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MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
F I G U R E E - 1
Geometric Stress-Concentration Factor Kt for a Shaft with a Shoulder Fillet in Axial tension
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Kt
r / d
1.30
1.01
1.02
1.051.10
1.20
1.50
1.15
1.071.05
dD
r
P P
2.0D / d =
D / d A b2.00 1.014 70 0.300 351.50 0.999 57 0.282 211.30 0.996 82 0.257 511.20 0.962 72 0.255 271.15 0.980 84 0.224 851.10 0.984 50 0.208 181.07 0.984 98 0.195 481.05 1.004 80 0.170 761.02 1.012 20 0.124 741.01 0.984 13 0.104 74
K A rdt
b
where :
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Kt
r / dF I G U R E E - 2Geometric Stress-Concentration Factor Kt for a Shaft with a Shoulder Fillet in Bending
1.011.02
1.031.05
1.101.20
1.502.0
3.0
6.0D / d = D / d A b6.00 0.878 68 0.332 433.00 0.893 34 0.308 602.00 0.908 79 0.285 981.50 0.938 36 0.257 591.20 0.970 98 0.217 961.10 0.951 20 0.237 571.07 0.975 27 0.209 581.05 0.981 37 0.196 531.03 0.980 61 0.183 811.02 0.960 48 0.177 111.01 0.919 38 0.170 32
K A rdt
b
where :
dD
r
M M
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
F I G U R E E - 3
Geometric Stress-Concentration Factor Kt for a Shaft with a Shoulder Fillet in Torsion
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Kt
r / d
1.201.09
1.33
T T
dD
r
2.0D / d =
D / d A b2.00 0.863 31 0.238 651.33 0.848 97 0.231 611.20 0.834 25 0.216 491.09 0.903 37 0.126 92
K A rdt
b
where :
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
F I G U R E E - 4
Geometric Stress-Concentration Factor Kt for a Grooved Shaft in Axial Tension
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Kt
r / d
1.15
1.30
1.01
1.02
1.031.10
1.20
1.50 2.0
1.05
P Pd
D r1.07D / d =
D / d A b 0.993 72 0.393 52
2.00 0.993 83 0.382 311.50 0.998 08 0.369 551.30 1.004 90 0.355 451.20 1.010 70 0.337 651.15 1.026 30 0.316 731.10 1.027 20 0.294 841.07 1.023 80 0.276 181.05 1.027 20 0.252 561.03 1.036 70 0.216 031.02 1.037 90 0.187 551.01 1.000 30 0.156 09
K A rdt
b
where :
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
F I G U R E E - 5
Geometric Stress-Concentration Factor Kt for a Grooved Shaft in Bending
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Kt
r / d
2.0
D / d = 1.051.07
1.10
1.301.15
1.03
1.02
1.01
M M
dD rK A r
dtb
where :
D / d A b 0.948 01 0.333 02
2.00 0.936 19 0.330 661.50 0.938 94 0.323 801.30 0.942 99 0.315 041.20 0.946 81 0.305 821.15 0.953 11 0.297 391.12 0.955 73 0.288 861.10 0.954 54 0.282 681.07 0.967 74 0.264 521.05 0.987 55 0.241 341.03 0.990 33 0.215 171.02 0.977 53 0.197 931.01 0.993 93 0.152 38
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
F I G U R E E - 6
Geometric Stress-Concentration Factor Kt for a Grooved Shaft in Torsion
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Kt
r / d
1.20
1.011.02
1.05
D / d = 1.10
1.30
2.0
dD r
T T
D / d A b 0.881 26 0.252 04
2.00 0.890 35 0.240 751.30 0.894 60 0.232 671.20 0.901 82 0.223 341.10 0.923 11 0.197 401.05 0.938 53 0.169 411.02 0.968 77 0.126 051.01 0.972 45 0.101 62
K A rdt
b
where :
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
F I G U R E E - 7
Geometric Stress-Concentration Factor Kt for a Shaft with a Transverse Hole in Bending
on surface of shaft at hole
1.50 2.0Kt
d / D0 0.05 0.10 0.15 0.20 0.25 0.30
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3.0
2.9
d
D
M M
K
dD
t
1 589 90
0 635 50
.
. log
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
F I G U R E E - 8
Geometric Stress-Concentration Factor Kt for a with a Transverse Hole in Torsion
below shaft surface in holeon surface of shaft at hole
Kt
d / D
2.62.72.82.93.03.13.23.33.43.5
4.0
0 0.05 0.10 0.15 0.20 0.25 0.30
3.63.73.83.9
d
D
T T
B
A KdD
dD
dD
dD
dD
tA
+ +
3 921 50 24 435
234 06 1 200 5
3 059 5 3042 4
2 3
4 5
. .
. .
. .
K dD
dD
dD
dD
dD
dD
tB
+ +
+ +
3 9702 9 292
27 159 30 231
393 19 650 39
15 451
2 3
4 5
6
. .
. .
. .
.
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
F I G U R E E - 9
Geometric Stress-Concentration Factor Kt for a Filleted Flat Bar in Axial tension
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Kt
r / d
1.01
1.02
1.05
1.101.20
1.501.15
1.07
3.0
2.0D / d =
1.30
d
D
h
r
P P
2.00 1.099 60 0.320 771.50 1.076 90 0.295 581.30 1.054 40 0.270 211.20 1.035 10 0.250 841.15 1.014 20 0.239 351.10 1.013 00 0.215 351.07 1.014 50 0.193 661.05 0.987 97 0.138 481.02 1.025 90 0.169 781.01 0.976 62 0.106 56
D / d A b
K A rdt
b
where :
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Kt
r / dF I G U R E E - 1 0Geometric Stress-Concentration Factor Kt for a Filleted Flat Bar in Bending
1.07
1.011.02 1.03 1.05
1.101.20
2.0
3.0
6.0D / d =
6.00 0.895 79 0.358 473.00 0.907 20 0.333 332.00 0.932 32 0.303 041.30 0.958 80 0.272 691.20 0.995 90 0.238 291.10 1.016 50 0.215 481.07 1.019 90 0.203 331.05 1.022 60 0.191 561.03 1.016 60 0.178 021.02 0.995 28 0.170 131.01 0.966 89 0.154 17
D / d A b
K A rdt
b
where :
dD
h
M Mr1.30
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
F I G U R E E - 1 1
Geometric Stress-Concentration Factor Kt for a Notched Flat Bar in Axial tension
1.15
2.0D / d =
Kt
r / d0.05 0.10 0.15 0.20 0.25 0.300.02
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0 1.50
1.30
1.20
1.02
1.01
1.03
1.051.07
1.10
P P
D h
r
d 1.109 50 0.417 12
3.00 1.113 90 0.409 232.00 1.133 90 0.385 861.50 1.132 60 0.365 921.30 1.158 60 0.332 601.20 1.147 50 0.315 071.15 1.095 20 0.325 171.10 1.085 10 0.299 971.07 1.091 20 0.268 571.05 1.090 60 0.241 631.03 1.051 80 0.222 161.02 1.054 00 0.188 791.01 1.042 60 0.141 45
D / d A b
K A rdt
b
where :
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 0.05 0.10 0.15 0.20 0.25 0.30
Kt
r / dF I G U R E E - 1 2Geometric Stress-Concentration Factor Kt for a Notched Flat Bar in Bending
1.02
1.01
1.03
1.05
1.07 D / d = 1.10
1.15
1.20
1.502.0
0.970 79 0.356 723.00 0.971 94 0.350 472.00 0.968 01 0.349 151.50 0.983 15 0.333 951.30 0.982 88 0.326 061.20 0.990 55 0.313 191.15 0.993 04 0.302 631.10 1.007 10 0.283 791.07 1.014 70 0.261 451.05 1.025 00 0.240 081.03 1.029 40 0.211 611.02 1.037 40 0.184 281.01 1.060 50 0.133 69
D / d A b
K A rdt
b
where :
1.30M M
D h
r
d
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
F I G U R E E - 1 3
Geometric Stress-Concentration Factor Kt for a Flat Bar with Transverse Hole in Axial tension
Kt
d / W
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
0 0.300.10 0.400.20 0.60 0.700.50
P PW d
h
for dW
K dW
dW
dW
dW
dW
t
+
+ +
0 65
3 003 9 3 753
7 973 5
9 265 9
1 814 5
2 968 4
2
3
4
5
. :
. .
.
.
.
.
MACHINE DESIGN - An Integrated Approach, 2ed by Robert L. Norton, Prentice-Hall 2000
1.52.0
1.0
0.50
0.25
0
F I G U R E E - 1 4
Geometric Stress-Concentration Factor Kt for a Flat Bar with Transverse Hole in Bending
d / hKt
d / W
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 0.300.10 0.400.20 0.60 0.700.50
0.25 2.687 50 0.751 280.50 2.466 20 0.772 151.00 2.240 00 0.787 391.50 2.024 30 0.808 212.00 2.105 60 0.798 78 1.808 20 0.667 02
d / h A b
for and
for
where :
dh
dW
K dW
dW
dW
dh
K Ae
t
tb d W
+ ( )[ ]
0 0 65
2 994 7 3 483 3
5 826 8 4 198 6
0 25
2 3
. :
. .
. .
. :
M M
W d
h
