Useful Tables Appendix A Appendix Outline A–1 Standard SI Prefixes 961 A–2 Conversion Factors 962 A–3 Optional SI Units for Bending, Torsion, Axial, and Direct Shear Stresses 963 A–4 Optional SI Units for Bending and Torsional Deflections 963 A–5 Physical Constants of Materials 963 A–6 Properties of Structural-Steel Angles 964 A–7 Properties of Structural-Steel Channels 966 A–8 Properties of Round Tubing 968 A–9 Shear, Moment, and Deflection of Beams 969 A–10 Cumulative Distribution Function of Normal (Gaussian) Distribution 977 A–11 A Selection of International Tolerance Grades—Metric Series 978 A–12 Fundamental Deviations for Shafts—Metric Series 979 A–13 A Selection of International Tolerance Grades—Inch Series 980 A–14 Fundamental Deviations for Shafts—Inch Series 981 A–15 Charts of Theoretical Stress-Concentration Factors K t 982 A–16 Approximate Stress-Concentration Factors K t and K ts for Bending a Round Bar or Tube with a Transverse Round Hole 987 A–17 Preferred Sizes and Renard (R-series) Numbers 989 A–18 Geometric Properties 990 A–19 American Standard Pipe 993 A–20 Deterministic ASTM Minimum Tensile and Yield Strengths for HR and CD Steels 994 A–21 Mean Mechanical Properties of Some Heat-Treated Steels 995 A–22 Results of Tensile Tests of Some Metals 997 A–23 Mean Monotonic and Cyclic Stress-Strain Properties of Selected Steels 998 A–24 Mechanical Properties of Three Non-Steel Metals 1000 A–25 Stochastic Yield and Ultimate Strengths for Selected Materials 1002 A–26 Stochastic Parameters from Finite Life Fatigue Tests in Selected Metals 1003 959 shi20361_app_A.qxd 6/3/03 3:42 PM Page 959
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Useful Tables Appendix AAppendix Outline
A–1 Standard SI Prefixes 961
A–2 Conversion Factors 962
A–3 Optional SI Units for Bending, Torsion, Axial, and Direct Shear Stresses 963
A–4 Optional SI Units for Bending and Torsional Deflections 963
A–5 Physical Constants of Materials 963
A–6 Properties of Structural-Steel Angles 964
A–7 Properties of Structural-Steel Channels 966
A–8 Properties of Round Tubing 968
A–9 Shear, Moment, and Deflection of Beams 969
A–10 Cumulative Distribution Function of Normal (Gaussian) Distribution 977
A–11 A Selection of International Tolerance Grades—Metric Series 978
A–12 Fundamental Deviations for Shafts—Metric Series 979
A–13 A Selection of International Tolerance Grades—Inch Series 980
A–14 Fundamental Deviations for Shafts—Inch Series 981
A–15 Charts of Theoretical Stress-Concentration Factors Kt 982
A–16 Approximate Stress-Concentration Factors Kt and Kts for Bending a Round Baror Tube with a Transverse Round Hole 987
A–17 Preferred Sizes and Renard (R-series) Numbers 989
A–18 Geometric Properties 990
A–19 American Standard Pipe 993
A–20 Deterministic ASTM Minimum Tensile and Yield Strengths for HR and CD Steels 994
A–21 Mean Mechanical Properties of Some Heat-Treated Steels 995
A–22 Results of Tensile Tests of Some Metals 997
A–23 Mean Monotonic and Cyclic Stress-Strain Properties of Selected Steels 998
A–24 Mechanical Properties of Three Non-Steel Metals 1000
A–25 Stochastic Yield and Ultimate Strengths for Selected Materials 1002
A–26 Stochastic Parameters from Finite Life Fatigue Tests in Selected Metals 1003
959
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A–27 Finite Life Fatigue Strengths of Selected Plain Carbon Steels 1004
A–28 Decimal Equivalents of Wire and Sheet-Metal Gauges 1005
A–29 Dimensions of Square and Hexagonal Bolts 1007
A–30 Dimensions of Hexagonal Cap Screws and Heavy Hexagonal Screws 1008
A–31 Dimensions of Hexagonal Nuts 1009
A–32 Basic Dimensions of American Standard Plain Washers 1010
A–33 Dimensions of Metric Plain Washers 1011
A–34 Gamma Function 1012
960 Mechanical Engineering Design
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Useful Tables 961
Name Symbol Factor
exa E 1 000 000 000 000 000 000 =1018
peta P 1 000 000 000 000 000 =1015
tera T 1 000 000 000 000 =1012
giga G 1 000 000 000 =109
mega M 1 000 000 =106
kilo k 1 000 =103
hecto‡ h 100 =102
deka‡ da 10 =101
deci‡ d 0.1 =10−1
centi‡ c 0.01 =10−2
milli m 0.001 =10−3
micro µ 0.000 001 =10−6
nano n 0.000 000 001 =10−9
pico p 0.000 000 000 001 =10−12
femto f 0.000 000 000 000 001 =10−15
atto a 0.000 000 000 000 000 001 =10−18
∗ If possible use multiple and submultiple prefixes in steps of 1000.†Spaces are used in SI instead of commas to group numbers to avoid confusion with the practice in some European countriesof using commas for decimal points.‡Not recommended but sometimes encountered.
Table A–1
Standard SI Prefixes∗†
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962 Mechanical Engineering Design
Multiply Input By Factor To Get Output Multiply Input By Factor To Get OutputX A Y X A Y
Pa · sdegree (angle) 0.0174 radian, radfoot, ft 0.305 meter, mfoot2, ft2 0.0929 meter2, m2
foot/minute, 0.0051 meter/second, m/sft/minfoot-pound, ft · lbf 1.35 joule, Jfoot-pound/ 1.35 watt, Wsecond, ft · lbf/s foot/second, ft/s 0.305 meter/second, m/sgallon (U.S.), gal 3.785 liter, Lhorsepower, hp 0.746 kilowatt, kW inch, in 0.0254 meter, m inch, in 25.4 millimeter, mm inch2, in2 645 millimeter2, mm2
inch of mercury 3.386 kilopascal, kPa(32◦F)kilopound, kip 4.45 kilonewton, kNkilopound/inch2, 6.89 megapascal, MPakpsi (ksi) (N/mm2)mass, lbf · s2/in 175 kilogram, kgmile, mi 1.610 kilometer, km
∗Approximate.†The U.S. Customary system unit of the pound-force is often abbreviated as lbf to distinguish it from the pound-mass, which is abbreviated as lbm.
Table A–2
Conversion Factors A to Convert Input X to Output Y Using the Formula Y = AX∗
mile/hour, mi/h 1.61 kilometer/hour, km/hmile/hour, mi/h 0.447 meter/second, m/smoment of inertia, 0.0421 kilogram-meter2,lbm ·ft2 kg · m2
moment of inertia, 293 kilogram-millimeter2,lbm · in2 kg · mm2
moment of section 41.6 centimeter4, cm4
(second moment of area), in4
ounce-force, oz 0.278 newton, Nounce-mass 0.0311 kilogram, kgpound, lbf† 4.45 newton, Npound-foot, 1.36 newton-meter,lbf · ft N · mpound/foot2, lbf/ft2 47.9 pascal, Papound-inch, lbf · in 0.113 joule, Jpound-inch, lbf · in 0.113 newton-meter,
N · m∗ m4 m Pa N∗ m2 PaN · m cm4 cm MPa (N/mm2) N† mm2 MPa (N/mm2)N · m† mm4 mm GPa kN m2 kPakN · m cm4 cm GPa kN† mm2 GPaN · mm† mm4 mm MPa (N/mm2)
∗Basic relation.†Often preferred.
Bending Deflection Torsional DeflectionF, w l l I E y T l J G θ
N∗ m m4 Pa m N · m∗ m m4 Pa radkN† mm mm4 GPa mm N · m† mm mm4 GPa radkN m m4 GPa µm N · mm mm mm4 MPa (N/mm2) radN mm mm4 kPa m N · m cm cm4 MPa (N/mm2) rad
∗Basic relation.†Often preferred.
Table A–4
Optional SI Units forBending Deflectiony = f (Fl3/El ) or y = f (wl4/El ) andTorsional Deflectionθ = Tl/GJ
Table A–3
Optional SI Units forBending Stressσ = Mc/l, Torsion Stressτ = Tr/J, Axial Stress σ= F/A, and DirectShear Stressτ = F/A
Table A–5
Physical Constants of Materials
Modulus of Modulus ofElasticity E Rigidity G Poisson’s Unit Weight w
Material Mpsi GPa Mpsi GPa Ratio v lbf/in3 lbf/ft3 kN/m3
w = weight per foot, lbf/ftm = mass per meter, kg/mA = area, in2 (cm2)I = second moment of area, in4 (cm4)k = radius of gyration, in (cm)y = centroidal distance, in (cm)Z = section modulus, in3, (cm3)
∗These sizes are also available in aluminum alloy.
Table A–7
Properties of Structural-Steel Channels (Continued)
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968 Mechanical Engineering Design
wa = unit weight of aluminum tubing, lbf/ftws = unit weight of steel tubing, lbf/ftm = unit mass, kg/mA = area, in2 (cm2)I = second moment of area, in4 (cm4)J = second polar moment of area, in4 (cm4)k = radius of gyration, in (cm)Z = section modulus, in3 (cm3)
d, t = size (OD) and thickness, in (mm)
Size, in wa ws A l k Z J
1 × 18 0.416 1.128 0.344 0.034 0.313 0.067 0.067
1 × 14 0.713 2.003 0.589 0.046 0.280 0.092 0.092
1 12 × 1
8 0.653 1.769 0.540 0.129 0.488 0.172 0.257
1 12 × 1
4 1.188 3.338 0.982 0.199 0.451 0.266 0.399
2 × 18 0.891 2.670 0.736 0.325 0.664 0.325 0.650
2 × 14 1.663 4.673 1.374 0.537 0.625 0.537 1.074
2 12 × 1
8 1.129 3.050 0.933 0.660 0.841 0.528 1.319
2 12 × 1
4 2.138 6.008 1.767 1.132 0.800 0.906 2.276
3 × 14 2.614 7.343 2.160 2.059 0.976 1.373 4.117
3 × 38 3.742 10.51 3.093 2.718 0.938 1.812 5.436
4 × 316 2.717 7.654 2.246 4.090 1.350 2.045 8.180
4 × 38 5.167 14.52 4.271 7.090 1.289 3.544 14.180
Size, mm m A l k Z J
12 × 2 0.490 0.628 0.082 0.361 0.136 0.163
16 × 2 0.687 0.879 0.220 0.500 0.275 0.440
16 × 3 0.956 1.225 0.273 0.472 0.341 0.545
20 × 4 1.569 2.010 0.684 0.583 0.684 1.367
25 × 4 2.060 2.638 1.508 0.756 1.206 3.015
25 × 5 2.452 3.140 1.669 0.729 1.336 3.338
30 × 4 2.550 3.266 2.827 0.930 1.885 5.652
30 × 5 3.065 3.925 3.192 0.901 2.128 6.381
42 × 4 3.727 4.773 8.717 1.351 4.151 17.430
42 × 5 4.536 5.809 10.130 1.320 4.825 20.255
50 × 4 4.512 5.778 15.409 1.632 6.164 30.810
50 × 5 5.517 7.065 18.118 1.601 7.247 36.226
Table A–8
Properties of RoundTubing
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Useful Tables 969
Table A–9
Shear, Moment, andDeflection of Beams(Note: Force andmoment reactions arepositive in the directionsshown; equations forshear force V andbending moment Mfollow the signconventions given inSec. 4–2.)
1 Cantilever—end load
R1 = V = F M1 = Fl
M = F(x − l)
y = Fx2
6E I(x − 3l)
ymax = − Fl3
3E I
2 Cantilever—intermediate load
R1 = V = F M1 = Fa
MA B = F(x − a) MBC = 0
yA B = Fx2
6E I(x − 3a)
yBC = Fa2
6E I(a − 3x)
ymax = Fa2
6E I(a − 3l)
x
F
l
y
R1
M1
x
V
+
x
M
–
x
F
CBA
l
y
R1
M1
a b
x
V
+
x
M
–
(continued)
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970 Mechanical Engineering Design
Table A–9
Shear, Moment, andDeflection of Beams(Continued)(Note: Force andmoment reactions arepositive in the directionsshown; equations forshear force V andbending moment Mfollow the signconventions given inSec. 4–2.)
3 Cantilever—uniform load
R1 = wl M1 = wl2
2
V = w(l − x) M = −w
2(l − x)2
y = wx2
24E I(4lx − x2 − 6l2)
ymax = − wl4
8E I
4 Cantilever—moment load
R1 = 0 M1 = MB M = MB
y = MB x2
2E Iymax = MB l2
2E I
x
l
w
y
R1
M1
x
V
+
x
M
–
MB
xB
A
l
y
R1
M1
x
V
x
M
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Useful Tables 971
5 Simple supports—center load
R1 = R2 = F
2VA B = R1
VA B = R1 VBC = −R2
MA B = Fx
2MBC = F
2(l − x)
yA B = Fx
48E I(4x2 − 3l2)
ymax = − Fl3
48E I
6 Simple supports—intermediate load
R1 = Fb
lR2 = Fa
l
VA B = R1 VBC = −R2
MA B = Fbx
lMBC = Fa
l(l − x)
yA B = Fbx
6E Il(x2 + b2 − l2)
yBC = Fa(l − x)
6E Il(x2 + a2 − 2lx)
Table A–9
Shear, Moment, andDeflection of Beams(Continued)(Note: Force andmoment reactions arepositive in the directionsshown; equations forshear force V andbending moment Mfollow the signconventions given inSec. 4–2.)
x
F
CBA
l
y
R1 R2
l / 2
x
V
+
–
x
M
+
x
F
CB
a
A
l
y
R1 R2
b
x
V
+
–
x
M
+
(continued)
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972 Mechanical Engineering Design
7 Simple supports—uniform load
R1 = R2 = wl
2V = wl
2− wx
M = wx
2(l − x)
y = wx
24E I(2lx2 − x3 − l3)
ymax = − 5wl4
384E I
8 Simple supports—moment load
R1 = R2 = MB
lV = MB
l
MA B = MB x
lMBC = MB
l(x − l)
yA B = MB x
6E Il(x2 + 3a2 − 6al + 2l2)
yBC = MB
6E Il[x3 − 3lx2 + x(2l2 + 3a2) − 3a2l]
Table A–9
Shear, Moment, andDeflection of Beams(Continued)(Note: Force andmoment reactions arepositive in the directionsshown; equations forshear force V andbending moment Mfollow the signconventions given inSec. 4–2.)
x
l
w
y
R1 R2
x
V
+
–
x
M
+
xC
BA
a
l
y
R1
R2
b
MB
x
V
+
x
M
+
–
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Useful Tables 973
Table A–9
Shear, Moment, andDeflection of Beams(Continued)(Note: Force andmoment reactions arepositive in the directionsshown; equations forshear force V andbending moment Mfollow the signconventions given inSec. 4–2.)
9 Simple supports—twin loads
R1 = R2 = F VA B = F VBC = 0
VC D = −F
MA B = Fx MBC = Fa MC D = F(l − x)
yA B = Fx
6E I(x2 + 3a2 − 3la)
yBC = Fa
6E I(3x2 + a2 − 3lx)
ymax = Fa
24E I(4a2 − 3l2)
10 Simple supports—overhanging load
R1 = Fa
lR2 = F
l(l + a)
VA B = − Fa
lVBC = F
MA B = − Fax
lMBC = F(x − l − a)
yA B = Fax
6E Il(l2 − x2)
yBC = F(x − l)
6E I[(x − l)2 − a(3x − l)]
yc = − Fa2
3E I(l + a)
x
F F
DB C
a
A
l
y
R1 R2
a
x
V
+
–
x
M
+
x
F
CBA
y
R2
R1
al
x
V
+
–
x
M
–
(continued)
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974 Mechanical Engineering Design
11 One fixed and one simple support—center load
R1 = 11F
16R2 = 5F
16M1 = 3Fl
16
VA B = R1 VBC = −R2
MA B = F
16(11x − 3l) MBC = 5F
16(l − x)
yA B = Fx2
96E I(11x − 9l)
yBC = F(l − x)
96E I(5x2 + 2l2 − 10lx)
12 One fixed and one simple support—intermediate load
R1 = Fb
2l3(3l2 − b2) R2 = Fa2
2l3(3l − a)
M1 = Fb
2l2(l2 − b2)
VA B = R1 VBC = −R2
MA B = Fb
2l3[b2l − l3 + x(3l2 − b2)]
MBC = Fa2
2l3(3l2 − 3lx − al + ax)
yA B = Fbx2
12E Il3[3l(b2 − l2) + x(3l2 − b2)]
yBC = yA B − F(x − a)3
6E I
Table A–9
Shear, Moment, andDeflection of Beams(Continued)(Note: Force andmoment reactions arepositive in the directionsshown; equations forshear force V andbending moment Mfollow the signconventions given inSec. 4–2.)
xCA
ly
R2
B
F
R1
M1
l / 2
x
V
+
–
x
M
+
–
xCA
ly
R2
B
Fa b
R1
M1
x
V
+
–
x
M
+
–
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Useful Tables 975
13 One fixed and one simple support—uniform load
R1 = 5wl
8R2 = 3wl
8M1 = wl2
8
V = 5wl
8− wx
M = −w
8(4x2 − 5lx + l2)
y = wx2
48E I(l − x)(2x − 3l)
ymax = − wl4
185E I
14 Fixed supports—center load
R1 = R2 = F
2M1 = M2 = Fl
8
VA B = −VBC = F
2
MA B = F
8(4x − l) MBC = F
8(3l − 4x)
yA B = Fx2
48E I(4x − 3l)
ymax = − Fl3
192E I
Table A–9
Shear, Moment, andDeflection of Beams(Continued)(Note: Force andmoment reactions arepositive in the directionsshown; equations forshear force V andbending moment Mfollow the signconventions given inSec. 4–2.)
x
l
y
R1
R2M1ymax
0.4215l
x
V
+
–
5l / 8
x
M
+
–
l /4
x
l
y
A B
F
C
R1 R2
M1 M2
l / 2
x
V
+
–
x
M
+
– –
(continued)
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976 Mechanical Engineering Design
15 Fixed supports—intermediate load
R1 = Fb2
l3(3a + b) R2 = Fa2
l3(3b + a)
M1 = Fab2
l2M2 = Fa2b
l2
VA B = R1 VBC = −R2
MA B = Fb2
l3[x(3a + b) − al]
MBC = MA B − F(x − a)
yA B = Fb2 x2
6E Il3[x(3a + b) − 3al]
yBC = Fa2(l − x)2
6E Il3[(l − x)(3b + a) − 3bl]
16 Fixed supports—uniform load
R1 = R2 = wl
2M1 = M2 = wl2
12
V = w
2(l − 2x)
M = w
12(6lx − 6x2 − l2)
y = − wx2
24E I(l − x)2
ymax = − wl4
384E I
Table A–9
Shear, Moment, andDeflection of Beams(Continued)(Note: Force andmoment reactions arepositive in the directionsshown; equations forshear force V andbending moment Mfollow the signconventions given inSec. 4–2.)
A Selection ofInternational ToleranceGrades—Metric Series(Size Ranges Are forOver the Lower Limitand Including the UpperLimit. All Values Arein Millimeters)Source: Preferred Metric Limitsand Fits, ANSI B4.2-1978.See also BSI 4500.
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Useful Tables 979
Table A–12
Fundamental Deviations for Shafts—Metric Series(Size Ranges Are for Over the Lower Limit and Including the Upper Limit. All Values Are in Millimeters)Source: Preferred Metric Limits and Fits , ANSI B4.2-1978. See also BSI 4500.
Basic Upper-Deviation Letter Lower-Deviation LetterSizes c d f g h k n p s u
A Selection ofInternational ToleranceGrades—Inch Series(Size Ranges Are forOver the Lower Limit and Including the UpperLimit. All Values Are inInches, Converted fromTable A–11)
shi20361_app_A.qxd 6/3/03 3:43 PM Page 980
981
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60
+0.0
001
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7−0
.000
60
+0.0
001
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6.40
–7.2
0−0
.009
1−0
.005
7−0
.001
7−0
.000
60
+0.0
001
+0.0
011
+0.0
017
+0.0
043
+0.0
083
7.20
–8.0
0−0
.009
4−0
.006
7−0
.002
0−0
.000
60
+0.0
002
+0.0
012
+0.0
020
+0.0
048
+0.0
093
8.00
–9.0
0−0
.010
2−0
.006
7−0
.002
0−0
.000
60
+0.0
002
+0.0
012
+0.0
020
+0.0
051
+0.0
102
9.00
–10.
00−0
.011
0−0
.006
7−0
.002
0−0
.000
60
+0.0
002
+0.0
012
+0.0
020
+0.0
055
+0.0
112
10.0
0–11
.20
−0.0
118
−0.0
075
−0.0
022
−0.0
007
0+0
.000
2+0
.001
3+0
.002
2+0
.006
2+0
.012
411
.20–
12.6
0−0
.013
0−0
.007
5−0
.002
2−0
.000
70
+0.0
002
+0.0
013
+0.0
022
+0.0
067
+0.0
130
12.6
0–14
.20
−0.0
142
−0.0
083
−0.0
024
−0.0
007
0+0
.000
2+0
.001
5+0
.002
4+0
.007
5+0
.015
414
.20–
16.0
0−0
.015
7−0
.008
3−0
.002
4−0
.000
70
+0.0
002
+0.0
015
+0.0
024
+0.0
082
+0.0
171
Table
A–1
4
Fund
amen
tal D
evia
tions
for S
hafts
—In
ch S
erie
s (S
ize
Rang
es A
re fo
r Ove
rthe
Low
er L
imit
and
Incl
udin
gth
e U
pper
Lim
it. A
ll Va
lues
Are
inIn
ches
, Con
verte
d fro
m T
able
A–1
2)
shi20361_app_A.qxd 6/3/03 3:43 PM Page 981
982 Mechanical Engineering Design
Table A–15
Charts of Theoretical Stress-Concentration Factors K*t
Figure A–15–1
Bar in tension or simplecompression with a transversehole. σ0 = F/A, whereA = (w − d )t and t is thethickness.
Kt
d
d/w0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
2.0
2.2
2.4
2.6
2.8
3.0
w
Figure A–15–2
Rectangular bar with atransverse hole in bending.σ0 = Mc/I, whereI = (w − d )h3
/12.
Kt
d
d/w0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
1.0
1.4
1.8
2.2
2.6
3.0
w
MM0.25
1.0
2.0
�
d /h = 0
0.5h
Kt
r
r /d0
1.5
1.2
1.1
1.05
1.0
1.4
1.8
2.2
2.6
3.0
dww /d = 3
0.05 0.10 0.15 0.20 0.25 0.30
Figure A–15–3
Notched rectangular bar intension or simple compression.σ0 = F/A, where A = dt and tis the thickness.
shi20361_app_A.qxd 6/3/03 3:43 PM Page 982
Useful Tables 983
Table A–15
Charts of Theoretical Stress-Concentration Factors K*t (Continued)
1.5
1.10
1.05
1.02
w/d = �
Kt
r
r /d0 0.05 0.10 0.15 0.20 0.25 0.30
1.0
1.4
1.8
2.2
2.6
3.0
dw MM
1.02
Kt
r/d0 0.05 0.10 0.15 0.20 0.25 0.30
1.0
1.4
1.8
2.2
2.6
3.0
r
dD
D/d = 1.50
1.05
1.10
Kt
r/d0 0.05 0.10 0.15 0.20 0.25 0.30
1.0
1.4
1.8
2.2
2.6
3.0
r
dD
D/d = 1.02
3
1.31.1
1.05 MM
Figure A–15–4
Notched rectangular bar inbending. σ0 = Mc/I, wherec = d/2, I = td 3/12, and t isthe thickness.
Figure A–15–5
Rectangular filleted bar intension or simple compression.σ0 = F/A, where A = dt and tis the thickness.
Figure A–15–6
Rectangular filleted bar inbending. σ0 = Mc/I, wherec = d/2, I = td3
/12, t is thethickness.
*Factors from R. E. Peterson, “Design Factors for Stress Concentration,” Machine Design, vol. 23, no. 2, February 1951, p. 169; no. 3, March 1951, p. 161, no. 5, May 1951, p. 159; no. 6, June 1951,p. 173; no. 7, July 1951, p. 155. Reprinted with permission from Machine Design, a Penton Media Inc. publication.
(continued)
shi20361_app_A.qxd 6/3/03 3:43 PM Page 983
984 Mechanical Engineering Design
Table A–15
Charts of Theoretical Stress-Concentration Factors K*t (Continued)
Plate loaded in tension by apin through a hole. σ0 = F/A,where A = (w − d)t . Whenclearance exists, increase Kt
35 to 50 percent. (M. M. Frochtand H. N. Hill, “Stress Concentration Factorsaround a Central Circular Hole in a PlateLoaded through a Pin in Hole,” J. Appl.Mechanics, vol. 7, no. 1, March 1940, p. A-5.)
dh
t
Kt
d /w0 0.1 0.2 0.3 0.4 0.60.5 0.80.7
1
3
5
7
9
11
w
h/w = 0.35
h/w � 1.0
h/w = 0.50
(continued)
*Factors from R. E. Peterson, “Design Factors for Stress Concentration,” Machine Design, vol. 23, no. 2, February 1951, p. 169; no. 3, March 1951, p. 161, no. 5, May 1951, p. 159; no. 6, June 1951,p. 173; no. 7, July 1951, p. 155. Reprinted with permission from Machine Design, a Penton Media Inc. publication.
shi20361_app_A.qxd 6/3/03 3:43 PM Page 985
Table A–15
Charts of Theoretical Stress-Concentration Factors K*t (Continued)
*Factors from R. E. Peterson, “Design Factors for Stress Concentration,” Machine Design, vol. 23, no. 2, February 1951, p. 169; no. 3, March 1951, p. 161, no. 5, May 1951, p. 159; no. 6, June 1951,p. 173; no. 7, July 1951, p. 155. Reprinted with permission from Machine Design, a Penton Media Inc. publication.
986 Mechanical Engineering Design
Figure A–15–13
Grooved round bar in tension.σ0 = F/A, whereA = πd 2/4.
Figure A–15–14
Grooved round bar inbending. σ0 = Mc/l, wherec = d/2 and I = πd4
/64.
Figure A–15–15
Grooved round bar in torsion.τ0 = Tc/J, where c = d/2and J = πd4
/32.
Kt
r /d0 0.05 0.10 0.15 0.20 0.25 0.30
1.0
1.4
1.8
2.2
2.6
3.0
D/d = 1.50
1.05
1.02
1.15
d
r
D
Kt
r /d0 0.05 0.10 0.15 0.20 0.25 0.30
1.0
1.4
1.8
2.2
2.6
3.0
D/d = 1.501.02
1.05
d
r
D MM
Kts
r /d0 0.05 0.10 0.15 0.20 0.25 0.30
1.0
1.4
1.8
2.2
2.6
D/d = 1.30
1.02
1.05
d
r
D
TT
shi20361_app_A.qxd 6/3/03 3:43 PM Page 986
Useful Tables 987
Table A–16
Approximate Stress-Concentration Factor Kt
for Bending of a RoundBar or Tube with aTransverse Round HoleSource: R. E. Peterson, StressConcentration Factors, Wiley,New York, 1974, pp. 146,235.
The nominal bending stress is σ0 = M/Znet where Znet is a reduced valueof the section modulus and is defined by
Znet = π A
32D(D4 − d4)
Values of A are listed in the table. Use d = 0 for a solid bar
Approximate Stress-Concentration Factors Kts for a Round Bar or Tube Having a Transverse Round Hole andLoaded in Torsion Source: R. E. Peterson, Stress Concentration Factors, Wiley, New York, 1974, pp. 148, 244.
TTD a d
The maximum stress occurs on the inside of the hole, slightly below the shaft surface. The nominal shear stress is τ0 = T D/2Jnet ,where Jnet is a reduced value of the second polar moment of area and is defined by
Jnet = π A(D4 − d4)
32
Values of A are listed in the table. Use d = 0 for a solid bar.
Preferred Sizes andRenard (R-Series)Numbers (When a choice can bemade, use one of thesesizes; however, not allparts or items areavailable in all the sizesshown in the table.)
Deterministic ASTM Minimum Tensile and Yield Strengths for Some Hot-Rolled (HR) and Cold-Drawn (CD) Steels [The strengths listed are estimated ASTM minimum values in the size range 18 to 32 mm (3
4 to 114 in). These
strengths are suitable for use with the design factor defined in Sec. 1–10, provided the materials conform toASTM A6 or A568 requirements or are required in the purchase specifications. Remember that a numberingsystem is not a specification. See Table 1–1 for certain ASTM steels.] Source: 1986 SAE Handbook, p. 2.15.
1 2 3 4 5 6 7 8Tensile Yield
SAE and/or Proces- Strength, Strength, Elongation in Reduction in BrinellUNS No. AISI No. sing MPa (kpsi) MPa (kpsi) 2 in, % Area, % Hardness
Mean Mechanical Properties of Some Heat-Treated Steels[These are typical properties for materials normalized and annealed. The properties for quenched and tempered(Q&T) steels are from a single heat. Because of the many variables, the properties listed are global averages. Inall cases, data were obtained from specimens of diameter 0.505 in, machined from 1-in rounds, and of gaugelength 2 in. unless noted, all specimens were oil-quenched.] Source: ASM Metals Reference Book, 2d ed., American
Society for Metals, Metals Park, Ohio, 1983.
1 2 3 4 5 6 7 8Tensile Yield
Temperature Strength Strength, Elongation, Reduction BrinellAISI No. Treatment °C (°F) MPa (kpsi) MPa (kpsi) % in Area, % Hardness
Mean Mechanical Properties of Some Heat-Treated Steels[These are typical properties for materials normalized and annealed. The properties for quenched and tempered(Q&T) steels are from a single heat. Because of the many variables, the properties listed are global averages. Inall cases, data were obtained from specimens of diameter 0.505 in, machined from 1-in rounds, and of gaugelength 2 in. Unless noted, all specimens were oil-quenched.] Source: ASM Metals Reference Book, 2d ed., American
Society for Metals, Metals Park, Ohio, 1983.
shi20361_app_A.qxd 6/3/03 3:43 PM Page 996
997
Table
A–2
2
Resu
lts o
f Ten
sile
Tests
of S
ome
Met
als*
Sour
ce:J
. Dat
sko,
“So
lid M
ater
ials,
” ch
ap. 7
in Jo
seph
E. S
higl
ey a
nd C
harle
s R.
Misc
hke
(eds
.-in-
chie
f), S
tand
ard
Han
dboo
k of
Mac
hine
Des
ign,
2nd
ed.,
McG
raw
-Hill,
New
Yor
k, 1
996,
pp.
7.4
7–7.
50.
Stre
ngth
(Te
nsi
le)
Yie
ldU
ltim
ate
Fract
ure
,Coef
fici
ent
Stra
inS y
,S u
,σ
f,σ
0,
Stre
ngth
,Fr
act
ure
Num
ber
Mate
rial
Conditio
nM
Pa
(kpsi
)M
Pa
(kpsi
)M
Pa
(kpsi
)M
Pa
(kpsi
)Ex
ponen
t m
Stra
in ε
f
1018
Stee
lA
nnea
led
220
(32.
0)34
1(4
9.5)
628
(91.
1)†
620
(90.
0)0.
251.
0511
44St
eel
Ann
eale
d35
8(5
2.0)
646
(93.
7)89
8(1
30)†
992
(144
)0.
140.
4912
12St
eel
HR
193
(28.
0)42
4(6
1.5)
729
(106
)†75
8(1
10)
0.24
0.85
1045
Stee
lQ
&T
600°
F15
20(2
20)
1580
(230
)23
80(3
45)
1880
(273
)†0.
041
0.81
4142
Stee
lQ
&T
600°
F17
20(2
50)
1930
(210
)23
40(3
40)
1760
(255
)†0.
048
0.43
303
Stai
nles
sA
nnea
led
241
(35.
0)60
1(8
7.3)
1520
(221
)†14
10(2
05)
0.51
1.16
steel
304
Stai
nles
sA
nnea
led
276
(40.
0)56
8(8
2.4)
1600
(233
)†12
70(1
85)
0.45
1.67
steel
2011
Alu
min
umT6
169
(24.
5)32
4(4
7.0)
325
(47.
2)†
620
(90)
0.28
0.10
allo
y20
24A
lum
inum
T429
6(4
3.0)
446
(64.
8)53
3(7
7.3)
†68
9(1
00)
0.15
0.18
allo
y70
75A
lum
inum
T654
2(7
8.6)
593
(86.
0)70
6(1
02)†
882
(128
)0.
130.
18al
loy
*Valu
es fr
om on
e or t
wo he
ats an
d beli
eved
to be
attai
nable
using
prop
er pu
rchas
e spe
cifica
tions
. The
frac
ture s
train
may v
ary as
muc
h as 1
00 pe
rcent.
† Deriv
ed va
lue.
shi20361_app_A.qxd 6/3/03 3:43 PM Page 997
Table
A–2
3
Mea
n M
onot
onic
and
Cyc
lic S
tress
-Stra
in P
rope
rties
of S
elec
ted
Stee
lsSo
urce
: ASM
Met
als
Refe
renc
e Bo
ok,2
nd e
d., A
mer
ican
Soc
iety
for M
etal
s, M
etal
s Pa
rk,
Ohi
o, 1
983,
p. 2
17.
True
Fatigue
Tensi
leSt
rain
Stre
ngth
Fatigue
Fatigue
Fatigue
Hard
-St
rength
Red
uct
ion
at
Modulu
s of
Coef
fici
ent
Stre
ngth
Duct
ility
Duct
ility
Ori
enta
-D
escr
iption
nes
sS u
tin
Are
aFr
act
ure
Elast
icity E
σ′ f
Exponen
tCoef
fici
ent
Exponen
tG
rade
(a)
tion (
e)(f
)H
BM
Pa
ksi
%ε
fG
Pa
10
4psi
MPa
ksi
bε
′ Fc
A53
8A (b
)L
STA
405
1515
220
671.
1018
527
1655
240
−0.0
650.
30−0
.62
A53
8B (b
)L
STA
460
1860
270
560.
8218
527
2135
310
−0.0
710.
80−0
.71
A53
8C (b
)L
STA
480
2000
290
550.
8118
026
2240
325
−0.0
70.
60−0
.75
AM
-350
(c)
LH
R, A
1315
191
520.
7419
528
2800
406
−0.1
40.
33−0
.84
AM
-350
(c)
LC
D49
619
0527
620
0.23
180
2626
9039
0−0
.102
0.10
−0.4
2G
aine
x (c
)LT
HR
shee
t53
077
580.
8620
029
.280
511
7−0
.07
0.86
−0.6
5G
aine
x (c
)L
HR
shee
t51
074
641.
0220
029
.280
511
7−0
.071
0.86
−0.6
8H
-11
LA
usfo
rmed
660
2585
375
330.
4020
530
3170
460
−0.0
770.
08−0
.74
RQC
-100
(c)
LTH
R pl
ate
290
940
136
430.
5620
530
1240
180
−0.0
70.
66−0
.69
RQC
-100
(c)
LH
R pl
ate
290
930
135
671.
0220
530
1240
180
−0.0
70.
66−0
.69
10B6
2L
Q&
T43
016
4023
838
0.89
195
2817
8025
8−0
.067
0.32
−0.5
610
05-1
009
LTH
R sh
eet
9036
052
731.
320
530
580
84−0
.09
0.15
−0.4
310
05-1
009
LTC
D s
heet
125
470
6866
1.09
205
3051
575
−0.0
590.
30−0
.51
1005
-100
9L
CD
she
et12
541
560
641.
0220
029
540
78−0
.073
0.11
−0.4
110
05-1
009
LH
R sh
eet
9034
550
801.
620
029
640
93−0
.109
0.10
−0.3
910
15L
Nor
mal
ized
8041
560
681.
1420
530
825
120
−0.1
10.
95−0
.64
1020
LH
R pl
ate
108
440
6462
0.96
205
29.5
895
130
−0.1
20.
41−0
.51
1040
LA
s fo
rged
225
620
9060
0.93
200
2915
4022
3−0
.14
0.61
−0.5
710
45L
Q&
T22
572
510
565
1.04
200
2912
2517
8−0
.095
1.00
−0.6
610
45L
Q&
T41
014
5021
051
0.72
200
2918
6027
0−0
.073
0.60
−0.7
010
45L
Q&
T39
013
4519
559
0.89
205
3015
8523
0−0
.074
0.45
−0.6
810
45L
Q&
T45
015
8523
055
0.81
205
3017
9526
0−0
.07
0.35
−0.6
910
45L
Q&
T50
018
2526
551
0.71
205
3022
7533
0−0
.08
0.25
−0.6
810
45L
Q&
T59
522
4032
541
0.52
205
3027
2539
5−0
.081
0.07
−0.6
011
44L
CD
SR26
593
013
533
0.51
195
28.5
1000
145
−0.0
80.
32−0
.58
998
shi20361_app_A.qxd 6/3/03 3:43 PM Page 998
1144
LD
AT30
510
3515
025
0.29
200
28.8
1585
230
−0.0
90.
27−0
.53
1541
FL
Q&
T fo
rgin
g29
095
013
849
0.68
205
29.9
1275
185
−0.0
760.
68−0
.65
1541
FL
Q&
T fo
rgin
g26
089
012
960
0.93
205
29.9
1275
185
−0.0
710.
93−0
.65
4130
LQ
&T
258
895
130
671.
1222
032
1275
185
−0.0
830.
92−0
.63
4130
LQ
&T
365
1425
207
550.
7920
029
1695
246
−0.0
810.
89−0
.69
4140
LQ
&T,
DAT
310
1075
156
600.
6920
029
.218
2526
5−0
.08
1.2
−0.5
941
42L
DAT
310
1060
154
290.
3520
029
1450
210
−0.1
00.
22−0
.51
4142
LD
AT33
512
5018
128
0.34
200
28.9
1250
181
−0.0
80.
06−0
.62
4142
LQ
&T
380
1415
205
480.
6620
530
1825
265
−0.0
80.
45−0
.75
4142
LQ
&T
and
400
1550
225
470.
6320
029
1895
275
−0.0
90.
50−0
.75
defo
rmed
4142
LQ
&T
450
1760
255
420.
5420
530
2000
290
−0.0
80.
40−0
.73
4142
LQ
&T
and
475
2035
295
200.
2220
029
2070
300
−0.0
820.
20−0
.77
defo
rmed
4142
LQ
&T
and
450
1930
280
370.
4620
029
2105
305
−0.0
90.
60−0
.76
defo
rmed
4142
LQ
&T
475
1930
280
350.
4320
530
2170
315
−0.0
810.
09−0
.61
4142
LQ
&T
560
2240
325
270.
3120
530
2655
385
−0.0
890.
07−0
.76
4340
LH
R, A
243
825
120
430.
5719
528
1200
174
−0.0
950.
45−0
.54
4340
LQ
&T
409
1470
213
380.
4820
029
2000
290
−0.0
910.
48−0
.60
4340
LQ
&T
350
1240
180
570.
8419
528
1655
240
−0.0
760.
73−0
.62
5160
LQ
&T
430
1670
242
420.
8719
528
1930
280
−0.0
710.
40−0
.57
5210
0L
SH, Q
&T
518
2015
292
110.
1220
530
2585
375
−0.0
90.
18−0
.56
9262
LA
260
925
134
140.
1620
530
1040
151
−0.0
710.
16−0
.47
9262
LQ
&T
280
1000
145
330.
4119
528
1220
177
−0.0
730.
41−0
.60
9262
LQ
&T
410
565
227
320.
3820
029
1855
269
−0.0
570.
38−0
.65
950C
(d)
LTH
R pl
ate
159
565
8264
1.03
205
29.6
1170
170
−0.1
20.
95−0
.61
950C
(d)
LH
R ba
r15
056
582
691.
1920
530
970
141
−0.1
10.
85−0
.59
950X
(d)
LPl
ate
chan
nel
150
440
6465
1.06
205
3062
591
−0.0
750.
35−0
.54
950X
(d)
LH
R pl
ate
156
530
7772
1.24
205
29.5
1005
146
−0.1
00.
85−0
.61
950X
(d)
LPl
ate
chan
nel
225
695
101
681.
1519
528
.210
5515
3−0
.08
0.21
−0.5
3
Notes
:(a)
AISI/
SAE g
rade,
unles
s othe
rwise
indic
ated.
(b) A
STM
desig
natio
n. (c)
Prop
rietar
y des
ignati
on. (
d) S
AE H
SLA g
rade.
(e) O
rienta
tion o
f axis
of sp
ecim
en, r
elativ
e to r
olling
direc
tion;
L is l
ongit
udina
l (pa
rallel
to ro
lling d
irecti
on);
LT is
long t
ransv
erse (
perpe
ndicu
larto
rollin
g dire
ction
). (f)
STA
, solu
tion t
reated
and a
ged;
HR, h
ot rol
led; C
D, co
ld dra
wn; Q
&T, q
uenc
hed a
nd te
mpere
d; CD
SR, c
old dr
awn s
train
reliev
ed; D
AT, dr
awn a
t tem
perat
ure; A
, ann
ealed
.
From
ASM
Metal
s Refe
rence
Boo
k, 2n
d edit
ion, 1
983;
ASM
Intern
ation
al, M
ateria
ls Pa
rk, O
H 44
073-0
002;
table
217
. Rep
rinted
by pe
rmiss
ion of
ASM
Intern
ation
al ®
, www
.asmi
nterna
tiona
l.org.
999
shi20361_app_A.qxd 6/3/03 3:43 PM Page 999
Fatigue
Shea
rSt
ress
-Te
nsi
leCom
pre
ssiv
eM
odulu
sM
odulu
s of
Endura
nce
Bri
nel
lConce
ntr
ation
AST
MSt
rength
Stre
ngth
of
Ruptu
reEl
ast
icity,
Mpsi
Lim
it*
Hard
nes
sFa
ctor
Num
ber
S ut,
kpsi
S uc, k
psi
S su, k
psi
Tensi
on
†To
rsio
nS e
, k
psi
HB
Kf
2022
8326
9.6–
143.
9–5.
610
156
1.00
2526
9732
11.5
–14.
84.
6–6.
011
.517
41.
0530
3110
940
13–1
6.4
5.2–
6.6
1420
11.
1035
36.5
124
48.5
14.5
–17.
25.
8–6.
916
212
1.15
4042
.514
057
16–2
06.
4–7.
818
.523
51.
2550
52.5
164
7318
.8–2
2.8
7.2–
8.0
21.5
262
1.35
6062
.518
7.5
88.5
20.4
–23.
57.
8–8.
524
.530
21.
50
*Poli
shed
or m
achin
ed sp
ecim
ens.
† The m
odulu
s of e
lastic
ity of
cast
iron i
n com
pressi
on co
rresp
onds
clos
ely to
the u
pper
value
in th
e ran
ge gi
ven f
or ten
sion a
nd is
a mo
re co
nstan
t valu
e tha
n tha
t for
tensio
n.
Table
A–2
4
Mec
hani
cal P
rope
rties
of T
hree
Non
-Ste
el M
etal
s(a
) Typ
ical
Pro
perti
es o
f Gra
y C
ast I
ron
[The
Am
eric
an S
ocie
ty fo
r Tes
ting
and
Mat
eria
ls (A
STM
) num
berin
g sy
stem
for g
ray
cast
iron
is su
ch th
at th
e nu
mbe
rs c
orre
spon
d to
the
min
imum
tens
ile s
treng
thin
kps
i. Th
us a
n A
STM
No.
20
cast
iron
has
a m
inim
um te
nsile
stre
ngth
of 2
0 kp
si. N
ote
parti
cula
rly th
at th
eta
bula
tions
are
typi
calo
f sev
eral
hea
ts.]
1000
shi20361_app_A.qxd 6/3/03 3:43 PM Page 1000
Table A–24
Mechanical Properties of Three Non-Steel Metals (Continued)(b) Mechanical Properties of Some Aluminum Alloys [These are typical properties for sizes of about 1
2 in; similar properties can be obtained by using proper purchase specifications. The values given for fatigue strength correspond to 50(107) cycles of completelyreversed stress. Alluminum alloys do not have an endurance limit. Yield strengths were obtained by the0.2 percent offset method.]
Aluminum Strength Elongation BrinellAssociation Yield, Sy, Tensile, Su, Fatigue, Sf, in 2 in, Hardness
Number Temper MPa (kpsi) MPa (kpsi) MPa (kpsi) % HB
Wrought:2017 O 70 (10) 179 (26) 90 (13) 22 452024 O 76 (11) 186 (27) 90 (13) 22 47
Dimensions of Metric Plain Washers (All Dimensions in Millimeters)
Washer Minimum Maximum Maximum Washer Minimum Maximum MaximumSize* ID OD Thickness Size* ID OD Thickness
1.6 N 1.95 4.00 0.70 10 N 10.85 20.00 2.301.6 R 1.95 5.00 0.70 10 R 10.85 28.00 2.801.6 W 1.95 6.00 0.90 10 W 10.85 39.00 3.50
2 N 2.50 5.00 0.90 12 N 13.30 25.40 2.802 R 2.50 6.00 0.90 12 R 13.30 34.00 3.502 W 2.50 8.00 0.90 12 W 13.30 44.00 3.50
2.5 N 3.00 6.00 0.90 14 N 15.25 28.00 2.802.5 R 3.00 8.00 0.90 14 R 15.25 39.00 3.502.5 W 3.00 10.00 1.20 14 W 15.25 50.00 4.00
3 N 3.50 7.00 0.90 16 N 17.25 32.00 3.503 R 3.50 10.00 1.20 16 R 17.25 44.00 4.003 W 3.50 12.00 1.40 16 W 17.25 56.00 4.60
3.5 N 4.00 9.00 1.20 20 N 21.80 39.00 4.003.5 R 4.00 10.00 1.40 20 R 21.80 50.00 4.603.5 W 4.00 15.00 1.75 20 W 21.80 66.00 5.10
4 N 4.70 10.00 1.20 24 N 25.60 44.00 4.604 R 4.70 12.00 1.40 24 R 25.60 56.00 5.104 W 4.70 16.00 2.30 24 W 25.60 72.00 5.60
5 N 5.50 11.00 1.40 30 N 32.40 56.00 5.105 R 5.50 15.00 1.75 30 R 32.40 72.00 5.605 W 5.50 20.00 2.30 30 W 32.40 90.00 6.40
6 N 6.65 13.00 1.75 36 N 38.30 66.00 5.606 R 6.65 18.80 1.75 36 R 38.30 90.00 6.406 W 6.65 25.40 2.30 36 W 38.30 110.00 8.50
8 N 8.90 18.80 2.308 R 8.90 25.40 2.308 W 8.90 32.00 2.80
N = narrow; R = regular; W = wide.*Same as screw or bolt size.
Useful Tables 1011
shi20361_app_A.qxd 6/3/03 3:43 PM Page 1011
Table A–34
Gamma Function*Source: Reprinted withpermission from William H.Beyer (ed.), Handbook ofTables for Probability andStatistics, 2nd ed., 1966.Copyright CRC Press, BocaRaton, Florida.