REFERENCES 1. Datsko, J., Material Properties and Manufacturing Process, John Wiley and Sons, New York, 1966. 2. Datsko, J. Material in Design and Manufacturing, Malloy, Ann Arbor, Michigan, 1977. 3. ASM Metals Handbook, American Society for Metals, Metals Park, Ohio, 1988. 4. Machine Design, 1981 Materials Reference Issue, Penton/IPC, Cleveland, Ohio, Vol. 53, No. 6, March 19, 1981. 5. Lingaiah, K., Machine Design Data Handbook, Vol. II (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986. 6. Lingaiah, K., and B. R. Narayana Iyengar, Machine Design Data Handbook, Vol. I (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986. 7. Technical Editor Speaks, the International Nickel Company, New York, 1943. 8. Shigley, J. E., Mechanical Engineering Design, Metric Edition, McGraw-Hill Book Company, New York, 1986. 9. Deutschman, A. D., W. J. Michels, and C. E. Wilson, Machine Design—Theory and Practice, Macmillan Pub- lishing Company, New York, 1975. 10. Juvinall, R. C., Fundaments of Machine Components Design, John Wiley and Sons, New York, 1983. 11. Lingaiah, K., and B. R. Narayana Iyengar, Machine Design Data Handbook, Engineering College Co-opera- tive Society, Bangalore, India, 1962. 12. Lingaiah, K., Machine Design Data Handbook, Vol. II (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1981 and 1984. 13. Lingaiah, K., and B. R. Narayana Iyengar, Machine Design Data Handbook, Vol. I (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1983. 14. SAE Handbook, 1981. 15. Lessels, J. M., Strength and Resistance of Metals, John Wiley and Sons, New York, 1954. 16. Siegel, M. J., V. L. Maleev, and J. B. Hartman, Mechanical Design of Machines, 4th edition, International Textbook Company, Scranton, Pennsylvania, 1965. 17. Black, P. H., and O. Eugene Adams, Jr., Machine Design, McGraw-Hill Book Company, New York, 1963. 18. Niemann, G., Maschinenelemente, Springer-Verlag, Berlin, Erster Band, 1963. 19. Faires, V. M., Design of Machine Elements, 4th edition, Macmillan Company, New York, 1965. 20. Nortman, C. A., E. S. Ault, and I. F. Zarobsky, Fundamentals of Machine Design, Macmillan Company, New York, 1951. 21. Spotts, M. F., Design of Machine Elements, 5th edition, Prentice-Hall of India Private Ltd., New Delhi, 1978. 22. Vallance, A., and V. L. Doughtie, Design of Machine Members, McGraw-Hill Book Company, New York, 1951. 23. Decker, K H., Maschinenelemente, Gestalting und Bereching, Carl Hanser Verlag, Munich, Germany, 1971. 24. Decker, K H., and Kabus, B. K., Maschinenelemente-Aufgaben, Carl Hanser Verlag, Munich, Germany, 1970. 25. ISO and BIS standards. 26. Metals Handbook, Desk Edition, ASM International, Materials Park, Ohio, 1985 (formerly the American Society for Metals, Metals Park, Ohio, 1985). 27. Edwards, Jr., K. S., and R. B. McKee, Fundamentals of Mechanical Components Design, McGraw-Hill Book Company, New York, 1991. 28. Shigley, J. E., and C. R. Mischke, Standard Handbook of Machine Design, 2nd edition, McGraw-Hill Book Company, New York, 1996. 29. Structural Alloys Handbook, Metals and Ceramics Information Center, Battelle Memorial Institute, Colum- bus, Ohio, 1985. 30. Wood Handbook and U. S. Forest Products Laboratory. 31. SAE J1099, Technical Report of Fatigue Properties. 32. Ashton, J. C., I. Halpin, and P. H. Petit, Primer on Composite Materials-Analysis, Technomic Publishing Co., Inc., 750 Summer Street, Stanford, Conn 06901, 1969. 33. Baumeister, T., E. A. Avallone, and T. Baumeister III, Mark’s Standard Handbook for Mechanical Engineers, 8th edition, McGraw-Hill Book Company, New York, 1978. 34. Norton, Refractories, 3rd edition, Green and Stewart, ASTM Standards on Refractory Materials Handbook (Committee C-8). PROPERTIES OF ENGINEERING MATERIALS 1.81 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. PROPERTIES OF ENGINEERING MATERIALS BIBLIOGRAPHY Black, P. H., and O. Eugene Adams, Jr., Machine Design, McGraw-Hill Book Company, New York, 1983. Decker, K H., Maschinenelemente, Gestalting und Bereching, Carl Hanser Verlag, Munich, Germany, 1971. Decker, K H., and Kabus, B. K., Maschinenelemente-Aufgaben, Carl Hanser Verlag, Munich, Germany, 1970. Deutschman, A. D., W. J. Michels, and C. E. Wilson, Machine Design—Theory and Practice, Macmillan Publish- ing Company, New York, 1975. Faires, V. M., Design of Machine Elements, 4th edition, McGraw-Hill Book Company, New York, 1965. Honger, O. S. (ed.), (ASME) Handbook for Metals Properties, McGraw-Hill Book Company, New York, 1954. ISO standards. Juvinall, R. C., Fundaments of Machine Components Design, John Wiley and Sons, New York, 1983. Lessels, J. M., Strength and Resistance of Metals, John Wiley and Sons, New York, 1954. Lingaiah, K., and B. R. Narayana Iyengar, Machine Design Data Handbook, Engineering College Co-operative Society, Bangalore, India, 1962. Mark’s Standard Handbook for Mechanical Engineers, 8th edition, McGraw-Hill Book Company, New York, 1978. Niemann, G., Maschinenelemente, Springer-Verlag, Berlin, Erster Band, 1963. Norman, C. A., E. S. Ault, and I. E. Zarobsky, Fundamentals of Machine Design, McGraw-Hill Book Company, New York, 1951. SAE Handbook, 1981. Shigley, J. E., Mechanical Engineering Design, Metric Edition, McGraw-Hill Book Company, New York, 1986. Siegel, M. J., V. L. Maleev, and J. B. Hartman, Mechanical Design of Machines, 4th edition, International Text- book Company, Scranton, Pennsylvania, 1965. Spotts, M. F., Design of Machine Elements, 5th edition, Prentice-Hall of India Private Ltd., New Delhi, 1978. Vallance, A., and V. L. Doughtie, Design of Machine Members, McGraw-Hill Book Company, New York, 1951. 1.82 CHAPTER ONE Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. PROPERTIES OF ENGINEERING MATERIALS CHAPTER 2 STATIC STRESSES IN MACHINE ELEMENTS SYMBOLS 3;4;5 A area of cross section, m 2 (in 2 ) A w area of web, m 2 (in 2 ) a constant in Rankine’s formula b radius of area of contact, m (in) bandwidth of contact, m (in) width of beam, m (in) c distance from neutral surface to extreme fiber, m (in) D diameter of shaft, m (in) C 1 constant in straight-line formula F load, kN (lbf) F c compressive force, kN (lbf) F t tensile force, kN (lbf) F shear force, kN (lbf) F cr crushing load, kN (lbf) e deformation, total, m (in) eccentricity, as of force equilibrium, m (in) unit volume change or volumetric strain e t thermal expansion, m (in) E modulus of elasticity, direct (tension or compression), GPa (Mpsi) E c combined or equivalent modulus of elasticity in case of composite bars, GPa (Mpsi) G modulus of rigidity, GPa (Mpsi) M b bending moment, N m (lbf ft) M t torque, torsional moment, N m (lbf ft) i number of turns I moment of inertia, area, m 4 or cm 4 (in 4 ) mass moment of inertia, N s 2 m (lbf s 2 ft) I xx , I yy moment of inertia of cross-sectional area around the respective principal axes, m 4 or cm 4 (in 4 ) J moment of inertia, polar, m 4 or cm 4 (in 4 ) k radius of gyration, m (in) k 0 polar radius of gyration, m (in) k t torsional spring constant, J/rad or N m/rad (lbf in/rad) 2.1 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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Source: MACHINE DESIGN DATABOOK l length, m (in) l 0 length of rod, m (in) L length, m (in) n speed, rpm (revolutions per minute) coefficient of end condition n 0 speed, rps (revolutions per second) l, m, n direction cosines (also with subscripts) P power, kW (hp) pitch or threads per meter T temperature, 8C(8F) ÁT temperature difference, 8C(8F) r radius of the rod or bar subjected to torsion, m (in) (Fig. 2-18) q shear flow Q first moment of the cross-sectional area outside the section at which the shear flow is required v velocity, m/s (ft/min or fpm) V volume, m 3 (in 3 ) shear force, kN (lbf) ÁV volume change, m 3 (in 3 ) Z section modulus, m 3 (in 3 ) deformation of contact surfaces, m (in) coefficient of linear expansion, m/m/K or m/m/8 C ðin=in=8F) shearing strain, rad/rad xy , yz , zx shearing strain components in xyz coordinates, rad/rad deformation or elongation, m (in) " strain, mm/m (min/in) " T thermal strain, mm/m (min/in) " x , " y , " z strains in x, y, and z directions, mm/m (min/in) angular distortion, rad angle, deg angular twist, rad (deg) angle made by normal to plane nn with the x axis, deg bulk modulus of elasticity, GPa (Mpsi) Poisson’s ratio radius of curvature, m (in) stress, direct or normal, tensile or compressive (also with subscripts), MPa (psi) b bearing pressure, MPa (psi) bending stress, MPa (psi) c compressive stress (also with subscripts), MPa (psi) hydrostatic pressure, MPa (psi) sc compressive strength, MPa (psi) cr stress at crushing load, MPa (psi) e elastic limit, MPa (psi) s strength, MPa (psi) t tensile stress, MPa (psi) st tensile strength, MPa (psi) x , y , z stress in x, y, and z directions, MPa (psi) 1 , 2 , 3 principal stresses, MPa (psi) y yield stress, MPa (psi) sy yield strength, MPa (psi) u ultimate stress, MPa (psi) su ultimate strength, MPa (psi) 0 principal direct stress, MPa (psi) 00 normal stress which will produce the maximum strain, MPa (psi) 2.2 CHAPTER TWO Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. STATIC STRESSES IN MACHINE ELEMENTS normal stress on the plane nn at any angle to x axis, MPa (psi) shear stress (also with subscripts), MPa (psi) s shear strength, MPa (psi) xy , yz , zx shear stresses in xy, yz, and zx planes, respectively, MPa (psi) shear stress on the plane at any angle with x axis, MPa (psi) ! angular speed, rad/s Other factors in performance or in special aspects are included from time to time in this chapter and, being applicable only in their immediate context, are not given at this stage. (Note: and with initial subscript s designates strength properties of material used in the design which will be used and observed throughout this Machine Design Data Handbook.) SIMPLE STRESS AND STRAIN The stress in simple tension or compression (Fig. 2-1a, 2-1b) The total elongation of a member of length l (Fig. 2-2a) FIGURE 2-1 Strain, deformation per unit length t ¼ F t A ; c ¼ F c A ð2-1Þ ¼ Fl AE ð2-2Þ " ¼ l ¼ E ð2-3Þ Particular Formula STATIC STRESSES IN MACHINE ELEMENTS 2.3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. STATIC STRESSES IN MACHINE ELEMENTS FIGURE 2-2 Young’s modulus or modulus of elasticity The shear stress (Fig. 2-1c) Shear deformation due to torsion (Fig. 2-18) Shear strain (Fig. 2-2c) The shear modulus or modulus of rigidity from Eq. (2-7) Poisson’s ratio Poisson’s ratio may be computed with sufficient accuracy from the relation The shear or torsional modulus or modulus of rigidity is also obtained from Eq. (2-10) The bearing stress (Fig. 2-3c) STRESSES Unidirectional stress (Fig. 2-4) The normal stress on the plane at any angle with x axis E ¼ " ð2-4Þ ¼ F A ð2-5Þ ¼ L G ð2-6Þ ¼ G ¼ a l ð2-7Þ G ¼ ð2-8Þ ¼ lateral strain/axial strain ¼ " t " a ð2-9Þ ¼ E 2G À 1 ð2-10Þ G ¼ E 2ð1 þÞ ð2-11Þ b ¼ F bd 2 ð2-12Þ ¼ x cos 2 ð2-13Þ Particular Formula 2.4 CHAPTER TWO Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. STATIC STRESSES IN MACHINE ELEMENTS FIGURE 2-3 Knuckle joint for round rods. FIGURE 2-4 A bar in uniaxial tension. 3;4 The shear stress on the plane at any angle with x axis Principal stresses Angles at which principal stresses act Maximum shear stress Angles at which maximum shear stresses act ¼ x 2 sin 2 ð2-14Þ 1 ¼ x and 2 ¼ 0 ð2-15Þ 1 ¼ 08 and 2 ¼ 908 ð2-16Þ max ¼ x 2 ð2-17Þ 1 ¼ 458 and 2 ¼ 1358 ð2-18Þ Particular Formula STATIC STRESSES IN MACHINE ELEMENTS 2.5 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. STATIC STRESSES IN MACHINE ELEMENTS The normal stress on the plane at an angle þð=2Þ (Fig. 2-4d) The shear stress on the plane at an angle þð=2Þ (Fig. 2-4d) Therefore from Eqs. (2-13) and (2-19), (2-14), and (2-20) PURE SHEAR (FIG. 2-5) The normal stress on the plane at any angle The shear stress on the plane at any angle The principal stress Angles at which principal stresses act Maximum shear stresses Angles at which maximum shear stress act FIGURE 2-5 An element in pure shear. BIAXIAL STRESSES (FIG. 2-6) The normal stress on the plane at any angle The shear stress on the plane at any angle The shear stress at ¼ 0 The shear stress at ¼ 458 0 ¼ x cos 2 þ 2 ¼ x cos 2 ð2-19Þ 0 ¼ x sin þ 2 cos þ 2 ¼ 1 2 x sin 2 ð2-20Þ ¼ 0 and ¼À 0 ð2-21Þ ¼ xy sin 2 ð2-22Þ ¼ xy cos 2 ð2-23Þ 1 ¼ xy and 2 ¼À xy ð2-24Þ 1 ¼ 458 and 2 ¼ 1358 ð2-25Þ max ¼ xy ¼ ð2-26Þ 1 ¼ 0 and 2 ¼ 908 ð2-27Þ FIGURE 2-6 An element in biaxial tension. ¼ x þ y 2 þ x À y 2 cos 2 ð2-28Þ ¼ x À y 2 sin 2 ð2-29Þ ¼ 0 ð2-30Þ max ¼ð x À y Þ=2 ð2-31Þ Particular Formula 2.6 CHAPTER TWO Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. STATIC STRESSES IN MACHINE ELEMENTS BIAXIAL STRESSES COMBINED WITH SHEAR (FIG. 2-7) The normal stress on the plane at any angle The shear stress in the plane at any angle The maximum principal stress The minimum principal stress Angles at which principal stresses act Maximum shear stress Angles at which maximum shear stress acts The equation for the inclination of the principal planes in terms of the principal stress (Fig. 2-8) x σ y σ y σ x τ xy σ θ τ θ τ xy τ xy τ xy σ x y θ θ n n (a) (b) σ y σ x τ xy τ xy θ θ FIGURE 2-7 An element in plane state of stress. ¼ x þ y 2 þ x À y 2 cos 2 þ xy sin 2 ð2-32Þ ¼ x À y 2 sin 2 À xy cos 2 ð2-33Þ 1 ¼ x þ y 2 þ x À y 2 2 þ 2 xy 1=2 ð2-34Þ 2 ¼ x þ y 2 À x À y 2 2 þ 2 xy 1=2 ð2-35Þ 1;2 ¼ 1 2 arctan 2 xy x À y ð2-36Þ where 1 and 2 are 1808 apart max ¼ x À y 2 2 þ 2 xy 1=2 ¼ 1 À 2 2 ð2-37Þ ¼ 1 2 arctan x À y 2 xy ð2-38Þ tan ¼ 1 À x xy ð2-39Þ FIGURE 2-8 Particular Formula STATIC STRESSES IN MACHINE ELEMENTS 2.7 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. STATIC STRESSES IN MACHINE ELEMENTS MOHR’S CIRCLE Biaxial field combined with shear (Fig. 2-9) Maximum principal stress 1 Minimum principal stress 2 Maximum shear stress max FIGURE 2-9 Mohr’s circle for biaxial state of stress. TRIAXIAL STRESS (Figs. 2-10 and 2-11) The normal stress on a plane nn, whose direction cosines are l, m, n The shear stress on a plane normal nn, whose direc- tion cosines are l, m, n The principal stresses The cubic equation for general state of stress in three dimensions from the theory of elasticity The maximum shear stresses on planes parallel to x, y, and z which are designated as 1 is the abscissa of point F 2 is the abscissa of point G max is the ordinate of point H ¼ x l 2 þ y m 2 þ z n 2 ð2-40Þ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 x l 2 þ 2 y m 2 þ 2 z n 2 q ð2-41Þ 1;2;3 ¼ x ; y ; z ð2-42Þ 3 Àð x þ y þ z Þ 2 þð x y þ y z þ z x À 2 xy À 2 yz À 2 zx Þ Àð x y z þ 2 xy yz zx À x 2 zy À y 2 zx À z 2 xy Þ ¼ 0 ð2-43Þ The three roots of this cubic equation give the magni- tude of the principal stresses 1 , 2 , and 3 . ð max Þ 1 ¼ 2 À 3 2 ; ð max Þ 2 ¼ 1 À 3 2 ; ð max Þ 3 ¼ 1 À 2 2 ð2-44Þ Particular Formula 2.8 CHAPTER TWO Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. 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STATIC STRESSES IN MACHINE ELEMENTS [...]... 1:046F 2 4 2 2 1 À 1 1 À 2 þ E1 E2 d1 d2 d2 À d1 31=3 2 7 7 7 5 2- 114Þ Refer to Fig 2- 28a " a ¼ 0: 721 Fd1 2 2 1 À 1 1 À 2 þ E1 E2 #1=3 2- 115Þ 31=3 2 F cðmaxÞ ¼ 0:9186 7 2 2 4 2 1 À 1 1 À 2 2 5 þ d1 E1 E2 2- 116Þ where d ¼ d1 (Fig 2- 27c) Contact of cylindrical surfaces Cylindrical surface on cylindrical surface, axis parallel (Fig 2- 27a and Fig 2- 28b) The width of band of contact 2 ... stress, 2l D G 32l Mt D4 D at circumference ðD4 À D4 Þ 1 2 16D1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D2 þ D2 1 2 ¼ 0:354 D2 þ D2 1 2 8 B h A b b2 h 16 a 1 4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 þ h2 2l D1 G 32l Mt ðD4 À D4 Þ G 1 2 at outer circumference 16ðb2 þ h2 Þl Mt G b3 h3 ðb2 þ h2 Þl G bh2 h>b 2b2 h 9 at A b a h>b rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 þ h2 12 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0 :28 9 b2 þ h2 mðb2 þ h2 Þl Mt... Þh 3ð2b þ b0 Þ ð6b2 þ 6bb0 þ b2 Þh2 0 12 3b þ b0 Þ rffiffiffiffi I A D4 64 D 2 D3 32 D 4 2b þ b0 h 2 D2 4 2 ðD À D2 Þ 2 4 1 Section modulus, Z ¼ I=c Radiusffiffiffiffiffiffiffiffiffi p of gyration, k ¼ I=A qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D2 þ D2 1 2 ðD4 À D4 Þ 2 64 1 ¼ ðR4 À R4 Þ 2 4 1 D1 ¼ R1 2 ab ba3 64 a 2 ba2 32 a 4 bh 2 bh3 36 ÁÁÁ bh2 24 0 :23 6h ðD4 À D4 Þ 1 2 32D1 4 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 þ R2 1 2 Downloaded from... 0.041 0.0 52 28 52 4184 689 20 67 1378 20 67 827 690 385–600 100–300 20 0–300 120 100 0.053–0.066 1 723 –3445 25 0–500 0.066 124 0 180 0. 126 24 80 360 0.0 92 0.090 0.091 0.095 lb/in3 Density, 20 0 1 72 138–413 2. 8 4 24 1–689 310 414 72. 5 85 100 415 GPa 29 25 20 –60 0.4 0.6 35–100 45 60 10.5 12. 3 14.5 60 Mpsi Modulis of elasticity, Eg 30 3.7 45–50 45–50 54 6.5 81–90 81–90 1.5 6.4 2. 2 2. 8 5.0 2. 7 11.5 4.0 2. 8 lin/in8F... STRESSES IN MACHINE ELEMENTS 2. 22 CHAPTER TWO Particular Formula Cylindrical surface in contact with a flat surface (Fig 2- 27c): The width of band of contact " Fd1 2b ¼ 1:6 L 2 2 1 À 1 1 À 2 þ E1 E2 #1 =2 2- 121 Þ 31 =2 F 1 ¼ 0:7986 2- 122 Þ 2 2 7 4Ld1 1 À 1 1 À 2 5 þ E1 E2 2 The maximum compressive stress cðmaxÞ where d ¼ d1 (Fig 2- 27c) Deformation of cylinder between two plates Ád1 ¼ 4F L 2 1 À... a ¼ 0: 721 6F 4 2 2 1 À 1 1 À 2 þ E1 E2 d1 d2 d1 þ d2 2 2 1 À 1 1 À 2 þ E1 E2 1 1 À d1 d2 2- 110Þ 31=3 2 7 7 7 5 2- 111Þ 31=3 7 7 7 5 2- 1 12 2 The maximum compressive stress cðmaxÞ 31=3 1 1 2 À 6 7 d1 d2 7 ¼ 0:9186F 7 6 2 2 4 1 À 1 1 À 2 2 5 þ E1 E2 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 20 04 The McGraw-Hill... of band of contact 2 6F 6 2b ¼ 1:66 4L 2 2 1 À 1 1 À 2 þ E1 E2 1 1 þ d1 d2 2 The maximum compressive stress Cylindrical surface in contact with a circular groove (Fig 2- 27b) The width of band of contact cðmaxÞ 31 =2 7 7 7 5 31 =2 1 1 þ 6F 7 d1 d2 7 ¼ 0:7986 6 2 2 7 4L 1 À 1 1 À 2 5 þ E1 E2 2 6F 6 2b ¼ 1:66 4L 2 2 1 À 1 1 À 2 þ E1 E2 1 1 À d1 d2 2 cðmaxÞ Distribution of pressure... Copyright © 20 04 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website 0.4 0.4 0.4 4 0 .2 0.4 5 4 0.5 0.001–0.01 0 .2 0 .2 0.5 0.8 5–10 127 1 02 13 0. 025 –0 .25 5 5–13 20 .5 Â10À3 in 10 .2 10 .2 10 .2 1 02. 0 Â10À3 mm 7.64 2. 43 2. 62 1.11 1.49 1.43–1.75 1.78 3.40 2. 48 2. 43 2. 46 2. 56 g/cm3 3100 4498 5510 27 56 MPa 450 650 800 400 kpsi Tensile strength, st 0 .28 3 0.090... combined with rigidity Refer to Fig 2- 29 For sandwich construction of honeycomb structure Refer to Fig 2- 30 FIGURE 2- 29 Sandwich fabricated panel FIGURE 2- 30 Honeycomb The moment of inertia of sandwich panel, Fig 2- 30 Simplified Eq (2- 124 ) after neglecting powers of h The flexural rigidity 3 Bh Hc þ h 2 þ 2Bh I 2 2 12 H I ¼ BhHc h þ c 2 D ¼ EI 2- 124 Þ 2- 125 Þ 2- 126 Þ where E ¼ modulus of elasticity... composite FIGURE 2- 31 A unit cube foam subject to a tensile load The deflection for a beam panel according to Castigliano’s theorem ¼ FIGURE 2- 32 Phantom load ð ð FIGURE 2- 33 The deflection at midspan (Fig 2- 32) L =2 @U @ ¼ @F @F @U @ ¼ ¼ @W @W 2 Mb dx þ 2EI ð V 2 dx 2GA 2 Mb dx þ 2EI ð V 2 dx 2GA 2- 1 32 W ¼0 2- 133aÞ 5FL3 FL þ 2- 133bÞ 349EI 8GA where W is the phantom load (Fig 2- 32) ¼ Downloaded . 2 2- 32 ¼ x À y 2 sin 2 À xy cos 2 2- 33Þ 1 ¼ x þ y 2 þ x À y 2 2 þ 2 xy 1 =2 2- 34Þ 2 ¼ x þ y 2 À x À y 2 2 þ 2 xy 1 =2 2- 35Þ 1 ;2 ¼ 1 2 arctan 2 xy x À. x cos 2 þ 2 ¼ x cos 2 2- 19Þ 0 ¼ x sin þ 2 cos þ 2 ¼ 1 2 x sin 2 2- 20Þ ¼ 0 and ¼À 0 2- 21Þ ¼ xy sin 2 2- 22 ¼ xy cos 2 2- 23Þ 1 ¼. xy and 2 ¼À xy 2- 24Þ 1 ¼ 458 and 2 ¼ 1358 2- 25Þ max ¼ xy ¼ 2- 26Þ 1 ¼ 0 and 2 ¼ 908 2- 27Þ FIGURE 2- 6 An element in biaxial tension. ¼ x þ y 2 þ x À y 2 cos 2 2- 28Þ ¼ x À