = 100 ksi
(a) Standard tensile test of
 proposed material. Tensile
 strength, S = 100 ksi
+�
JUVINALL: Machine Design
Fig. 6-7 W-199
+�
+�
Uniaxial
compression Uniaxial
tension
Principal Mohr circle
must lie within these
bounds to avoid failure
For biaxial stresses (i.e., �3 = 0),
�1 and �2 must plot within this
area to avoid failure
0
+�2
+�10
Suc Sut Suc
Sut
Suc
Sut
(a) Mohr circle plot (b) �1 – �2 plot
+�
+�
JUVINALL: Machine Design
Fig. 6-8 W-200
Principal Mohr
circle must lie
within these
bounds to avoid
failure
Uniaxial tension
Syt
+�2
+�1
Syt
Syt
0
For biaxial stresses (i.e., �3 = 0),
�1 and �2 must plot within this
area to avoid failure
(a) Mohr circle plot (b) �1 – �2 plot
JUVINALL: Machine Design
Fig. 6-9 W-201
Principal plane
Principal planes
Octahedral plane
+�2
(0, 100)
(–100, 100) (100, 100)
(100, 0)(–100, 0)
(–100, –100)
(0, –100)
(100, –100)
+�1
JUVINALL: Machine Design
Fig. 6-10 W-202
(–58, 58)
(58, –58)
(50, –50)
0
Shear diagonal (�1 = –�2)
Distortion energy theory
Normal stress theory
Shear stress
theory
Note: �3 = 0
+�
+�
JUVINALL: Machine Design
Fig. 6-11 W-203
Principal Mohr circle must
lie within these bounds
to avoid failure
SutSuc
+�2
+�1
Sut
Suc
Suc
+Sut
0
For biaxial stresses (i.e., �3 = 0),
�1 and �2 must plot within this
area to avoid failure
(a) Mohr circle plot (b) �1 – �2 plot
0
JUVINALL: Machine Design
Fig. 6-12 W-204
+�2
+�1
SutSuc
Sut
Suc
0
Shear diagonal
JUVINALL: Machine Design
Fig. 6-13 W-205
�2 = –25 ksi
�2 = –25 ksi
�1 = 35 ksi �1 = 35 ksi
Note: �3 = 0
Steel,
Sy = 100 ksi
JUVINALL: Machine Design
Fig. 6-14 W-206
–25
–100
�2 (ksi)
�1 (ksi)
35 58 66 100
(58, –58)
0
Normal load
point
Limiting
points
� theory
D.E. theory
� theory
Load line
Shear diagonal
S
tr
es
s 
(%
 o
f 
ul
ti
m
at
e 
st
re
ng
th
)
Load (% of ultimate load)
0 50
SF = 2 based on
load, Eq. 6.10
SF = 2 based on
strength, Eq. 6.9
Fracture
100
50
100
JUVINALL: Machine Design
Fig. 6-15 W-207
Fr
eq
ue
nc
y 
p(
x)
 a
nd
 p
(y
)
Strength (x), and stress (y) (MPa or ksi)
0 40 70
JUVINALL: Machine Design
Fig. 6-16 W-208
x (strength)y (stress)
�y �x
Fr
eq
ue
nc
y 
p(
z)
Margin of safety, z, where z = x – y
300
JUVINALL: Machine Design
Fig. 6-17 W-209
z (margin of safety)
�z
Fr
eq
ue
nc
y 
p(
x)
Quantity x
0 � x1
�1
�1 < �2 < �3
�2
�3
x2
JUVINALL: Machine Design
Fig. 6-18 W-210
Fr
eq
ue
nc
y 
p(
x)
Quantity x
–3� –2� –1� � +1� +2� +3�
JUVINALL: Machine Design
Fig. 6-19 W-211
0.13% 0.13%
2.14% 2.14%
13.60% 13.60%
34.13% 34.13%
of total
area
Inflection point Inflection point
%
 r
el
ia
bi
lit
y
(%
 o
f 
su
rv
iv
or
s 
or
 %
 c
um
ul
at
iv
e 
pr
ob
ab
ili
ty
 o
f 
su
rv
iv
al
)
Number of standard deviations, k
–4 –3 –2 –1 0 +1 +2 +3 +4
0.01
0.05
0.1
0.2
0.5
1
2
5
10
20
30
40
50
60
70
80
90
95
98
99
99.8
99.9
99.99
%
 o
f 
fa
ilu
re
s 
or
 P
, 
%
 c
um
ul
at
iv
e 
pr
ob
ab
ili
ty
 o
f 
fa
ilu
re
99.99
99.9
99.8
99
98
95
80
70
60
50
40
30
20
10
5
2
1
0.5
0.2
0.1
0.05
0.01
JUVINALL: Machine Design
Fig. 6-20 W-212
�
–k�
% of failures
Fatigue life, strength, etc.
Extreme
values
k = –4, 99.99683% reliability
k = –5, 99.9999713% reliability
k = –6, 99.9999999013% reliability
% of
survivors
Fr
eq
ue
nc
y 
p(
z)
Torque z (N • m)
(5.22)0
JUVINALL: Machine Design
Fig. 6-21 W-213
z = x – y
�z
Fr
eq
ue
nc
y 
p(
x)
 a
nd
 p
(y
)
Torque x and y (N • m)
(a)
(b)
0 (14.8) 20.0
One bolt in
500 twists off
x (bolt twist-
off strength)
y (wrench
twist-off torque)
�x�y
�x = 1 N • m
�y = 1.5 N • m
k�z
One bolt in
500 twists off
JUVINALL: Machine Design
Fig. P6-13 W-214
�1 = 200 MPa
�2 = 100 MPa
�2
�1 �1 = 150 MPa
�2 = –100 MPa
�2
�1 ba
JUVINALL: Machine Design
Fig. P6-23 W-215
�x �x = 50 MPa
Sy = 500 MPa
�xy = 100 MPa
�xy
k
JUVINALL: Machine Design
Fig. 7-1 W-216
c
k
m
(b)(a) (c)
k
m
m
S u
 a
nd
 S
y 
(k
si
)
Average strain rate (s–1)
10–6 10–5 10– 4 10–3 10–2 10–1 1 101 102 103
0
10
20
30
40
50
60
70
80
90
100
S y
 /
S u
 (%
)
E
lo
ng
at
io
n 
(%
)
0
10
20
30
40
50
60
70
80
90
100
JUVINALL: Machine Design
Fig. 7-2 W-217
Yield strength Sy
Ultimate strength Su
Total elongation
Ratio Sy /Su
�
k
(a) (b) (c)
Elastic-strain energy stored
in structure = Fe�Force
Fe
W O
h
Deflection
Work of falling weight = W (h + �)
Guide rod
h
�
�st
1
2
JUVINALL: Machine Design
Fig. 7-3a-c W-218
W
k
W
d
L /2
L /2
2d
JUVINALL: Machine Design
Fig. 7-4 W-219
(b)
d
L
(a)
�d2
4
Area = A = 
L
Bumper of
cross section A;
volume = AL 
h
JUVINALL: Machine Design
Fig. 7-5 W-220
W
 1 in. × 3 in., I = bh3/12 = 6.46 in.4
2 × 4 white pine
E = 106 psi
Mod. of rupture = 6 ksi
JUVINALL: Machine Design
Fig. 7-6 W-221
30 in.
12 in.
60 in.
100 lb/in. 100 lb/in.5
8
5
8
 Z = I/c = 3.56 in.3 
 100 lb
100-mm
dia
120-mm
dia
20-mm
dia
JUVINALL: Machine Design
Fig. 7-7 W-222
20 mm20 mm
250 mm
To
rs
io
na
l d
ef
le
ct
io
n 
of
 s
ha
ft
 (
de
g)
Shaft radius (mm)
5.0 7.5 10.0 12.5 15.0
0
5
10
15
20
25
30
35
40
JUVINALL: Machine Design
Fig. 7-7b W-223
S
ha
ft
 s
he
ar
 s
tr
es
s 
(M
P
a)
Shaft radius (mm)
5.0 7.5 10.0 12.5 15.0
100
200
300
400
500
600
700
Aluminum
Cast iron
Steel
Aluminum
Cast iron
Steel
JUVINALL: Machine Design
Fig. 7-8 W-224
Ki = 1.5
Ki = 1.5
d
JUVINALL: Machine Design
Fig. 7-9 W-225
Ki = 1.5
Ki = 3
Ki = 1.5
d
d
2
Ki = 3.4
A = 700 mm2
JUVINALL: Machine Design
Fig. 7-10 W-226
"Very long"
(>10d)
"Negligible"
Ki = 3.5
A = 600 mm2
Shank
Head
Ki = 3.4
A = 300 mm2
Ki =1.5
Ki = 3.0
Ki = 1.5
A = 600 mm2
(a) Original design (b) Modified design
d
JUVINALL: Machine Design
Fig. 7-10 W-229
K = 1.55
K = 4
Drop
weight
24 mm dia.
K = 1.4
30 mm dia.
JUVINALL: Machine Design
Fig. 7-11 W-227
(a)
Axial hole
(b)
"Very long"
K = 2
K = 2
1-in dia.
JUVINALL: Machine Design
Fig. 7-13 W-232
0.1-in dia. hole
Steel cable
A = 2.5 in.2
E = 12 × 106
JUVINALL: Machine Design
Fig. P7-2 W-228
JUVINALL: Machine Design
Fig. P7-5 W-228
K = 5000 N/mm
L = 5 m 
v = 4 km/hr 
m = 1400 kg
Rope
JUVINALL: Machine Design
Fig. P7-11 W-230
(a)
Original design New design
(b)
 Thread:
 Area = 600 mm2
K = 3.9
Thread:
Area = A
 K = 2.6
Area = A
K =
2.6
"Very long"
A= 600 mm2
K = 3.9
K = 1.3
K = 1.3
Platform
Area = 800 mm2
Area = 800 mm2
dia. = 36 mm
K = 2.2
250 mm
(Fracture
location)
3 mm
(negligible)
JUVINALL: Machine Design
Fig. P7-12 W-231
K = 1.5
Hole dia., d
A = 800 mm2
K = 3.8
(a)
Original design
(b)
Modified design
Assume that hole
drilled to this depth,
does not significantly
change the K = 3.8
factor at the thread.
JUVINALL: Machine Design
Fig. 8-2 W-234
Small region behaves plastically
Main body behaves elastically
0.300"
C
R
110-Volts AC
Flexible
coupling
JUVINALL: Machine Design
Fig. 8-3 W-235
Weights
Revolution
counter
Test specimen
9 "78
Motor
++
++
Fa
ti
gu
e 
st
re
ng
th
, 
or
P
ea
k 
al
te
rn
at
in
g 
st
re
ss
 S
 (
ks
i (
lo
g)
)
Life N (cycles (log))
103 104 105 106 107 108
10
20
30
40
50
60
70
80
100
JUVINALL: Machine Design
Fig. 8-4 W-236
(c) Log-log coordinates
Sn (endurance limit)'
'
'
"Knee" of curve
8:7 ratio
Not broken
7:1
ratio
Life N (cycles (log))
(a) Linear coordinates (not used for obvious reasons)
(b) Semilog coordinates
Sn (endurance limit)Fa
ti
gu
e 
st
re
ng
th
, 
or
P
ea
k 
al
te
rn
at
in
g 
st
re
ss
 S
 (
ks
i)
103 104 105 106 107 108
0
10
20
30
40
50
Not broken
Life N (cycles � 106)
Sn (endurance limit)Fa
ti
gu
e 
st
re
ng
th
, 
or
P
ea
k 
al
te
rn
at
in
g 
st
re
ss
 S
 (
ks
i)
0 10 20 30 40 50 60 70 80 90 100
0
10
20
30
40
50
Not broken
+++++
+
++++
++
++
++
+
+
+
+
++
++
+
++
++
++
++++
++
++
++
++
S/
S u
 (l
og
)
Life N (cycles(log)) Sn = 0.5 Su
(in ksi, Sn � 0.25 � Bhn;
in MPa, Sn � 1.73 � Bhn) 
103 1042 4 6 1052 4 6 1062 4 6 1072
Not broken
4 6
0.4
0.5
0.6
0.8
0.9
1.0
0.7
JUVINALL: Machine Design
Fig. 8-5 W-237
S = 0.9Su (in ksi, S � 0.45 � Bhn; in MPa, S � 3.10 � Bhn)
Sn
'
'
'
'
E
nd
ur
an
ce
 li
m
it
 
S n
 (k
si
)
'
'
E
nd
ur
an
ce
 li
m
it
 
S n
 (M
P
a)
Hardness (Rockwell C)
0 10 20 30 40 50
0.25 Bhn
60
187 229 285
Hardness (HB)
375 477 653
70
0
20
100
SAE 4063
SAE 5150
SAE 4052
SAE 4140
200
300
400
500
600
700
800
900
40
60
80
100
120
140
JUVINALL: Machine Design
Fig. 8-6 W-238
Actual maximum stress
Calculated maximum
stress (Mc /I ) 
JUVINALL: Machine Design
Fig. 8-7 W-239
MM
P
ea
k 
al
te
rn
at
in
g 
be
nd
in
g 
st
re
ss
 S
 (
ks
i (
lo
g)
S 
(M
P
a 
(l
og
))
Life N (cycles (log))
103 104 105 106 107
Wrought
Permanent
mold cast
Sand cast
108 109
5
6
7
8
10
12
14
16
18
20
30
35
25
40
50
60
70
80
50
75
100
150
200
250
300
400
500
JUVINALL: Machine Design
Fig. 8-8 W-240
Fa
ti
gu
e 
st
re
ng
th
 a
t 
5
 �
 1
0
8
 c
yc
le
s
S n
 (
ks
i)
S n
 (
M
P
a)
Tensile strength Su (ksi)
Su (MPa)
0 10 20 30
Alloys represented:
1100-0, H12, H14, H16, H18
3003-0, H12, H14, H16, H18
5052-0, H32, H34, H36, H38
2014-0, T4, and T6
2024-T3, T36 and T4
6061-0, T4 and T6
6063-0, T42, T5, T6
7075-T6
40 50
0 50 100 150 200 250 300 350 400 450 500 550
60 70
0 0
50
100
150
10
20
30
JUVINALL: Machine Design
Fig. 8-9 W-241
Sn = 19 ksi
Sn = 0.4Su'
''
'
P
ea
k 
al
te
rn
at
in
g 
st
re
ss
 S
 (
ks
i (
lo
g)
)
S
 (
M
P
a 
(l
og
))
Life N (cycles (log))
105 1062 4 6 8 1072 4 6 8 1082 4 6 8
5
6
50
75
100
150
200
7
8
9
10
12
14
16
18
20
25
30
35
40
JUVINALL: Machine Design
Fig. 8-10 W-242
Sand-cast
Extruded and forged
R
at
io
,
(l
og
)
pe
ak
 a
lt
er
na
ti
ng
 s
tr
es
s,
 S
 o
r 
S s
S u
Life, N (cycles (log))
103
Torsion
Axial (no eccentricity)
Bending
Sn = Sn = 0.5Su'
'
'
Sn = 0.9Sn = 0.45Su
Sn = 0.58Sn = 0.29Su
S103 = 0.9Su
S103 = 0.75Su
S103 = 0.9Sus (≈ 0.72Su)
104 105 106 107
0.1
0.3
0.5
1.0
JUVINALL: Machine Design
Fig. 8-11 W-243
–1.2
Reversed bending
Reversed torsion
Reversed bending
DE theory
–0.8
–0.6
–0.4
–0.2
0.2
0.4
0.6
0.8
1.2
–1.2 –0.8 –0.4
Note: Dotted portion is
superfluous for completely
reversed stresses
0 0.4 0.8 1.2
�1
Sn
JUVINALL: Machine Design
Fig. 8-12 W-245
�1
Sn
�2
Sn
–1.0
1.0
S
ur
fa
ce
 f
ac
to
r 
C s
Tensile strength Su (ksi)
60 80 100 120 140 160
Su (GPa)
180 200 220 240 260
120 160 200 240 280 320
Hardness (HB)
360 400 440 480 520
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
JUVINALL: Machine Design
Fig. 8-13 W-246
0.4 1.81.61.41.21.00.80.6
Mirror-polished
Fine-ground or
commercially
polished
Machined or cold-drawn
Hot-rolled
As forged
Corroded in salt water
Corroded in
tap water
JUVINALL: Machine Design
Fig. 8-14 W-247
Equal
surface
stresses
(a) d = (0.3" or 7.6 mm)
(b) d > (0.3" or 7.6 mm)
(c) d < (0.3" or 7.6 mm)
0
+
–
�min
�m = mean stress; �a = alternating stress (or stress amplitude)
�max = maximum stress; �min = minimum stress
�m = (�max + �min)/2
�a = (�max – �min)/2
S
tr
es
s
JUVINALL: Machine Design
Fig. 8-15 W-248
�max
�max
�a
�m
�m �a
�a
�min
0 Sy–Sy
A' A
Sn
Sy
F
E
A"
D
C
G
H
106 ~
Values from S–N curve
105 ~
104 ~
10 3
 ~
10 4
 ~
10 5
 ~
10 6
 ~
103 ~
H'
B
�m (tension)–�m (compression) Su
JUVINALL: Machine Design
Fig. 8-16 W-249
�a
M
ax
im
um
 s
tr
es
s 
�
m
ax
 (
%
 o
f 
S u
)
Minimum stress �min (% of Su)
–100 –80 0 20 40 60 80 100
0
10
20
30
40
50
60
70
80
90
100 
JUVINALL: Machine Design
Fig. 8-17 W-250
–60 –40 –20
–3
0
–2
0
40
50
M
ea
n 
str
es
s �
m
 (%
 of
 S u
)
60
80
70
10
0
90
–1
0
10
30
20
60
50
40
Alternating stress �
a (%
 of S
u ) 20
30
10
90
70
80
Su
10
3-cycle life
10
4
10
61
0
5
10
7
3 × 1
03
3 ×
 10
4
JUVINALL: Machine Design
Fig. 8-18 W-251
–2
0
–1
0
M
ax
im
um
 s
tr
es
s 
�
m
ax
 (
ks
i)
Minimum stress �min (ksi)
–80 –60 0 20 40 60 80
0
10
20
30
40
50
60
70
80
–20–40
50
40
Alternating stress �
a (ksi) 20
30
10
70
60
10
3-cycle
 life
10
4
10
5
10
9
10
6
10
7
4 × 
10
4
4 ×
 10
5
Su
40
50
60
70
80
10
30
M
ea
n 
str
es
s �
m
 (k
si)
20
JUVINALL: Machine Design
Fig. 8-19 W-252
M
ax
im
um
 s
tr
es
s 
�
m
ax
 (
ks
i)
Minimum stress �min (ksi)
–80 0 20 40 60 80
0
10
20
30
40
50
60
70
80
–40–60 –20
–3
0
–1
0
–2
0
40
50
60
70
80
10
30
M
ea
n 
str
es
s �
m
 (k
si)
20
50
40
Alternating stress �
a (ksi) 20
30
10
70
60
10
3 -cycl
e life
10
4
10
5
10
9
10
6 10
7
4 ×
 10
4
4 ×
 10
5
Sn
–Sn
Sy
Su
0
(a)
(b)
(c)
(d)
(e)
( f )
C
al
cu
la
te
d 
fl
uc
tu
at
in
g 
ax
ia
l s
tr
es
s
(i
gn
or
in
g 
yi
el
di
ng
)
JUVINALL: Machine Design
Fig. 8-20 W-253
�a
�m
�a
�a
�m
0
d < 2.0 in.
P(t)P(t)
P(t)
t
Commercially
polished surface
Sy = 120 ksi
Su = 150 ksi
JUVINALL: Machine Design
Fig. 8-21 W-254
20 = 0.67
A
10 3
 ~
10 4
 ~
10 5 ~
10 6 ~
Axial loading stresses in ksi
Axial loading stresses in ksi
1
�a
�a
Sy
�m
40
Point O
80
100
112 ksi
92 ksi
61 ksi
75 ksi
120
–120 –100 –80 –60 –40 –20 0 20 40
(used in Sample Problem 8.2)
60 80 100 120 150
–�m (compression) +�m (tension) SySy Su
JUVINALL: Machine Design
Fig. 8-22 W-255
P
ea
k 
al
te
rn
at
in
g 
st
re
ss
, 
S 
(l
og
)
Life N (cycles (log))
S = 0.75Su = 0.75(150) = 112
'Sn = SnCLCGCS
 = (0.5 × 150)(1)(0.9)(0.9) = 61
103 104 105 106 107
61
75
92
112
3 2
C
al
cu
la
te
d 
no
m
in
al
 s
tr
es
s 
S
Life N (cycles)
103 104 105
Unnotched specimensNotched specimens
106
(a) Unnotched specimen ("u")
(b) Notched specimen ("n") (c) Illustration of fatigue stress concentration factor, Kf
107
Kf = 
Sn(u) 
Sn(u) 
Sn(n) Sn(n) 
JUVINALL: Machine Design
Fig. 8-23 W-256
d
d
Notch radius r (in.)
0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
Notch radius r (mm)
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0
0.1
0.2
0.3
q
0.4
0.5
0.6
0.7
0.8
0.9
Use these values with bending and axial loads
Use these values with torsion
Steel
Su (ksi) and Bhn
as marked
1.0
JUVINALL: Machine Design
Fig. 8-24 W-257
Aluminum alloy (based on 2024-T6 data)
200 (
400 B
hn) 180 (360 Bh
n)
120 (240
 Bhn)
140 (
280 B
hn)
100
 (20
0 Bh
n)
80 
(16
0 B
hn)
80 (160
 Bhn)
60 (12
0 Bhn)
60 
(12
0 B
hn)
50 
(10
0 B
hn)
100
200
d
c
c'
b
a
b'
280
300
0 100 200 300
106 ~ Life
105 ~ Life
104 ~ Life
103 ~ Life
400 450
�m, tension (MPa) Su
Sy
�
a
 (
M
P
a)
0
–300
300
300
600
0
(a) (b) (c) (d)
(a) (b') (c') (d')
Calculated
stresses
Actual
stresses
Constant-
life
fatigue
diagram
C
al
cu
la
te
d 
no
tc
h 
st
re
ss
(P
/A
)K
f (
M
P
a)
A
ct
ua
l n
ot
ch
 s
tr
es
s
(P
/A
)K
f 
+
 �
re
si
du
al
 (
M
P
a)
JUVINALL: Machine Design
Fig. 8-25 W-258
d'
Commercial ground finish
Heat-treated alloy steel,
Su = 1.2 GPa, Sy = 1.0 GPa
T = 1000 ± 250 N • m
T = 1000 ± 250 N • m
D/d = 1.2 
 r/d = 0.05
 SF = 2.0 
JUVINALL: Machine Design
Fig. 8-26 W-259
d
r
D
100
150
1200
B'
B
A
NB
NB'
NA
(0.58)(0.9)(0.87) = 272 MPa
�max = Ssy
106 ~ = ∞ life
Assuming 10 mm < d < 50 mm
2
116
200
300
–200 –100 0
0'
100 200
Sn = SnCLCGCS = '
300 400
Mean torsional stress �m (MPa)
500 600 700 800 900
Ssy ≈ 0.58(1000) = 580 Sus ≈ 0.8(1200) = 960
A
lt
er
na
ti
ng
 t
or
si
on
al
 s
tr
es
s
� a
 (
M
P
a)
JUVINALL: Machine Design
Fig. 8-27 W-260
A
lt
er
na
ti
ng
 b
en
di
ng
 s
tr
es
s
�
ea
 (
M
P
a)
Mean bending stress �em (MPa)
0 100
(15.7, 65.0)
"Operating point"
200 300 400 500 600 700 800 900
0
100
200
300 "Failure point"
�max = Sy
Sy = 750
Su = 900
10 6 ~ = ∞ life
JUVINALL: Machine Design
Fig. 8-28 W-261
900
r = 5 mm rad., machined surface
D = 18 mm (bearing bore)
d = 16 mm (shaft dia.)
50 mm
f = 0.6 (between the object
and the disk)
T = 12 N • m (friction torque)
Su = 900 MPa
Sy = 750 MPa
' (1)(0.9)(0.72) = 291 MPa
2
Sn = SnCLCGCS = 
100 mm
Ft Fn
S
tr
es
s 
(k
si
)
(a)
Stress-time plot
(b)
S-N curve
–80
–40
0
40
80
JUVINALL: Machine Design
Fig. 8-29 W-262
R
ev
er
se
d 
st
re
ss
 S
 (
ks
i (
lo
g)
)
N (cycles (log))
103 104 105 106 107
40
50
60
140
120
100
80
Representive 20-second test
1
.6
 ×
 1
0
4
3
.8
 ×
 1
0
4
1
0
5
0
–100
–200
–300
100
200
300
2~
a
3~
(a)
Stress-time plot
2~ 1~
1~
B
en
di
ng
 s
tr
es
s 
(M
P
a)
σ
a
 (
M
P
a)
R
ev
er
se
d 
st
re
ss
 S
 (
M
P
a)
�m (MPa)
�m – �a plot
(b)
Sy Su
N (cycles)
(c)
(d)
S-N plot
100 200 300 400 500
103 104 105 106 107 108
0
100
200
300
400
100
150
200
250
300
400
500
JUVINALL: Machine Design
Fig. 8-30 W-263
b c
b d''
c
b'
b
a'
a
c'
d
d'
c''
d'
b''
d
Representative 6-sec test
c'
a' b'
2
.5
 ×
 1
0
3
3
.5
 ×
 1
0
6
2
 ×
 1
0
4
Bending stress at
critical notch
Part
Aluminum alloy
Sy = 410 MPa
Su = 480 MPa
P(t)
0
Pmax
Pmax
T
(d) Strength
(c) Total stress, (a) + (b)
(a) Load stress
(b) Residual stress
C
om
pr
es
si
ve
 s
tr
es
s 
(k
si
)
Te
ns
ile
 s
tr
es
s 
an
d 
st
re
ng
th
 (
ks
i)
JUVINALL: Machine Design
Fig. 8-31 W-264
Axis of specimen
symmetry and
axis of load
(1) (2)
P
JUVINALL: Machine Design
Fig. P8-26 W-265
30 mm
30 mm
P
P
P
30 mm
r = 2.5 mm
r = 2.5 mm
35 mm
30 mm
JUVINALL: Machine Design
Fig. P8-27 W-266
3 in.3 in.
1 in. dia. 1 in. dia.
1
4
2 in. 1 in.
2 in.
F lb
1 in. dia.
1 R8
1 R8
1 R16
F
lb2
F
lb2
JUVINALL: Machine Design
Fig. P8-28 W-267
24 mm 24 mm20 mm
2-mm rad. 0.8-mm rad.
JUVINALL: Machine Design
Fig. P8-30 W-268
High-carbon
steel, 490 Bhn,
machined finish
1
0.1094 in.
3 in.
4
8
r = in.
Kt = 1.7
F
4 in.
JUVINALL: Machine Design
Fig. P8-37 W-268a
1
0.050 in.
0.191-in. rad.
0.125-in. dia.
2 in.
0
+80
–16
Time
N
om
in
al
 s
tr
es
s
(M
P
a)
JUVINALL: Machine Design
Fig. P8-38 W-268b
60 mm50 mm
1.5 rad. 5-mm rad. 5-mm rad.
50 mm60 mm
JUVINALL: Machine Design
Fig. P8-39 W-268c
-in. dia. hole1
16
1.0-in. dia.1.2-in. dia.
0.1-in. rad.
0.1-in. rad.
To
rq
ue
7000 lb • in.
3000 lb • in.
Time
JUVINALL: Machine Design
Fig. P8-44 W-268d
Helical
spur gear
Pump
Fillet
25-mm solid
round shaft
500 N
750 N2000 N
Bending Kf = 2.0
Torsional Kf = 1.5
Axial Kf = 1.8
50
 mm
250-mm dia.
Forces act at 500-mm dia.
Fx = 0.2625FyFz = 0.3675Fy
C
B
Ax
Forces act at 375-mm dia. (2)
120 dia. Keyway
(Kf = 1.6 for bend and torsion; 1.0
for axial load. Use CS = 1 with these values.)
80 dia.
B
E
C D
A
(1)
Fx = 1.37 kN
Fz = 5.33 kN
Fy = 1.37 kN
Fy
D
y
z
JUVINALL: Machine Design
Fig. P8-45 W-268e
550
400
450
400
JUVINALL: Machine Design
Fig. P8-46 W-268f
To
rs
io
n 
st
re
ss
 (
ks
i)
0
–10
–20
–30
10
20
30
30 seconds
JUVINALL: Machine Design
Fig. 9-1 W-269a
+
+
+
+
+
+
+
+
+
+
+
Electrolyte
Fe2+ ions in solution
Iron electrode with surplus
of electrons
~ ~ ~
~
~
~
~
~
~
~~
~
~ ~
JUVINALL: Machine Design
Fig. 9-2 W-269b
Electrolyte
Exposed iron (anode or cathode)
Plating, as tin or zinc (cathode or anode)
~ ~~ ~~
~ ~
~~
~~ ~
~ ~ ~ ~
~
~ ~
~
~
JUVINALL: Machine Design
Fig. 9-3 W-269d
Electrolyte
~
~
~
~
~ ~
~
~
~
~
~
~
~
~
~
A B
JUVINALL: Machine Design
Fig. 9-4 W-269e
Magnesium
anode
Zinc strips between steel spring leaves
Outlet
Inlet
(a) Water tank
(c) Leaf spring
(d) Ship
(b) Underground pipe
Magnesium
anode
Insulated copper wire
Zinc anodes
JUVINALL: Machine Design
Fig. 9-5 W-269f
Insulated copper wire
+–
Steel tank
Steel
Rust particles Rust particles
(a)
Rust begins at center of drop
(b)
"Crevice corrosion"
JUVINALL: Machine Design
Fig. 9-6 W-269g
Steel Steel
Steel bolt and nut
Nonporous, pliable
electrical insulator
JUVINALL: Machine Design
Fig. 9-7 W-270
Aluminum plates
JUVINALL: Machine Design
Fig. 9-8a W-271a
Salt water
Strong
acids
Strong
alkalis
Aerated
water
U-V
radiation
A Excellent
B Good
C Poor
D BadOrganic solvents
Ceramics,
Glasses
KFRP
Polymers
PTFE, PP
 Epoxies, PS, PVC
HDPE, LDPE, Polyesters
Phenolics
Nylons
PMMA
Composites
GFRP
CFRP
A B C D D
Alloys
Alloys
Ceramics
Glasses
Lead alloys
Steels
Ti-alloys Cu-
alloys
Al-
alloys C-steels
Cast ironsNi-alloys
Ceramics,
Glasses
KFRP
GFRPCFRP Polymers
 Many
 elastomers
 PTFE
 PVC
PMMA
Nylons
LDPE
Epoxies, HDPE
polyesters, PP,
phenolics, PS
Filled
 polymers
All
All
Alloys
AllAll
All
Composites
KFRP
GFRP
CFRP
Polymers
PS
PVC
Most
elastomers
Phenomics
Polyesters
PU
LDPE
HDPE
Epoxies
Nylons
PP
PTFE
Composites
Polymers
PTFE
Epoxies
LDPE/HDPE
PP PS PVC
Nylons
Polyesters
Phenolics
PMMAAlloys
Lead alloys
Nickel alloys
S-steels
Cu-alloys
Al-alloys
Cast irons
Low alloy
steels
C-
 steels
Ti-alloys CFRP
KFRP
GFRP
Composites Ceramics,
Glasses
All
Alloys
Gold
Lead
PTFE
PVC
HDPE
Nylons
LDPE, Epoxies
Elastomers
Alloys
Ti-alloys
Cast
irons
C-steel
Al-alloys
Ni-alloys
S-steels
Polyesters
Phenolics
PS
PMMA
PU Composites
CFRP
CFRP
KFRP
Ceramics,
Glasses
Glasses
Vitreous
ceramics
Mg 0 Zr02
Al203
Si C
Si3N4
Si02
Alloys
Al-alloys Cu-alloys
Zn-alloys
Ni-alloys
Steels
S-steels
Cast irons
Ti-alloys
C AB
Polymers Nylons
PMMA Elastomers
Phenomics
Polyesters LDPE/HDPE
P.V.,PS,PP,PTFE
PVC,EpoxyComposites
GFRP
KFRP
CFRPCeramics,
Glasses
Si02
Glasses
Vitreous
 ceramics
Si C, Si3N4
Al203
Zr02
Graphites
Polymers
JUVINALL: Machine Design
Fig. 9-9 W-272
Mo Cr Co Ni Fe Nb Pt Zr Ti Cu Au Ag Al Zn Mg Cd Sn Pb In
W
Mo
Cr
Two liquid phases
Increasing
compatibility;
hence,
increasing
wear rate
One liquid phase, solid
solubility below 0.1%
Solid solubility between
1 and 0.1%
Solid solubility above 1%
Identical metals
Co
Ni
Fe
Nb
Pt
Zr
Ti
Cu
Au
Ag
Al
Zn
Mg
Cd
Sn
Pb
In
JUVINALL: Machine Design
Fig. 9-11 W-274
Wear coefficient, K
10–2 10–3 10–4 10–5 10–6
Unlubed Poorlube
Good
lube Excellent lube
Unlubed Excellent lubePoorlube
Poor
lube
Poor
lube
Good
lube
Excellent
lube
Good
lube
Unlubed
Unlubed Good lube Exc.
lube
Unlubed Lubed
2-body 3-bodyHigh abr.concentr.
Low abr.
concentr.
Unlubed LubedFretting
Abrasive
wear
Adhesive
wear
Nonmetal on metal or nonmetal
Incompatible metals
Partly compatible
Compatible
metals
Identical
metals
JUVINALL: Machine Design
Fig. 9-12 W-275
r = 16 mm
F = 20 N
n = 80 rpm
Copper pin
80 Vickers
Pin Pin
DiskDisk
Initial profiles Final profiles
t = 2 ht = 0 h
Disk volume lost
Pin volume lost = 2.7 mm3
= 0.65 mm3Steel disk
210 Brinell
JUVINALL: Machine Design
Fig. 9-13 W-276
Contact area
(a)
Two spheres
(b)
Two parallel cylinders
Contact area
x
z
y
JUVINALL: Machine Design
Fig. 9-14 W-277
a
p
p
p0
R1
R2
z
x
L
b
y
y
a
p0
D
is
ta
nc
e 
be
lo
w
 s
ur
fa
ce
–p0 –0.8p0 –0.4p0 0.4p00
Stress
4a
(a)
Two spheres
(a is defined in Fig. 9.13a)
3a
2a
a
0
JUVINALL: Machine Design
Fig. 9-15 W-278
p0 = max. contact
pressure
�z
�max
�x = �y
D
is
ta
nc
e 
be
lo
w
 s
ur
fa
ce
–p0 –0.8p0 –0.4p0 0.4p00
Stress
7b
(b)
Two parallel cylinders
(b is defined in Fig. 9.13b)
6b
5b
4b
3b
2b
b
0
�z
p0 = max. contact
pressure
�y
�max
�x
–0.6p0 –0.4p0 –0.2p0 0 0.2p0
0
0.1p0
0.2p0
0.3p0
JUVINALL: Machine Design
Fig. 9-16 W-279
�y ≈ –0.1p0
�max ≈ 0.3p0
�x ≈ –0.25p0
�z ≈ –0.7p0
One plane of maximum shear stress
�z ≈ –0.7p0
+�
+�
�y ≈ –0.1p0
�x ≈ –0.25p0
S
tr
es
s 
� y
z
Distance y from load plane
–4b –3b –2b –b 0 b 2b 3b 4b
–0.3p0
–0.2p0
–0.1p0
0
0.1p0
0.2p0
0.3p0
A
A B
F
F
b
B
�yz �yz
�z �z
�y �y
JUVINALL: Machine Design
Fig. 9-17 W-280
p0 = max contact pressure
0.5b below surface
A B
A B
y
JUVINALL: Machine Design
Fig. 9-18 W-281
�yt = 2fp0
�yt = 2fp0
�yzt = fp0
�yzt = fp0
�yt = –2fp0
�yt = –2fp0
p0 = maximum contact pressure
f = coefficient of friction
Loaded cylinder
(resists rotation to
cause some sliding)
Driving cylinder
y y
z
z
Direction of rotation
Direction of rotation
b b
JUVINALL: Machine Design
Fig. 9-19 W-282
Hard-bronze bearing
alloy spherical seat
10 mm
2000 N
Hardened-
steel sphere
10.1 mm
M
ax
im
um
 c
on
ta
ct
 s
tr
es
s
p 0
 (
M
P
A
)
Sphere radius, R1 (mm)
5.00 5.01 5.02 5.03 5.04
50
100
150
200
250
JUVINALL: Machine Design
Fig. 9-19b W-283
Cast iron
Copper
Steel
C
om
pu
te
d 
m
ax
im
um
 e
la
st
ic
 c
on
ta
ct
 s
tr
es
s
p 0
 o
r 
�
z 
(k
si
)
Life N (cycles (log))
105 106 107 108 109 1010
100
150
200
300
400
500
600
700
800
JUVINALL: Machine Design
Fig. 9-21 W-285
Spur gears–high-quality
manufacture, case-hardened
steel, 60 Rockwell C (630 Bhn)
Roller bearings
Angular-contact ball bearings
Radial ball bearings
Parallel rollers
1
C
Protected ("noble", more cathodic)C
C
C
C
X
C
C
C
C
C
C
C
C
C
C
C
C
CC
JUVINALL: Machine Design
Tab. 9-1 W-269c
2
10Key:
11
12
13
14
15
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Gold, platinum, gold-platinum alloys
C
C
C
X
X
X
X
X
X
X
C
X
X
X
F
F
X
X
F
C
C
C
C
C
C
X
X
X
C
X
X
X
F
F
X
X
F
C
C
C
C
C
C
X
X
C
X
X
X
F
F
X
X
F
C
C
C
C
C
C
C
C
C
C
C
F
F
C
C
F
C
C
C
C
C
C
C
P
P
X
F
F
P
X
F
C
C
C
C
C
C
X
X
X
F
F
X
X
F
C
C
C
C
C
C
P
X
F
F
P
P
F
C
C
C
C
C
X
X
F
F
X
X
F
C
C
C
C
C
X
F
F
X
X
F
C
C
C
C
C
F
F
X
X
F
C
C
C
C
F
F
P
X
F
C
C
C
F
F
C
P
F
C
C
F
F
X
X
F
C
F
F
C
P
F
F
F
C
C
F
F
F
F
F
F
F
F
C
FF
Rhodium, graphite, palladium
Silver, high-silver alloys
Titanium
Nickel, manel, cobalt, high-nickel and
high-cobalt alloys
Nickel-copper alloys per QQ-N-281,
QQ-N-286, and MIL-N-20184
Steel, AISI 301, 302, 303, 304, 316,
321, 347*, A286
Copper, bronze, brass, copper alloys per QQ-C-551,
QQ-B-671, MIL-C 20159, silver solder per QQ-5-561
Commercial yellow brass and bronze;
QQ-B-611 brass
Leaded brass, naval brass, leaded bronze
Steel, AISI, 431, 440; AM 355; PH steels
Chromium plate, tungsten, molybdenum
Steel, AISI 410, 416, 420
Tin, indium, tin-lead solder
Lead, lead-tin solder
Aluminum , 2024, 2014, 7075
Steel, (except corrosion-resistant types), iron
Aluminum, 1100, 3003, 5052, 6063,
6061, 356
Cadmium and zinc plate, galvanized steel,
beryllium, cald aluminum
Magnesium
Legend:
X – Not compatible
C – Compatible
P – Compatible if not exposed within two miles
 of a body of salt water
F – Compatible only when finished with at least
 one coat of primer
*Applicable forms: 301, 302, 321, and 347 sheet
and plate; 304 and 321 tubing; 302, 303, 316, 321,
and 347 bar and forgings; 302 and 347 casting;
and 302 and 316 wire.
 These materials must be finished with at least
one coat of primer.
C
+
Corroded ("active", more cathodic)
–
JUVINALL: Machine Design
Prob. 9-1 W-269
Rivets
Total exposed area = 100 cm2
Metal plates
Total exposed area = 1 m2
Chromium-plated steel cap screws
Total exposed area = 110 cm2
301 Stainless steel plates
Total exposed area = 1.5 m2
Electrolytic environment
JUVINALL: Machine Design
Prob. 9-4 W-286
Drain plug
(steel)
Insert rod
(magnesium)
Oil
Crankcase
(steel)
JUVINALL: Machine Design
Prob. 9-8d W-287
100 N 100 N
Latch
closed
Latch
open
30 cycles/day, every day
Steel, 100 Bhn
Steel, 300 Bhn
JUVINALL: Machine Design
Prob. 9-12 W-287a
30 mm
Locking plate
Arm
Geneva wheel
JUVINALL: Machine Design
Prob. 9-20 W-288
100-mm
radius
JUVINALL: Machine Design
Fig. 10-1 W-289
�
L
p
End of thread
�
L
p
End of thread
End of thread
(a)
Single thread–right hand
(b)
Double thread–left hand
Pitch dia. dp
Crest
 p
4
 p
8
Root
Axis of thread
30�
p
JUVINALL: Machine Design
Fig. 10-2 W-290
Major dia. d
Root (or minor) dia. dr
60�
Nut tolerance zone
Basic profile
(as shown in
Fig. 10.2)
Screw
Basic profile
Screw tolerance zone
JUVINALL: Machine Design
Fig. 10-3 W-291
Nut
p
2
p
2
JUVINALL: Machine Design
Fig. 10-4 W-292
2� = 29�
5�
45�
0.663p
0.163p
p
p
2
p
2
d
dr
p
2
2� = 29�
(a) Acme
(c) Square (d) Modified square (e) Buttress
(b) Acme stub
p
dmdr
0.3p
dm dr d
p
p
2
p
2
dm dr d
p p
dmdr
� = 5�
� = 7�
dm
d
d
a
JUVINALL: Machine Design
Fig. 10-5 W-293
(c)(b)(a)
Force F
dc
 Weight 
A
A
L
q
JUVINALL: Machine Design
Fig. 10-6 W-294
�
�dm
fn
w
n
n cos �n
Section A A
(normal to thread)
 Scale 4:1 
�n
�n
q fn
dm
JUVINALL: Machine Design
Fig. 10-7 W-295
�n
�
h
h
b
A
A
B
B
 Section B-B
(normal to thread)
 Section A-A
(through screw axis)
 tan �n = 
 Screw axis
b
h
 tan �
 
= bh cos �
�
b/cos ��
E
ff
ic
ie
nc
y,
 e
 (%
)
Helix angle, �
0� 10� 20� 30� 40� 50� 60� 70� 80� 90�
0
10
20
30
40
50
60
70
80
90
100
JUVINALL: Machine Design
Fig. 10-8 W-296
e =
cos �n – f tan � 
cos �n + f cos � 
 , where 
�n = tan
–1 (tan 14 � cos �)12
f = 0
.01
f = 0
.02
f = 0
.05
f = 0
.10
f = 0
.15
f = 0
.20
a
JUVINALL: Machine Design
Fig. 10-10 W-298
Force F
f = 0.12
fc = 0.09
1-in. double-thread
Acme screw
dc = 1.5 in.
Weight = 1000 lb
 Force
flow
lines
Nut
A - shear fracture
 line for nut
 thread stripping
B - shear fracture
 line for bolt
 thread stripping
B
A
JUVINALL: Machine Design
Fig. 10 -11 W-299
dr
di
dp
d
 1 
 Total = P 
 Total = P 
Clamped
member
 2 
 3 
 Bolt
t
JUVINALL: Machine Design
Fig. 10-12 W-300
Clamped member
Bolt
Nut
JUVINALL: Machine Design
Fig. 10-13 W-301
Pilot surface
of bolt
Material
being
compressed
JUVINALL: Machine Design
Fig. 10-14 W-302
Motor
Material
being
compressed
Spur gears
Ball thrust
bearings
Ball thrust
bearings
Thrust
washers
(b) Screws in tension (good)(a) Screws in compression (poor)
Thrust
washers
Motor
Flat washer
(a) Screw (b) Bolt and nut (c) Stud and nut (d) Threaded rod and nuts
JUVINALL: Machine Design
Fig. 10-15 W-303
0.65d
1.5d
d
(a) Hexagon head
(b) Square head
(d) Flat head (f ) Oval head
(h) Hex socket headless setscrew
(j) Round head with Phillips socket
(c) Round head
(e) Fillister head
(g) Hexagon socket head (i) Carriage bolt
JUVINALL: Machine Design
Fig. 10-16 W-304
JUVINALL: Machine Design
Fig. 10-17 W-305
(a)
Conventional screwdriver
will tighten but not
loosen the screw
(Plug in socket)
(b)
Special tool required to
tighten or loosen screw
(5-sided head) ("Spanner head")
(c)
Break-away heads
T4
T3
JUVINALL: Machine Design
Fig. 10-18 W-307
y
 Mohr circles 
Fi
Fi
Fi
Fi
y x
Fi
Fi
� +��
+�
�max = per max � theory
Sy
2
Stresses with torques applied
Stresses after
torques are relieved
x'
x (�, –�)
y'
y
T2
T1
B
ol
t 
te
ns
io
n
Bolt elongation
Torqued tension,
galvanized
(high friction)
Torqued tension,
galvanized and
lubricated
Torqued tension,
black oxide
JUVINALL: Machine Design
Fig. 10-19 W-308
Direct tension,
black oxide
Direct tension,
galvanized
JUVINALL: Machine Design
Fig. 10-20 W-309
(a)
Helical (split) type
(b)
Twisted-tooth type
(Teeth may be external,
as in this illustration,
or internal.)
JUVINALL: Machine Design
Fig. 10-21 W-310
(b)(a)
(a)
Insert nut (Nylon insert is compressed when
nut seats to provide both locking and sealing.)
(c)
Single thread nut (Prongs pinch bolt thread
when nut is tightened. This type of nut is
quickly applied and used for light loads.)
JUVINALL: Machine Design
Fig. 10-22 W-311
(b)
Spring nut (Top of nut pinches
bolt thread when nut is tightened.) 
Spring- top nut
(Upper part of nut is tapered.
Segments press against bolt threads.)
Starting Fully locked
Nylon-insert nuts
(Collar or plug of nylon exerts friction
grip on bolt threads.)
Distorted nut (Portion of nut is distorted
to provide friction grip on bolt threads.)
(a) (b) (c)
JUVINALL: Machine Design
Fig. 10-23 W-312
JUVINALL: Machine Design
Fig. 10-24 W-313
Fe
Fe Fe
(a)
Complete joint
(b)
Free body without
external load
Fb = Fi Fc = Fi
(c)
Free body with
external load
Fb Fc
(a) (b) (c)
(d)
g
JUVINALL: Machine Design
Fig. 10-25 W-314
Fe Fb
Fc
Fb
Fb
Fc
Fc
Fc
F b
 a
nd
 F
c
Fc = Fi
F b
 =
 F i
 an
d 
F e
Fb
Soft
gasket
(Separating force per bolt)
0 Fe
Fi
(a) (b) (c)
g
JUVINALL: Machine Design
Fig. 10-26 W-315
Fe
Fb
Fc
Fb
Fb
Fc
Fb
"O-ring"
gasket
(d)
F b
 a
nd
 F
c
Fb = Fi
Fc = Fi – Fe 
Fc = 0
(Separating force per bolt)
0
"Rubber"
portion of
bolt
Fe
Fi
Fo
rc
e
External load Fe
0
Fi
Fc
Fe
Fb
Fc = 0
Fb = Fe 
Fb = Fi + 
JUVINALL: Machine Design
Fig. 10-27 W-316
�Fb
�Fc
C A
Bkb
kb + kc
Fe
kc
kb + kc
Fluctuations
in Fb and Fc
corresponding
to fluctuations
in Fe between
0 and C
Fc = Fi – 
Conical effective
clamped volume
(Hexagonal bolt
head and nut)
30°
JUVINALL: Machine Design
Fig. 10-28 W-317
d2
d3
d1
g
d
(a)
Bolt bending caused by nonparallelism
of mating surfaces. (Bolt will bend
when nut is tightened.)
Connecting
rod and cap
P
A
a
(b)
Bolt bending caused by deflection
of loaded members. (Note tendency
to pivot about A; hence, bending is
reduced if dimension a is increased.) 
a
A
P
JUVINALL: Machine Design
Fig. 10-29 W-318
JUVINALL: Machine Design
Fig. 10-30 W-319
Pillow block
Rotating
shaft
Metric
(ISO) screw
9 kN
F
F
2
F
2
F
2
F
2
(a) (b)
Normal load, carried by
friction forces
Overload, causing shear failure
F
JUVINALL: Machine Design
Fig. 10-31 W-320
150
150
500
400
100
24 kN24 kN
150
D
A
D
E
JUVINALL: Machine Design
Fig. 10-32 W-321
48
144-kN applied
overload
JUVINALL: Machine Design
Fig. 10-33 W-322
F
F
V
F
100
150
CG of bolt group
cross section
200
180
4848
144 kN
144 kN (150 mm) =
21.6 kN � m
200
180
180
Su = 830
S
tr
es
s,
 �
 (M
P
a)
� = 0.0032 @ Sy = 660 on idealized curve
Strain, �
0 0.01 0.02 0.03 0.04
Fluctuation in thread root stress – Case 2, Fi = 35.3 kN
Fluctuation in thread root stress – Case 1, Fi = 10 kN
12% elongation @ Su specified for class 8.8
0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
0
100
200
300
400
500
600
700
800
900
JUVINALL: Machine Design
Fig. 10-34ab W-323
Sp = 660
Sp = 600
505
Fo
rc
e 
(k
N
)
Bolt tight,
machine not
yet turned on
38.3
35.3
Case 2 – Fi = 38.3 kN
(bolt tightened to full
yield strength)
Bolt yields slightly, with no
increase in load or stress during
first application of Fe 
29.3
4
0
10
20
30
40
Fb
Machine
operating at
normal load
Machine
turned off
Case 1 – Fi = 10 kN
Fc
Fb
Fe
Fc9
13
Time
(a) Fluctuation in Fb and Fc caused by fluctuations in Fe
(b) Idealized (not actual) stress–strain curve for class 8.8 bolt steel
A
lt
er
na
ti
ng
 s
tr
es
s,
 �
a
 (
M
P
a)
Mean stress, �m (MPa)
0
After initial
tightening
After shut-down
following normal operation
(c) Mean stress-alternating stress diagram for plotting thread root stresses
130
77
200 400 600 800
0
100
200
300
400
JUVINALL: Machine Design
Fig. 10-34 W-324
� Life
Su = 830
Sy = 660
 4 
 2 
 1 3 
During normal
operation
Operation at overload on verge
of causing eventual fatigue failure
Sn = SnCLCS CG = (1)(1)(0.9) = 373 MPa
830
2
'
Steel bolt, '' – 13 UNC,
grade 5 with cut threads
E
xt
er
na
l l
oa
d 
F e
Time
(b)
Fluctuating separating
force versus time
(a)
Simplified model of machine
members bolted together
g = 2''
Fmax
JUVINALL: Machine Design
Fig. 10-35a-c W-325, 326a
0 to Fmax
Steel
member
0 to Fmax,
fluctuating
external force
Fe
1
2
�
a
 (
ks
i)
�m (ksi)
0
�a = 37
�a = 23
�a = 22.7
20 40 60 80 100 120
0
20
40
60
Limiting point for case a
Limiting point for case b
Sn = S 'nCLCGCS = (1)(0.9)(1) = 54 ksi
120
2
Sy = 120
Sy = 92
�a = 37
�a = 23
�a = 22.7
Limiting point for case a
Limiting point for case b
Sn = SnCLCGCS = (1)(0.9)(1) = 54 ksi'
120
2
(c)
Fatigue diagram for thread root
Su = 120
Sy = 92
Fe
"O-ring" gasket
250 mm
Aluminum cover plate,
E = 70 GPa
Cast-iron cylinder,
E = 100 GPa
Class 8.8
steel bolt
350 mm
g/2
g/2
JUVINALL: Machine Design
Fig. 10-36 W-327
JUVINALL: Machine Design
Fig. P10-1 W-328
a
f = 0.13
fc = 0.10
1-in. double-thread
Acme screw
dc = 2.0 in.
Weight = 10,000 lb
Force F
JUVINALL: Machine Design
Fig. P10-09 W-330
5 in.
1/2 in. Acme thread
dc = 5/8 in.
 Fe = 0 to 8,000 lb
kc = 6kb
Fe
Fe
JUVINALL: Machine Design
Fig. P10-17 W-329
JUVINALL: Machine Design
Fig. P10.26 W-331
(1)
1000 N
Spring
washer
1000 N
(2)
1000 N1000 N
A
A
Spring washer
JUVINALL: Machine Design
Fig. P10-28 W-332
JUVINALL: Machine Design
Fig. P10-39 W-333
280 mm
140 mm
230 mm
JUVINALL: Machine Design
Fig. P10-41 W-334
Fo
rc
e 
(k
N
)
Time
15 kN 15 kN
30 kN
0
20
40
60
80 Fb and Fc
Fe
Light load Light load
Heavy load
Initial
tighten
JUVINALL: Machine Design
Fig. P10-44 W-335
22
22
22
22
22
22
22
22
22
22
22
22
22 222222
JUVINALL: Machine Design
Table 10-4 W-306
JUVINALL: Machine Design
Fig. 11-1 W-336
Before setting
After setting
Full tubular
Bifurcated (split)
Metal-piercing
JUVINALL: Machine Design
Fig. 11-2 W-337
(c)
Compression
(a)
Semitubular
(b)
Self-piercing
JUVINALL: Machine Design
Fig. 11-3 W-338
"Built-up" lightweight structure
Acute corner
Back (blind) side
not accessible
Back (blind) side not accessible
Blind
side upset
Blind
side upset
Drive pin
blind rivet
JUVINALL: Machine Design
Fig. 11-4 W-339
Open-end
break mandrel
blind rivet
Blind
side upset
Pull-through
blind rivet
Blind
side upset
Closed-end
break mandrel
blind rivet
Blind
side upset
Mandrel head collapses
as rivet is expanded
and pulled through rivet
Trim or grind
mandrelPulling
head
Mandrel breaks
after seating and
rivet expansion
Self-plugging
blind rivet
(b) (c)(a)
JUVINALL: Machine Design
Fig. 11-5 W-340
60�
JUVINALL: Machine Design
Fig. 11-6 W-341
(a) (c) (d)(b)
45�
60�
FF
h t
t = 0.707
h
h
t
h
(a)
A
B
C
D
(b)
(d)
Transverse loading
50 mm
(a' )
Convex
weld bead
(a" )
Concave weld
bead (poor
practice)
(c)
Parallel loading
(e)
Transverse loading
F
A
B
C
D
50
 mm
F
JUVINALL: Machine Design
Fig. 11-7 W-342
1052 + 202
J
T
802 + 452
J
T
690.0
t
525.8
t
691.9
t
131.4
t690.0
t
80
t
674.1
t
80
t
5600 N • m
20 kN
295.7
t
y
G
B A
JUVINALL: Machine Design
Fig. 11-8 W-343
(a)
(b) (c)
100
–
x–
XX
C
B
Y
G
A
Y
150
300
20 kN
T (80)
J
525.8
t
105
8020
G
B
T
=
T (105)
J =
T (20)
J
131.4
t
=
T (45)
J
295.7
t
Torsional stresses Torsional plus direct shear stresses
=
B
C
A
B
A
X
X
120
160
10 kN
60
70
(a) (b) Stresses on weld AB
121.2
t
� =26.3
t
� =
124
tResultant stress
=
JUVINALL: Machine Design
Fig. 11-9 W-344
D
L /2
L /2
G (CG of total weld group)
G' (CG of this weld segment)
b
a
y
Y'
Y' Y
Y
X'X'
X
t
X
JUVINALL: Machine Design
Fig. 11-10 W-345
�
a
 (k
si
)
�m (ksi)
190 50 62
13.6
JUVINALL: Machine Design
Fig. 11-11 W-346
= = 0.5
�a
�m
30
60
JUVINALL: Machine Design
Fig. 11-12 W-347
(a) Adhesive-bonded metal lap joint (b) Brazed tubing fittings (c) Glued wood joint
 Removing this
material reduces
stress concentration
at bond edges
F
JUVINALL: Machine Design
Fig. P11-4 W-348
15 mm
Weld length = 90 mm
Sy = 400 MPa
SF
 
= 3
E70 series weld 
F
3.0 in.
F
F
JUVINALL: Machine Design
Fig. P11-07 W-349
E60 series welding rods
Sy = 50 ksi (plates)
h
 
= 0.375 in.
SF
 
= 3
Note: There are two
3 in. welds.
100 mm
Note: Each plate has two 75 mm
welds and one 100 mm weld.
60 kN
JUVINALL: Machine Design
Fig. P11-11 W-350
75
mm
55
mm
4 in.
3 in.
JUVINALL: Machine Design
Fig. P11-12 W-351
4000
lb
Note: There are two 4 in. welds.
Fixed
end
Spline
Spline
Generous
radius
Bearing
Bearing
Torsion bar
portion
(a)
Torsion bar with splined ends
(type used in auto suspensions, etc.)
(b)
Rod with bent ends serving as torsion bar spring
(type used for auto hood and trunk counterbalancing, etc.)
JUVINALL: Machine Design
Fig. 12-1 W-352
d
JUVINALL: Machine Design
Fig. 12-2 W-353
D
�
F
End surface
ground flat (c)
Tension spring
(a)
Compression spring
(ends squared and ground)
D
d
F
F
d
FD
2
T =
FD
2
T =
F
F
F
F
d
(d)
Top portion of tension
spring shown as a free
body in equalibrium
D
F
F
JUVINALL: Machine Design
Fig. 12-3 W-354
(a)
Straight torsion bar
(b)
Curved torsion bar
P
la
ne
 m
P
la
ne
 n
 0 
 0 
� =
� �
� �
Tc
J
Tc
J
Tc
J
Tc
J
� =
T
b
dc
a
T
T
T
Preferred range,
ends ground 
K
w
 
an
d 
K
s 
Spring index, C = D/d 
2 4 6 8 10 12 14
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
2
4
6
8
10
12
14
16
18
JUVINALL: Machine Design
Fig. 12-4 W-355
K
w
C 
an
d 
K
sC
 
 Preferred range, ends not ground 
Ks
KwC
Kw
KsC
Ks = 1 + (shear correction only,
 use for static loading) 
Kw = + (shear and curvature 
 corrections, use for
 fatigue loading) 
0.5
C
0.615
C
4C – 1
4C – 4
JUVINALL: Machine Design
Fig. 12-5 W-356
JUVINALL: Machine Design
Fig. 12-6 W-357
M
in
im
um
 u
lt
im
at
e 
te
ns
ile
 s
tr
en
gt
h 
(M
P
a)
M
in
im
um
 u
lt
im
at
e 
te
ns
ile
 s
tr
en
gt
h 
(k
si
)
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1
Wire diameter (mm)
Wire diameter (in.)
1.00.10 10.0 100.0
2 3 4 5 6 7 8 9 1
0
50
100
150
200
250
300
350
400
450
500
0
1000
1500
2000
2500
3000
0.0400.0200.0080.004 0.080 0.200 0.400 0.800
JUVINALL: Machine Design
Fig. 12-7 W-358
ASTM A229
ASTM A313
(302)
ASTM A228 music wire (cold-drawn steel)
ASTM A401 (Cr-Si steel)
ASTM A230
(oil-tempered carbon steel)
ASTM A232 (Cr-Va steel)
ASTM A229
(oil-tempered carbon steel)
ASTM A227
(cold-drawn carbon steel)
ASTM A313
(302 stainless steel)
ASTM B159
(phosphor bronze)
Inconel alloy X-750 (spring temper)
ASTM A227
JUVINALL: Machine Design
Fig. 12-8 W-359
(a)
Ls = (Nt + 1)d
(c)
Ls = (Nt + 1)d
(b)
Ls = Nt d
(d)
Ls = Ntd
(b)(a)
Contoured
and plate
(d)(c)
JUVINALL: Machine Design
Fig. 12-9 W-360
R
at
io
, 
de
fl
ec
ti
on
–f
re
e 
le
ng
th
, 
�
/L
f
Ratio, free length–mean diameter, Lf /D
2 3 4 5 6
Unstable
Stable
7 8 9 10 11
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
JUVINALL: Machine Design
Fig. 12-10 W-361
A
A- end plates are constrained parallel
 (buckling pattern as in Fig. 5.27c)
B- one end plate is free to tip
 (buckling pattern as in Fig. 5.27b )
B
1
2
JUVINALL: Machine Design
Fig. 12-11 W-362
Lf
Ls
Fs
D + d
 � 1.5 in.
(Spring
free) (Spring
with
min. load)
(Spring
with
max. load)
105 lb
60 lb
(Spring
solid)
Cash
allowance
� 2.5 in.
in.
Life N (cycles (log))
JUVINALL: Machine Design
Fig. 12-12 W-363
S
tr
es
s 
S 
(%
 S
u
)(
lo
g)
103 104 105 106
30
20
40
50
60
70
80
0.9Sus � 0.72 Su
0.54 Su
0.395 Su
Su
2
CLCSCGSn =
Su
2
= (0.58)(1)(1)
= 0.29 Su
� a
/S
u
�m /Su
0.1 0.2
(0.38, 0.38)
(0.325,
0.325)
(0.265, 0.265)
(0.215, 0.215)
0.72
0.3 0.4 0.5 0.6 0.7 0.80
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
JUVINALL: Machine Design
Fig. 12-13 W-364
103�
104�
105�
106 + �
0.54
0.395
0.29
Region of interest
0
0
�m = 0
= 1
�a
�m
0
� 1
�a
�m
P
Static load
0
= 0
�a
�m
� m
ax
/S
u
�min /Su
0.20 0.40 0.60 0.800
0.20
0.40
0.60
0.80
JUVINALL: Machine Design
Fig. 12-14 W-365
103 �
104 �
105 �
106 + �
P
0.76
0.65
0.53
0.43
To
rs
io
na
l s
tr
es
s 
S s
, 
m
ax
 (
%
 S
u
)
Life N, (cycles)
104
Shot-peened wire
103 105 106 107
30
40
50
60
80
70
JUVINALL: Machine Design
Fig. 12-15 W-366
Design curves [1]
Non-shot-peened wire
Calculated curve (from Fig. 12.14)
Note: For zero-to-max torsional
stress fluctuation
76
65
53
43
� m
ax
 (
M
P
a)
�min (MPa)
0 200 400
689
800
510
600 800
(965, 965)
(862, 862)
(Static load line)
(Load line, slope 600/300
for Sample Problem 12.2)
1000
200
400
600
800
1000
JUVINALL: Machine Design
Fig. 12-16 W-367
Infinite life without
shot peening
Infinite life with
shot peening
JUVINALL: Machine Design
Fig. 12-17 W-368
Without presetting
Load stress
Load stress
plus residual
stress
With presetting
–�
0
+�
�resid from presetting
JUVINALL: Machine Design
Fig. 12-18 W-369
25 mm
600 N 
300 N 
600 N 
Squared and
ground ends,
ASTM A232
spring wire
300 N 
Key
Cam
n =
650
rpm Shaft
�� + 25 
� m
ax
 (
M
P
a)
�min (MPa)
0 200 400 600 800 1000 1200
200
400
600
800
975
750
540
1000
1200
JUVINALL: Machine Design
Fig. 12-19 W-369A
�max
�min
600
300
=
D
r2
r4 B
d
d
F
D
A
F
r1
r3
JUVINALL: Machine Design
Fig. 12-20 W-370
Bending stress at Sec. A:
� =
16FD
�d3
r1
r3
Torsional stress at Sec. B:
� =
8FD
�d3
r4
r2
F
JUVINALL: Machine Design
Fig. 12-21 W-371
(b)
Semi-elliptic
6FL
bh2
L L
� = 
12FL3
Ebh3
� = 
(c)
Full-elliptic
 2F 
 2F 
6FL
bh2
L L
� = 
6FL3
Ebh3
� = 
 2F 
6FL
bh2
� = 
6FL3
Ebh3
� = 
(a)
Quarter-elliptic
(simple cantilever)
L F F F
JUVINALL: Machine Design
Fig. 12-22 W-372
F
L
x
JUVINALL: Machine Design
Fig. 12-23 W-373
(a)
t
h
b
w
F
L
(b)
t is constant; w varies linearly with L
(c)
w is constant; t varies parabolically with L
L
h
b
If � and t are
constant, then x /w
must be constant.
If � and w are
constant, then x /t2
must be constant.
Mc
I
6Fx
wt2
� = =
F
b
h
Half of nth leaf
Half of nth leaf
n leaves
Half of 3rd leaf
Half of 3rd leaf
Half of 2nd leaf
Half of 2nd leaf
Main leafb
L L
h
F
JUVINALL: Machine Design
Fig. 12-24 W-374
F
h
b
n
(a) (b)
Clips
Shackle (permits
small fluctuations
in spring length)
Fixed pivot
Fixed pivot
JUVINALL: Machine Design
Fig. 12-25 W-375
2F
Bolt, Kf = 1.3
�a
�m
�
a
 (
M
P
a)
 �m (MPa)
 �a = 525
0
Design overload point
= 0.67
400 800 1200 1600
400
800
JUVINALL: Machine Design
Fig. 12-26 W-376
� life, bending
Sn
Sy Su
F = 1000 to 5000 N
(b)(a)
k = 30 N/mm
h = 7 mm
F
6FL3
Ebh3
FL3
Eh3
L = 682
L = 682 L = 682
b = 416
b = 416 b = 333
L = 682
JUVINALL: Machine Design
Fig. 12-27 W-377
� = = 0.0144 ; F
�
Eh3
L3
k = = 69.33
6FL3
Ebh3
FL3
Eh3
�1 = = 0.0180
F
�1
Eh3
L3
k1 = = 55.55
Eh3
L3
k = 76.30
4FL3
Ebh3
FL3
Eh3
�2 = = 0.0482
Eh3
L3
k2 = 20.75
(a) Triangular-plate solution to Sample Problem 12.4
(b) Trapezoidal plate solution to Sample Problem 12.5
 + =
k = k1 + k2
8383
D
a
F
d
F
JUVINALL: Machine Design
Fig. 12-28 W-378
Thickness = h
b
JUVINALL: Machine Design
Fig. 12-29 W-379
FF
 a
D
d
D
h
Fa
ct
or
s 
fo
r 
in
ne
r 
su
rf
ac
e 
st
re
ss
 c
on
ce
nt
ra
ti
on
K
i, 
ro
un
d 
an
d 
K
i, 
re
ct
Spring index, C = or
2 4 6 8 10 12
1.0
1.1
1.2
1.3
1.4
1.5
1.6
JUVINALL: Machine Design
Fig. 12-30 W-380
Ki, round
Ki, rect
Belleville Wave Slotted Finger Curve Internally slotted
(as used in automotive clutches)
JUVINALL: Machine Design
Fig. 12-31 W-381
In series
JUVINALL: Machine Design
Fig. 12-32 W-382
In parallel In series-parallel
JUVINALL: Machine Design
Fig. 12-33 W-383
+ + + +
Storage drum Output drum Storage drum Output drum
(a) Constant-force extension springs
(b) Electric motor brush spring
(c) Two forms of constant spring motors
JUVINALL: Machine Design
Fig. 12-34 W-384
End attached
to door
Fixed
end
Torsion bar
Center of gravity
of 60-lb door
Door stop
JUVINALL: Machine Design
Fig. P12-3 W-385
24 in.
110�
Deflection
Support
Spring
Retainer
Nut
Force
Fo
rc
e
Threaded bolt
JUVINALL: Machine Design
Fig. P12-11 W-386
Deflection
C
B
A
JUVINALL: Machine Design
Fig. P12-15 W-387
F = 3.0 kN
Di
Do
 Do = 45 mm
 do = 8 mm
 No = 5
do
di
 Di = 25 mm
 di = 5 mm
 Ni = 10 
F
F = 45 to 90 lb
Deflection = 0.5 in.
D = 2 in. 
JUVINALL: Machine Design
Fig. P12-28 W-388
F
Squared and
ground end
0
+
–
3600 engine rpm
1800 camshaft rpm
"Reversal point"
Valve lift is 0.384 in.
(maximum-on "nose" of cam)
"Reversal point"
Valve lift is 0.201 in.
Va
lv
e 
ac
ce
le
ra
ti
on
JUVINALL: Machine Design
Fig. P12-34 W-389
Cam angle
Key
Cam
Shaft
Stationary guide
Oscillating assembly
Roller follower
Spring
Adjusting nut
Cap screw
JUVINALL: Machine Design
Fig. P12-35 W-390
Support
e
JUVINALL: Machine Design
Fig. P12-37 W-392
F
Tire
Stationary
support
Handle
Brake
shoe
Spring
Pin stops
Pivot A
35 mm
Stationary
support
JUVINALL: Machine Design
Fig. P12-39 W-391
25 mm shaft
Torsion springs
Cable
Cable
110 mm dia.
110 mm dia.
JUVINALL: Machine Design
Fig. P12-46 W-393
JUVINALL: Machine Design
Fig. 13-1 W-395
Main bearing
Connecting rod
Connecting rod bearing
Thrust bearing
(flanged portion of main bearing)
Main bearing
Crankshaft
Main bearing cap
Connecting rod bearing cap
JUVINALL: Machine Design
Fig. 13-2 W-396
(a) Hydrodynamic
(surface separated)
(b) Mixed film
(intermittent local contact)
(c) Boundary (continuous
and extensive local contact)
JUVINALL: Machine Design
Fig. 13-3 W-397
(a)
At rest
W
Oil inlet
W
(b)
Slow rotation
(boundary lubrication)
W
Bearing
Journal
Minimum film
thickness, h0
(c)
Fast rotation
(hydrodynamic lubrication)
Oil flow
W
e
W
Resultant oil
film force
W
�n/P
f
A
JUVINALL: Machine Design
Fig. 13-4 W-398
Boundary lubrication
Mixed-film lubrication
Hydrodynamic lubrication
(viscosity × rps ÷ load per unit of projected bearing area)
JUVINALL: Machine Design
Fig. 13-5 W-399
T
Cross-sectional area, A
where G = shear modulus
(b)
At equilibrium, torque T
produces elastic displacement,
�, across a solid element
F
h h
Fh
AG
�
� =
Surface velocity, U
where � = absolute viscosity
(c)
At equilibrium, torque T
produces laminar flow
velocity, U, across a fluid
element
F
Fh
A�U =
(a)
Rubber element
Fluid element
A
bs
ol
ut
e 
vi
sc
os
it
y 
(m
P
a 
• s
)
A
bs
ol
ut
e 
vi
sc
os
it
y 
(�
re
yn
)
Temperature (°C)
Temperature (°F)
10 20 30 40 50 60 70 80 90 100 110 120 130 140
28026024022020018016014012010080
0.3
0.4
0.5
0.6
0.7
0.9
1.0
2
3
4
5
10
2
3
5
102
2
3
103
2
3
4
5
10
2
3
4
5
102
2
3
5
103
2
3
5
104
JUVINALL: Machine Design
Fig. 13-6 W-400
SAE 70
20
40
50
60
JUVINALL: Machine Design
Fig. 13-7 W-401
Overflow rim
Oil
Level of liquid
in bath
Saybolt viscometer
Kinematic viscosity,
58 s at 100°C
Bottom of bath
Orifice
Bath
JUVINALL: Machine Design
Fig. 13-8 W-402
D
R
L
c
n
JUVINALL: Machine Design
Fig. 13-9 W-403
5000 N
D = 100 mm
R = 50 mm n = 600 rpm
Oil viscosity,
50 mPa • s
c = 0.05 mm
L = 80 mm
JUVINALL: Machine Design
Fig. 13-10 W-404
Journal
Oil hole
W Partial bronze
bearing
Oil level
JUVINALL: Machine Design
Fig. 13-11 W-405
Rotating journal
Fixed bearing
Lubricant
Lubricant flow
Coordinates:
x = tangential
y = radial
z = axial
W
dx
dy
(� + dy) dx dz
� dx dz
dx
dyp dy dz
∂�
∂y
(p + dx) dy dzdpdx
JUVINALL: Machine Design
Fig. 13-12 W-406
y
h Lubricant flow
Stationary bearing
Rotating journal
U
JUVINALL: Machine Design
Fig. 13-13 W-407
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 0.01 0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 42 6 8 10
M
in
im
um
 f
ilm
 t
hi
ck
ne
ss
 v
ar
ia
bl
e,
h 0 c
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
E
cc
en
tr
ic
it
y 
ra
ti
o,
 e
/c
Bearing characteristic number, S =
2R
c
�n
P
Optimum zone
Min. friction
Max.load
L /D = ∞
1
1
2
1
4
JUVINALL: Machine Design
Fig. 13-14 W-408
1
2
3
4
5
10
20
30
40
50
100
200
0 0.01 0.02 0.04 0.1 0.2 0.4 0.6 0.8 1.0 2 4 6 8 100.08
C
oe
ff
ic
ie
nt
 o
f 
fr
ic
ti
on
 v
ar
ia
bl
e,
f
R c
L /D =
∞
Bearing characteristic number, S =
2R
c
�n
P
1
4
1
2
1
JUVINALL: Machine Design
Fig. 13-15 W-409
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.2
0.3
0.1
0 0.01 0.02 0.04 0.06 0.1 0.2 0.4 0.6 0.81.0 2 4 6 8 10
M
in
im
um
 f
ilm
 p
re
ss
ur
e 
ra
ti
o,
P
p m
ax
 (
ga
ge
)
L /D = ∞
1
Bearing characteristic number, S =
2R
c
�n
P
1
2
1
4
JUVINALL: Machine Design
Fig. 13-16 W-410
100
90
80
70
60
50
40
20
30
10
0 0.01 0.02 0.04
* Defined in Figure 13.20
0.06 0.1 0.2 0.4 0.6 0.8 1.0 2 4 6 8 10
P
os
it
io
n 
of
 m
in
im
um
 f
ilm
 t
hi
ck
ne
ss
, 
�
 (
de
g*
)
L /D = ∞
1
Bearing characteristic number, S =
2R
c
�n
P
1
2
1
4
JUVINALL: Machine Design
Fig. 13-17 W-411
100
90
80
70
60
50
40
30
20
10
0 0.01 0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 42 6 8
Te
rm
in
at
in
g 
po
si
ti
on
 o
f 
fi
lm
, 
�
p 0
 (
de
g*
)
25
20
15
10
5
0
P
os
it
io
n 
of
 m
ax
im
um
 f
ilm
 p
re
ss
ur
e,
 �
p m
ax
 (
de
g*
)
L /D = ∞ 1
1
∞
�p0
�pmax
Bearing characteristic number, S =
2R
c
�n
P
1
2
1
2
1
4
1
4
* Defined in Figure 13.20
JUVINALL: Machine Design
Fig. 13-18 W-412
6
5
4
3
2
1
0 0.01 0.02 0.04 0.1 0.2 0.4 0.6 0.81.0 2 4 6 8 10
Fl
ow
 v
ar
ia
bl
e,
Q
Rc
nL
L /D =
L /D =
L /D = 1
L /D = ∞
Bearing characteristic number, S =
2R
c
�n
P
1
4
1
2
JUVINALL: Machine Design
Fig. 13-19 W-413
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.01 0.02 0.04 0.1 0.2 0.4 0.6 1.0 2 4 6 8 10
Fl
ow
 r
at
io
,
Q s Q
L /D =
L /D = ∞
1
Bearing characteristic number, S =
2R
c
�n
P
1
4
1
2
JUVINALL: Machine Design
Fig. 13-20 W-414
W
e
n
Oil of viscosity �
and flow rate Q
R = D/2
Average film pressure = P =
Film pressure, p
W
DL
h0
�p0
�
pmax
�pmax
JUVINALL: Machine Design
Fig. 13-21 W-415
1000 lb
D = 2.0 in.
R = 1.0 in. n = 3000 rpm
SAE 20 Oil
Tavg = 130°F
c = 0.0015 in.
L = 1.0 in.
JUVINALL: Machine Design
Fig. 13-23 W-417
Oil hole
Steel backing
Bearing material
Axial groove
O
il 
fi
lm
 p
re
ss
ur
e
JUVINALL: Machine Design
Fig. 13-24 W-418
Grooved
bearing
Oil inlet hole
Ungrooved bearing
2
Circumferential
groove
L
2
L
D
JUVINALL: Machine Design
Fig. 13-25 W-419
"Rifle drilled" passage
in connecting rod*
Circumferential groove
in main bearing
Piston
Piston pin or wrist pin
Drilled passage in crankshaft
Circumferential groove in rod bearing
Circumferential groove in main bearing
*If omitted, piston pin bearing is splash lubricated.
Oil in Oil in
JUVINALL: Machine Design
Fig. 13-26 W-420
W = 17 kN
D = 150 mm
R = 75 mm n = 1800 rpm
Force feed,
SAE 10 oil
Tavg = 82°C
c = ? mm
L = ? mm
f = ?
Qs = ?
Power loss = ?
Oil temperature rise = ?
f, 
co
ef
fi
ci
en
t 
of
 f
ri
ct
io
n
h 0
, 
m
in
im
um
 o
il 
fi
lm
 t
hi
ck
ne
ss
 (
m
m
)
Q 
an
d 
Q s
, 
oi
l f
lo
w
 r
at
e 
(c
m
3
/s
)
c, radial clearance (mm)
*As defined in Fig. 13.13
0 0.05 0.10
Optimum band*
0.15
0
0.001
0
0.005
0.010
0.015
0.020
50
100
150
200
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.010
JUVINALL: Machine Design
Fig. 13-27 W-421
M
ax
. 
lo
ad M
in
. 
fr
ic
ti
on
h0
Qs
Q
f
JUVINALL: Machine Design
Fig. 13-28 W-422
a
a > b
b Pads
Ro
Ri
Runner
JUVINALL: Machine Design
Fig. P13-12 W-423
D = 4.0 in.
R = 2.0 in. n = 900 rpm
SAE 10 Oil
Tavg = 150°F
c = 0.002 in.
L = 6.0 in.
JUVINALL: Machine Design
Fig. P13-27 W-424
JUVINALL: Machine Design
Fig. P13-29D W-425
4.5 kN
D = ? in.
R = ? in. n = 660 rpm
SAE ? Oil
Tavg = ?°C
c = ? in.
L = ? L = ?
4
JUVINALL: Machine Design
Fig. 14-1b W-426
3
(b)
Steps in assembly
21
(a)
Relative proportions of bearings
with same bore dimension
(b)
Relative proportions of bearings
with same outside diameter
JUVINALL: Machine Design
Fig. 14-2 W-427
(LL00) (L00)
Light
series
(200)
Medium
series
(300)
Medium
series
(300)
Extra-
light
series
(L00)
Extra-
light
series
Extra-
extra-
light
series
(LL00)
Extra-
extra-
light
series
Light
series
(200)
Loading
grooves
(a) Filling notch (loading groove) type
JUVINALL: Machine Design
Fig. 14-3a W-428
(c) Double row
JUVINALL: Machine Design
Fig. 14-3c W-428
(d) Internal self-aligning
JUVINALL: Machine Design
Fig. 14-3d W-428
(e) External self-aligning
JUVINALL: Machine Design
Fig. 14-3e W-428
JUVINALL: Machine Design
Fig. 14-4 W-429
One
shield
Two
shields
One seal Two seals Shield
and seal
Snap ring
Snap ring
shield and
seal
Snap ring
and two
shields
Snap ring
and one
shield
Snap ring
and two
seals
Snap ring
and one
seal
JUVINALL: Machine Design
Fig. 14-5 W-430
Added
stabilizing ring
(b) One-direction locating (c) Two-direction locating
JUVINALL: Machine Design
Fig. 14-8 W-433
Bearing axis
Common
apex
Crowned roller body
Spherical roller head
Roller axis
(d) Idler sheave
(unground bearing)
(e) Rod end bearing
JUVINALL: Machine Design
Fig. 14-10 W-436
JUVINALL: Machine Design
Fig. 14-10h W-437
(h) Integral spindle, shown with V-belt pulley
JUVINALL: Machine Design
Fig. 14-11 W-438 
dS dH
r
r
+
+
P
er
ce
nt
ag
e 
of
 f
ai
lu
re
s
Life
1 2 3 4 5 6 7 8 9 10 11 12
2
4
6
8
10
12
14
16
18
20
22
24
JUVINALL: Machine Design
Fig. 14-12 W-439
Median
Li
fe
 a
dj
us
tm
en
t 
re
lia
bi
lit
y 
fa
ct
or
 K
r
Reliability r (%)
90 91 92 93 94 95 96 97 98 99 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
JUVINALL: Machine Design
Fig. 14-13 W-440
1800 rpm
Radial bearing
JUVINALL: Machine Design
Fig. 14-14 W-441
1800 rpm
Angular bearing
Ft = 1.5 kN, Fr = 1.2 kN
Light-to-moderate impact
Eight hours/day operation
1800 rpm
Case a: 90 percent reliability
JUVINALL: Machine Design
Fig. 14-15 W-442
Case b: 30,000-hour life
No. 211 radial-contact bearing,
C = 12.0 kN
Fr = 1.2 kN
Ft = 1.5 kN
Light-to-moderate impact,
Ka = 1.5
21 mm
100 mm
55 mm
1000 rpm
Ka = 1.0 (uniform load)
Fr
No. 207 radial-
contact bearing
JUVINALL: Machine Design
Fig. 14-16 W-443
R
ad
ia
l l
oa
d 
(k
N
)
0
1
1 2 3 1
Time
3
2
4
5
6
7
20%
100%
50% 30%
Note spacers
JUVINALL: Machine Design
Fig. 14-17 W-444
JUVINALL: Machine Design
Fig. 14-18 W-445
F1
L1
JUVINALL: Machine Design
Prob. 14-6 W-446
F2
2L1
F2
3L1
3500 rpm
JUVINALL: Machine Design
Prob. 14-10 W-447
No. 204 radial ball bearing
Fr = 1000 N, Ft = 250 N
90% reliability
Light-moderate shock loading
L = ? hr life
Gear Shaft Bearing
JUVINALL: Machine Design
Prob. 14-19 W-449
JUVINALL: Machine Design
Prob. 14-20 W-448
150-mm dia.
Gear
120-mm dia.
1.2 kN
20°
B
A
300 mm
100
mm
60
mm
60
mm
Clamping supports
Chain sprocket
Rotating shaft
Chain
JUVINALL: Machine Design
Prob. 14-21d W-450
1.75 ft 0.75 ft
600 lb 600 lb
2.25 ft
Right-angle gearing
Parallel gearing
JUVINALL: Machine Design
Fig. 15-1 W-451
JUVINALL: Machine Design
Fig. 15-2 W-452
JUVINALL: Machine Design
Fig. 15-3 W-453
Line of centers
Point of contact
Pitch point
Common normal (to tooth surfaces
at point of contact)
Driving gear
P
Driven gear
JUVINALL: Machine Design
Fig. 15-4 W-454
Involute curves
Base circle
Base pitch, pb
JUVINALL: Machine Design
Fig. 15-5 W-455
�p
�g
Gear
pitch
circle
Pinion
pitch
circle
P (pitch point)
c
dp
dp
JUVINALL: Machine Design
Fig. 15-6 W-456
Pinion
base
circle
� (pressure angle)
�p
�g
Gear
base
circle
b
P
a
JUVINALL: Machine Design
Fig. 15-7 W-457
Base circle
Pitch circle
Pitch circle
Pinion
a
P
c
f
e
d
g
b
�
�
Base circle
Gear
rp
rg
JUVINALL: Machine Design
Fig. 15-8 W-458
rg
Addendum circle
Dedendum
Angle of
approach
p
Angle of
recess
Position of
teeth leaving
contact
0g
0p
Pitch circle
Addendum
Addendum
Dedendum circle
Base circle
Pitch circle
Addendum circle
Angle of
approach
Dedendum
Angle of
recess
Pinion (driving)
Position
of teeth
entering
contact
Base circle
Dedendum circle
Gear (driven)
c
b
a
n
n
�
rp
JUVINALL: Machine Design
Fig. 15-9 W-459
Working
depth
Whole
depth
Addendum
Dedendum
Clearance
To
p 
lan
d
Fa
ce
Fl
an
k
Bo
tto
m
 la
nd
Circular pitch p
Pitch circle
Fillet
radius
Dedendum
circle Clearance circle
(mating teeth extend
to this circle)
Addendum circle
Tooth
thickness t
Fa
ce
 w
id
th
 b
t0
Width of
space
18
36
32
30
2880
64
40
48
16
1
4
20
2
2
24
26
6
5
41
2
11
10
7
8
9
JUVINALL: Machine Design
Fig. 15-10 W-460
Pinion
Rack
Circular pitch
p
JUVINALL: Machine Design
Fig. 15-11 W-461
�
JUVINALL: Machine Design
Fig. 15-12 W-462
Pitch circle
Base circle
�Base circle
Pitch circle Dedendum
circle
Addendum
circle
�
�
JUVINALL: Machine Design
Fig. 15-14 W-464
Gear blank rotates
in this direction
Rack cutter reciprocates in a direction
perpendicular to this page
Driving gear
Driven gear
Base circle
Base circle
02
01
�2
�1
�
�
JUVINALL: Machine Design
Fig. 15-15 W-465
Interference is on flank
of driver during approach
(This portion of profile
is not an involute)
(This portion of profile
is not an involute)
Pitch point, P
�
Addendum circlesa
b
P = 6 teeth/in.
� = 20°
�p
�g
JUVINALL: Machine Design
Fig. 15-16 W-466
= –3.0
rg
rp
c = 4 in.
Pitch circle
(gear)
JUVINALL: Machine Design
Fig. 15-17 W-467
dg
dp
P
P
Fr
Fr
Pitch circle
(pinion)
(Driving pinion rotates clockwise)
F
F
�
�
Ft
Ft
�g
�p
N = 12 teeth (input pinion)
P = 3
600 rpm; 25 hp
(a)
(b)
JUVINALL: Machine Design
Fig. 15-18 W-468
a
b c
N = 36 teeth
(idler)
N = 28 teeth
(output gear)
Resultant force (applied by shaft to gear) = (1313 + 478) 2 = 2533 lb.
45°
Vab = 478 lb
Hab = 1313 lb
Vcb = 1313 lb
20°
20°
b
Hcb = 478 lb
c
a
rf
Fr
Ft
x
F
a
F
Constant-
strengh
parabola
JUVINALL: Machine Design
Fig. 15-20 W-470
t
h
b
Le
w
is
 f
or
m
 f
ac
to
r 
Y
Number of teeth N (Rack)
12 15 17 20 24 30 35 40 4550 60 80 125 275 ∞
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
JUVINALL: Machine Design
Fig. 15-21 W-471
� = 1
4 
°1
2
� =
 25
°
� =
 20
°
� =
 20
°, s
tub
 tee
th
Lo
ad
Driving and driven gears
0
F
2
Time
Time
Fa = Fm =
Driving gear Idler gear Driven gear
0
(b) Stress fluctuation
Sn
�m
�a
Su
JUVINALL: Machine Design
Fig. 15-22 W-472
1 revolution
F
Lo
ad
0
Idler gear
40% higher fat. strength
for o-max loading
(driver and driven)
Fat. strength
for reversed
loading (idler)
Fa = F
Fm = 0
1 revolution
F
F
�a �m
�a
G
eo
m
et
ry
 f
ac
to
r 
J
Number of teeth N
(b) 25° full-depth teeth
12 15 17 20 24 30 40 50 80 275 ∞
0.15
0.20
0.25
Load applied at
tip of tooth
(no sharing)
Load applied at
highest point of
single-tooth
contact
(sharing)
85
1000
50
25
17
0.30
0.35
0.40
0.45
0.50
0.55
0.60
JUVINALL: Machine Design
Fig. 15-23 W-473
G
eo
m
et
ry
 f
ac
to
r 
J
Number of teeth N
(b) 20° full-depth teeth
12 15 17 20 24 30 40 50 80 275 ∞
0.15
0.20
0.25
Load applied at
tip of tooth
(no sharing)
Load applied at
highest point of
single-tooth
contact
(sharing)
85
50
25
35
17
0.30
0.35
0.40
0.45
0.50
0.55
0.60
Num
ber
 of 
teet
h in
 ma
ting
 gea
r
Num
ber
 of 
teet
h in
 ma
ting
 gea
r
1000
12545 6035
12545 6035
Ve
lo
ci
ty
 f
ac
to
r 
K
v
Pitch line velocity V (ft/min)
* Limited to about 350 Bhn
E D
C
B
A
0 1000 2000 3000 4000 5000 6000 7000
1
2
3
4
5
0 10 20
Pitch line velocity V (m/s)
30
JUVINALL: Machine Design
Fig. 15-24 W-474
Hob
s, sh
apin
g cu
tters
*
High precision, sh
aved and ground
Highest precision, shaved and ground
Ho
bs
, f
or
m
 cu
tte
rs*
Precision,
 shaved an
d ground
Pinion
Gear
Steel, 290 Bhn
(manufacture of pinion and gear corresponds
to curve D, Fig. 15.24)
P = 10
20° full-depth teeth
Steel, 330 Bhn
Np = 18 (teeth)
JUVINALL: Machine Design
Fig. 15-25 W-475
Electric
motor
1720 rpm
Conveyor
drive
(involves
moderate
shock
torsional
loading)
860 rpm
Vgn = Vpn
Vgn = Vpn
Vp = Vg
Vg
Vp
Vgt Vpt = Vgt
Common
normal
Common
normal
Gear
(driver)
Gear
(driver)
Common
tangent
(a) General contact position
 sliding velocity as shown
(b) Teeth in contact at pitch point
no sliding
Pinion
(driven)
Pinion
(driven)
Common
tangent
Sliding
velocity
�
JUVINALL: Machine Design
Fig. 15-26 W-476
Vpt
Surface fatigue life (cycles)
104
CLi
105 106 107 108 109 1010 1011
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
JUVINALL: Machine Design
Fig. 15-27 W-477
JUVINALL: Machine Design
Fig. 15-28 W-477A
Win = 100 hp
3600 rpm
•
900 rpm
Negligible shock loading
Life: 5 years, 2000 hours/year
 Full power: 10 percent of time
 Half power: 90 percent of time
Failure in 5 years: 10 percent likely
JUVINALL: Machine Design
Fig. 15-29 W-478
Motor
(input)
Driven machine
(output)
p1
g1
g2
p2
a c
b
(a)
With three planets (typical)
JUVINALL: Machine Design
Fig. 15-30 W-479
P
P
Ring
Planet
Arm
Sun
R
A S
P
(b)
With one planet (for analysis only)
P
R
A S
(R = input; A = output; S = fixed member)
JUVINALL: Machine Design
Fig. 15-31 W-479A
R/2
2Ti
2Ti /3R
2Ti /3R
4Ti /3R 4Ti /3R
R + S
4
Ti
R P
A
3R
R + S
4
2Ti
3R
2Ti
3R
4Ti
3R To
Ti
�i
�o
S
R
S
R
4Ti
R
4Ti
3R
To =
= = 1 +
= Ti 1 +
(R = input; A = output; S = fixed member)
JUVINALL: Machine Design
Fig. 15-32 W-480
P
R
V
S
�0
�0
�i
�i
A
R
2 R + S
4
V
2
V
R/2
V/2=
S
R�0
�i = 1 + 
(R + S)/4
JUVINALL: Machine Design
Fig. 15-33 W-481
P
P
R
S
90° = 17 teeth (ring)12
Planet will
fit here
Planet will
fit here 90° = 5 teeth (sun)
Planet will
NOT fit here
Planet will
NOT fit here
JUVINALL: Machine Design
Prob. 15-21 W-482
Driven machine
coupled to this
shaft
45 teeth
P = 5, � = 25°
15 teeth
45 teeth
25
mm
100
mm
25
mm
1 kW, 1200-rpm
motor coupled
to this shaft
c
B
b
A
a
JUVINALL: Machine Design
Prob. P15-23 W-482A
A
B
36T
64T
24T, P = 6
18T, P = 9
2''
To driven
machine
8''
2''
Coupled to 20 lb.in.
torque motor
JUVINALL: Machine Design
Prob. 15-26 W-483
a
a
Motor
Driven machine
32T
24T To driven
machine
1''
B
A
JUVINALL: Machine Design
Prob. 15-27 W-484
90°2.0''
16T
1700-rpm
motor
100-lb.in.
torque
(b)(a)
JUVINALL: Machine Design
Prob. 15-45 W-485
3
3
4
4
2
7
6
78
9
4
1
Low (L)
Neutral (N)
High (H)
3
2
Member
pushes here to
disengage pawl
Hub can
"overrun"
in this
direction
5
JUVINALL: Machine Design
Prob. P15-47 W-485A
P2 P1
P2
S2
P1
S1
Input
Output
Arm
JUVINALL: Machine Design
Prob. P15-50 W-485B
P1 P2
Input
S1 (100 teeth)
P2 (102 teeth)
P1 (101 teeth)
S2 (99 teeth)
Output
Arm
Reverse brake band
holds S2 fixed
Low brake band
holds S3 fixed
S3 (21 teeth)
P3 (33 teeth) P1 (27 teeth)
P2 (24 teeth)
S1 (27 teeth)
S2 (30 teeth)
OutputInput
JUVINALL: Machine Design
Prob. 15-51 W-486
JUVINALL: Machine Design
Fig. 16-1 W-487
(b) Rotated spur gear laminations
approach a helical gear as laminations
approach zero thickness.
p
pn
pn
pa
�n
p
�
� Section NN
(normal plane) 
 Section RR
(in plane of rotation) 
JUVINALL: Machine Design
Fig. 16-4 W-490
Rb R
b
N
N
c
d
a
�
e
 Section NN
(normal plane) 
 Section RR
(plane of rotation) 
d
2 cos2 �
JUVINALL: Machine Design
Fig. 16-5 W-491
Re = 
R
d
N
N
R
�
�n
�
F
 Top of tooth 
 Pitch
cylinder
 Spur gear
(helical gear with � = 0�)
 
d
JUVINALL: Machine Design
Fig. 16-6 W-492
Fa
Fr
Ft
Fr
Ft
Ft
Isometric view
showing helical
gear forces
�
 Top of tooth 
 Pitch
cylinder
Helical gear 
Section RR
(plane of rotation)
Section NN
(normal plane)
Fr
Ft
Ft
�
�
Fa
Fb
Fr
F
Fb
R
N
N
R
Np = 18 (teeth)
Pn = 14
�n = 20�
(a)
Electric motor
 hp 1800 rpm
 (normal
plane)
Input shaft of
driven machine
600 rpm
� = 30�
(right hand)
JUVINALL: Machine Design
Fig. 16-07 W-493
Fr
Fa
Ft
(b)
Isometric view of
motor shaft and pinion
Direction of
rotation 
� = 30�
(left hand)
1
2
G
eo
m
et
ry
 f
ac
to
r 
J
Helix angle �
0� 5� 10� 15� 20� 25� 30� 35�
0.40
0.30
0.50
0.60
0.70
JUVINALL: Machine Design
Fig. 16-8 W-494
J-
fa
ct
or
 m
ul
ti
pl
ie
r
N
um
be
r 
of
 t
ee
th
Te
et
h 
in
 m
at
in
g 
ge
ar
Helix angle �
0� 5� 10� 15� 20� 25� 30� 35�
0.95
0.90
1.00
500
150
75
50
30
12
14
16
18
20
30
60
150
500
20
1.05
 Developed back
cone radius, rbg
rbp�p
�p
b
Pitch cone
length, L
 Dedendum
 Dedendum
 Addendum
 Pinion back cone
 Pitch cone
angles
 Gear
pitch cone
dp
JUVINALL: Machine Design
Fig. 16-9 W-495
 Gear pitch
dia., dg 
Gear
back
cone
 Pinion
pitch
cone 
Spiral
angle
Circular pitch
Face advance
�
Mean
radius
JUVINALL: Machine Design
Fig. 16-10 W-496
b
Ft
Ft
Fa
Fr
Fn
Fn
F
Fr
 Note: Fn is normal
to the pitch cone.
�
d
2
b
2
dav
2
JUVINALL: Machine Design
Fig. 16-12 W-498
�
JUVINALL: Machine Design
Fig. 16-13 W-499
G
eo
m
et
ry
 f
ac
to
r 
J
Number of teeth in gear for which geometry factor is desired
0 10 20 30 40 50 60 70 80 90 100
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
0.34
0.36
0.38
15
20
40
30
50
80
Teeth in mating gear
60
100
0.40
JUVINALL: Machine Design
Fig. 16-13 W-517
 250 mm 
Load
Motor
Rotation
 140 mm 
A
B
C
D
140 mm 
65
mm
JUVINALL: Machine Design
Fig. 16-14 W-500
G
eo
m
et
ry
 f
ac
to
r 
J
Number of teeth in gear for which geometry factor is desired
0 20 40
100
80
60
50
40
12
30
25
20 15
60
Teeth in mating gear
80 100
0.16
0.20
0.24
0.28
0.32
0.36
G
eo
m
et
ry
 f
ac
to
r 
I 
Number of teeth in pinion NP
0 10 20 30 40 50
0.05
0.06
0.07
0.08
0.09
0.10
0.11
JUVINALL: Machine Design
Fig. 16-15 W-502
Ng = 100
Ng = 70
Ng = 50
15 Teeth in gear
90
80
60
40
30
25
20
G
eo
m
et
ry
 f
ac
to
r 
I 
Number of teeth in pinion NP
0 10 20 30 40 50
0.06
0.08
0.10
0.12
0.14
0.16
0.18
JUVINALL: Machine Design
Fig. 16-16 W-503
Ng = 100
30 Teeth in gear
15
20 25
50
40
60
80
�S
JUVINALL: Machine Design
Fig. 16-17 W-504
�R
A
P
P
 Fixed arm, A 
R
P (planet)
R (ring)
S (sun)
S
P
JUVINALL: Machine Design
Fig. 16-18 W-505
 Arm
(input member)
Right axleLeft axle
P
P
RS
JUVINALL: Machine Design
Fig. 16-19 W-506
 Worm lead
angle, �, and
gear helix
angle, �
 Center
distance
c
Keyway
 Axial pitch, P 
 Lead, L
Note: � and � are
measured on pitch
surfaces.
 Worm
outside dia.,
dw, out 
 Pitch
dia., dw
 Pitch
dia., dg
 Face
width, b
Fwt
Fwr
Fwa
 Worm-driving
torque 
JUVINALL: Machine Design
Fig. 16-20 W-507
Fgt
Fgr
Fga
JUVINALL: Machine Design
Fig. 16-21 W-508
fFn cos �
Fn sin �n
Fn cos �n
Fn cos �n cos � 
Fn
Fn cos �n sin � 
�n
Direction of
Fga and Fwt
Direction of
Fgt and Fwa
Direction of
Fgr and Fwr
(a) Worm driving (as in Fig. 16.20) (b) Gear driving (same direction of rotation)
�Fn 
fFn sin �
�
fFn cos �
Direction of
Fga and Fwt
Direction of
Fgr and Fwr
Direction of
Fgt and Fwa
fFn sin �
fFn
Fn cos �n sin � 
�n
Fn cos �n
Fn sin �n
Fn cos �n
Fn
Fn cos �n cos � 
� 
JUVINALL: Machine Design
Fig. 16-22 W-509
Vs
Vw
Vg Gear
rotation
�
 Worm
 Gear
 Worm rotation
C
oe
ff
ic
ie
nt
 o
f 
fr
ic
ti
on
 f
Sliding velocity Vs (ft /min)
1 2 4 6 10 2 4 6 100 2 4 6 1000 2 4 6 10,0000
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0
JUVINALL: Machine Design
Fig. 16-23 W-510
 Worm: Steel, hardened and ground
Nw = 2,
RH, p = in., �n =14 �
c = 5 in.
JUVINALL: Machine Design
Fig. 16-24 W-511
 Gear 
 60 rpm 
Worm
Gear: Bronze
Motor
2 hp., 1200 rpm
5
8
1
2
Worm rpm, nw 
C
oe
ff
ic
ie
nt
 C
 
0 400 800 1200 1600
0
10
20
30
40
50
60
70
80
JUVINALL: Machine Design
Fig. 16-25 W-512
ft
 �
 lb
m
in
 �
 ft
2
 �
 �
F
With fan 
(as in Fig. 16.26)
Without fan 
c ≈ 6 in.
JUVINALL: Machine Design
Fig. 16-27 W-514
 Gear 
Worm: hardened steel
rpm =1200
Gear: Chill-cast bronze
Speed ratio, 11:1
Worm
JUVINALL: Machine Design
Table 16-1 W-501
p
b
JUVINALL: Machine Design
Fig. P16-5 W-516
�
Pa
40 teeth 60 teeth
20 teethOutput
JUVINALL: Machine Design
Fig. P16-08 W-515
24 teeth Input
JUVINALL: Machine Design
Fig. P16-14 W-518
Motor
Output
50 teeth
20 teeth
� = 0.50 rad
left hand
25 teeth
� = 0.35 rad
right hand
A
B 125
 100
 200
50 teeth
 Gear
Pinion
 1000 rpm
 400 rpm
 Bevel gears:
35 hp
Np = 36
Ng = ?
b = 2 in.
� = 20�
P = 6
JUVINALL: Machine Design
Fig. P16-19 W-519
 Pinion 
 1500 rpm
 Gear
A B
 3 in. 3 in.
 Bevel gears:
 50 hp
Np = 30
Ng = 60
b = 3 in.
� = 20�
P = 6
Flexible
coupling to
machine
JUVINALL: Machine Design
Fig. P16-23D W-520
 Nw = 2
Ng = 55
P = ?
JUVINALL: Machine Design
Fig. P16-30 W-521
c = 8 in. Gear 
Worm
 Gear material: Chill-cast bronze
Worm material: Hardened steel
Nw = 3 p = 0.5 in. f = 0.029
Ng = 45 �n = 20�
c = 4.5 in.
b =
1.0 in.
 1200
 rpm 
JUVINALL: Machine Design
Fig. P16-34 W-522
JUVINALL: Machine Design
Fig. 17-1 W-523
(a) Square key
d
w
w
w
2
(b) Flat key
w ≈ d/4 w ≈ d/4; h ≈ 3w/4
d
h
h
w
2
(c) Round key
Key usually has drive
fit; is often tapered
(d) Kennedy keys
Keys are tapered and
driven tightly; for
heavy-duty service
(e) Woodruff key
Widely used in automotive and
machine tool industries
( f ) Gib-head key
Usually tapered, giving tight
fit when driven into place;
gib head facilitates removal
(g) Feather key
Key is screwed to shaft; hub is free to
slide axially – easier sliding is obtained
with two keys spaced 180° apart
JUVINALL: Machine Design
Fig. 17-2 W-524
d
D
(a) Straight round pin (b) Tapered round pin
(c) Split tubular spring pin Grooves are produced by rolling,
and provide spring action to
retain pin
(d) Grooved pin
JUVINALL: Machine Design
Fig. 17-3 W-525
Basic Inverted
E-ring
External rings (fit on shaft)
(a) Conventional type, fitting in grooves
(b) Push-on type – no grooves required
Teeth deflect when installed to "bite in" and resist removal
(less positive than conventional type)
Basic
Internal rings (fit in housing)
Inverted
I
I Section II
External ring (fit on shaft)
I
I Section II
Internal ring (fit in housing)
4-spline 6-spline 10-spline
(a) Straight-sided (b) Involute
16-spline
JUVINALL: Machine Design
Fig. 17-4 W-526
JUVINALL: Machine Design
Fig. 17-5a W-527
�st
Gravitational
force, w
Mass, m
Shaft of spring rate k = w/�st
(a) Single mass
JUVINALL: Machine Design
Fig. 17-5b W-527
m1
w1 w2
w3
m2
�1 �2 �3
m3
w1 w2
w5
m1 m2
m3
m4
m5
w3
w4
(b) Multiple masses
JUVINALL: Machine Design
Fig. 17-5c W-527
�st
(c) Shaft mass only
50 300
Track
sprockets
Track
50
60
T1
A B
C
T2
Chain
30°
Chain
sprocket
100 diameter
Track sprocket
250 diameter
Track
Fc (= 2500 N)
FT (= 1000 N)
(a) General arrangement
JUVINALL: Machine Design
Fig. 17-6a W-528
d
JUVINALL: Machine Design
Fig. 17-6b-d W-530
55 Small gap or
spring washer
(b) Shaft layout
d
A
T1 T2
B
C
S
A T1 S T2
2490Vertical forces
C
B
325 2165
50
245
Torque
62,500
55 50 60
95,800
125,000
(c) Loading diagrams
VV
MV
T1 S T2
Horizontal forces
B
CA
687.5 1250
937.5
VH
MH
500
(Ft /2)
500
(Ft /2)
80,300
90,600
75,000
�
ea
 (
M
P
a)
�em (MPa)
�ea
�em
(d) Fatigue diagram
0 100 200
"Design overload" point
300 400 450
530
500
100
= 2.9
200
165
Sn = S' CLCGCS = (0.5)(550)(1)(0.9)(0.78) = 186n
113,700 130,000
JUVINALL: Machine Design
Fig. 17-7 W-531
d/4
d
(c) Shear failure of a tightly fitted key
d/4
d/8
d
(b) Key tightly fitted at top and bottom(a) Loosely fitted key
JUVINALL: Machine Design
Fig. 17-8 W-532
Sled-runner keyway Profiled keyway
Fatigue stress concentration factor, Kf*
Steel
Annealed
(less than 200 Bhn)
Quenched and drawn
(over 200 Bhn)
1.3
Bending
1.6
* Base nominal stress on total shaft section.
1.3
Torsion
1.6
1.6
Bending
2.0
1.3
Torsion
1.6
JUVINALL: Machine Design
Fig. 17-9 W-533
(b) Constant-stress,
 constant strain
 shear coupling
JUVINALL: Machine Design
Fig. 17-10 W-534
(a) Basic shear-type coupling
Bonded rubber element
(c) Tube form shear coupling
JUVINALL: Machine Design
Fig. 17-12 W-536
(a) Basic Oldham type (b) Modified type
JUVINALL: Machine Design
Fig. 17-13 W-537
JUVINALL: Machine Design
Fig. P17-1 W-538
20 in.
Flexible coupling
Motor 0.25-in.-dia. shaft
JUVINALL: Machine Design
Fig. P17-7 W-539
600 mm600 mm
50 kg
25-mm dia.
JUVINALL: Machine Design
Fig. P17-11 W-540
40 in. 30 in.20 in.
120 lb
80 lb
2-in.-dia. shaft
JUVINALL: Machine Design
Fig. P17-13a-f W-541,542,543
Driver
56 kw
Bearing (2)
Shaft
Driven
28 kw
Driven
28 kw
(b) Gear input shaft
(a) Connecting shaft
(c) Hydroelectric generator shaft
(d) Idler gear shaft
Bearings Shaft
Electric
generator
rotor
Hydraulic
turbine
Driver
Shaft
Bearing (2)
Driven
Idler
(e) Gear countershaft ( f ) Stationary countershaft
Shaft
Needle bearing (2)
Shaft
DriverDriven
Driver Driven
Coupling (2)Motor
Bearing (2)
Shaft
Driven machine
JUVINALL: Machine Design
Fig. P17-14 W-544
5 in.
2 in.
Bearing A
Bearing B
Fr = 450 lb
Fa = 400 lb
Ft = 800 lb
3 in. rad
JUVINALL: Machine Design
Fig. P17-15 W-545
125 mm
50 mm
B
A
Fr = 2.4 kN
Ft = 4.0 kN
Fa = 1.5 kN
Note: Gear forces act
at a 75-mm radius
from shaft axis.
Chain sprocket
JUVINALL: Machine Design
Fig. P17-16 W-546
(a)
Stationary shaft
Clamping supports
Chain sprocket
(b)
Rotating shaft
Clamping supports
Driving
shaft
Driven
shaft
Provision for
axial movement
Ring element
subjected to clamping
pressure, p
Friction lining
material
JUVINALL: Machine Design
Fig. 18-1 W-547
dr
rri
ro
Release
lever
To release
To transmission
Housing
Cover
Spring
Flywheel
Friction
planes
Engine
crankshaft
Pressure plate
Clutch plate
(driven disk)
Release
bearing
JUVINALL: Machine Design
Fig. 18-2 W-548
Oil passage
Input
Oil passage
Piston
Oil chamber
(pressurized to
engage clutch)
Seals
Bushing
Key
Key
Output
Disks b – driven disks (3 disks, 6 friction surfaces)
Disks a – driving disks (4 disks, 6 friction surfaces)
JUVINALL: Machine Design
Fig. 18-3 W-549
ri ro
dr
F
Cone
� Cone
angle
Spline (sliding fit)
Shifting groove
Spring
Key
Cup
(a) (b)
dr
sin �
Local pressure = p
JUVINALL: Machine Design
Fig. 18-5 W-551
r
�
ri
ro
Lever
(a)
Brake assembly
a A
F
Shoe
(block)
O
Drum
Direction of rotation
JUVINALL: Machine Design
Fig. 18-6 W-552
(b)
Shoe and lever as a free body
(c)
Drum as a free body
(d)
Lever proportions for a
self-locking brake
F
O
Ov
Oh
A
r
b
Av
fN
fN
N
N
Inertial and/or
load torque, T
Ah
c
b
a
JUVINALL: Machine Design
Fig. 18-7 W-553
6
23
1
80
80
All dimensions in millimeters
1
4
6
(rotation)
23
4
400
300
250
rad.
45°
300 Shoe width, 80 mm
f = 0.20
pmax = 0.40 N/mm
2
400
120
120
(a)
(b)
(c)
( f )
(d) (e)
5
5
H25 = 4F
H52 = 4F
V26 = 1.41F
H54 = 4FH34 = 4FH43 = 4F
H62 = 7.07FH26 = 7.07F
V16 = 0.70F
H16 =
3.46F
T = 880F
H36 = 10.53FH63 = 10.53F
V63 = 0.2H63
V36 = 2.11F
H13 = 6.53F
V13 = 2.11F
V12 = 2.41F
H12 = 3.07F O12
O16
O13
V62 = 0.2H62
V52 = F
H45 = 4F
V25 = F
O25
F
45°
90° 90°
F
A'
�n
�
�
JUVINALL: Machine Design
Fig. 18-8 W-554
O3
O3 O2
A
B
�
'
�
JUVINALL: Machine Design
Fig. 18-9 W-555
O3
d�
O2
A
dN
f dN
d cos (180° – �)
= –d cos �
d si
n (
18
0° 
– �
)
= d
 sin
 �
Drum rotation
Note: d = O2O3
 b = width of shoe
B
r �1
�2
c
F
�
180° – �
JUVINALL: Machine Design
Fig. 18-10 W-558
300
 rpm
C = 500
200
Spring
compressed
to force F
Force to
release brake
Cast-iron drum
Molded composite
shoe lining of
width b = 50
All dimensions in millimeters
(a) Complete brake
(b)
Drum and right shoe
F
150
150 150
300
200
150
O2
O3
�1
�150
45°
45°
�2
d
JUVINALL: Machine Design
Fig. 18-10 W-556
O2
N
Pivot P
F
fN
�
2
r f
r
�
2
JUVINALL: Machine Design
Fig. 18-12 W-557
P
f dN2 + f dN2
r
rf
f dN1
dN2
dN1
dN2
��
f dN2
f dN2
'
'
'
Drum
Rotation
Adjusting
cam
Brake lining
Anchor pins
Hydraulic wheel cylinder
Return spring
O2
O3
JUVINALL: Machine Design
Fig. 18-13 W-559
C
r
d �1
�2
Anchor pin
Hydraulic wheel cylinder
Forward
rotation
Adjusting cam
and guide
Brake shoe
Brake liningAnchor pin
Hydraulic wheel cylinder
Brake drum
Adjusting cam
and guide
JUVINALL: Machine Design
Fig. 18-14 W-560
Return
spring
P1
P1
P2
F
P2
a
Band of width = b
Rotation
Cutting plane for
free-body diagrams
JUVINALL: Machine Design
Fig. 18-15 W-561
�
�
c
r
d�/2d�/2
P + dP P
Rotation
dN
d�
JUVINALL: Machine Design
Fig. 18-16 W-562
P1
s
P2
Band of width = b
Rotation
JUVINALL: Machine Design
Fig. 18-17 W-563
�
a
F
c
P1
P2
Band width, b = 80 mm
Rotation
JUVINALL: Machine Design
Fig. 18-18 W-564
� = 270° Friction coefficient, f = 0.20
Maximum lining pressure,
pmax = 0.5 MPa
a = 150 mm
F
c = 700 mm
s = 35 mm
r = 250 mm
Pads of diameter = 60 mm
125 mm
320 mm
pmax = 500 kPa
f = 0.30
JUVINALL: Machine Design
Fig. P18-12 W-567
4m/s
1000 kg
JUVINALL: Machine Design
Fig. P18-14 W-565
JUVINALL: Machine Design
Fig. P18-17 W-568
Electric
motor
Gear
reducer
Friction clutch
T = 6 N • m, 600 rpm
Rotary inertial load,
I = 0.7 N • m • s2
JUVINALL: Machine Design
Fig. P18-17 W-569
Rotation
F = 1500 N
200 mm
340 mm
400 mm 500 mm
JUVINALL: Machine Design
Fig. P18-22 W-570
Rotation
A
F
240 mm
250 mm 320 mm
400 mm
150 mm
JUVINALL: Machine Design
Fig. P18-23 W-571
500 mm
Spring
300 mm
400 mm
350 mm
Woven lining
Cast- iron
drum
JUVINALL: Machine Design
Fig. P18-24 W-572
2
5
3
4
6
1
18 in.
25 in.
150
5 in.
5 in.
23 in.
18 in.
30 in.
Rotation
5
JUVINALL: Machine Design
Fig. P18-31 W-573
Rotation
F = 300 N
500 mm
�
JUVINALL: Machine Design
Prob. 18-33 W-574
55
258°
240
F
75
72
370
JUVINALL: Machine Design
Prob. 18-34 W-575
Wt.
s
a
c
270°
JUVINALL: Machine Design
Fig. 19-1 W-576
�
Motor
rotation
(a) Manual adjustment
(b) Pivoted, overhung motor
(c) Weighted idler pulley
Adjustment
Tight
side
Pivot
Pivot
Overhang
Idler
Weight
Tight
side
JUVINALL: Machine Design
Fig. 19-2 W-577
0.50 in.
0.31 in.
0.66 in.
0.41 in. 0.53 in.
0.75 in.
0.91 in.
A
0.38 in.
0.32 in.3 V
0.62 in.
0.54 in.
0.88 in.
5 V
8 V
D
E
C
B
(a) Standard sizes A, B, C, D, and E
(b) High-capacity sizes 3V, 5V, and 8V
0.88 in.
1.25 in.
1.50 in.
1.0 in.
JUVINALL: Machine Design
Fig. 19-4 W-579
2�
≈ 36°
dN
dN2
dN/2
sin �
(a) (b)
JUVINALL: Machine Design
Fig. 19-5 W-581
Tension-
carrying cords
Fabric cover
Rubber
JUVINALL: Machine Design
Fig. 19-7 W-583
p
�r Pitch
circle
(a)
rc
p
(b)
A
B
AB
rc
r
Chordal rise, r – rc
JUVINALL: Machine Design
Fig. 19-9 W-584A
Pitch p
(a)
JUVINALL: Machine Design
Fig. 19-10 W-584B
A
A
r
r4
(D/2)
r3
D
Ti
�i �o
To
Input
shaft
Oil particle
Impeller
Gasket
Case
Turbine
Fluid
circulation
Oil seal
Output shaft
Core or inner
shroud
r2
r1
�i
Blades
Section AA
P
er
ce
nt
 r
at
ed
 t
or
qu
e
Input speed �i (rpm)
0 200 400 600 800 1,000 1,200 1,400 1,600 1,800
0
40
80
120
160
200
240
280
320
360
JUVINALL: Machine Design
Fig. 19-11 W-584C
12 8
7
5
20
100
16 14
10
6
4
3
2
Percent slip
Maximum
coupling
torque
Electric motor
torque curve
Turbine
Fluid
circulation
Input
shaft Output
shaft
Impeller
Reactor
JUVINALL: Machine Design
Fig. 19-12 W-585
Turbine
Input
shaft Output
shaft
Impeller
One-way
clutchReactor
JUVINALL: Machine Design
Fig. 19-13 W-586
To
rq
ue
 r
at
io
Speed ratio
0 0.2 0.4 0.6 0.8 1.0
0.8
1.2
1.6
2.0
2.4
2.8
3.2
E
ff
ic
ie
nc
y 
(%
)
0
20
40
60
80
100
JUVINALL: Machine Design
Fig. 19-14 W-587
Converter efficiency
Coupling
efficiency
Converter
torque ratio
Coupling torque ratio
JUVINALL: Machine Design
Fig. P19-3 W-588
�
�
�
�
�2
c
�1
r2
r1
JUVINALL: Machine Design
Fig. P19-4 W-589
A
B
C
D
JUVINALL: Machine Design
Fig. P19-8 W-590
V-belt
� = 18°
f = 0.20
Belt maximum tension = 1300 N
Belt unit weight = 1.75 N/m
r = 100 mm
Pulley radius
� = 170°
n = 4000 rpm
JUVINALL: Machine Design
Fig. P19-15 W-591
Electric motor
n = 1780 rpm
55% rated power
Fluid coupling—
performance curves—
Fig. 19.11
Driven
machine
JUVINALL: Machine Design
Fig. U19-1 W-580
Multiple V-belt, � = 18°, size 5V
Unit weight = 0.012 lb/in.
Power input = 25 hp
Pmax = P1 = 150 lb
f = 0.20
3.7 in. dia.
Driving
pulley
Number of belts = ?
Driven
pulley
n = 1750
rpm
165° angle of wrap
1.44 –2.99
B1 engaged
–4.31Reverse
B3 engaged
1.00 1.00
C1 engaged
1.004
C2 engaged
1.44 1.00
B1 engaged
39%
61%
39%
61%
1.443
C2 engaged
1.00
(b) Power flow block diagram
(c) Gear shift pattern(a) Internal power flow diagram
2.53
C1 engaged
2.532
B2 engaged
1.44 2.53
B1 engaged
3.661
–Neutral
Torque
ratio
Tout/Tin
Front
planetary
train
Fluid
coupling
Rear
planetary
train
Gear
No clutches or brakes engaged
B2 engaged
Gear Ratio
Neutral –
1 3.66
2 2.53
3 1.44
4 1
Reverse –4.31
C1 B1 C2 B2 B3
S1, P1, R1 S2, P2, R2 S3, P3, R3
B3
B2B1
C2C1
Neutral
S1, P1, R1 S2, P2, R2 S3, P3, R3
B2B1
C2 B3C1
1
S1, P1, R1 S2, P2, R2 S3, P3, R3
B3
B2B1
C2C1
2
S1, P1, R1 S2, P2, R2 S3, P3, R3
B3
B2B1
C2C1
3
S1, P1, R1 S2, P2, R2 S3, P3, R3
B3
B2B1
C2C1
4
S1, P1, R1 S2, P2, R2 S3, P3, R3
B3
B2B1
C2C1
Reverse
Fluid
coupling
Gear
interface
Bearing
JUVINALL: Machine Design
Fig. 20-2 W-594
JUVINALL: Machine Design
Fig. 20-3 W-595
Input torque
Ti
54-tooth ring
R1
×
Ti
3
TiP
81
TiP
81
TiP
81
TiP
81
TiP
81
TiP
81
TiP
81
TiP
40.5
P1
S1
TiP
40.5
TiP
40.5
TiP
40.5A1
TiP
81
P
27
15-tooth planet
12-tooth sun
P
27
P
12
P
19.5
P
12
P
7.5
Torque from B1:
TB1 =
TB1 = 0.44Ti
(3)
TiP
40.5 P
19.5
Output torque:
To =
To = 1.44Ti
(3)
Arm
To
JUVINALL: Machine Design
Fig. 20-4 W-596
TiP
67.5
TiP
67.5
TiP
67.5
Ti
3
P
22.5
TiP
Ti
67.5
TiP
67.5
S2
6
P
TiP
33.75
TiP
67.5
R2
34.5
P
TiP
33.75
TiP
33.75
TiP
33.75A2
P
28.5
TiP
33.75 P
28.5
Output torque:
To = (3)
To = 2.53Ti
Arm
22.5
45-tooth sun
69-tooth ring
•
P
TiP
67.5 P
34.5TB2 = (3)
TB2 = 1.53Ti
P2
12-tooth planet
JUVINALL: Machine Design
Fig. 20-5 W-597
TiP
67.5
34.5TiP
675
69TiP
675
TiP
67.5
34.5TiP
67.5
34.5TiP
675
TiP
67.5
TiP
67.5
TiP
67.5
TiP
67.5
TiP
Ti
67.5
S2
TiP
33.75
34.5
P
10
P
34.5
10
•
TiP
33.75
69TiP
675
A2, A3
P
28.5
P
18
TiP
33.75
69TiP
675P
28.5
Output torque:
To = – 3
To = –2.99Ti
P
18
Arms
22.5
45-tooth sun
P
P2
12-tooth planet
P3
16-tooth planet
R2, S3
69-tooth ring
and 20-tooth sun
JUVINALL: Machine Design
Fig. 20-5 W-598
34.5TiP
675
34.5TiP
675
34.5TiP
675
34.5TiP
675
P
26
Torque from reverse lock, B3
TB3 = (3)
TB3 = 3.99Ti
26 R3
52-tooth ring
P
JUVINALL: Machine Design
Fig. 20-6 W-599
To
TiP
40.5
TiP
81
S1
24-tooth sun
TiP
81
TiP
81 19.5
P
TiP
40.5
TiP
40.5
Output torque:
To = 1.00Ti
TiP
81 P
12
Torque from C1:
TC1 = 3
TC1 = 0.44Ti
A1
TC1
TC1
Arm
12
P
0.0117Ti P
Tf
Tf P
67.5
TC2P
Clutch
torque
TC2
103.5
P
28.5
Arm
A2
22.5
45-tooth sun
P 34.5
P
P2
12-tooth
planet
69-tooth ring
R2
S2
To
P
28.5
Output torque:
To = 0.117Ti P (3)
To = 1.00Ti
Tf P
67.5
TC2P
103.5
For equilibrium of P2:
∴ Planet pin force = 0.0117Ti P
=
Tf + TC2 = Ti
Tf = 0.39Ti
TC2 = 0.61Ti
JUVINALL: Machine Design
Fig. 20-7 W-600
JUVINALL: Machine Design
Fig. B-1 W-601
h
h
b
d
b
Rectangle
Triangle
Circle
d
Hollow circle
y
y
di
Rod
Disk
Rectangular prism
Cylinder
y
d
d
b
x
x
z
z
y
y
t
JUVINALL: Machine Design
Fig. B-2 W-602
L
c
L
a
z
y
d
x
z
Hollow cylinder
L
y
do
di
x
z
Tempering temperature (°F)
Reduction of area
400
%
ksi
600 800 1000 1200
0
20
40
60
60
80
100
120
140
160
180
200
220
240
JUVINALL: Machine Design
Fig. C-5a W-603
4130
4130 1095
1050
1095
1050
1095
1030, 1040
1095, 4130
1040
1040
1030
1030
1050
1030, 1040, 4130
1050
Elongation
Ultimate strength
Yield strength
Tempering temperature (°F)
Reduction of area
400
%
ksi
600 800 1000 1200
0
20
40
60
60
80
100
120
140
160
180
200
JUVINALL: Machine Design
Fig. C-5b W-604
Elongation
Ultimate strength
Yield strength
1095
1050
1040
1050
1040
1040
1040
1050
1095
1095
1050
1095
Tempering temperature (°F)
Reduction of area
400
%
ksi
600 800 1000 1200
0
20
40
60
100
140
120
160
200
180
220
260
240
280
300
JUVINALL: Machine Design
Fig. C-5c W-605
Elongation
Ultimate strength
Yield strength
4340
9255
4140
4340
9255
4340
4140
9255
9255
4140
4140, 4340
Diameter of test specimen (in.)
Diameter of test specimen (mm)
0 1 2 3 4
50
60
70
80
90
ksi MPa
100
110
120
130
140
150
160
170
180
190 1300
1200
4340
4340
4140
3140
4140
3140
1040
1040
1100
1000
900
800
700
600
500
400
0 200 400 600 800
Su
Sy
1000
JUVINALL: Machine Design
Fig. C-6 W-606
–PL
P
P
�
�max
V = P
M = –PL
+
0
0
–
V
M
JUVINALL: Machine Design
Fig. D-1(1) W-607
L
x
JUVINALL: Machine Design
Fig. D-1(2) W-607
V = P
M = –Pa
+
0
0
–
V
M
–Pa
P
P
b
�
�max
x
a
�max
M = –wL2/2
+
0
0
–
V
M
JUVINALL: Machine Design
Fig. D-1(3) W-608
wL
V = wL
wL2
2
w
x
L
JUVINALL: Machine Design
Fig. D-1(4) W-608
0
0
–
V
M
–Mb
–Mb
Mb
P
�
�max
x
L
+
+
0
0
–
V
M
JUVINALL: Machine Design
Fig. D-2(1) W-609
�
L
x
P
2
LP
2
P
P/2
–P/2
PL/4
2
+
+
0
0
–
V
M
JUVINALL: Machine Design
Fig. D-2(2) W-609
�
L
x
b
Pa
L
Pb
L
P
Pb/L
Pab/L –Pa/L
a
+
+
0
0
– –
V
M
JUVINALL: Machine Design
Fig. D-2(3) W-610
L
x
w
wL
wL /2
wL2
2
2
wL
2
wL
2
+
0
0
–
–
V
M
JUVINALL: Machine Design
Fig. D-2(4) W-610
L
x
a
PL
P
P
Pb
a
a
–Pb/a
–Pb
b
�
�max
z
+
+
0
0
– –
V
M
JUVINALL: Machine Design
Fig. D-2(5) W-611
a
L
x
M0
M0
L
b
M0
L
M0
L
M0a
L
M0b
L
0
–
–
0
V
M
JUVINALL: Machine Design
Fig. D-2(6) W-611
a a
L
x
M0
M0
x'
b
�max
a
M0
M0
a
M0
�
–
JUVINALL: Machine Design
Fig. D-3(1) W-612
�
+
+
0
0
–
–
V
M
PL
8
P
x
L
–
–
–
PL
8
PL
8
– PL
8
PL
8
P
2
P
2
P
2
P
2
L
2
JUVINALL: Machine Design
Fig. D-3(2) W-612
+
+
0
0
–
– –
V
M
Pb2
L3
P
x
a b
L
–
–
Pab2
L2
Pa2b
L2
(3a + b)
Pb2
L3
2Pa2b2
L3
Pab2
L2
(3a + b)
Pb2
L3
(a + 3b)
Pb2
L3
– Pa
2b
L2
(a + 3b)
JUVINALL: Machine Design
Fig. D-3(3) W-612
+
+
0
0
–
–
V
M
x
w
�
L
–
–
wL2
12
– wL
2
12
– wL
2
12
wL2
24
wL2
12
wL
2
wL
2
wL
2
wL
2
JUVINALL: Machine Design
Fig. D-4 W-613
107
9
5
.0
0
1
2
2
.1
7
1
4
4
.8
1
 R
O
O
T
1
7
5
.8
4
 P
IT
C
H
2
0
6
.8
8
 O
.D
.
2
5
8
2
.2
1
 N
 • 
m
1
0
1
.6
8
5
.0
0
8
2
.6
3
152
276
400
530
646
680
716
1060
A shaft with integral worm, dimensions in millimeters.
RB
RA
8.68 kN
10
9
8
7
654
3
2
1
1
h hole
s shaft
Class
of fit
Bar
graph
(basic
hole
system)
2 3 4 5 6 7 8
Loose fit Free fit Medium fit Snug fit Wringing fit Tight fit
Medium
force fit
Heavy
force and
shrink fit
.0216 (.0025) .0112 (.0013) .0069 (.0008) .0052 (.0006) .0052 (.0006) .0052 (.0006) .0052 (.0006) .0052 (.0006)
.0216 (.0025) .0112 (.0013) .0069 (.0008) .0035 (.0004) .0035 (.0004) .0052 (.0006) .0052 (.0006) .0052 (.0006)
.0073 (.0025)
Note: Numbers in the table are for use with all dimensions in millimeters, except for those in parentheses, which are for use with inches.
.0041 (.0014) .0026 (.0009) 0 (0)
Cb
Cs
Ca
Ci 0 (0) .00025 (.00025) .0005 (.0005) .0010 (.0010)
JUVINALL: Machine Design
Fig. E-1 W-614
a
a
h h h h s h h hs
s
s
sa
s
s
JUVINALL: Machine Design
p754 b1 W-???
JUVINALL: Machine Design
p754b2 W-604
	transparencies.pdf
	transparencies.pdf
	Chapter 1
	F01
	F01-01a
	F01-02
	F01-03a
	F01-03b
	F01-03c
	F01-04
	F01-05
	F01-06
	F01-07
	F01-08
	F01-09
	F01-10
	F01-11
	F01-12
	F01-13
	P01
	P01-18
	P01-23
	P01-26
	P01-29
	P01-42
	P01-49
	Chapter 2
	F02
	F02-01
	F02-02
	F02-03
	F02-04
	F02-05
	F02-06
	F02-07
	F02-08
	F02-09
	F02-10
	F02-11
	F02-12
	F02-13
	F02-14
	F02-15
	F02-16
	F02-17
	F02-18
	F02-19
	P02
	P02-02
	P02-03
	P02-04
	P02-06
	P02-07
	P02-08
	P02-09
	P02-10
	P02-11
	P02-12
	P02-13
	P02-14
	P02-15
	P02-16
	P02-17
	P02-18
	P02-19
	P02-20
	P02-21
	P02-22
	P02-23
	P02-24
	P02-25
	P02-26
	P02-27
	P02-28
	P02-29
	P02-31
	Chapter 3
	F03
	F03-01
	F03-02
	F03-03
	F03-04
	F03-05
	F03-06
	F03-07
	F03-08
	F03-11
	F03-12
	F03-13
	P03
	P03-14
	Chapter 4
	F04
	F04-01
	F04-02
	F04-03
	F04-04
	F04-05
	F04-06
	F04-07
	F04-08
	F04-09
	F04-10
	F04-11
	F04-12
	F04-13
	F04-14
	F04-15
	F04-16
	F04-17
	F04-18
	F04-19
	F04-20
	F04-21
	F04-22
	F04-23
	F04-24
	F04-25
	F04-26
	F04-27
	F04-28
	F04-29
	F04-30
	F04-31
	F04-32
	F04-33
	F04-34
	F04-35
	F04-36
	F04-37
	F04-38
	F04-39
	F04-40
	F04-41
	F04-42
	F04-43
	F04-44
	F04-45
	F04-61
	P04
	P04-02
	P04-10
	P04-11
	P04-18
	P04-19
	P04-21
	P04-23
	P04-24
	P04-25
	P04-27
	P04-29
	P04-30
	P04-34
	P04-36
	P04-40
	P04-38
	P04-41
	P04-46
	P04-49
	P04-52
	P04-52
	P04-54
	P04-55
	P04-65
	Chapter 5
	F05
	F05-01
	F05-02
	F05-03
	F05-04
	F05-05
	F05-06
	F05-07
	F05-08
	F05-09
	F05-10
	F05-11
	F05-12
	F05-13
	F05-14
	F05-15
	F05-16
	F05-17
	F05-18
	F05-19
	F05-20
	F05-21a
	F05-21b
	F05-21c
	F05-21d
	F05-22
	F05-23
	F05-24
	F05-25
	F05-26
	F05-27
	F05-28
	F05-29
	F05-30
	F05-31
	F05-32
	F05-33
	F05-34
	F05-35
	F05-36
	F05-37
	F05-38
	T05
	T05-01
	T05-02
	P05
	P05-04
	P05-09
	P05-14
	P05-15
	P05-16
	P05-17
	P05-19
	P05-20
	P05-21
	P05-22
	P05-23
	P05-27
	P05-29
	Chapter 6
	F06
	F06-02
	F06-03
	F06-04
	F06-05
	F06-06
	F06-07
	F06-08
	F06-09
	F06-10
	F06-11
	F06-12
	F06-13
	F06-14
	F06-15
	F06-16
	F06-17
	F06-18
	F06-19
	F06-20
	F06-21
	P06
	P06-13
	P06-23
	Chapter 7
	F07
	F07-01
	F07-02
	F07-03a-c
	F07-04
	F07-05
	F07-06
	F07-07
	F07-07b
	F07-08
	F07-09
	F07-10 W-226
	F07-10 W-229
	F07-11
	F07-13
	P07
	P07-02
	P07-05
	P07-11
	P07-12
	Chapter 8
	F08
	F08-02
	F08-03
	F08-04
	F08-05
	F08-06
	F08-07
	F08-08
	F08-09
	F08-10
	F08-11
	F08-12
	F08-13
	F08-14
	F08-15
	F08-16
	F08-17
	F08-18
	F08-19
	F08-20
	F08-21
	F08-22
	F08-23
	F08-24
	F08-25
	F08-26
	F08-27
	F08-28
	F08-29
	F08-30
	F08-31
	P08
	P08-26
	P08-27
	P08-28
	P08-30
	P08-37
	P08-38
	P08-39
	P08-44
	P08-45
	P08-46
	Chapter 9
	F09
	F09-01
	F09-02
	F09-03
	F09-04
	F09-05
	F09-06
	F09-07
	F09-08a
	F09-09
	F09-11
	F09-12
	F09-13
	F09-14
	F09-15
	F09-16
	F09-17
	F09-18
	F09-19
	F09-19b
	F09-21
	T09
	T09-01
	P09
	P09-01
	P09-04
	P09-08d
	P09-12
	P09-20
	Chapter 10
	F10
	F10-01
	F10-02
	F10-03
	F10-04
	F10-05
	F10-06
	F10-07
	F10-08
	F10-10
	F10-11
	F10-12
	F10-13
	F10-14
	F10-15
	F10-16
	F10-17
	F10-18
	F10-19
	F10-20
	F10-21
	F10-22
	F10-23
	F10-24
	F10-25
	F10-26
	F10-27
	F10-28
	F10-29
	F10-30
	F10-31
	F10-32
	F10-33
	F10-34-ab
	F10-34
	F10-35a-c
	F10-36
	P10
	P10-01
	P10-09
	P10-17
	P10.26
	P10-28
	P10-39
	P10-41
	P10-44
	T10
	T10-04
	Chapter 11
	F11
	F11-01
	F11-02
	F11-03
	F11-04
	F11-05
	F11-06
	F11-07
	F11-08
	F11-09
	F11-10
	F11-11
	F11-12
	F11-04
	F11-07
	P11
	P11-11
	P11-12
	Chapter 12
	F12
	F12-01
	F12-02
	F12-03
	F12-04
	F12-05
	F12-06
	F12-07
	F12-08
	F12-09
	F12-10
	F12-11
	F12-12
	F12-13
	F12-14
	F12-15
	F12-16
	F12-17
	F12-18
	F12-19
	F12-20
	F12-21
	F12-22
	F12-23
	F12-24
	F12-25
	F12-26
	F12-27
	F12-28
	F12-29
	F12-30
	F12-31
	F12-32
	F12-33
	F12-34
	P12
	P12-03
	P12-11
	P12-15
	P12-28
	P12-34
	P12-35
	P12-37
	P12-39
	P12-46
	Chapter 13
	F13
	F13-01
	F13-02
	F13-03
	F13-04
	F13-05
	F13-06
	F13-07
	F13-08
	F13-09
	F13-10
	F13-11
	F13-12
	F13-13
	F13-14
	F13-15
	F13-16
	F13-17
	F13-18
	F13-19
	F13-20
	F13-21
	F13-23
	F13-24
	F13-25
	F13-26
	F13-27
	F13-28
	P13
	P13-12
	P13-27
	P13-29D
	Chapter 14
	F14
	F14-1b
	F14-2
	F14-3a
	F14-3c
	F14-3d
	F14-3e
	F14-4
	F14-5
	F14-8
	F14-10
	F14-10h
	F14-11
	F14-12
	F14-13
	F14-14
	F14-15
	F14-16
	F14-17
	F14-18
	P14
	P14-06
	P14-10
	P14-19
	P14-20
	P14-21d
	Chapter 15
	F15
	F15-01
	F15-02
	F15-03
	F15-04
	F15-05
	F15-06
	F15-07
	F15-08
	F15-09
	F15-10
	F15-11
	F15-12
	F15-14
	F15-15
	F15-16
	F15-17
	F15-18
	F15-20
	F15-21
	F15-22
	F15-23
	F15-24
	F15-25
	F15-26
	F15-27
	F15-28
	F15-29
	F15-30
	F15-31
	F15-32
	F15-33
	P15
	P15-21
	P15-23
	P15-26
	P15-27
	P15-45
	P15-47
	P15-50
	P15-51
	Chapter 16
	F16
	F16-01
	F16-04
	F16-05
	F16-06
	F16-07
	F16-08
	F16-09
	F16-10
	F16-12
	F16-13
	F16-13
	F16-14
	F16-15
	F16-16
	F16-17
	F16-18
	F16-19
	F16-20
	F16-21
	F16-22
	F16-23
	F16-24
	F16-25
	F16-27
	T16
	T16-01
	P16
	P16-05
	P16-08
	P16-14
	P16-19
	P16-23D
	P16-30
	P16-34
	Chapter 17
	F17
	F17-01
	F17-02
	F17-03
	F17-04
	F17-05a
	F17-05b
	F17-05c
	F17-06a
	F17-6b-d
	F17-07
	F17-08
	F17-09
	F17-10
	F17-12
	F17-13
	P17
	P17-01
	P17-07
	P17-11
	P17-13a-f
	P17-14
	P17-15
	P17-16
	Chapter 18
	F18
	F18-01
	F18-02
	F18-03
	F18-05
	F18-06
	F18-07
	F18-08
	F18-09
	F18-10 W-556
	F18-12
	F18-13
	F18-14
	F18-15
	F18-16
	F18-17
	F18-18
	P18
	P18-12
	P18-14
	P18-17
	P18-17
	P18-22
	P18-23
	P18-24
	P18-31
	P18-33
	P18-34
	Chapter 19
	F19
	F19-01
	F19-02
	F19-04
	F19-05
	F19-07
	F19-09
	F19-10
	F19-11
	F19-12
	F19-13
	F19-14
	P19
	P19-03
	P19-04
	P19-08
	P19-15
	U19
	U19-01
	Chapter 20
	F20
	F20-02
	F20-03
	F20-04
	F20-05
	F20-05 W-598
	F20-06
	F20-07
	Appendix
	FB
	FB-01
	FB-02
	FC
	FC-05a
	FC-05b
	FC-05c
	FC-06
	FD
	FD-01(1)
	FD-01(2)
	FD-01(3)
	FD-01(4)
	FD-02(1)
	FD-02(2)
	FD-02(3)
	FD-02(4)
	FD-02(5)
	FD-02(6)
	FD-03(1)
	FD-03(2)
	FD-03(3)
	FD-04
	FE
	FE-01
	p754 b1
	p754b2