Design of Machine Elements. Databook

Transcription

1 Design of Machine Elements Databook

2 Fatigue Failure Strain-Life method: Mansion-Coffin relation between fatigue life and total strain (Strain-Life method): Δε 2 = σ F E (2N)b + ε F (2N) c, Δε := total strain amplitude, N := number of cycles, E := Young's modulus σ F := Fatigue strength coefficient, b := Fatigue strength exponent ε F := Fatigue ductility coefficient, c := Fatigue ductility exponent For values of the coefficients and the exponents for a few materials see Table A-2. Stress-Life method: Fatigue strength (S f ): The fatigue strength reduces with number of cycles. After about 0 6 cycles, for steel specimen it becomes constant and equal to the endurance limit. At 0 cycles, the fatigue strength is given by: S f = f.s ut. The fatigue strength fraction f is given in Fig-6-8 (below) for the ultimate strength ( S ut ) between 490 MPa and 400 MPa. For S ut < 0 MPa, f=0.9. Fatigue strength fraction f at 0 cycles as a function of ultimate strength: Figure 6 8 Fatigue strength fraction, f, of S ut at 0 cycles for S e S9 e 0.S ut at 0 6 cycles. f S ut, kpsi The ultimate strength is given in kpsi unit. While using the figure, convert to MPa using kpsi = 6.89 MPa. Between 0 and 0 6 cycles: S f = an b,where a = ( fs ut )2 and b = S e log fs ut. S e

3 Endurance limit ( S e ) for the R. R. Moore s rotating beam specimen (shown below): 0.S ut S ut 400 MPa S e = 00 MPa S ut > 400 MPa For actual mechanical component endurance limit ( S e ) at the critical location is different (less) from that of the R. R. Moore rotary specimen ( S e ). The endurance limit for the actual component is given by the following Marin equation: S e = k a k b k c k d k e k f S e, where k a = surface condition modification factor k b = size modification factor k c = load modification factor k d = temperature modification factor k e = reliability factor k f = miscellaneous-effect modification factor. Surface Condition Modification Factor: b k a = as ut a and b are given in table 6-2(below) Figure 6 9 Test-specimen geometry for the R. R. Moore rotating-beam machine. The bending moment is uniform, M Fa, over the curved length and at the highest-stressed section at the mid-point of the beam. F a 0.0 in F in 9 8 in R. F a F Table 6 2 Parameters for Marin Surface Modification Factor, Eq. (6 9) Factor a Exponent Surface Finish S ut, kpsi S ut, MPa b Ground Machined or cold-drawn Hot-rolled As-forged Size Modification Factor: From C. J. Noll and C. Lipson, Allowable Working Stresses, Society for Experimental Stress Analysis, vol., no. 2, 946 p. 29. Reproduced by O.J. Horger (ed.) Metals Engineering Design ASME Handbook, McGraw-Hill, New York. Copyright 9 by The McGraw-Hill Companies, Inc. Reprinted by permission. For bending and torsion: k b =.24 d d mm.d 0. < d 24 mm For axial loading: k b = (however a loading factor k c 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 d e is used for calculating the size factor k b, in place of d. For a few non-rotating specimen they are given below.

4 Equivalent diameter and 9% stress area for structural shapes undergoing non-rotating bending Table 6 A 0.9s Areas of Common Nonrotating Structural Shapes d A 0.9s d 2 d e 0.0d b 2 A 0.9s 0.0hb h d e 0.808hb 2 a b 2 2 t f A 0.9s e 0.0at f 0.0ba t f. 0.02a axis - axis 2-2 a 2 x b t f 2 A 0.9s e 0.0ab 0.02xa 0.t f (b 2 x) axis - axis 2-2. Load Modification factor k c : k c = bending 0.8 axial 0.9 torsion 4. Temperature Modification factor k d : We will take this factor to be unity, i.e., k d =.. Reliability factor k e : Given in table 6- (below) Table 6 Reliability Factors k e Corresponding to 8 Percent Standard Deviation of the Endurance Limit Reliability, % Transformation Variate z a Reliability Factor k e Miscellaneous-effect Modification factor k f : We will take this factor to be unity, i.e., k f =.

5 Notch sensitivity factors q and q shear 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 (K t or K ts ) and the notch sensitivity factor (q or q shear ) are: For bending and axial loading: K f = + q(k t ) For Shear: K fs = + q shear (K ts ) For the notch sensitivity factor q and q shear see figures 6-20 and 6-2 below. Figure 6 20 Notch-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 0.-in (4-mm) ordinate. (From George Sines and J. L. Waisman (eds.), Metal Fatigue, McGraw-Hill, New York. Copyright 969 by The McGraw-Hill Companies, Inc. Reprinted by permission.) Notch sensitivity q S ut = 200 kpsi (.4 GPa) (.0) (0.) (0.4) Notch radius r, mm 0.4 Steels Alum. alloy Notch radius r, in Figure 6 2 Notch-sensitivity curves for materials in reversed torsion. For larger notch radii, use the values of q shear corresponding to r 0. in (4 mm). Notch sensitivity q shear S ut = 200 kpsi 0 (.0) 00 (0.) 60 (0.4) (.4 GPa) Notch radius r, mm Steels Alum. alloy Notch radius r, in The notch radius is given in inches. Use the conversion in = 2.4 mm to interpret the results. 2 2

6 Bolted Joints Threads: Figure 8 Terminology 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 4 chamfer 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 := (D maj )major diameter or largest diameter; Root Crest d p := (D p ) pitch diameter between d and d r ; d r := (D min )minor or smallest diameter, p := pitch (distance along the thread axis between adjacent thread forms) A t := tensile-stress area (area of an unthreaded rod with same tensile strength as the threaded rod) Metric Thread Specification: For example, in the specification M X 2., M - denotes metric thread, nominal major diameter is mm and pitch is 2.mm. See Table 8- for thread diameters and areas (next page). Some important quantities for bolted joints (fasteners): Washer thickness: t (from Table A-2 or A-) Nut thickness (bolted joints): Thread angle 2α H (Table A-) Grip length: l := The length between bolt and nut faces (Fig a) l := h + t 2 / 2 (for t 2 d) h + d (for t 2 > d) Tensile-stress area: A t (Table 8-) For Cap-Screws (Fig b) l + H ( Fig a) Fastener (bolt) length: L> (Table A- for standard values) l +.d ( Fig b) 2d + 6mm, (L 2mm, d 48mm) Threaded length: L T = 2d + 2mm, (2< L 200mm) 2d + 2mm, (L > 200mm) Tensile-stress (thread) area: A t (Table 8-); CS area of unthreaded part: A d = πd 2 / 4 Unthreaded length in grip: l d = L L T ; Threaded length in grip: l t = l l d A Fastener (bolt) Stiffness: k b = d A t E (by considering springs in series - show) A d l t + A t l d

7 Table 8 Diameters and Areas of Coarse-Pitch and Fine- Pitch Metric Threads.* Nominal Coarse-Pitch Series Fine-Pitch Series Major Tensile- Minor- Tensile- Minor- Diameter Pitch Stress Diameter Pitch Stress Diameter d p Area A t Area A r p Area A t Area A r mm mm mm 2 mm 2 mm mm 2 mm *The equations and data used to develop this table have been obtained from ANSI B.-94 and B The minor diameter was found from the equation d r d p, and the pitch diameter from d p d p. The mean of the pitch diameter and the minor diameter was used to compute the tensile-stress area.

8 Useful tables from Appendix.

9 Table A Often preferred. Physical Constants of Materials Modulus of Modulus of Elasticity E Rigidity G Poisson s Unit Weight w Material Mpsi GPa Mpsi GPa Ratio N lbf/in lbf/ft kn/m Aluminum (all alloys) Beryllium copper Brass Carbon steel Cast iron (gray) Copper Douglas fir Glass Inconel Lead Magnesium Molybdenum Monel metal Nickel silver Nickel steel Phosphor bronze Stainless steel (8-8) Titanium alloys Table A A Selection of International Tolerance Grades 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 B See also BSI 400. Basic Tolerance Grades Sizes IT6 IT IT8 IT9 IT0 IT

10 Table A 2 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 B See also BSI 400. Basic Upper-Deviation Letter Lower-Deviation Letter Sizes c d f g h k n p s u

11 Design'of'Machine'Elements' Databook'

12 04 Mechanical Engineering Design Table A 2 Conversion Factors A to Convert Input X to Output Y Using the Formula Y AX* Multiply Input By Factor To Get Output Multiply Input By Factor To Get Output X A Y X A Y British thermal 0 joule, J unit, Btu Btu/second, Btu/s.0 kilowatt, kw calorie 4.9 joule, J centimeter of. kilopascal, kpa mercury (0 C) centipoise, cp 0.00 pascal-second, Pa? s degree (angle) 0.04 radian, rad foot, ft 0.0 meter, m foot 2, ft meter 2, m 2 foot/minute, 0.00 meter/second, m/s ft/min foot-pound, ft? lbf. joule, J foot-pound/. watt, W second, ft? lbf/s foot/second, ft/s 0.0 meter/second, m/s gallon (U.S.), gal.8 liter, L horsepower, hp 0.46 kilowatt, kw inch, in meter, m inch, in 2.4 millimeter, mm inch 2, in 2 millimeter 2, mm 2 inch of mercury.86 kilopascal, kpa (2 F) kilopound, kip 4.4 kilonewton, kn kilopound/inch 2, 6.89 megapascal, MPa kpsi (ksi) (N/mm 2 ) mass, lbf? s 2 /in kilogram, kg mile, mi.60 kilometer, km mile/hour, mi/h.6 kilometer/hour, km/h mile/hour, mi/h 0.44 meter/second, m/s moment of inertia, kilogram-meter 2, lbm? ft 2 kg? m 2 moment of inertia, 29 kilogram-millimeter 2, lbm? in 2 kg? mm 2 moment of section 4.6 centimeter 4, cm 4 (second moment of area), in 4 ounce-force, oz 0.28 newton, N ounce-mass 0.0 kilogram, kg pound, lbf 4.4 newton, N pound-foot, lbf? ft.6 newton-meter, N? m pound/foot 2, lbf/ft pascal, Pa pound-inch, lbf? in 0. joule, J pound-inch, lbf? in 0. newton-meter, N? m pound/inch, lbf/in newton/meter, N/m pound/inch 2, psi 6.89 kilopascal, kpa (lbf/in 2 ) pound-mass, lbm 0.44 kilogram, kg pound-mass/ 0.44 kilogram/second, second, lbm/s kg/s quart (U.S. liquid), qt 946 milliliter, ml section modulus, in.4 centimeter, cm slug 4.6 kilogram, kg ton (short 2000 lbm) 90 kilogram, kg yard, yd 0.94 meter, m *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.

13 Table A Often preferred. Physical Constants of Materials Modulus of Modulus of Elasticity E Rigidity G Poisson s Unit Weight w Material Mpsi GPa Mpsi GPa Ratio N lbf/in lbf/ft kn/m Aluminum (all alloys) Beryllium copper Brass Carbon steel Cast iron (gray) Copper Douglas fir Glass Inconel Lead Magnesium Molybdenum Monel metal Nickel silver Nickel steel Phosphor bronze Stainless steel (8-8) Titanium alloys Table A A Selection of International Tolerance Grades 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 B See also BSI 400. Basic Tolerance Grades Sizes IT6 IT IT8 IT9 IT0 IT

14 Table A 2 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 B See also BSI 400. Basic Upper-Deviation Letter Lower-Deviation Letter Sizes c d f g h k n p s u

15 Useful Tables 04 Table A 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.) Fraction of Inches, 2,, 2, 8, 2,, 4,, 8,, 2,, 9 8,, 4, 8,, 4, 2, 4, 2, 2 4, 2 2, 2 4,, 4, 2, 4, 4, 4 4, 4 2, 4 4,, 4, 2, 4, 6, 6 2,, 2, 8, 8 2, 9, 9 2, 0, 0 2,, 2, 2, 2 2,, 2, 4, 4 2,, 2,, 2,, 2, 8, 8 2, 9, 9 2, 20 Decimal Inches 0.00, 0.02, 0.0, 0.020, 0.02, 0.02, 0.040, 0.0, 0.06, 0.08, 0.0, 0.2, 0., 0.20, 0.24, 0.0, 0.40, 0.0, 0.60, 0.80,.00,.20,.40,.60,.80, 2.0, 2.4, 2.6, 2.8,.0,.2,.4,.6,.8, 4.0, 4.2, 4.4, 4.6, 4.8,.0,.2,.4,.6,.8, 6.0,.0,., 8., 9.0, 9., 0.0, 0.,.0,., 2.0, 2.,.0,., 4.0, 4.,.0,.,.0,.,.0,., 8.0, 8., 9.0, 9., 20 Millimeters 0.0, 0.06, 0.08, 0.0, 0.2, 0., 0.20, 0.2, 0.0, 0.40, 0.0, 0.60, 0.0, 0.80, 0.90,.0,.,.2,.4,.,.6,.8, 2.0, 2.2, 2., 2.8,.0,., 4.0, 4.,.0,., 6.0, 6.,.0, 8.0, 9.0, 0,, 2, 4,, 8, 20, 22, 2, 28, 0, 2,, 40, 4, 0, 60, 80, 00, 20, 40, 0, 80, 200, 20, 00 st choice, R:,.6, 2., 4, 6., 0 2d choice, R0:.2, 2,.,, 8 Renard Numbers* d choice, R20:.2,.4,.8, 2.24, 2.8,., 4.,.6,., 9 4th choice, R40:.06,.8,.2,.,.,.9, 2.2, 2.6, 2.6,,.,., 4.2, 4.,., 6, 6.,., 8., 9. *May be multiplied or divided by powers of 0.

16 04 Mechanical Engineering Design Table A Charts of Theoretical Stress-Concentration Factors K* t Figure A.0 Bar in tension or simple compression with a transverse hole. s 0 FyA, where A (w 2 d)t and t is the thickness F w d F K t d/w Figure A 2.0 d Rectangular bar with a transverse hole in bending. s 0 McyI, where I (w 2 d)h y K t.8 d/h = ` M w h M d/w Figure A Notched rectangular bar in tension or simple compression. s 0 FyA, where A dt and t is the thickness K t.8 w/d = F w r d F r/d

17 Useful Tables 0 Table A Charts of Theoretical Stress-Concentration Factors K* t (Continued) Figure A 4 Notched rectangular bar in bending. s 0 McyI, where c dy2, I td y2, and t is the thickness w/d = `. M w r d M K t r/d Figure A.0 Rectangular filleted bar in tension or simple compression. s 0 FyA, where A dt and t is the thickness D/d =.0 F D r d F K t r/d Figure A 6.0 Rectangular filleted bar in bending. s 0 McyI, where c dy2, I td y2, t is the thickness M D r d M K t.8.4 D/d = r/d (Continued) *Factors from R. E. Peterson, Design Factors for Stress Concentration, Machine Design, vol. 2, no. 2, February 9, p. 9; no., March 9, p., no., May 9, p. 9; no. 6, June 9, p. ; no., July 9, p.. Reprinted with permission from Machine Design, a Penton Media Inc. publication.

18 06 Mechanical Engineering Design Table A Charts of Theoretical Stress-Concentration Factors K* t (Continued) Figure A 2.6 Round shaft with shoulder fillet in tension. s 0 FyA, where A pd 2 y F D r d F K t.8 D/d = r/d Figure A 8.0 Round shaft with shoulder fillet in torsion. t 0 TcyJ, where c dy2 and J pd 4 y T D r d T 2.2 K ts D/d = r/d Figure A 9.0 Round shaft with shoulder fillet in bending. s 0 McyI, where c dy2 and I pd 4 y. 2.6 M D r d M 2.2 K t.8 D/d = r/d

19 Useful Tables 0 Table A Charts of Theoretical Stress-Concentration Factors K* t (Continued) Figure A 0 Round shaft in torsion with transverse hole T D T d B A K.2 ts K ts, A J c = D dd 2 6 (approx) 2.8 K ts, B d/d Figure A Round shaft in bending with a transverse hole. s 0 My[(pD y2) 2 (dd 2 y6)], approximately M D d M K t d/d Figure A 2 Plate loaded in tension by a pin through a hole. s 0 FyA, where A (w 2 d)t. When clearance exists, increase K t to 0 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., no., March 940, p. A-.) t 9 h h/w = 0. d w F/2 F/2 K t F h/w = 0.0 h/w $ d/w (Continued) *Factors from R. E. Peterson, Design Factors for Stress Concentration, Machine Design, vol. 2, no. 2, February 9, p. 9; no., March 9, p., no., May 9, p. 9; no. 6, June 9, p. ; no., July 9, p.. Reprinted with permission from Machine Design, a Penton Media Inc. publication.

20 08 Mechanical Engineering Design Table A Charts of Theoretical Stress-Concentration Factors K* t (Continued) Figure A Grooved round bar in tension. s 0 FyA, where A pd 2 y F D r d F 2.2 K t.8.02 D/d = r/d Figure A 4 Grooved round bar in bending. s 0 McyI, where c dy2 and I pd 4 y M D r d M K t.8.02 D/d = r/d Figure A 2.6 r Grooved round bar in torsion. t 0 TcyJ, where c dy2 and J pd 4 y T D d T.8 K ts D/d = r/d *Factors from R. E. Peterson, Design Factors for Stress Concentration, Machine Design, vol. 2, no. 2, February 9, p. 9; no., March 9, p., no., May 9, p. 9; no. 6, June 9, p. ; no., July 9, p.. Reprinted with permission from Machine Design, a Penton Media Inc. publication.

21 Useful Tables 09 Table A Charts of Theoretical Stress-Concentration Factors K* t (Continued) Figure A Round shaft with flat-bottom groove in bending and/or tension. s 0 4F pd 2M 2 pd Source: W. D. Pilkey and D. F. Pilkey, Peterson s Stress- Concentration Factors, rd ed. John Wiley & Sons, Hoboken, NJ, 2008, p K t F M D r a r d t F M r t a/t (Continued)

22 040 Mechanical Engineering Design Table A Charts of Theoretical Stress-Concentration Factors K* t (Continued) Figure A Round shaft with flat-bottom groove in torsion. t 0 T pd Source: W. D. Pilkey and D. F. Pilkey, Peterson s Stress- Concentration Factors, rd ed. John Wiley & Sons, Hoboken, NJ, 2008, p T D r a r d t T r t K ts a/t

23 Useful Tables 04 Table A Approximate Stress- Concentration Factor K t of a Round Bar or Tube with a Transverse Round Hole and Loaded in Bending Source: R. E. Peterson, Stress- Concentration Factors, Wiley, New York, 94, pp. 46, 2. M D a d M The nominal bending stress is s 0 MyZ net where Z net is a reduced value of the section modulus and is defined by Z net pa 2D (D4 2 d 4 ) Values of A are listed in the table. Use d 0 for a solid bar d/d a/d A K t A K t A K t (Continued)

24 042 Mechanical Engineering Design Table A (Continued) Approximate Stress-Concentration Factors K ts 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, 94, pp. 48, 244. T D a d T The maximum stress occurs on the inside of the hole, slightly below the shaft surface. The nominal shear stress is t 0 TDy2J net, where J net is a reduced value of the second polar moment of area and is defined by Values of A are listed in the table. Use d 0 for a solid bar. J net pa(d4 2 d 4 ) 2 d/d a/d A K ts A K ts A K ts A K ts A K ts

25 048 Mechanical Engineering Design 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 8 to 2 mm ( 4 to 4 in). These strengths are suitable for use with the design factor defined in Sec. 0, provided the materials conform to ASTM A6 or A68 requirements or are required in the purchase specifications. Remember that a numbering system is not a specification.] Source: 986 SAE Handbook, p 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 G HR 00 (4) 0 (24) 0 86 CD 0 (48) 280 (4) G HR 20 (4) 80 (26) CD 0 () 00 (44) G00 0 HR 40 (0) 90 (2.) CD 90 (6) 20 (4) 8 40 G HR 400 (8) 220 (2) 2 0 CD 440 () 0 (4) G HR 80 () 20 (0) 2 0 CD 40 (68) 90 () 40 G HR 40 (68) 260 (.) CD 20 (6) 440 () 2 49 G00 0 HR 00 (2) 20 (9.) CD 0 (80) 460 (6) 2 G HR 20 (6) 290 (42) CD 90 (8) 490 () 2 0 G HR 0 (82) 0 (4) 40 CD 60 (9) 0 () 2 9 G HR 620 (90) 40 (49.) 9 CD 690 (00) 80 (84) G HR 680 (98) 0 (4) G HR 0 (2) 420 (6.) G HR 80 (20) 460 (66)

26 Useful Tables 049 Table A 2 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 0.0 in, machined from -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, M e t a l s Park, Ohio, Tensile Yield Temperature Strength Strength, Elongation, Reduction Brinell AISI No. Treatment C ( F) MPa (kpsi) MPa (kpsi) % in Area, % Hardness 00 Q&T* 20 (400) 848 (2) 8 (94) 4 49 Q&T* (600) 800 () 62 (90) 9 40 Q&T* 42 (800) (06) 9 (84) Q&T* 40 (000) 669 (9) () Q&T* 60 (200) 86 (8) 44 () Normalized 92 (00) 2 () 4 (0) Annealed 80 (00) 40 (62) (46) 040 Q&T 20 (400) 9 () 9 (86) Q&T 42 (800) 8 (0) 2 (80) Q&T 60 (200) (92) 44 (6) Normalized 900 (0) 90 (86) 4 (4) 28 0 Annealed 90 (40) 9 () () Q&T* 20 (400) 20 () 80 () Q&T* 42 (800) 090 (8) 9 () Q&T* 60 (200) (04) 8 (8) Normalized 900 (0) 48 (08) 42 (62) Annealed 90 (40) 66 (92) 6 () Q&T 42 (800) 080 (6) 6 () 4 4 Q&T 40 (000) 96 (40) 669 (9) 4 2 Q&T 60 (200) 800 () 24 (6) Normalized 900 (0) 6 (2) 42 (6) Annealed 90 (40) 626 (9) 2 (4) Q&T (600) 260 (8) 8 (8) 0 0 Q&T 42 (800) 20 (6) 2 (2) Q&T 40 (000) 090 (8) 66 (98) 2 Q&T 60 (200) 896 (0) 2 (80) Normalized 900 (0) 00 (4) 00 (2) 9 29 Annealed 90 (40) 68 (9) 80 () Q&T (600) 460 (22) 280 (86) Q&T 40 (000) 896 (0) 6 () (Continued)

27 00 Mechanical Engineering Design Table A 2 (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 0.0 in, machined from -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, Tensile Yield Temperature Strength Strength, Elongation, Reduction Brinell AISI No. Treatment C ( F) MPa (kpsi) MPa (kpsi) % in Area, % Hardness 40 Q&T* 20 (400) 0 (26) 460 (22) Q&T* (600) 00 (2) 80 (200) 4 4 Q&T* 42 (800) 280 (86) 90 () Q&T* 40 (000) 00 (0) 90 (2) Q&T* 60 (200) 84 (8) 0 (02) Normalized 80 (00) 60 (9) 46 (6) Annealed 86 (8) 60 (8) 6 (2) Q&T 20 (400) 0 (2) 40 (28) Q&T (600) 0 (22) 40 (208) Q&T 42 (800) 20 (8) 40 () 49 0 Q&T 40 (000) 9 (8) 84 (2) Q&T 60 (200) 8 (0) 6 (9) Normalized 80 (00) 020 (48) 6 (9) Annealed 8 (00) 6 (9) 4 (6) Q&T (600) 20 (20) 90 (20) *Water-quenched Q&T 42 (800) 40 (2) 60 (98) Q&T 40 (000) 0 (0) 080 (6) 60 Q&T 60 (200) 96 (40) 8 (24)

28 0 Table A 22 Results of Tensile Tests of Some Metals* Source: J. Datsko, Solid Materials, chap. 2 in Joseph E. Shigley, Charles R. Mischke, and Thomas H. Brown, Jr. (eds.-in-chief), Standard Handbook of Machine Design, rd ed., McGraw-Hill, New York, 2004, pp Strength (Tensile) Yield Ultimate Fracture, Coefficient Strain S y, S u, S f, S 0, Strength, Fracture Number Material Condition MPa (kpsi) MPa (kpsi) MPa (kpsi) MPa (kpsi) Exponent m Strain f 08 Steel Annealed 220 (2.0) 4 (49.) 628 (9.) 620 (90.0) Steel Annealed 8 (2.0) 6 (9.) 898 (0) 992 (44) Steel HR 9 (28.0) 424 (6.) 29 (06) 8 (0) Steel Q&T 600 F 20 (220) 80 (20) 280 (4) 880 (2) Steel Q&T 600 F 20 (20) 90 (280) 240 (40) 60 (2) Stainless Annealed 24 (.0) 60 (8.) 20 (22) 40 (20) 0.. steel 04 Stainless Annealed 26 (40.0) 68 (82.4) 00 (2) 20 (8) steel 20 Aluminum T6 9 (24.) 24 (4.0) 2 (4.2) 620 (90) alloy 2024 Aluminum T4 296 (4.0) 446 (.8) (.) 689 (00) alloy 0 Aluminum T6 42 (8.6) 9 (86.0) 06 (02) 882 (28) alloy *Values from one or two heats and believed to be attainable using proper purchase specifications. The fracture strain may vary as much as 00 percent. Derived value.

29 02 Table A 2 Mean Monotonic and Cyclic Stress-Strain Properties of Selected Steels Source: ASM Metals Reference Book, 2nd ed., American Society for Metals, Metals Park, Ohio, 98, p. 2. True Fatigue Tensile Strain Strength Fatigue Fatigue Fatigue Hard- Strength Reduction at Modulus of Coefficient Strength Ductility Ductility Orienta- Description ness S ut in Area Fracture Elasticity E S9 f Exponent Coefficient Exponent Grade (a) tion (e) (f) HB MPa ksi % E f GPa 0 6 psi MPa ksi b E9 F c A8A (b) L STA A8B (b) L STA A8C (b) L STA AM-0 (c) L HR, A AM-0 (c) L CD Gainex (c) LT HR sheet Gainex (c) L HR sheet H- L Ausformed RQC-00 (c) LT HR plate RQC-00 (c) L HR plate B62 L Q&T LT HR sheet LT CD sheet L CD sheet L HR sheet L Normalized L HR plate L As forged L Q&T L Q&T L Q&T L Q&T L Q&T L Q&T L CDSR

30 0 44 L DAT F L Q&T forging F L Q&T forging L Q&T L Q&T L Q&T, DAT L DAT L DAT L Q&T L Q&T and deformed 442 L Q&T L Q&T and deformed 442 L Q&T and deformed 442 L Q&T L Q&T L HR, A L Q&T L Q&T L Q&T L SH, Q&T L A L Q&T L Q&T C (d) LT HR plate C (d) L HR bar X (d) L Plate channel X (d) L HR plate X (d) L Plate channel Notes: (a) AISI/SAE grade, unless otherwise indicated. (b) ASTM designation. (c) Proprietary designation. (d) SAE HSLA grade. (e) Orientation of axis of specimen, relative to rolling direction; L is longitudinal (parallel to rolling direction); LT is long transverse (perpendicular to rolling direction). (f) STA, solution treated and aged; HR, hot rolled; CD, cold drawn; Q&T, quenched and tempered; CDSR, cold drawn strain relieved; DAT, drawn at temperature; A, annealed. From ASM Metals Reference Book, 2nd edition, 98; ASM International, Materials Park, OH ; table 2. Reprinted by permission of ASM International,

31 04 Table A 24 Mechanical Properties of Three Non-Steel Metals (a) Typical Properties of Gray Cast Iron [The American Society for Testing and Materials (ASTM) numbering system for gray cast iron is such that the numbers correspond to the minimum tensile strength in kpsi. Thus an ASTM No. 20 cast iron has a minimum 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 Concentration ASTM Strength Strength of Rupture Elasticity, Mpsi Limit* Hardness Factor Number S ut, kpsi S uc, kpsi S su, kpsi Tension Torsion S e, kpsi H B K f *Polished or machined specimens. The modulus of elasticity of cast iron in compression corresponds closely to the upper value in the range given for tension and is a more constant value than that for tension.

32 Useful Tables 0 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 2 in; similar properties can be obtained by using proper purchase specifications. The values given for fatigue strength correspond to 0(0 ) cycles of completely reversed stress. Alluminum alloys do not have an endurance limit. Yield strengths were obtained by the 0.2 percent offset method.] Aluminum Strength Elongation Brinell Association Yield, S y, Tensile, S u, Fatigue, S f, in 2 in, Hardness Number Temper MPa (kpsi) MPa (kpsi) MPa (kpsi) % H B Wrought: Cast: 20 O 0 (0) 9 (26) 90 () O 6 () 86 (2) 90 () 22 4 T 4 (0) 482 (0) 8 (20) H2 () (9) (8) 20 H (24) 9 (26) 6 (9.) H4 86 (2) 24 (4) 0 () 2 6 H8 24 (4) 26 (40) 0 () 6 02 H2 86 (2) 24 (4) () 8 62 H6 24 (4) 269 (9) 24 (8) * T6 (24) 248 (6) 69 (0) T 2 (2) 24 (4) 8 (2).0 00 T6 20 (0) 289 (42) 0 (). 0.0* T6 2 (2) 24 () 62 (9).0 80 *Sand casting. Permanent-mold casting. T 248 (6) 262 (8) 62 (9) 0. 8 (c) Mechanical Properties of Some Titanium Alloys Yield, S y Strength Elongation Hardness (0.2% offset) Tensile, S ut in 2 in, (Brinell or Titanium Alloy Condition MPa (kpsi) MPa (kpsi) % Rockwell) Ti-A Annealed 20 (0) 2 (40) 0 HB Ti-0A Annealed 0 (4) 80 () 2 2 HB Ti-0.2 Pd Annealed 280 (40) 40 (0) HB Ti- Al-2. Sn Annealed 60 (0) 90 () 6 HRC Ti-8 Al- Mo- V Annealed 900 (0) 96 (40) 9 HRC Ti-6 Al-6 V-2 Sn Annealed 90 (40) 00 (0) 4 8 HRC Ti-6Al-4V Annealed 80 (20) 900 (0) 4 6 HRC Ti- V- Cr- Al Sol. aging 20 () 26 (8) 8 40 HRC Commercially pure alpha titanium.

33 08 Table A 2 Finite Life Fatigue Strengths of Selected Plain Carbon Steels Source: Compiled from Table 4 in H. J. Grover, S. A. Gordon, and L. R. Jackson, Fatigue of Metals and Structures, Bureau of Naval Weapons Document NAVWEPS , 960. Tensile Yield Strength Strength Stress Cycles to Failure Material Condition BHN* kpsi kpsi RA* 0 4 4(0 4 ) 0 4(0 ) 0 6 4(0 6 ) Furnace cooled 00 Air-cooled Normal WQT Forged HR, N N, AC WQT MN N WQT As Rec. 6 Rb OQT OQT *BHN Brinell hardness number; RA fractional reduction in area.

34 Useful Tables 06 Table A 29 Dimensions of Square and Hexagonal Bolts H W R Head Type Nominal Square Regular Hexagonal Heavy Hexagonal Structural Hexagonal Size, in W H W H R min W H R min W H R min Nominal Size, mm M M M M M M M M M M M

35 062 Mechanical Engineering Design Table A 0 Dimensions of Hexagonal Cap Screws and Heavy Hexagonal Screws (W Width across Flats; H Height of Head; See Figure in Table A 29) Minimum Type of Screw Nominal Fillet Cap Heavy Height Size, in Radius W W H Nominal Size, mm M M M M M M M M M M M

36 Useful Tables 06 Table A Dimensions of Hexagonal Nuts Height H Nominal Width Regular Thick or Size, in W Hexagonal Slotted JAM Nominal Size, mm M M M M M M M M M M M

37 Table A 2 Basic Dimensions of American Standard Plain Washers (All Dimensions in Inches) 0 Fastener Washer Diameter Size Size ID OD Thickness # # # # N W N W N W N W N W N W N W N W N W N W N W N W N W N W N narrow; W wide; use W when not specified.

38 Useful Tables 06 Table A Dimensions of Metric Plain Washers (All Dimensions in Millimeters) Washer Minimum Maximum Maximum Washer Minimum Maximum Maximum Size* ID OD Thickness Size* ID OD Thickness.6 N N R R W W N N R R W W N N R R W W N N R R W W N N R R W W N N R R W W N N R R W W N N R R W W N R W N narrow; R regular; W wide. *Same as screw or bolt size.