Design of Machine Elements Databook - ME14 -...

Design of Machine Elements

Databook

Fatigue Failure Strain-Life method:

Mansion-Coffin relation between fatigue life and total strain (Strain-Life method):

Δε2

= ′σ F

E(2N )b + ′εF (2N )c ,

Δε := total strain amplitude, N := number of cycles, E := Young's modulus′σ F := Fatigue strength coefficient, b := Fatigue strength exponent′εF := Fatigue ductility coefficient, c := Fatigue ductility exponent

For values of the coefficients and the exponents for a few materials see Table A-23.

Stress-Life method:

Fatigue strength ( Sf ): The fatigue strength reduces with number of cycles. After about 106 cycles, for steel specimen it becomes constant and equal to the endurance limit.

At 103 cycles, the fatigue strength is given by:

Sf = f .Sut .

The fatigue strength fraction f is given in Fig-6-18 (below) for the ultimate strength (Sut ) between 490 MPa and 1400 MPa. For Sut < 350 MPa, f=0.9.

Fatigue strength fraction f at 103 cycles as a function of ultimate strength:

The ultimate strength is given in kpsi unit. While using the figure, convert to MPa using 1 kpsi = 6.89 MPa.

Between 103 and 106 cycles:

Sf = aNb ,where

a = ( fSut )2

Se and b = −

13

log fSutSe

⎛⎝⎜

⎞⎠⎟

.

Fatigue Failure Resulting from Variable Loading 293

The process given for finding f can be repeated for various ultimate strengths. Figure 6–18 is a plot of f for 70 # Sut # 200 kpsi. To be conservative, for Sut , 70 kpsi, let f 5 0.9. For an actual mechanical component, S9e is reduced to Se (see Sec. 6–9) which is less than 0.5 Sut. However, unless actual data is available, we recommend using the value of f found from Fig. 6–18. Equation (a), for the actual mechanical component, can be written in the form

Sf 5 a Nb (6–13)

where N is cycles to failure and the constants a and b are defined by the points 103, (Sf)103 and 106, Se with (Sf)103 5 f Sut. Substituting these two points in Eq. (6–13) gives

a 5( f Sut)

2

Se (6–14)

b 5 213

log af Sut

Seb (6–15)

If a completely reversed stress srev is given, setting Sf 5 srev in Eq. (6–13), the num-ber of cycles-to-failure can be expressed as

N 5 asrev

ab1yb

(6–16)

Note that the typical S-N diagram, and thus Eq. (6–16), is only applicable for com-pletely reversed loading. For general fluctuating loading situations, it is necessary to obtain an equivalent, completely reversing, stress that is considered to be equally as damaging as the actual fluctuating stress (see Ex. 6–12, p. 321). Low-cycle fatigue is often defined (see Fig. 6–10) as failure that occurs in a range of 1 # N # 103 cycles. On a log-log plot such as Fig. 6–10 the failure locus in this range is nearly linear below 103 cycles. A straight line between 103, f Sut and 1, Sut (transformed) is conservative, and it is given by

Sf $ Sut N(log f )y3 1 # N # 103 (6–17)

70 80 90 100 110 120 130 140 150 160 170 200180 190

Sut , kpsi

f

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9Figure 6–18Fatigue strength fraction, f,of Sut at 103 cycles for Se 5 S9e 5 0.5Sut at 106 cycles.

bud98209_ch06_273-349.indd 93 10/7/13 1:16 PM f-496 bud98209_ch06_273-349.indd Page 293 10/7/13 1:16 PM f-496 /204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles/204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles

Endurance limit ( ′Se ) for the R. R. Moore’s rotating beam specimen (shown below):

′Se =0.5Sut Sut ≤ 1400 MPa

700 MPa Sut > 1400 MPa

⎧⎨⎪

⎩⎪For actual mechanical component endurance limit (Se ) at the critical location is different (less) from that of the R. R. Moore rotary specimen ( ′Se ). The endurance limit for the actual component is given by the following Marin equation:

Se = kakbkckdkek f ′Se, whereka = surface condition modification factorkb = size modification factorkc = load modification factorkd = temperature modification factorke = reliability factork f = miscellaneous-effect modification factor

1. Surface Condition Modification Factor: ka = aSut

b

a and b are given in table 6-2(below)

2. Size Modification Factor:

For bending and torsion: kb =1.24d−0.107 2.79 ≤ d ≤ 51 mm

1.51d−0.157 51 < d ≤ 254 mm

⎧⎨⎪

⎩⎪

For axial loading: kb = 1 (however a loading factor kc should be used).

In the above equation is for a rotating bar of circular cross-section, and d is the corresponding diameter. When the cross-section is not circular, or the bar is not rotating, an equivalent diameter de is used for calculating the size factor kb , in place of d. For a few non-rotating specimen they are given below.

296 Mechanical Engineering Design

Table 6–2

Parameters for Marin Surface Modification Factor, Eq. (6–19)

Factor a ExponentSurface Finish Sut, kpsi Sut, MPa b

Ground 1.34 1.58 20.085

Machined or cold-drawn 2.70 4.51 20.265

Hot-rolled 14.4 57.7 20.718

As-forged 39.9 272. 20.995

From C. J. Noll and C. Lipson, “Allowable Working Stresses,” Society for Experimental Stress Analysis, vol. 3, no. 2, 1946 p. 29. Reproduced by O.J. Horger (ed.) Metals Engineering Design ASME Handbook, McGraw-Hill, New York. Copyright © 1953 by The McGraw-Hill Companies, Inc. Reprinted by permission.

EXAMPLE 6–3 A steel has a minimum ultimate strength of 520 MPa and a machined surface. Estimate ka.

Solution From Table 6–2, a 5 4.51 and b 520.265. Then, from Eq. (6–19)

Answer ka 5 4.51(520)20.265 5 0.860

Again, it is important to note that this is an approximation as the data is typically quite scattered. Furthermore, this is not a correction to take lightly. For example, if in the previous example the steel was forged, the correction factor would be 0.540, a significant reduction of strength.

Size Factor kb

The size factor has been evaluated using 133 sets of data points.15 The results for bending and torsion may be expressed as

kb 5 µ (dy0.3)20.107 5 0.879d20.107 0.11 # d # 2 in0.91d20.157 2 , d # 10 in(dy7.62)20.107 5 1.24d20.107 2.79 # d # 51 mm1.51d20.157 51 , d # 254 mm

(6–20)

For axial loading there is no size effect, so

kb 5 1 (6–21)

but see kc. One of the problems that arises in using Eq. (6–20) is what to do when a round bar in bending is not rotating, or when a noncircular cross section is used. For example, what is the size factor for a bar 6 mm thick and 40 mm wide? The approach to be

15Charles R. Mischke, “Prediction of Stochastic Endurance Strength,” Trans. of ASME, Journal of Vibration, Acoustics, Stress, and Reliability in Design, vol. 109, no. 1, January 1987, Table 3.

bud98209_ch06_273-349.indd Page 296 10/7/13 1:16 PM f-496 bud98209_ch06_273-349.indd Page 296 10/7/13 1:16 PM f-496 /204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles/204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles


device is the R. R. Moore high-speed rotating-beam machine. This machine subjects the specimen to pure bending (no transverse shear) by means of weights. The test specimen, shown in Fig. 6–9, is very carefully machined and polished, with a final polishing in an axial direction to avoid circumferential scratches. Other fatigue-testing machines are available for applying fluctuating or reversed axial stresses, torsional stresses, or combined stresses to the test specimens. To establish the fatigue strength of a material, quite a number of tests are neces-sary because of the statistical nature of fatigue. For the rotating-beam test, a constant bending load is applied, and the number of revolutions (stress reversals) of the beam required for failure is recorded. The first test is made at a stress that is somewhat under the ultimate strength of the material. The second test is made at a stress that is less than that used in the first. This process is continued, and the results are plotted as an S-N diagram (Fig. 6–10). This chart may be plotted on semilog paper or on log-log paper. In the case of ferrous metals and alloys, the graph becomes horizontal after the material has been stressed for a certain number of cycles. Plotting on log paper emphasizes the bend in the curve, which might not be apparent if the results were plotted by using Cartesian coordinates. The ordinate of the S-N diagram is called the fatigue strength Sf; a statement of this strength value must always be accompanied by a statement of the number of cycles N to which it corresponds.

Figure 6–9Test-specimen geometry for the R. R. Moore rotating-beam machine. The bending moment is uniform, M 5 Fa, over the curved length and at the highest-stressed section at the mid-point of the beam.

7163

0.30 in

in

9 in R.78

aF F

aF F

Figure 6–10An S-N diagram plotted from the results of completely reversed axial fatigue tests. Material: UNS G41300 steel, normalized; Sut 5 116 kpsi; maximum Sut 5 125 kpsi. (Data from NACA Tech. Note 3866, December 1966.)

100

50

100

101 102 103 104 105 106 107 108

Number of stress cycles, N

Se

Sut

Fat

igue

str

engt

h S f

, kp

si

Low cycle High cycle

Finite life Infinitelife


Equivalent diameter and 95% stress area for structural shapes undergoing non-rotating bending

3. Load Modification factor kc :

kc =1 bending0.85 axial0.59 torsion

⎧

⎨⎪

⎩⎪

4. Temperature Modification factor kd : We will take this factor to be unity, i.e., kd = 1.

5. Reliability factor ke : Given in table 6-5 (below)

5. Miscellaneous-effect Modification factor k f : We will take this factor to be

unity, i.e., k f = 1.


Loading Factor kc

Estimates of endurance limit, such as that given in Eq. (6–8), are typically obtained from testing with completely reversed bending. With axial or torsional loading, fatigue tests indicate different relationships between the endurance limit and the ultimate strength for each type of loading.17 These differences can be accounted for with a load factor to adjust the endurance limit obtained from bending. Though the load factor is actually a function of the ultimate strength, the variation is minor, so it is appropriate to specify average values of the load factor as

kc 5 •1 bending0.85 axial0.59 torsion

(6–26)

Note that the load factor for torsion is very close to the prediction from the distortion energy theory, Eq. (5–21), where for ductile materials the shear strength is 0.577 times the normal strength. This implies that the load factor for torsion is mainly accounting for the difference in shear strength versus normal strength. Therefore, use the torsion load factor only for pure torsional fatigue loading. When torsion is combined with

Table 6–3

A0.95s Areas of Common Nonrotating Structural Shapes

A0.95s 5 0.01046d 2

de 5 0.370d

A0.95s 5 0.05hb

de 5 0.8081hb

A0.95s 5 e 0.10atf

0.05ba tf . 0.025a

axis 1-1axis 2-2

A0.95s 5 e 0.05ab0.052xa 1 0.1tf (b 2 x)

axis 1-1axis 2-2

d

b

h

2

2

11

1

2 2

1

a

btf

122

1

a

b tfx

17H. J. Grover, S. A. Gordon, and L. R. Jackson, Fatigue of Metals and Structures, Bureau of Naval Weapons, Document NAVWEPS 00-2500435, 1960; R. G. Budynas and J. K. Nisbett, op. cit., pp. 332–333.



where za is defined by Eq. (1–5) and values for any desired reliability can be deter-mined from Table A–10. Table 6–5 gives reliability factors for some standard specified reliabilities.

Miscellaneous-Effects Factor kf

Though the factor kf is intended to account for the reduction in endurance limit due to all other effects, it is really intended as a reminder that these must be accounted for, because actual values of kf are not always available. Residual stresses may either improve the endurance limit or affect it adversely. Generally, if the residual stress in the surface of the part is compression, the endurance limit is improved. Fatigue failures appear to be tensile failures, or at least to be caused by tensile stress, and so anything that reduces tensile stress will also reduce the pos-sibility of a fatigue failure. Operations such as shot peening, hammering, and cold rolling build compressive stresses into the surface of the part and improve the endur-ance limit significantly. Of course, the material must not be worked to exhaustion. The endurance limits of parts that are made from rolled or drawn sheets or bars, as well as parts that are forged, may be affected by the so-called directional charac-teristics of the operation. Rolled or drawn parts, for example, have an endurance limit in the transverse direction that may be 10 to 20 percent less than the endurance limit in the longitudinal direction. Parts that are case-hardened may fail at the surface or at the maximum core radius, depending upon the stress gradient. Figure 6–19 shows the typical triangular stress distribution of a bar under bending or torsion. Also plotted as a heavy line in this figure are the endurance limits Se for the case and core. For this example the

Reliability, % Transformation Variate za Reliability Factor ke

50 0 1.000

90 1.288 0.897

95 1.645 0.868

99 2.326 0.814

99.9 3.091 0.753

99.99 3.719 0.702

99.999 4.265 0.659

99.9999 4.753 0.620

Table 6–5

Reliability Factors ke Corresponding to 8 Percent Standard Deviation of the Endurance Limit

Se (case)

! or "

Se (core)

Case

Core

Figure 6–19The failure of a case-hardened part in bending or torsion. In this example, failure occurs in the core.


Notch sensitivity factors q and qshear and stress concentration: In fatigue loading

scenario, the effect of stress concentration is reduced. This is captured by a notch sensitivity factor. The relations between fatigue stress concentration factor (K f or K fs ) , the stress concentration factor (Kt or Kts ) and the notch sensitivity factor (q or qshear ) are:

For bending and axial loading: K f = 1+ q(Kt −1)

For Shear: K fs = 1+ qshear (Kts −1)

For the notch sensitivity factor q and qshear see figures 6-20 and 6-21 below.

The notch radius is given in inches. Use the conversion 1 in = 25.4 mm to interpret the results.


6–10 Stress Concentration and Notch SensitivityIn Sec. 3–13 it was pointed out that the existence of irregularities or discontinuities, such as holes, grooves, or notches, in a part increases the theoretical stresses significantly in the immediate vicinity of the discontinuity. Equation (3–48) defined a stress-concentration factor Kt (or Kts), which is used with the nominal stress to obtain the maximum result-ing stress due to the irregularity or defect. It turns out that some materials are not fully sensitive to the presence of notches and hence, for these, a reduced value of Kt can be used. For these materials, the effective maximum stress in fatigue is,

smax 5 Kf s0 or tmax 5 Kfst0 (6–30)

where Kf is a reduced value of Kt and s0 is the nominal stress. The factor Kf is com-monly called a fatigue stress-concentration factor, and hence the subscript f. So it is convenient to think of Kf as a stress-concentration factor reduced from Kt because of lessened sensitivity to notches. The resulting factor is defined by the equation

Kf 5maximum stress in notched specimen

stress in notch-free specimen (a)

Notch sensitivity q is defined by the equation

q 5Kf 2 1

Kt 2 1 or qshear 5

Kfs 2 1

Kts 2 1 (6–31)

where q is usually between zero and unity. Equation (6–31) shows that if q 5 0, then Kf 5 1, and the material has no sensitivity to notches at all. On the other hand, if q 5 1, then Kf 5 Kt, and the material has full notch sensitivity. In analysis or design work, find Kt first, from the geometry of the part. Then specify the material, find q, and solve for Kf from the equation

Kf 5 1 1 q(Kt 2 1) or Kfs 5 1 1 qshear(Kts 2 1) (6–32)

Notch sensitivities for specific materials are obtained experimentally. Published experimental values are limited, but some values are available for steels and alumi-num. Trends for notch sensitivity as a function of notch radius and ultimate strength are shown in Fig. 6–20 for reversed bending or axial loading, and Fig. 6–21 for

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0

0.2

0.4

0.6

0.8

1.0

Notch radius r, in

Notch radius r, mm

Not

ch s

ensi

tivity

q

S ut = 200 kpsi

(0.4)

60

100

150 (0.7)

(1.0)(1.4 GPa)

Steels

Alum. alloy

Figure 6–20Notch-sensitivity charts for steels and UNS A92024-T wrought aluminum alloys subjected to reversed bending or reversed axial loads. For larger notch radii, use the values of q corresponding to the r 5 0.16-in (4-mm) ordinate. (From George Sines and J. L. Waisman (eds.), Metal Fatigue, McGraw-Hill, New York. Copyright © 1969 by The McGraw-Hill Companies, Inc. Reprinted by permission.)



reversed torsion. In using these charts it is well to know that the actual test results from which the curves were derived exhibit a large amount of scatter. Because of this scatter it is always safe to use Kf 5 Kt if there is any doubt about the true value of q. Also, note that q is not far from unity for large notch radii. Figure 6–20 has as its basis the Neuber equation, which is given by

Kf 5 1 1Kt 2 1

1 1 2ayr (6–33)

where 1a is defined as the Neuber constant and is a material constant. Equating Eqs. (6–31) and (6–33) yields the notch sensitivity equation

q 51

1 11a2r

(6–34)

correlating with Figs. 6–20 and 6–21 as

Bending or axial: 1a 5 0.246 2 3.08(1023)Sut 1 1.51(1025)S2ut 2 2.67(1028)S3

ut (6–35a)

Torsion: 1a 5 0.190 2 2.51(1023)Sut 1 1.35(1025)S2ut 2 2.67(1028)S3

ut (6–35b)

where the equations apply to steel and Sut is in kpsi. Equation (6–34) used in conjunction with Eq. pair (6–35) is equivalent to Figs. 6–20 and 6–21. As with the graphs, the results from the curve fit equations provide only approximations to the experimental data. The notch sensitivity of cast irons is very low, varying from 0 to about 0.20, depending upon the tensile strength. To be on the conservative side, it is recommended that the value q 5 0.20 be used for all grades of cast iron.

Figure 6–21Notch-sensitivity curves for materials in reversed torsion. For larger notch radii, use the values of qshear corresponding to r 5 0.16 in (4 mm).

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0

0.2

0.4

0.6

0.8

1.0

Notch radius r, in

Notch radius r, mm

Not

ch s

ensi

tivity

qsh

ear

Steels

Alum. alloy

S ut = 200 kpsi (1.4 GPa)

60 (0.4)100 (0

.7)150 (1.0)

EXAMPLE 6–6 A steel shaft in bending has an ultimate strength of 690 MPa and a shoulder with a fillet radius of 3 mm connecting a 32-mm diameter with a 38-mm diameter. Estimate Kf using:(a) Figure 6–20.(b) Equations (6–33) and (6–35).


Bolted Joints Threads:

Note: The MJ profile has a rounded fillet at the root (external thread), and a larger minor diameter. Used when high fatigue strength is required.

d := (Dmaj )major diameter or largest diameter; dr := (Dmin )minor or smallest diameter, dp := (Dp ) pitch diameter between d and dr; p := pitch (distance along the thread axis between adjacent thread forms)At := tensile-stress area (area of an unthreaded rod with same tensile strength as the threaded rod) Metric Thread Specification: For example, in the specification M16 X 2.5, M - denotes metric thread, nominal major diameter is 16 mm and pitch is 2.5mm. See Table –8-1 for thread diameters and areas (next page). Some important quantities for bolted joints (fasteners):

Washer thickness: t (from Table A-32 or A-33)Nut thickness (bolted joints): H (Table A-31)Grip length: l := The length between bolt and nut faces (Fig a)

l :=h + t2 / 2 (for t2 ≤ d) h + d (for t2 > d)

⎧⎨⎩

For Cap-Screws (Fig b)

Tensile-stress area: At (Table 8-1)

Fastener (bolt) length: L> l + H ( Fig a) l +1.5d ( Fig b)⎧⎨⎩

(Table A-17 for standard values)

Threaded length: LT = 2d + 6mm, (L ≤ 125mm, d ≤ 48mm) 2d +12mm, (125< L ≤ 200mm)2d + 25mm, (L > 200mm)

⎧⎨⎪

⎩⎪

Tensile-stress (thread) area: At (Table 8-1); CS area of unthreaded part: Ad = πd 2 / 4 Unthreaded length in grip: ld = L − LT ; Threaded length in grip: lt = l − ld

Fastener (bolt) Stiffness: kb =AdAtE

Adlt + Atld (by considering springs in series - show)

Screws, Fasteners, and the Design of Nonpermanent Joints 403

threads. The MJ profile has a rounded fillet at the root of the external thread and a larger minor diameter of both the internal and external threads. This profile is espe-cially useful where high fatigue strength is required. Tables 8–1 and 8–2 will be useful in specifying and designing threaded parts. Note that the thread size is specified by giving the pitch p for metric sizes and by giving the number of threads per inch N for the Unified sizes. The screw sizes in Table 8–2 with diameter under 1

4 in are numbered or gauge sizes. The second column in Table 8–2 shows that a No. 8 screw has a nominal major diameter of 0.1640 in. A great many tensile tests of threaded rods have shown that an unthreaded rod having a diameter equal to the mean of the pitch diameter and minor diameter will have the same tensile strength as the threaded rod. The area of this unthreaded rod is called the tensile-stress area At of the threaded rod; values of At are listed in both tables. Two major Unified thread series are in common use: UN and UNR. The differ-ence between these is simply that a root radius must be used in the UNR series. Because of reduced thread stress-concentration factors, UNR series threads have improved fatigue strengths. Unified threads are specified by stating the nominal major diameter, the number of threads per inch, and the thread series, for example, 5

8 in-18 UNRF or 0.625 in-18 UNRF. Metric threads are specified by writing the diameter and pitch in millimeters, in that order. Thus, M12 3 1.75 is a thread having a nominal major diameter of 12 mm and a pitch of 1.75 mm. Note that the letter M, which precedes the diameter, is the clue to the metric designation.

Figure 8–1Terminology of screw threads. Sharp vee threads shown for clarity; the crests and roots are actually flattened or rounded during the forming operation.

Major diameter

Pitch diameter

Minor diameter

Pitch p

45° chamfer

Thread angle 2αRootCrest

Figure 8–2Basic profile for metric M and MJ threads.d 5 major diameterdr 5 minor diameterdp 5 pitch diameterp 5 pitch H 5 13

2 p

Internal threads

External threads

H4

H4

5H8

3H8

H8

Hp4

p2

p

p

2

p8

30°

60°

60°

dr

dp

d



Nominal Coarse-Pitch Series Fine-Pitch Series Major Tensile- Minor- Tensile- Minor- Diameter Pitch Stress Diameter Pitch Stress Diameter d p Area At Area Ar p Area At Area Ar mm mm mm2 mm2 mm mm2 mm2

1.6 0.35 1.27 1.07

2 0.40 2.07 1.79

2.5 0.45 3.39 2.98

3 0.5 5.03 4.47

3.5 0.6 6.78 6.00

4 0.7 8.78 7.75

5 0.8 14.2 12.7

6 1 20.1 17.9

8 1.25 36.6 32.8 1 39.2 36.0

10 1.5 58.0 52.3 1.25 61.2 56.3

12 1.75 84.3 76.3 1.25 92.1 86.0

14 2 115 104 1.5 125 116

16 2 157 144 1.5 167 157

20 2.5 245 225 1.5 272 259

24 3 353 324 2 384 365

30 3.5 561 519 2 621 596

36 4 817 759 2 915 884

42 4.5 1120 1050 2 1260 1230

48 5 1470 1380 2 1670 1630

56 5.5 2030 1910 2 2300 2250

64 6 2680 2520 2 3030 2980

72 6 3460 3280 2 3860 3800

80 6 4340 4140 1.5 4850 4800

90 6 5590 5360 2 6100 6020

100 6 6990 6740 2 7560 7470

110 2 9180 9080

*The equations and data used to develop this table have been obtained from ANSI B1.1-1974 and B18.3.1-1978. The minor diameter was found from the equation dr 5 d 2 1.226 869p, and the pitch diameter from dp 5 d 2 0.649 519p. The mean of the pitch diameter and the minor diameter was used to compute the tensile-stress area.

Table 8–1

Diameters and Areas of Coarse-Pitch and Fine-Pitch Metric Threads.*

Square and Acme threads, whose profiles are shown in Fig. 8–3a and b, respec-tively, are used on screws when power is to be transmitted. Table 8–3 lists the pre-ferred pitches for inch-series Acme threads. However, other pitches can be and often are used, since the need for a standard for such threads is not great. Modifications are frequently made to both Acme and square threads. For instance, the square thread is sometimes modified by cutting the space between the teeth so as to have an included thread angle of 10 to 15°. This is not difficult, since these threads are usually cut with a single-point tool anyhow; the modification retains most of the high efficiency inherent in square threads and makes the cutting simpler. Acme threads


Useful tables from Appendix.

Useful Tables 1015

Axial and Bending and Torsion Direct ShearM, T I, J c, r S, T F A S, T

N ? m* m4 m Pa N* m2 Pa

N ? m cm4 cm MPa (N/mm2) N† mm2 MPa (N/mm2)

N ? m† mm4 mm GPa kN m2 kPa

kN ? m cm4 cm GPa kN† mm2 GPa

N ? mm† mm4 mm MPa (N/mm2)

*Basic relation.†Often preferred.

Table A–3

Optional SI Units for Bending Stress s 5 Mcyl, Torsion Stress t 5 TryJ, Axial Stresss 5 FyA, and Direct Shear Stress t 5 FyA

Bending Deflection Torsional DeflectionF, w l l I E y T l J G U

N* m m4 Pa m N ? m* m m4 Pa rad

kN† mm mm4 GPa mm N ? m† mm mm4 GPa rad

kN m m4 GPa mm N ? mm mm mm4 MPa (N/mm2) rad

N mm mm4 kPa m N ? m cm cm4 MPa (N/mm2) rad


Table A–4

Optional SI Units for Bending Defl ectiony 5 f(Fl3yEl) or y 5 f (wl 4yEl) andTorsional Defl ectionu 5 TlyGJ

Modulus of Modulus of Elasticity E Rigidity G Poisson’s Unit Weight wMaterial Mpsi GPa Mpsi GPa Ratio N lbf/in3 lbf/ft3 kN/m3

Aluminum (all alloys) 10.4 71.7 3.9 26.9 0.333 0.098 169 26.6

Beryllium copper 18.0 124.0 7.0 48.3 0.285 0.297 513 80.6

Brass 15.4 106.0 5.82 40.1 0.324 0.309 534 83.8

Carbon steel 30.0 207.0 11.5 79.3 0.292 0.282 487 76.5

Cast iron (gray) 14.5 100.0 6.0 41.4 0.211 0.260 450 70.6

Copper 17.2 119.0 6.49 44.7 0.326 0.322 556 87.3

Douglas fi r 1.6 11.0 0.6 4.1 0.33 0.016 28 4.3

Glass 6.7 46.2 2.7 18.6 0.245 0.094 162 25.4

Inconel 31.0 214.0 11.0 75.8 0.290 0.307 530 83.3

Lead 5.3 36.5 1.9 13.1 0.425 0.411 710 111.5

Magnesium 6.5 44.8 2.4 16.5 0.350 0.065 112 17.6

Molybdenum 48.0 331.0 17.0 117.0 0.307 0.368 636 100.0

Monel metal 26.0 179.0 9.5 65.5 0.320 0.319 551 86.6

Nickel silver 18.5 127.0 7.0 48.3 0.322 0.316 546 85.8

Nickel steel 30.0 207.0 11.5 79.3 0.291 0.280 484 76.0

Phosphor bronze 16.1 111.0 6.0 41.4 0.349 0.295 510 80.1

Stainless steel (18-8) 27.6 190.0 10.6 73.1 0.305 0.280 484 76.0

Titanium alloys 16.5 114.0 6.2 42.4 0.340 0.160 276 43.4

Table A–5

Physical Constants of Materials

bud98209_appa_1011-1066.indd Page 1015 02/12/13 1:20 PM user-f-w-198 bud98209_appa_1011-1066.indd Page 1015 02/12/13 1:20 PM user-f-w-198 /204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles/204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles


Basic Tolerance Grades Sizes IT6 IT7 IT8 IT9 IT10 IT11

0–3 0.006 0.010 0.014 0.025 0.040 0.060

3–6 0.008 0.012 0.018 0.030 0.048 0.075

6–10 0.009 0.015 0.022 0.036 0.058 0.090

10–18 0.011 0.018 0.027 0.043 0.070 0.110

18–30 0.013 0.021 0.033 0.052 0.084 0.130

30–50 0.016 0.025 0.039 0.062 0.100 0.160

50–80 0.019 0.030 0.046 0.074 0.120 0.190

80–120 0.022 0.035 0.054 0.087 0.140 0.220

120–180 0.025 0.040 0.063 0.100 0.160 0.250

180–250 0.029 0.046 0.072 0.115 0.185 0.290

250–315 0.032 0.052 0.081 0.130 0.210 0.320

315–400 0.036 0.057 0.089 0.140 0.230 0.360

Table A–11

A Selection of International Tolerance Grades—Metric Series (Size Ranges Are for Over the Lower Limit and Including the Upper Limit. All Values Arein Millimeters)Source: Preferred Metric Limits and Fits, ANSI B4.2-1978. See also BSI 4500.

Table A–10

Cumulative Distribution Function of Normal (Gaussian) Distribution* (Continued)

ZA 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

3 0.00135 0.03968 0.03687 0.03483 0.03337 0.03233 0.03159 0.03108 0.04723 0.04481

4 0.04317 0.04207 0.04133 0.05854 0.05541 0.05340 0.05211 0.05130 0.06793 0.06479

5 0.06287 0.06170 0.07996 0.07579 0.07333 0.07190 0.07107 0.08599 0.08332 0.08182

6 0.09987 0.09530 0.09282 0.09149 0.010777 0.010402 0.010206 0.010104 0.011523 0.011260

za 21.282 21.643 21.960 22.326 22.576 23.090 23.291 23.891 24.417

F(za) 0.10 0.05 0.025 0.010 0.005 0.001 0.0005 0.0001 0.000005

R(za) 0.90 0.95 0.975 0.990 0.995 0.999 0.9995 0.9999 0.999995

*The superscript on a zero after the decimal point indicates how many zeros there are after the decimal point. For example, 0.04481 5 0.000 048 1.


Useful Tables 1031

Basic Upper-Deviation Letter Lower-Deviation Letter Sizes c d f g h k n p s u

0–3 20.060 20.020 20.006 20.002 0 0 10.004 10.006 10.014 10.018

3–6 20.070 20.030 20.010 20.004 0 10.001 10.008 10.012 10.019 10.023

6–10 20.080 20.040 20.013 20.005 0 10.001 10.010 10.015 10.023 10.028

10–14 20.095 20.050 20.016 20.006 0 10.001 10.012 10.018 10.028 10.033

14–18 20.095 20.050 20.016 20.006 0 10.001 10.012 10.018 10.028 10.033

18–24 20.110 20.065 20.020 20.007 0 10.002 10.015 10.022 10.035 10.041

24–30 20.110 20.065 20.020 20.007 0 10.002 10.015 10.022 10.035 10.048

30–40 20.120 20.080 20.025 20.009 0 10.002 10.017 10.026 10.043 10.060

40–50 20.130 20.080 20.025 20.009 0 10.002 10.017 10.026 10.043 10.070

50–65 20.140 20.100 20.030 20.010 0 10.002 10.020 10.032 10.053 10.087

65–80 20.150 20.100 20.030 20.010 0 10.002 10.020 10.032 10.059 10.102

80–100 20.170 20.120 20.036 20.012 0 10.003 10.023 10.037 10.071 10.124

100–120 20.180 20.120 20.036 20.012 0 10.003 10.023 10.037 10.079 10.144

120–140 20.200 20.145 20.043 20.014 0 10.003 10.027 10.043 10.092 10.170

140–160 20.210 20.145 20.043 20.014 0 10.003 10.027 10.043 10.100 10.190

160–180 20.230 20.145 20.043 20.014 0 10.003 10.027 10.043 10.108 10.210

180–200 20.240 20.170 20.050 20.015 0 10.004 10.031 10.050 10.122 10.236

200–225 20.260 20.170 20.050 20.015 0 10.004 10.031 10.050 10.130 10.258

225–250 20.280 20.170 20.050 20.015 0 10.004 10.031 10.050 10.140 10.284

250–280 20.300 20.190 20.056 20.017 0 10.004 10.034 10.056 10.158 10.315

280–315 20.330 20.190 20.056 20.017 0 10.004 10.034 10.056 10.170 10.350

315–355 20.360 20.210 20.062 20.018 0 10.004 10.037 10.062 10.190 10.390

355–400 20.400 20.210 20.062 20.018 0 10.004 10.037 10.062 10.208 10.435

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.

bud98209_appa_1011-1066.indd 31 02/12/13 1:21 PM user-f-w-198 bud98209_appa_1011-1066.indd Page 1031 02/12/13 1:21 PM user-f-w-198 /204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles/204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles

Design'of'Machine'Elements'Databook'


Multiply Input By Factor To Get Output Multiply Input By Factor To Get OutputX A Y X A Y

British thermal 1055 joule, Junit, Btu

Btu/second, Btu/s 1.05 kilowatt, kW

calorie 4.19 joule, J

centimeter of 1.333 kilopascal, kPamercury (0°C)

centipoise, cP 0.001 pascal-second, Pa ? s

degree (angle) 0.0174 radian, rad

foot, ft 0.305 meter, m

foot2, ft2 0.0929 meter2, m2

foot/minute, 0.0051 meter/second, m/sft/min

foot-pound, ft ? lbf 1.35 joule, J

foot-pound/ 1.35 watt, Wsecond, ft ? lbf/s

foot/second, ft/s 0.305 meter/second, m/s

gallon (U.S.), gal 3.785 liter, L

horsepower, 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, kN

kilopound/inch2, 6.89 megapascal, MPakpsi (ksi) (N/mm2)

mass, lbf ? s2/in 175 kilogram, kg

*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.

mile, mi 1.610 kilometer, km

mile/hour, mi/h 1.61 kilometer/hour, km/h

mile/hour, mi/h 0.447 meter/second, m/s

moment 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, N

ounce-mass 0.0311 kilogram, kg

pound, lbf† 4.45 newton, N

pound-foot, lbf ? ft 1.36 newton-meter, N ? m

pound/foot2, lbf/ft2 47.9 pascal, Pa

pound-inch, lbf ? in 0.113 joule, J

pound-inch, lbf ? in 0.113 newton-meter, N ? m

pound/inch, lbf/in 175 newton/meter, N/m

pound/inch2, psi 6.89 kilopascal, kPa(lbf/in2)

pound-mass, lbm 0.454 kilogram, kg

pound-mass/ 0.454 kilogram/second,second, lbm/s kg/s

quart (U.S. liquid), qt 946 milliliter, mL

section modulus, in3 16.4 centimeter3, cm3

slug 14.6 kilogram, kg

ton (short 2000 lbm) 907 kilogram, kg

yard, yd 0.914 meter, m

Table A–2

Conversion Factors A to Convert Input X to Output Y Using the Formula Y 5 AX*


Useful Tables 1015

Axial and Bending and Torsion Direct ShearM, T I, J c, r S, T F A S, T

N ? m* m4 m Pa N* m2 Pa

N ? m cm4 cm MPa (N/mm2) N† mm2 MPa (N/mm2)

N ? m† mm4 mm GPa kN m2 kPa

kN ? m cm4 cm GPa kN† mm2 GPa

N ? mm† mm4 mm MPa (N/mm2)


Table A–3

Optional SI Units for Bending Stress s 5 Mcyl, Torsion Stress t 5 TryJ, Axial Stresss 5 FyA, and Direct Shear Stress t 5 FyA

Bending Deflection Torsional DeflectionF, w l l I E y T l J G U

N* m m4 Pa m N ? m* m m4 Pa rad

kN† mm mm4 GPa mm N ? m† mm mm4 GPa rad

kN m m4 GPa mm N ? mm mm mm4 MPa (N/mm2) rad

N mm mm4 kPa m N ? m cm cm4 MPa (N/mm2) rad


Table A–4

Optional SI Units for Bending Defl ectiony 5 f(Fl3yEl) or y 5 f (wl 4yEl) andTorsional Defl ectionu 5 TlyGJ

Modulus of Modulus of Elasticity E Rigidity G Poisson’s Unit Weight wMaterial Mpsi GPa Mpsi GPa Ratio N lbf/in3 lbf/ft3 kN/m3

Aluminum (all alloys) 10.4 71.7 3.9 26.9 0.333 0.098 169 26.6

Beryllium copper 18.0 124.0 7.0 48.3 0.285 0.297 513 80.6

Brass 15.4 106.0 5.82 40.1 0.324 0.309 534 83.8

Carbon steel 30.0 207.0 11.5 79.3 0.292 0.282 487 76.5

Cast iron (gray) 14.5 100.0 6.0 41.4 0.211 0.260 450 70.6

Copper 17.2 119.0 6.49 44.7 0.326 0.322 556 87.3

Douglas fi r 1.6 11.0 0.6 4.1 0.33 0.016 28 4.3

Glass 6.7 46.2 2.7 18.6 0.245 0.094 162 25.4

Inconel 31.0 214.0 11.0 75.8 0.290 0.307 530 83.3

Lead 5.3 36.5 1.9 13.1 0.425 0.411 710 111.5

Magnesium 6.5 44.8 2.4 16.5 0.350 0.065 112 17.6

Molybdenum 48.0 331.0 17.0 117.0 0.307 0.368 636 100.0

Monel metal 26.0 179.0 9.5 65.5 0.320 0.319 551 86.6

Nickel silver 18.5 127.0 7.0 48.3 0.322 0.316 546 85.8

Nickel steel 30.0 207.0 11.5 79.3 0.291 0.280 484 76.0

Phosphor bronze 16.1 111.0 6.0 41.4 0.349 0.295 510 80.1

Stainless steel (18-8) 27.6 190.0 10.6 73.1 0.305 0.280 484 76.0

Titanium alloys 16.5 114.0 6.2 42.4 0.340 0.160 276 43.4

Table A–5

Physical Constants of Materials



Basic Tolerance Grades Sizes IT6 IT7 IT8 IT9 IT10 IT11

0–3 0.006 0.010 0.014 0.025 0.040 0.060

3–6 0.008 0.012 0.018 0.030 0.048 0.075

6–10 0.009 0.015 0.022 0.036 0.058 0.090

10–18 0.011 0.018 0.027 0.043 0.070 0.110

18–30 0.013 0.021 0.033 0.052 0.084 0.130

30–50 0.016 0.025 0.039 0.062 0.100 0.160

50–80 0.019 0.030 0.046 0.074 0.120 0.190

80–120 0.022 0.035 0.054 0.087 0.140 0.220

120–180 0.025 0.040 0.063 0.100 0.160 0.250

180–250 0.029 0.046 0.072 0.115 0.185 0.290

250–315 0.032 0.052 0.081 0.130 0.210 0.320

315–400 0.036 0.057 0.089 0.140 0.230 0.360

Table A–11

A Selection of International Tolerance Grades—Metric Series (Size Ranges Are for Over the Lower Limit and Including the Upper Limit. All Values Arein Millimeters)Source: Preferred Metric Limits and Fits, ANSI B4.2-1978. See also BSI 4500.

Table A–10

Cumulative Distribution Function of Normal (Gaussian) Distribution* (Continued)

ZA 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

3 0.00135 0.03968 0.03687 0.03483 0.03337 0.03233 0.03159 0.03108 0.04723 0.04481

4 0.04317 0.04207 0.04133 0.05854 0.05541 0.05340 0.05211 0.05130 0.06793 0.06479

5 0.06287 0.06170 0.07996 0.07579 0.07333 0.07190 0.07107 0.08599 0.08332 0.08182

6 0.09987 0.09530 0.09282 0.09149 0.010777 0.010402 0.010206 0.010104 0.011523 0.011260

za 21.282 21.643 21.960 22.326 22.576 23.090 23.291 23.891 24.417

F(za) 0.10 0.05 0.025 0.010 0.005 0.001 0.0005 0.0001 0.000005

R(za) 0.90 0.95 0.975 0.990 0.995 0.999 0.9995 0.9999 0.999995

*The superscript on a zero after the decimal point indicates how many zeros there are after the decimal point. For example, 0.04481 5 0.000 048 1.


Useful Tables 1031

Basic Upper-Deviation Letter Lower-Deviation Letter Sizes c d f g h k n p s u

0–3 20.060 20.020 20.006 20.002 0 0 10.004 10.006 10.014 10.018

3–6 20.070 20.030 20.010 20.004 0 10.001 10.008 10.012 10.019 10.023

6–10 20.080 20.040 20.013 20.005 0 10.001 10.010 10.015 10.023 10.028

10–14 20.095 20.050 20.016 20.006 0 10.001 10.012 10.018 10.028 10.033

14–18 20.095 20.050 20.016 20.006 0 10.001 10.012 10.018 10.028 10.033

18–24 20.110 20.065 20.020 20.007 0 10.002 10.015 10.022 10.035 10.041

24–30 20.110 20.065 20.020 20.007 0 10.002 10.015 10.022 10.035 10.048

30–40 20.120 20.080 20.025 20.009 0 10.002 10.017 10.026 10.043 10.060

40–50 20.130 20.080 20.025 20.009 0 10.002 10.017 10.026 10.043 10.070

50–65 20.140 20.100 20.030 20.010 0 10.002 10.020 10.032 10.053 10.087

65–80 20.150 20.100 20.030 20.010 0 10.002 10.020 10.032 10.059 10.102

80–100 20.170 20.120 20.036 20.012 0 10.003 10.023 10.037 10.071 10.124

100–120 20.180 20.120 20.036 20.012 0 10.003 10.023 10.037 10.079 10.144

120–140 20.200 20.145 20.043 20.014 0 10.003 10.027 10.043 10.092 10.170

140–160 20.210 20.145 20.043 20.014 0 10.003 10.027 10.043 10.100 10.190

160–180 20.230 20.145 20.043 20.014 0 10.003 10.027 10.043 10.108 10.210

180–200 20.240 20.170 20.050 20.015 0 10.004 10.031 10.050 10.122 10.236

200–225 20.260 20.170 20.050 20.015 0 10.004 10.031 10.050 10.130 10.258

225–250 20.280 20.170 20.050 20.015 0 10.004 10.031 10.050 10.140 10.284

250–280 20.300 20.190 20.056 20.017 0 10.004 10.034 10.056 10.158 10.315

280–315 20.330 20.190 20.056 20.017 0 10.004 10.034 10.056 10.170 10.350

315–355 20.360 20.210 20.062 20.018 0 10.004 10.037 10.062 10.190 10.390

355–400 20.400 20.210 20.062 20.018 0 10.004 10.037 10.062 10.208 10.435

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.


Useful Tables 1043

Fraction of Inches

164, 1

32, 116, 3

32, 18, 5

32, 316, 1

4, 516, 3

8, 716, 1

2, 916, 5

8, 1116, 3

4, 78, 1, 11

4, 112, 13

4, 2, 214, 21

2, 234, 3,

314, 31

2, 334, 4, 41

4, 412, 43

4, 5, 514, 51

2, 534, 6, 61

2, 7, 712, 8, 81

2, 9, 912, 10, 101

2, 11, 1112, 12,

1212, 13, 131

2, 14, 1412, 15, 151

2, 16, 1612, 17, 171

2, 18, 1812, 19, 191

2, 20

Decimal Inches

0.010, 0.012, 0.016, 0.020, 0.025, 0.032, 0.040, 0.05, 0.06, 0.08, 0.10, 0.12, 0.16, 0.20, 0.24, 0.30,

0.40, 0.50, 0.60, 0.80, 1.00, 1.20, 1.40, 1.60, 1.80, 2.0, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.2,

4.4, 4.6, 4.8, 5.0, 5.2, 5.4, 5.6, 5.8, 6.0, 7.0, 7.5, 8.5, 9.0, 9.5, 10.0, 10.5, 11.0, 11.5, 12.0, 12.5,

13.0, 13.5, 14.0, 14.5, 15.0, 15.5, 16.0, 16.5, 17.0, 17.5, 18.0, 18.5, 19.0, 19.5, 20

Millimeters

0.05, 0.06, 0.08, 0.10, 0.12, 0.16, 0.20, 0.25, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.0, 1.1, 1.2,

1.4, 1.5, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 8.0, 9.0, 10, 11, 12, 14,

16, 18, 20, 22, 25, 28, 30, 32, 35, 40, 45, 50, 60, 80, 100, 120, 140, 160, 180, 200, 250, 300

Renard Numbers*

1st choice, R5: 1, 1.6, 2.5, 4, 6.3, 10

2d choice, R10: 1.25, 2, 3.15, 5, 8

3d choice, R20: 1.12, 1.4, 1.8, 2.24, 2.8, 3.55, 4.5, 5.6, 7.1, 9

4th choice, R40: 1.06, 1.18, 1.32, 1.5, 1.7, 1.9, 2.12, 2.36, 2.65, 3, 3.35, 3.75, 4.25, 4.75, 5.3, 6, 6.7, 7.5, 8.5, 9.5

*May be multiplied or divided by powers of 10.

Table A–17

Preferred Sizes and Renard (R-Series) Numbers(When a choice can be made, use one of these sizes; however, not all parts or items are available in all the sizes shown in the table.)



Table A–15

Charts of Theoretical Stress-Concentration Factors K*t

Kt

d

F F

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–15–1Bar in tension or simple compression with a transverse hole. s0 5 FyA, where A 5 (w 2 d)t and t is the thickness.

Kt

r

FF

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–15–3Notched rectangular bar in tension or simple compression. s0 5 FyA, where A 5 dt and t is the thickness.

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

Figure A–15–2Rectangular bar with a transverse hole in bending.s0 5 McyI, where I 5 (w 2 d)h3y12.


Useful Tables 1035

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

Figure A–15–4Notched rectangular bar in bending. s0 5 McyI, wherec 5 dy2, I 5 td3y12, and t is the thickness.

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–15–6Rectangular filleted bar in bending. s0 5 McyI, wherec 5 dy2, I 5 td3y12, t is the thickness.

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

F F

Figure A–15–5Rectangular filleted bar in tension or simple compression. s0 5 FyA, where A 5 dt and t is the thickness.

*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)



Table A–15


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

r

FF

1.05

1.02

1.10

D/d = 1.50

dD

Figure A–15–7Round shaft with shoulder fillet in tension. s0 5 FyA, where A 5 pd 2y4.

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 = 3

1.02

1.5

1.10

1.05

r

MD dM

Figure A–15–9Round shaft with shoulder fillet in bending. s0 5 McyI, where c 5 dy2 and I 5 pd 4y64.

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

3.0

D/d = 21.09

1.20 1.33

r

TTD d

Figure A–15–8Round shaft with shoulder fillet in torsion. t0 5 TcyJ, wherec 5 dy2 and J 5 pd 4y32.


Useful Tables 1037

Table A–15


Kts

d /D0 0.05 0.10 0.15 0.20 0.25 0.30

2.4

2.8

3.2

3.6

4.0

Jc

TB

dT

!D3

16dD2

6= – (approx)

AD

Kts, A

Kts, B

Figure A–15–10Round shaft in torsion with transverse hole.

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

F

F/2 F/2

Figure A–15–12Plate loaded in tension by a pin through a hole. s0 5 FyA, where A 5 (w 2 d )t. When clearance exists, increase Kt 35 to 50 percent. (M. M. Frocht and H. N. Hill, “Stress-Concentration Factors around a Central Circular Hole in a Plate Loaded through a Pin in Hole,” J. Appl. Mechanics, vol. 7, no. 1, March 1940,p. A-5.)

Kt

d /D0 0.05 0.10 0.15 0.20 0.25 0.30

1.0

1.4

1.8

2.2

2.6

3.0d

D

MM

Figure A–15–11Round shaft in bending with a transverse hole. s0 5 My[(pD3y32) 2 (dD2y6)], approximately.


(Continued)



Table A–15


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 FF

Figure A–15–13Grooved round bar in tension. s0 5 FyA, where A 5 pd2y4.

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

Figure A–15–15Grooved round bar in torsion. t0 5 TcyJ, where c 5 dy2 and J 5 pd 4y32.

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

Figure A–15–14Grooved round bar in bending. s0 5 McyI, where c 5 dy2 and I 5 pd 4y64.



Useful Tables 1039

Table A–15


Figure A–15–16Round shaft with flat-bottom groove in bending and/or tension.

s0 54F

pd 2 132M

pd 3

Source: W. D. Pilkey and D. F. Pilkey, Peterson’s Stress-Concentration Factors, 3rd ed. John Wiley & Sons, Hoboken, NJ, 2008, p. 115.

Kt

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

1.00

0.5 0.6 0.7 0.8 0.91.0 2.0 3.0 4.0 5.0 6.01.0

a/t

0.03

0.04

0.05

0.07

0.15

0.60

d

ra

r

DM

Ft

MF

rt

0.10

0.20

0.40

(Continued)



Table A–15


Figure A–15–17Round shaft with flat-bottom groove in torsion.

t0 516T

pd3

Source: W. D. Pilkey and D. F. Pilkey, Peterson’s Stress-Concentration Factors, 3rd ed. John Wiley & Sons, Hoboken, NJ, 2008, p. 133

0.03

0.04

0.06

0.10

0.20

rt

0.5 0.6 0.7 0.8 0.91.0 2.01.0

2.0

3.0

4.0

5.0

6.0

3.0 4.0 5.0 6.0

d

ra

r

D

T

Tt

Kts

a/t

bud98209_appa_1011-1066.indd Page 1040 12/4/13 6:51 PM f-496 bud98209_appa_1011-1066.indd Page 1040 12/4/13 6:51 PM f-496 /204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles/204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles

Useful Tables 1041

The nominal bending stress is s0 5 MyZnet where Znet is a reduced value of the section modulus and is defined by

Znet 5pA32D

(D4 2 d 4)

Values of A are listed in the table. Use d 5 0 for a solid bar

d/D 0.9 0.6 0

a/D A Kt A Kt A Kt

0.050 0.92 2.63 0.91 2.55 0.88 2.42

0.075 0.89 2.55 0.88 2.43 0.86 2.35

0.10 0.86 2.49 0.85 2.36 0.83 2.27

0.125 0.82 2.41 0.82 2.32 0.80 2.20

0.15 0.79 2.39 0.79 2.29 0.76 2.15

0.175 0.76 2.38 0.75 2.26 0.72 2.10

0.20 0.73 2.39 0.72 2.23 0.68 2.07

0.225 0.69 2.40 0.68 2.21 0.65 2.04

0.25 0.67 2.42 0.64 2.18 0.61 2.00

0.275 0.66 2.48 0.61 2.16 0.58 1.97

0.30 0.64 2.52 0.58 2.14 0.54 1.94

M M

D d

aTable A–16

Approximate Stress-Concentration Factor Kt of a Round Bar or Tube with a Transverse Round Hole and Loaded in BendingSource: R. E. Peterson, Stress-Concentration Factors, Wiley, New York, 1974, pp. 146, 235.

(Continued)

bud98209_appa_1011-1066.indd Page 1041 12/4/13 6:55 PM f-496 bud98209_appa_1011-1066.indd Page 1041 12/4/13 6:55 PM f-496 /204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles/204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles


TTD a d

The maximum stress occurs on the inside of the hole, slightly below the shaft surface. The nominal shear stress is t0 5 TDy2Jnet, where Jnet is a reduced value of the second polar moment of area and is defined by

Jnet 5pA(D4 2 d 4)

32

Values of A are listed in the table. Use d 5 0 for a solid bar.

d/D 0.9 0.8 0.6 0.4 0a/D A Kts A Kts A Kts A Kts A Kts

0.05 0.96 1.78 0.95 1.77

0.075 0.95 1.82 0.93 1.71

0.10 0.94 1.76 0.93 1.74 0.92 1.72 0.92 1.70 0.92 1.68

0.125 0.91 1.76 0.91 1.74 0.90 1.70 0.90 1.67 0.89 1.64

0.15 0.90 1.77 0.89 1.75 0.87 1.69 0.87 1.65 0.87 1.62

0.175 0.89 1.81 0.88 1.76 0.87 1.69 0.86 1.64 0.85 1.60

0.20 0.88 1.96 0.86 1.79 0.85 1.70 0.84 1.63 0.83 1.58

0.25 0.87 2.00 0.82 1.86 0.81 1.72 0.80 1.63 0.79 1.54

0.30 0.80 2.18 0.78 1.97 0.77 1.76 0.75 1.63 0.74 1.51

0.35 0.77 2.41 0.75 2.09 0.72 1.81 0.69 1.63 0.68 1.47

0.40 0.72 2.67 0.71 2.25 0.68 1.89 0.64 1.63 0.63 1.44

Table A–16 (Continued)

Approximate Stress-Concentration Factors Kts for a Round Bar or Tube Having a Transverse Round Hole and Loaded in Torsion Source: R. E. Peterson, Stress-Concentration Factors, Wiley, New York, 1974, pp. 148, 244.



Table A–20

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 defi ned in Sec. 1–10, provided the materials conform to ASTM A6 or A568 requirements or are required in the purchase specifi cations. Remember that a numbering system is not a specifi cation.] Source: 1986 SAE Handbook, p. 2.15.

1 2 3 4 5 6 7 8 Tensile Yield SAE and/or Process- Strength, Strength, Elongation in Reduction in Brinell

UNS No. AISI No. ing MPa (kpsi) MPa (kpsi) 2 in, % Area, % Hardness

G10060 1006 HR 300 (43) 170 (24) 30 55 86

CD 330 (48) 280 (41) 20 45 95

G10100 1010 HR 320 (47) 180 (26) 28 50 95

CD 370 (53) 300 (44) 20 40 105

G10150 1015 HR 340 (50) 190 (27.5) 28 50 101

CD 390 (56) 320 (47) 18 40 111

G10180 1018 HR 400 (58) 220 (32) 25 50 116

CD 440 (64) 370 (54) 15 40 126

G10200 1020 HR 380 (55) 210 (30) 25 50 111

CD 470 (68) 390 (57) 15 40 131

G10300 1030 HR 470 (68) 260 (37.5) 20 42 137

CD 520 (76) 440 (64) 12 35 149

G10350 1035 HR 500 (72) 270 (39.5) 18 40 143

CD 550 (80) 460 (67) 12 35 163

G10400 1040 HR 520 (76) 290 (42) 18 40 149

CD 590 (85) 490 (71) 12 35 170

G10450 1045 HR 570 (82) 310 (45) 16 40 163

CD 630 (91) 530 (77) 12 35 179

G10500 1050 HR 620 (90) 340 (49.5) 15 35 179

CD 690 (100) 580 (84) 10 30 197

G10600 1060 HR 680 (98) 370 (54) 12 30 201

G10800 1080 HR 770 (112) 420 (61.5) 10 25 229

G10950 1095 HR 830 (120) 460 (66) 10 25 248


Useful Tables 1049

Table A–21

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. In all cases, data were obtained from specimens of diameter 0.505 in, machined from 1-in rounds, and of gauge length 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 8 Tensile Yield Temperature Strength Strength, Elongation, Reduction Brinell

AISI No. Treatment °C (°F) MPa (kpsi) MPa (kpsi) % in Area, % Hardness

1030 Q&T* 205 (400) 848 (123) 648 (94) 17 47 495

Q&T* 315 (600) 800 (116) 621 (90) 19 53 401

Q&T* 425 (800) 731 (106) 579 (84) 23 60 302

Q&T* 540 (1000) 669 (97) 517 (75) 28 65 255

Q&T* 650 (1200) 586 (85) 441 (64) 32 70 207

Normalized 925 (1700) 521 (75) 345 (50) 32 61 149

Annealed 870 (1600) 430 (62) 317 (46) 35 64 137

1040 Q&T 205 (400) 779 (113) 593 (86) 19 48 262

Q&T 425 (800) 758 (110) 552 (80) 21 54 241

Q&T 650 (1200) 634 (92) 434 (63) 29 65 192

Normalized 900 (1650) 590 (86) 374 (54) 28 55 170

Annealed 790 (1450) 519 (75) 353 (51) 30 57 149

1050 Q&T* 205 (400) 1120 (163) 807 (117) 9 27 514

Q&T* 425 (800) 1090 (158) 793 (115) 13 36 444

Q&T* 650 (1200) 717 (104) 538 (78) 28 65 235

Normalized 900 (1650) 748 (108) 427 (62) 20 39 217

Annealed 790 (1450) 636 (92) 365 (53) 24 40 187

1060 Q&T 425 (800) 1080 (156) 765 (111) 14 41 311

Q&T 540 (1000) 965 (140) 669 (97) 17 45 277

Q&T 650 (1200) 800 (116) 524 (76) 23 54 229

Normalized 900 (1650) 776 (112) 421 (61) 18 37 229

Annealed 790 (1450) 626 (91) 372 (54) 22 38 179

1095 Q&T 315 (600) 1260 (183) 813 (118) 10 30 375

Q&T 425 (800) 1210 (176) 772 (112) 12 32 363

Q&T 540 (1000) 1090 (158) 676 (98) 15 37 321

Q&T 650 (1200) 896 (130) 552 (80) 21 47 269

Normalized 900 (1650) 1010 (147) 500 (72) 9 13 293

Annealed 790 (1450) 658 (95) 380 (55) 13 21 192

1141 Q&T 315 (600) 1460 (212) 1280 (186) 9 32 415

Q&T 540 (1000) 896 (130) 765 (111) 18 57 262

(Continued)



Table A–21 (Continued)

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. In all cases, data were obtained from specimens of diameter 0.505 in, machined from 1-in rounds, and of gauge length 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 8 Tensile Yield Temperature Strength Strength, Elongation, Reduction Brinell

AISI No. Treatment °C (°F) MPa (kpsi) MPa (kpsi) % in Area, % Hardness

4130 Q&T* 205 (400) 1630 (236) 1460 (212) 10 41 467

Q&T* 315 (600) 1500 (217) 1380 (200) 11 43 435

Q&T* 425 (800) 1280 (186) 1190 (173) 13 49 380

Q&T* 540 (1000) 1030 (150) 910 (132) 17 57 315

Q&T* 650 (1200) 814 (118) 703 (102) 22 64 245

Normalized 870 (1600) 670 (97) 436 (63) 25 59 197

Annealed 865 (1585) 560 (81) 361 (52) 28 56 156

4140 Q&T 205 (400) 1770 (257) 1640 (238) 8 38 510

Q&T 315 (600) 1550 (225) 1430 (208) 9 43 445

Q&T 425 (800) 1250 (181) 1140 (165) 13 49 370

Q&T 540 (1000) 951 (138) 834 (121) 18 58 285

Q&T 650 (1200) 758 (110) 655 (95) 22 63 230

Normalized 870 (1600) 1020 (148) 655 (95) 18 47 302

Annealed 815 (1500) 655 (95) 417 (61) 26 57 197

4340 Q&T 315 (600) 1720 (250) 1590 (230) 10 40 486

Q&T 425 (800) 1470 (213) 1360 (198) 10 44 430

Q&T 540 (1000) 1170 (170) 1080 (156) 13 51 360

Q&T 650 (1200) 965 (140) 855 (124) 19 60 280

*Water-quenched


1051

Strength (Tensile)

Yield

Ultim

ate Fracture,

Coeffi cient Strain

S

y , S

u , S

f , S

0 , Strength,

FractureN

umber

Material

Condition M

Pa (kpsi)

MPa (k

psi) M

Pa (kpsi)

MPa (k

psi) Ex

ponent m

Strain !f

1018 Steel

Annealed

220 (32.0) 341 (49.5)

628 (91.1) † 620 (90.0)

0.25 1.05

1144 Steel

Annealed

358 (52.0) 646 (93.7)

898 (130) † 992 (144)

0.14 0.49

1212 Steel

HR

193 (28.0)

424 (61.5) 729 (106) †

758 (110) 0.24

0.85

1045 Steel

Q&

T 600°F

1520 (220) 1580 (230)

2380 (345) 1880 (273) †

0.041 0.81

4142 Steel

Q&

T 600°F

1720 (250) 1930 (280)

2340 (340) 1760 (255) †

0.048 0.43

303 Stainless

Annealed

241 (35.0) 601 (87.3)

1520 (221) † 1410 (205)

0.51 1.16

steel

304 Stainless

Annealed

276 (40.0) 568 (82.4)

1600 (233) † 1270 (185)

0.45 1.67

steel

2011 A

luminum

T

6 169 (24.5)

324 (47.0) 325 (47.2) †

620 (90) 0.28

0.10

alloy

2024 A

luminum

T

4 296 (43.0)

446 (64.8) 533 (77.3) †

689 (100) 0.15

0.18

alloy

7075 A

luminum

T

6 542 (78.6)

593 (86.0) 706 (102) †

882 (128) 0.13

0.18

alloy

*Values from

one or two heats and believed to be attainable using proper purchase specifi cations. T

he fracture strain may vary as m

uch as 100 percent.†D

erived value.

Table A–2

2

Results of T

ensile Tests of Som

e Metals*

Source: J. Datsko, “Solid M

aterials,” chap. 32 in Joseph E. Shigley, C

harles R. M

ischke, and Thom

as H. B

rown, Jr.

(eds.-in-chief), Standard Handbook of M

achine Design, 3rd ed., M

cGraw

-Hill, N

ew Y

ork, 2004, pp. 32.49–32.52.

bud98209_appa_1011-1066.indd Page 1051 02/12/13 1:21 PM user-f-w-198 bud98209_appa_1011-1066.indd Page 1051 02/12/13 1:21 PM user-f-w-198 /204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles /204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles

1052

True

Fatigue

Tensile

Strain

Strength

Fatigue Fatigue

Fatigue

Hard-

Strength Reduction

at M

odulus of Coeffi cient

Strength D

uctility D

uctility

Orienta-

Description

ness S

ut in A

rea Fracture

Elasticity E S

9f Ex

ponent Coeffi cient

Exponent

Grade (a)

tion (e) (f)

HB

MPa

ksi

%

Ef

GPa

10

6 psi M

Pa k

si b

E9F c

A538A

(b) L

ST

A

405 1515

220 67

1.10 185

27 1655

240 2

0.065 0.30

20.62

A538B

(b) L

ST

A

460 1860

270 56

0.82 185

27 2135

310 2

0.071 0.80

20.71

A538C

(b) L

ST

A

480 2000

290 55

0.81 180

26 2240

325 2

0.07 0.60

20.75

AM

-350 (c) L

H

R, A

1315 191

52 0.74

195 28

2800 406

20.14

0.33 2

0.84

AM

-350 (c) L

C

D

496 1905

276 20

0.23 180

26 2690

390 2

0.102 0.10

20.42

Gainex (c)

LT

H

R sheet

530

77 58

0.86 200

29.2 805

117 2

0.07 0.86

20.65

Gainex (c)

L

HR

sheet

510 74

64 1.02

200 29.2

805 117

20.071

0.86 2

0.68

H-11

L

Ausform

ed 660

2585 375

33 0.40

205 30

3170 460

20.077

0.08 2

0.74

RQ

C-100 (c)

LT

H

R plate

290 940

136 43

0.56 205

30 1240

180 2

0.07 0.66

20.69

RQ

C-100 (c)

L

HR

plate 290

930 135

67 1.02

205 30

1240 180

20.07

0.66 2

0.69

10B62

L

Q&

T

430 1640

238 38

0.89 195

28 1780

258 2

0.067 0.32

20.56

1005-1009 L

T

HR

sheet 90

360 52

73 1.3

205 30

580 84

20.09

0.15 2

0.43

1005-1009 L

T

CD

sheet 125

470 68

66 1.09

205 30

515 75

20.059

0.30 2

0.51

1005-1009 L

C

D sheet

125 415

60 64

1.02 200

29 540

78 2

0.073 0.11

20.41

1005-1009 L

H

R sheet

90 345

50 80

1.6 200

29 640

93 2

0.109 0.10

20.39

1015 L

N

ormalized

80 415

60 68

1.14 205

30 825

120 2

0.11 0.95

20.64

1020 L

H

R plate

108 440

64 62

0.96 205

29.5 895

130 2

0.12 0.41

20.51

1040 L

A

s forged 225

620 90

60 0.93

200 29

1540 223

20.14

0.61 2

0.57

1045 L

Q

&T

225

725 105

65 1.04

200 29

1225 178

20.095

1.00 2

0.66

1045 L

Q

&T

410

1450 210

51 0.72

200 29

1860 270

20.073

0.60 2

0.70

1045 L

Q

&T

390

1345 195

59 0.89

205 30

1585 230

20.074

0.45 2

0.68

1045 L

Q

&T

450

1585 230

55 0.81

205 30

1795 260

20.07

0.35 2

0.69

1045 L

Q

&T

500

1825 265

51 0.71

205 30

2275 330

20.08

0.25 2

0.68

1045 L

Q

&T

595

2240 325

41 0.52

205 30

2725 395

20.081

0.07 2

0.60

1144 L

C

DSR

265

930 135

33 0.51

195 28.5

1000 145

20.08

0.32 2

0.58

Table A–2

3

Mean M

onotonic and Cyclic Stress-Strain Properties of Selected Steels

Source: ASM

Metals R

eference Book, 2nd ed., A

merican Society for M

etals, Metals Park,

Ohio, 1983, p. 217.


1053

1144 L

D

AT

305

1035 150

25 0.29

200 28.8

1585 230

20.09

0.27 2

0.53

1541F L

Q

&T

forging 290

950 138

49 0.68

205 29.9

1275 185

20.076

0.68 2

0.65

1541F L

Q

&T

forging 260

890 129

60 0.93

205 29.9

1275 185

20.071

0.93 2

0.65

4130 L

Q

&T

258

895 130

67 1.12

220 32

1275 185

20.083

0.92 2

0.63

4130 L

Q

&T

365

1425 207

55 0.79

200 29

1695 246

20.081

0.89 2

0.69

4140 L

Q

&T

, DA

T

310 1075

156 60

0.69 200

29.2 1825

265 2

0.08 1.2

20.59

4142 L

D

AT

310

1060 154

29 0.35

200 29

1450 210

20.10

0.22 2

0.51

4142 L

D

AT

335

1250 181

28 0.34

200 28.9

1250 181

20.08

0.06 2

0.62

4142 L

Q

&T

380

1415 205

48 0.66

205 30

1825 265

20.08

0.45 2

0.75

4142 L

Q

&T

and 400

1550 225

47 0.63

200 29

1895 275

20.09

0.50 2

0.75

deform

ed

4142 L

Q

&T

450

1760 255

42 0.54

205 30

2000 290

20.08

0.40 2

0.73

4142 L

Q

&T

and 475

2035 295

20 0.22

200 29

2070 300

20.082

0.20 2

0.77

deform

ed

4142 L

Q

&T

and 450

1930 280

37 0.46

200 29

2105 305

20.09

0.60 2

0.76

deform

ed

4142 L

Q

&T

475

1930 280

35 0.43

205 30

2170 315

20.081

0.09 2

0.61

4142 L

Q

&T

560

2240 325

27 0.31

205 30

2655 385

20.089

0.07 2

0.76

4340 L

H

R, A

243

825 120

43 0.57

195 28

1200 174

20.095

0.45 2

0.54

4340 L

Q

&T

409

1470 213

38 0.48

200 29

2000 290

20.091

0.48 2

0.60

4340 L

Q

&T

350

1240 180

57 0.84

195 28

1655 240

20.076

0.73 2

0.62

5160 L

Q

&T

430

1670 242

42 0.87

195 28

1930 280

20.071

0.40 2

0.57

52100 L

SH

, Q&

T

518 2015

292 11

0.12 205

30 2585

375 2

0.09 0.18

20.56

9262 L

A

260

925 134

14 0.16

205 30

1040 151

20.071

0.16 2

0.47

9262 L

Q

&T

280

1000 145

33 0.41

195 28

1220 177

20.073

0.41 2

0.60

9262 L

Q

&T

410

565 227

32 0.38

200 29

1855 269

20.057

0.38 2

0.65

950C (d)

LT

H

R plate

159 565

82 64

1.03 205

29.6 1170

170 2

0.12 0.95

20.61

950C (d)

L

HR

bar 150

565 82

69 1.19

205 30

970 141

20.11

0.85 2

0.59

950X (d)

L

Plate channel 150

440 64

65 1.06

205 30

625 91

20.075

0.35 2

0.54

950X (d)

L

HR

plate 156

530 77

72 1.24

205 29.5

1005 146

20.10

0.85 2

0.61

950X (d)

L

Plate channel 225

695 101

68 1.15

195 28.2

1055 153

20.08

0.21 2

0.53

Notes: (a) A

ISI/SAE

grade, unless otherwise indicated. (b) A

STM

designation. (c) Proprietary designation. (d) SAE

HSL

A grade. (e) O

rientation of axis of specimen, relative to rolling direction;

L is longitudinal (parallel to rolling direction); L

T is long transverse (perpendicular to rolling direction). (f) ST

A, solution treated and aged; H

R, hot rolled; C

D, cold draw

n; Q&

T, quenched and

tempered; C

DSR

, cold drawn strain relieved; D

AT

, drawn at tem

perature; A, annealed. From

ASM

Metals R

eference Book, 2nd edition, 1983; A

SM International, M

aterials Park, OH

44073-0002; table 217. R

eprinted by permission of A

SM International ®, w

ww

.asminternational.org.


1054

Table A–2

4

Mechanical Properties of T

hree Non-Steel M

etals(a) T

ypical Properties of Gray C

ast Iron[T

he Am

erican Society for Testing and M

aterials (AST

M) num

bering system for gray cast iron is such that the num

bers correspond to the minim

um

tensile strength in kpsi. Thus an A

STM

No. 20 cast iron has a m

inimum

tensile strength of 20 kpsi. Note particularly that the tabulations are typical

of several heats.]

Fatigue

Shear

Stress-

Tensile

Compressive

Modulus

Modulus of

Endurance Brinell

ConcentrationA

STM

Strength Strength

of Rupture Elasticity, M

psi Lim

it* H

ardness Factor

Num

ber S

ut , kpsi

Suc , k

psi S

su , kpsi

Tension†

Torsion S

e , kpsi

HB

Kf

20 22

83 26

9.6–14 3.9–5.6

10 156

1.00

25 26

97 32

11.5–14.8 4.6–6.0

11.5 174

1.05

30 31

109 40

13–16.4 5.2–6.6

14 201

1.10

35 36.5

124 48.5

14.5–17.2 5.8–6.9

16 212

1.15

40 42.5

140 57

16–20 6.4–7.8

18.5 235

1.25

50 52.5

164 73

18.8–22.8 7.2–8.0

21.5 262

1.35

60 62.5

187.5 88.5

20.4–23.5 7.8–8.5

24.5 302

1.50

*Polished or machined specim

ens.†T

he modulus of elasticity of cast iron in com

pression corresponds closely to the upper value in the range given for tension and is a more constant value than that for tension.


Useful Tables 1055

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 45

2024 O 76 (11) 186 (27) 90 (13) 22 47

T3 345 (50) 482 (70) 138 (20) 16 120

3003 H12 117 (17) 131 (19) 55 (8) 20 35

H16 165 (24) 179 (26) 65 (9.5) 14 47

3004 H34 186 (27) 234 (34) 103 (15) 12 63

H38 234 (34) 276 (40) 110 (16) 6 77

5052 H32 186 (27) 234 (34) 117 (17) 18 62

H36 234 (34) 269 (39) 124 (18) 10 74

Cast:

319.0* T6 165 (24) 248 (36) 69 (10) 2.0 80

333.0† T5 172 (25) 234 (34) 83 (12) 1.0 100

T6 207 (30) 289 (42) 103 (15) 1.5 105

335.0* T6 172 (25) 241 (35) 62 (9) 3.0 80

T7 248 (36) 262 (38) 62 (9) 0.5 85

*Sand casting.†Permanent-mold casting.

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 specifi cations. The values given for fatigue strength correspond to 50(107) cycles of completely reversed stress. Alluminum alloys do not have an endurance limit. Yield strengths were obtained by the 0.2 percent offset method.]

(c) Mechanical Properties of Some Titanium Alloys

Yield, Sy Strength Elongation Hardness (0.2% offset) Tensile, Sut in 2 in, (Brinell orTitanium Alloy Condition MPa (kpsi) MPa (kpsi) % Rockwell)

Ti-35A† Annealed 210 (30) 275 (40) 30 135 HB

Ti-50A† Annealed 310 (45) 380 (55) 25 215 HB

Ti-0.2 Pd Annealed 280 (40) 340 (50) 28 200 HB

Ti-5 Al-2.5 Sn Annealed 760 (110) 790 (115) 16 36 HRC

Ti-8 Al-1 Mo-1 V Annealed 900 (130) 965 (140) 15 39 HRC

Ti-6 Al-6 V-2 Sn Annealed 970 (140) 1030 (150) 14 38 HRC

Ti-6Al-4V Annealed 830 (120) 900 (130) 14 36 HRC

Ti-13 V-11 Cr-3 Al Sol. ! aging 1207 (175) 1276 (185) 8 40 HRC

†Commercially pure alpha titanium.


1058

Tensile

Yield

Strength

Strength Stress Cycles to Failure

Material

Condition BH

N*

kpsi

kpsi

RA*

10

4 4(1

04)

10

5 4(1

05)

10

6 4(1

06)

10

7 10

8

1020

Furnace

58 30

0.63

37

34 30

28 25

cooled

1030

Air-cooled

135 80

45 0.62

51

47 42

38 38

38

1035

Norm

al 132

72 35

0.54

44

40 37

34 33

33

WQ

T

209 103

87 0.65

80

72 65

60 57

57 57

1040

Forged 195

92 53

0.23

40 47

33 33

1045

HR

, N

107

63 0.49

80 70

56 47

47 47

47

1050

N, A

C

164 92

47 0.40

50 48

46 40

38 34

34

WQ

T

1200 196

97 70

0.58

60 57

52 50

50 50

50

.56 MN

N

193

98 47

0.42 61

55 51

47 43

41 41

41

WQ

T

277 111

84 0.57

94 81

73 62

57 55

55 55

1200

1060

As R

ec. 67 R

b 134

65 0.20

65 60

55 50

48 48

48

1095

162

84 33

0.37 50

43 40

34 31

30 30

30

OQ

T

227 115

65 0.40

77 68

64 57

56 56

56 56

1200

10120

224

117 59

0.12

60 56

51 50

50 50

OQ

T

369 180

130 0.15

102

95 91

91 91

91

860

*BH

N 5

Brinell hardness num

ber; RA

5 fractional reduction in area.

Table A–2

7

Finite Life Fatigue Strengths of Selected Plain C

arbon Steels Source: C

ompiled from

Table 4 in H. J. G

rover, S. A. G

ordon, and L. R

. Jackson,

Fatigue of Metals and Structures, B

ureau of Naval W

eapons Docum

ent NAV

WE

PS 00-25-534, 1960.


Useful Tables 1061

Head Type

Nominal Square Regular Hexagonal Heavy Hexagonal Structural HexagonalSize, in W H W H Rmin W H Rmin W H Rmin

14 3

8 1164 7

16 1164 0.01

516 1

2 1364 1

2 732 0.01

38 9

16 14 9

16 14 0.01

716 5

8 1964 5

8 1964 0.01

12 3

4 2164 3

4 1132 0.01 7

8 1132 0.01 7

8 516 0.009

58 15

16 2764 15

16 2764 0.02 1 1

16 2764 0.02 1 1

16 2564 0.021

34 11

8 12 11

8 12 0.02 11

4 12 0.02 11

4 1532 0.021

1 112 21

32 112 43

64 0.03 158 43

64 0.03 158 39

64 0.062

118 111

16 34 111

16 34 0.03 113

16 34 0.03 113

16 1116 0.062

114 17

8 2732 17

8 2732 0.03 2 27

32 0.03 2 2532 0.062

138 2 1

16 2932 2 1

16 2932 0.03 2 3

16 2932 0.03 3 3

16 2732 0.062

112 21

4 1 214 1 0.03 23

8 1 0.03 238 15

16 0.062

NominalSize, mm

M5 8 3.58 8 3.58 0.2

M6 10 4.38 0.3

M8 13 5.68 0.4

M10 16 6.85 0.4

M12 18 7.95 0.6 21 7.95 0.6

M14 21 9.25 0.6 24 9.25 0.6

M16 24 10.75 0.6 27 10.75 0.6 27 10.75 0.6

M20 30 13.40 0.8 34 13.40 0.8 34 13.40 0.8

M24 36 15.90 0.8 41 15.90 0.8 41 15.90 1.0

M30 46 19.75 1.0 50 19.75 1.0 50 19.75 1.2

M36 55 23.55 1.0 60 23.55 1.0 60 23.55 1.5

Table A–29

Dimensions of Square and Hexagonal Bolts

H

R

W



Table A–30

Dimensions of Hexagonal Cap Screws and Heavy Hexagonal Screws (W 5 Width across Flats; H 5 Height of Head; See Figure in Table A–29)

Minimum Type of ScrewNominal Fillet Cap Heavy HeightSize, in Radius W W H

14 0.015 7

16 532

516 0.015 1

2 1364

38 0.015 9

16 1564

716 0.015 5

8 932

12 0.015 3

4 78 5

16

58 0.020 15

16 1 116 25

64

34 0.020 11

8 114 15

32

78 0.040 1 5

16 1 716 35

64

1 0.060 112 11

8 3964

114 0.060 17

8 2 2532

138 0.060 2 1

16 2 316 27

32

112 0.060 21

4 238 15

16

NominalSize, mm

M5 0.2 8 3.65

M6 0.3 10 4.15

M8 0.4 13 5.50

M10 0.4 16 6.63

M12 0.6 18 21 7.76

M14 0.6 21 24 9.09

M16 0.6 24 27 10.32

M20 0.8 30 34 12.88

M24 0.8 36 41 15.44

M30 1.0 46 50 19.48

M36 1.0 55 60 23.38


Useful Tables 1063

Table A–31

Dimensions of Hexagonal Nuts

Height HNominal Width Regular Thick orSize, in W Hexagonal Slotted JAM

14

716

732

932

532

516

12

1764

2164

316

38

916

2164

1332

732

716

1116

38

2964

14

12

34

716

916

516

916

78

3164

3964

516

58

1516

3564

2332

38

34 11

8 4164

1316

2764

78 1 5

16 34

2932

3164

1 112

5564 1 35

64

118 111

16 3132 1 5

32 3964

114 17

8 1 116 11

4 2332

138 2 1

16 11164 13

8 2532

112 21

4 1 932 11

2 2732

NominalSize, mm

M5 8 4.7 5.1 2.7

M6 10 5.2 5.7 3.2

M8 13 6.8 7.5 4.0

M10 16 8.4 9.3 5.0

M12 18 10.8 12.0 6.0

M14 21 12.8 14.1 7.0

M16 24 14.8 16.4 8.0

M20 30 18.0 20.3 10.0

M24 36 21.5 23.9 12.0

M30 46 25.6 28.6 15.0

M36 55 31.0 34.7 18.0


1064

Table A–32

Basic Dimensions of American Standard Plain Washers (All Dimensions in Inches)

Fastener Washer DiameterSize Size ID OD Thickness

#6 0.138 0.156 0.375 0.049

#8 0.164 0.188 0.438 0.049

#10 0.190 0.219 0.500 0.049

#12 0.216 0.250 0.562 0.065

14 N 0.250 0.281 0.625 0.065

14 W 0.250 0.312 0.734 0.065

516 N 0.312 0.344 0.688 0.065

516 W 0.312 0.375 0.875 0.083

38 N 0.375 0.406 0.812 0.065

38 W 0.375 0.438 1.000 0.083

716 N 0.438 0.469 0.922 0.065

716 W 0.438 0.500 1.250 0.083

12 N 0.500 0.531 1.062 0.095

12 W 0.500 0.562 1.375 0.109

916 N 0.562 0.594 1.156 0.095

916 W 0.562 0.625 1.469 0.109

58 N 0.625 0.656 1.312 0.095

58 W 0.625 0.688 1.750 0.134

34 N 0.750 0.812 1.469 0.134

34 W 0.750 0.812 2.000 0.148

78 N 0.875 0.938 1.750 0.134

78 W 0.875 0.938 2.250 0.165

1 N 1.000 1.062 2.000 0.134

1 W 1.000 1.062 2.500 0.165

118 N 1.125 1.250 2.250 0.134

118 W 1.125 1.250 2.750 0.165

114 N 1.250 1.375 2.500 0.165

114 W 1.250 1.375 3.000 0.165

138 N 1.375 1.500 2.750 0.165

138 W 1.375 1.500 3.250 0.180

112 N 1.500 1.625 3.000 0.165

112 W 1.500 1.625 3.500 0.180

158 1.625 1.750 3.750 0.180

134 1.750 1.875 4.000 0.180

178 1.875 2.000 4.250 0.180

2 2.000 2.125 4.500 0.180

214 2.250 2.375 4.750 0.220

212 2.500 2.625 5.000 0.238

234 2.750 2.875 5.250 0.259

3 3.000 3.125 5.500 0.284

N 5 narrow; W 5 wide; use W when not specifi ed.


Useful Tables 1065

Table A–33

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 2.30

1.6 R 1.95 5.00 0.70 10 R 10.85 28.00 2.80

1.6 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 2.80

2 R 2.50 6.00 0.90 12 R 13.30 34.00 3.50

2 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 2.80

2.5 R 3.00 8.00 0.90 14 R 15.25 39.00 3.50

2.5 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 3.50

3 R 3.50 10.00 1.20 16 R 17.25 44.00 4.00

3 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 4.00

3.5 R 4.00 10.00 1.40 20 R 21.80 50.00 4.60

3.5 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 4.60

4 R 4.70 12.00 1.40 24 R 25.60 56.00 5.10

4 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 5.10

5 R 5.50 15.00 1.75 30 R 32.40 72.00 5.60

5 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 5.60

6 R 6.65 18.80 1.75 36 R 38.30 90.00 6.40

6 W 6.65 25.40 2.30 36 W 38.30 110.00 8.50

8 N 8.90 18.80 2.30

8 R 8.90 25.40 2.30

8 W 8.90 32.00 2.80

N 5 narrow; R 5 regular; W 5 wide.*Same as screw or bolt size.


Design of Machine Elements Databook - ME14 -...

Documents

Transcript of Design of Machine Elements Databook - ME14 -...