DESIGN OF MACHINE ELEMENTS FOR STRENGTH 5.20 CHAPTER FIVE Particular FIGURE 5-10 The shapes of normal distribution curves for various and constant Formula FIGURE 5-11 The Gaussian (normal) distribution curve Refer to Table 5-8 for area under the standard normal distribution curve The area under normal distribution curve to the right of t (Fig 5-11) Error function or probability integral Btị ẳ Atị 5-107ị where Atị is the area to the left of t The area under the entire normal distribution curve is Atị ỵ Btị and is equal to unity The term BðtÞ can be found from Table 5-8 or by integrating the area under the curve x t2 erfxị ẳ p e dt ð5-108Þ Refer to Table 5-9 for erfðxÞ for various values of x ẳ s ỵ ð5-109Þ The resultant mean of subtracting the means of two populations ẳ s 5-110ị The resultant standard deviation for both subtraction and addition of two standard deviations s and ^ ^ ¼ ^ The resultant mean of adding the means of two populations (Fig 5-12) FIGURE 5-12 Distribution curves for two means of populations qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 þ 2 ^s ^ 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 ð5-111Þ DESIGN OF MACHINE ELEMENTS FOR STRENGTH DESIGN OF MACHINE ELEMENTS FOR STRENGTH 5.21 TABLE 5-7 Standard normal curve ordinates y ¼ pffiffiffiffiffiffi eÀt =2 2p t 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3989 3970 3910 3814 3683 3521 3332 3123 2897 2661 2420 2179 1942 1714 1497 1295 1109 0940 0790 0656 0540 0440 0355 0283 0224 0175 0136 0104 0079 0060 0044 0033 0024 0017 0012 0009 0006 0004 0003 0002 3989 3965 3902 3802 3668 3503 3312 3101 2874 2637 2396 2155 1919 1691 1476 1276 1092 0925 0775 0644 0529 0431 0347 0277 0219 0171 0132 0101 0077 0058 0043 0032 0023 0017 0012 0008 0006 0004 0003 0002 3989 3961 2894 3790 3653 3485 3292 3079 2850 2613 2371 2131 1895 1669 1456 1257 1074 0909 0761 0632 0519 0422 0339 0270 0213 0167 0129 0099 0075 0056 0042 0031 0022 0016 0012 0008 0006 0004 0003 0002 3988 3956 3885 3778 3637 3467 3271 3056 2827 2589 2347 2107 1872 1647 1435 1238 1057 0893 0748 0620 0508 0413 0332 0264 0208 0163 0126 0096 0073 0055 0040 0030 0022 0016 0011 0008 0005 0004 0003 0002 3986 3951 3876 3765 3621 3448 3251 3034 2803 2565 2323 2083 1849 1626 1415 1219 1040 0878 0734 0608 0498 0404 0325 0258 0203 0158 0122 0093 0071 0053 0039 0029 0021 0015 0011 0008 0005 0004 0003 0002 3984 3945 3867 3752 3605 3429 3230 3011 2780 2541 2299 2059 1826 1604 1394 1200 1023 0863 0721 0596 0488 0396 0317 0252 0198 0154 0119 0091 0069 0051 0038 0028 0020 0015 0010 0007 0005 0004 0002 0002 3982 3939 3857 3739 3589 3410 3209 2989 2756 2516 2275 2036 1804 1528 1374 1182 1006 0848 0707 0584 0487 0387 0310 0246 0194 0151 0116 0088 0067 0050 0037 0027 0020 0014 0010 0007 0005 0003 0002 0002 3980 3932 3847 3725 3572 3391 3187 2966 2932 2492 2251 2012 1781 1561 1354 1163 0989 0833 0694 0573 0468 0379 0303 0241 0189 0147 0113 0086 0065 0048 0036 0026 0019 0014 0010 0007 0005 0003 0002 0002 3977 3925 3836 3712 3555 3372 3166 2943 2709 2468 2227 1989 1758 1539 1334 1145 0973 0818 0681 0562 0459 0371 0297 0235 0184 0143 0110 0084 0063 0047 0035 0025 0018 0013 0009 0007 0005 0003 0002 0001 3973 3918 3815 3697 3538 3352 3144 2920 2685 2444 2203 1965 1736 1518 1315 1127 0957 0804 0669 0551 0449 0363 0290 0229 0180 0139 0107 0081 0061 0046 0034 0025 0018 0013 0009 0006 0004 0003 0002 0001 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 DESIGN OF MACHINE ELEMENTS FOR STRENGTH 5.22 CHAPTER FIVE TABLE 5-8 Areas under the standard normal distribution curve Atị ẳ t pffiffiffiffiffiffi eÀt =2 dt 2p t 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 0000 0398 0793 1179 1554 1915 2258 2580 2881 3159 3413 3643 3849 4032 4192 4332 4452 4554 4641 4713 4772 4821 4861 4893 4918 4938 4953 4965 4974 4981 4987 4990 4993 4995 4997 4998 4998 4999 4999 5000 0040 0438 0832 1217 1591 1950 2291 2612 2910 3186 3438 3665 3869 4049 4207 4345 4463 4564 4649 4719 4778 4826 4864 4896 4920 4940 4955 4966 4975 4982 4987 4991 4993 4995 4997 4998 4998 4999 4999 5000 0080 0478 0871 1255 1628 1985 2324 2642 2939 3212 3461 3686 3888 4066 4222 4357 4474 4573 4656 4726 4783 4830 4868 4898 4922 4941 4956 4967 4976 4982 4987 4991 4994 4995 4997 4998 4999 4999 4999 5000 0120 0517 0910 1293 1664 2019 2357 2673 2967 3238 3485 3708 3907 4082 4236 4370 4484 4582 4664 4732 4788 4834 4871 4901 4925 4943 4957 4968 4977 4983 4988 4991 4994 4996 4997 4998 4999 4999 4999 5000 0160 0557 0948 1331 1700 2054 2389 2704 2996 3264 3508 3729 3925 4099 4251 4382 4495 4591 4671 4738 4793 4838 4875 4904 4927 4945 4959 4969 4977 4984 4988 4992 4994 4996 4997 4998 4999 4999 4999 5000 0199 0596 0987 1368 1736 2088 2422 2734 3023 3289 3531 3749 3944 4115 4265 4394 4506 4599 4678 4744 4798 4842 4878 4906 4929 4946 4960 4970 4978 4984 4989 4992 4994 4996 4997 4998 4999 4999 4999 5000 0239 0636 1026 1406 1772 2123 2454 2764 3051 3315 3554 3770 3962 4131 4279 4406 4515 4608 4686 4750 4803 4846 4881 4909 4931 4948 4961 4971 4979 4985 4989 4992 4994 4996 4997 4998 4999 4999 4999 5000 0279 0675 1064 1443 1808 2157 2486 2794 3078 3340 3577 3790 3980 4147 4292 4418 4525 4616 4693 4756 4808 4850 4884 4911 4932 4949 4962 4972 4979 4985 4989 4992 4995 4996 4997 4998 4999 4999 4999 5000 0319 0714 1103 1480 1844 2190 2518 2823 3106 3365 3599 3810 3997 4162 4306 4429 4535 4625 4699 4761 4812 4854 4887 4913 4934 4951 4963 4973 4980 4986 4990 4993 4995 4996 4997 4998 4999 4999 4999 5000 0359 0754 1141 1517 1879 2224 2549 2852 3133 3389 3621 3830 4015 4177 4319 4441 4545 4633 4706 4767 4817 4857 4890 4916 4936 4952 4964 4974 4981 4986 4990 4993 4995 4997 4998 4998 4999 4999 4999 5000 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 DESIGN OF MACHINE ELEMENTS FOR STRENGTH 5.23 DESIGN OF MACHINE ELEMENTS FOR STRENGTH TABLE 5-9 Error function or probability integral erfðxÞ ¼ pffiffiffi p x 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 11246 22270 32863 42839 52050 60386 67780 74210 79691 84270 88021 91031 93401 95229 96611 97635 98379 98909 99279 99532 99702 99814 99886 99931 99959 99976 99987 99992 99996 99998 ðx eÀt dt 01128 12362 23352 33891 43797 52924 61168 68467 74800 80188 84681 88353 91296 93606 95385 96728 97721 98441 98952 99309 99552 99715 99822 99891 99935 99961 99978 99987 99993 99996 02256 13476 24430 34913 44747 53790 61941 69143 75381 80677 85084 88679 91553 93807 95538 96841 97804 98500 98994 99338 99572 99728 99831 99897 99938 99963 99979 99988 99993 99996 03384 14587 25502 35928 45689 54646 62705 69810 75952 81156 85478 88997 91805 94002 95686 96952 97884 98558 99035 99366 99591 99741 99839 99902 99941 99965 99980 99989 99994 99997 04511 15695 26570 36936 46623 55494 63459 70468 76514 81627 85865 89308 92051 94191 95830 97059 97962 98613 99074 99392 99609 99753 99846 99906 99944 99967 99981 99989 99994 99997 05637 16800 27633 37938 47548 56332 64203 71116 77067 82089 86244 89612 92290 94376 95970 97162 98038 98667 99111 99418 99626 99764 99854 99911 99947 99969 99982 99990 99994 99997 06762 17901 28690 38933 48466 57162 64938 71754 77610 82542 86614 89910 92524 94556 96105 97263 98110 98719 99147 99443 99642 99775 99861 99915 99950 99971 99983 99991 99995 99997 07886 18999 29742 39921 49375 57982 65663 72382 78144 82987 86977 90200 92751 94731 96237 97360 98181 98769 99182 99466 99658 99785 99867 99920 99952 99972 99984 99991 99995 99997 09008 20094 30788 40901 50275 58792 66378 73001 78669 83243 87333 90484 92973 94902 96365 97455 98249 98817 99216 99489 99673 99795 99874 99924 99955 99974 99985 99992 99995 99997 10128 21184 31828 41874 51167 59594 67084 73610 79184 83851 87680 90761 93190 95067 96490 97546 98315 98864 99248 99511 99688 99805 99880 99928 99957 99975 99986 99992 99996 99998 The standard variable tR (deviation multiplication factor) in order to determine the probability of failure or the reliability s À À tR ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ s 2 ^ s ỵ ^ ^ The reliability associated with tR R ẳ 0:5 ỵ AtR ị 5-112ị where subscripts s and refer to strength and stress, respectively ð5-113Þ where AðtR Þ is the area under a standard normal distribution curve Refer to Table 5-10 for typical values of R as a function of standardized variable tR 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 DESIGN OF MACHINE ELEMENTS FOR STRENGTH 5.24 CHAPTER FIVE Particular Formula TABLE 5-10 Reliability R as a function of tR Survival rate (R) % tR 50 90.00 95.00 98.00 99.00 99.90 99.99 1.288 1.645 2.050 2.330 3.080 3.700 A safety factor of is taken into account in determining the reliability from Eq (5-113) The fatigue strength reduction factor based on reliability CR ¼ À 0:08ðtR Þ If a factor of safety n0 is to be specified together with reliability, then Eq (5-112) is rewritten to give a new expression for tR s À n0 À n0 tR ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ s ^ 2 ỵ 2 ^s ^ The expression for safety factor n0 from Eq (5-115) n0 ¼ ¼ The best-fitting straight line which fits a set of scattered data points as per linear regression The equations for regression The correlation coefficient ð5-114Þ where tR is also called the deviation multiplication factor (DMF), taken from Table 5-10 À tR s q! 2 ỵ 2 ^s ^ tR ị ^ s y ẳ mx þ b ð5-115Þ ð5-116aÞ ð5-116bÞ ð5-117Þ where m is the slope and b is the intercept on the y axis P P P x y xy n mẳ 5-118aị À P Á2 P x x À n P P ym x 5-118bị bẳ n rẳ msx sy 5-119ị where r lies between and ỵ1 If r is negative, it indicates that the regression line has a negative slope If r ¼ 1, there is a perfect correlation, and if r ¼ 0, there is no correlation 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 DESIGN OF MACHINE ELEMENTS FOR STRENGTH DESIGN OF MACHINE ELEMENTS FOR STRENGTH The equation for frequency or density function according to Weibull f xị ẳ b x0 x À x0 À x0 À 1& b exp À x À x0 À x0 5.25 !' b ð5-120Þ The cumulative distribution function FðxÞ ¼ ðx x0 f ðxÞ dx ¼ À exp À x À x0 À x0 ! b ð5-121Þ Equation (5-121) after simplification ! x b FðxÞ ¼ À exp À ð5-122Þ REFERENCES Maleev, V L., and J B Hartman, Machine Design, International Textbook Company, Scranton, Pennsylvania, 1954 Shigley, J E., and L D Mitchell, Mechanical Engineering Design, McGraw-Hill Book Company, New York, 1983 Faires, V M., Design of Machine Elements, The Macmillan Company, New York, 1965 Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Engineering Co-operative Society, Bangalore, India, Bangalore, India, 1962 Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Vol I (SI and Customary Units), Suma Publishers, Bangalore, India, 1986 Lingaiah, K., Machine Design Data Handbook, Vol II (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986 Juvinall, R C., Fundamentals of Machine Component Design, John Wiley and Sons, New York, 1983 Deutschman, A D., W J Michels, and C E Wilson, Machine Design—Theory and Practice, Macmillan Publishing Company, New York, 1975 Edwards, Jr., K S., and R B McKee, Fundamentals of Mechanical Component Design, McGraw-Hill Publishing Company, New York, 1991 10 Norton, R L., Machine Design—An Integrated Approach, Prentice Hall International, Inc., Upper Saddle River, New Jersey, 1996 11 Lingaiah, K Machine Design Data Handbook, McGraw-Hill Publishing Company, New York, 1994 12 Metals Handbook, American Society for Metals, Vol 10, 8th edition, p 102, Metals Park, Ohio, 1975 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 Source: MACHINE DESIGN DATABOOK CHAPTER CAMS SYMBOLS3;4 a A Ac b B ao ¼ o þ i d dh Do E1 , E2 f f ðÞ F F Fn Ft h Ki , Ko L n N1 , N2 r Rc Ro Rp Rr R, S S S1 v w radius of circular area of contact, m (in) acceleration of the follower, m/s2 (in/s2 ) follower overhang, m (in) arc of pitch circle, m (in) half the band of width of contact, m (in) follower bearing length, m (in) distance between centers of rotation, m (in) diameter of shaft, m (in) hub diameter, m (in) minimum diameter of the pitch surface of cam, m (in) moduli of elasticity of the materials which are in contact, GPa (Mpsi) cam factor, dimensionless the desired motion of follower, as a function of cam angle applied load, kN (lbf ) total external load on follower (includes weight, spring force, inertia, friction, etc.), kN (lbf ) force normal to cam profile (Fig 6-6), kN (lbf ) side thrust, kN (lbf ) depth to the point of maximum shear, m (in) constants for input and output cams, respectively length of cylinder in contact, m (in) total distance through which the follower is to rise, m (in) cam speed, rpm forces normal to follower stem, kN (lbf ) radius of follower, m (in) radius of the circular arc, m (in) minimum radius of the pitch surface of the cam, m (in) pitch circle radius, m (in) radius of the roller, m (in) functions of i and o , in basic spiral contour cams displacement of the follower corresponding to any cam angle , m (in) initial compression spring force with weight w, at zero position, kN (lbf ) velocity of the follower, m/s (in/s) equivalent weight at follower ends, kN (lbf ) 6.1 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 CAMS 6.2 CHAPTER SIX cartesian coordinates of any point on the cam surface actual lift at follower end, m (in) rise of cam, m (in) radius of curvature of the pitch curve, m (in) radii of curvature of the contact surfaces, m (in) pressure angle, deg maximum pressure angle, deg angle through which cam is to rotate to effect the rise L, rad cam angle corresponding to the follower displacement S, rad angle rotated by the output-driven member, deg angle rotated by the input driver, deg angular velocity of cam, rad/s coefficient of friction between follower stem and its guide bearing Poisson’s ratios for the materials of contact surfaces maximum compressive stress, MPa (kpsi) shear stress, MPa (kpsi) x, y y yc 1 , 2 m o i ! 1 , 2 c;max Particular Cam factor Formula Ac L ð6-1Þ The length of arc of the pitch circle Ac ẳ Rp 6-2ị The pitch circle radius Rp ¼ f ¼ fL CAMS 6.10 CHAPTER SIX FIGURE 6-8 Harmonic motion characteristics S ¼ displacement, inches; V ¼ velocity, inches per degree; A ¼ acceleration, inches per degree2 (From ‘‘Plate Cam Design—with Emphasis on Dynamic Effects,’’ by M Kloomok and R V Muffley, Product Eng., February 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio 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 CAMS CAMS 6.11 FIGURE 6-9 Eighth-power polynomial motion characteristics S ¼ displacement, inches; V ¼ velocity, inches per degree; A ¼ acceleration, inches per degree2 (From ‘‘Plate Cam Design—with Emphasis on Dynamic Effects,’’ by M Kloomok and R V Muffley, Product Eng., February 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio 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 CAMS 6.12 CHAPTER SIX FIGURE 6-10 Cycloidal motion (From ‘‘Plate Cam Design—Radius of Curvature,’’ by M Kloomok and R V Muffley, Product Eng., September 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio 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 CAMS CAMS 6.13 FIGURE 6-11 Harmonic motion (From ‘‘Plate Cam Design—Radius of Curvature,’’ by M Kloomok and R V Muffley, Product Eng., September 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio 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 CAMS 6.14 CHAPTER SIX FIGURE 6-12 Eighth-power polynomial motion (From ‘‘Plate Cam Design—Radius of Curvature,’’ by M Kloomok and R V Muffley, Product Eng., September 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio 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 CAMS CAMS Particular 6.15 Formula TABLE 6-1 Cam factors for basic curves Types of motion Pressure angle , deg Uniform Modified uniform Simple harmonic Parabolic and cycloidal 10 15 20 25 30 35 40 45 5.67 3.73 2.75 2.14 1.73 1.43 1.19 1.00 5.84 3.99 3.10 2.58 2.27 2.06 1.92 1.82 8.91 5.85 4.32 3.36 2.72 2.24 1.87 1.57 11.34 7.46 5.50 4.28 3.46 2.86 2.38 2.00 The maximum shear stress max ẳ 0:295c;max 6-37ị The depth to the point of maximum shear h ẳ 0:786b 6-38ị For further data on characteristic equations of basic curves, different motion characteristics, cam factors, materials for cams and followers, and displacement ratios Refer to Tables 6-1 and Figures 6-7, 6-8 and 6-9 For materials of cams refer to Chapter on ‘‘Properties of Engineering Materials.’’ REFERENCES Rothbart, H A., Cams, John Wiley and Sons, New York, 1956 Marks, L S., Mechanical Engineers’ Handbook, McGraw-Hill Book Company, New York, 1951 Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Engineering College Co-operative Society, Bangalore, India, 1962 Lingaiah, K., Machine Design Data Handbook, Vol II (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986 Rothbart, H A., Mechanical Design and Systems Handbook, McGraw-Hill Book Company, New York, 1964 Shigley, J E., Theory of Machines, McGraw-Hill Book Company, New York, 1961 Mabie, H H., and F W Ocvirk, Mechanisms and Dynamics of Machinery, John Wiley and Sons, New York, 1957 Kent, R T., Mechanical Engineers’ Handbook—Design and Production, Vol II John Wiley and Sons, New York, 1961 Klcomok, M., and R V Muffley, ‘‘Plate Cam Design—with Emphasis on Dynamic Effects,’’ Product Eng., February 1955 10 Klcomok, M., and R V Muffley, ‘‘Plate Cam Design—Radius of Curvature,’’ Product Eng., February 1955 11 Varnum, E C., ‘‘Circular Nomogram—Theory and Practice Construction Technique,’’ Barber-Coleman Co., Product Eng 12 Gruenberg, R., ‘‘Nomogram for Parabolic Cam with Radially Moving Follower,’’, in Douglas C Greenwood, Editor, Engineering Data for Product Design, McGraw-Hill Book Company, New York, 1996 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 Source: MACHINE DESIGN DATABOOK CHAPTER PIPES, TUBES, AND CYLINDERS SYMBOLS5;6;9 d dc di e E h or t I K L p pc pcr pi po ri c r rðmaxÞ sa su ðmaxÞ max diameter of cylinder, m (in) diameter of contact surface in compound cylinder, m (in) inside diameter of cylinder or pipe or tube, m (in) outside diameter of cylinder or pipe or tube, m (in) factor for expanded tube ends modulus of elasticity, GPa (Mpsi) thickness of cylinder or pipe or tube, m (in) moment of inertia, area, m4 or cm4 (in4 ) constant maximum distance between supports or stiffening rings, m (in) maximum allowable working pressure, MPa (psi) unit pressure between the compound cylinders, MPa (psi) collapsing pressure, MPa (psi) internal pressure, MPa (psi) external pressure, MPa (psi) inside radius of tube or pipe, m (in) permissible working stress, from Table 7-1, MPa (psi) crushing stress, MPa (psi) radial stress (also with primes), MPa (psi) maximum radial stress, MPa (psi) maximum allowable stress value at design condition, MPa (psi) ultimate strength, MPa (psi) tangential stress (also with primes), MPa (psi) maximum tangential stress, MPa (psi) maximum shear stress, MPa (psi) Poisson’s ratio efficiency, from Table 7-4 Note: The initial subscript s, along with , which stands for strength, is used throughout this book 7.1 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 PIPES, TUBES, AND CYLINDERS 7.2 CHAPTER SEVEN Particular Formula LONG THIN TUBES WITH INTERNAL PRESSURE The permissible steam pressure in steel and iron pipes (Table 7-1) according to ASME Power Boiler Code pẳ 2sa h 1:625 103 ị 0:9 SI ð7-1aÞ where h, in m, and p and in MPa pẳ 2sa h 0:065ị 125 USCS ð7-1bÞ where h, in in, and p and in psi For tubes from 6.35 mm (0.25 in) to 127 mm (5 in) nominal diameter p¼ 2sa ðh À 2:54 Â 10À3 Þ SI ð7-2aÞ where h, in m, and p and in MPa pẳ 2sa h 0:1ị USCS 7-2bị where h, in in, and p and in psi For over 127 mm (5 in) diameter The minimum required thickness of ferrous tube up to and including 125 mm (5 in) outside diameter subjected to internal pressure as per ASME Power Boiler Code The maximum allowable working pressure (MAWP) from Eq (7-3) as per ASME Power Boiler Code h¼ pdo ỵ 0:005do ỵ e 2sa ỵ p 7-3ị where sa is the maximum allowable stress value at design condition and e is the thickness factor for expanded tube ends Refer to Table 7-1 for sa Refer to table 7-2 for e 2h À 0:01do À 2e p ẳ sa h 0:005do eị ¼ sa 2h À 0:01do À 2e 1:005d0 À h ỵ e For maximum allowable working pressure hẳ 7-4ị Refer to Table 9-1 The minimum required thickness of ferrous pipe under internal pressure as per ASME Power Boiler Code or pdo pri ỵC ẳ ỵC 2sa ỵ 2yp sa À ð1 À yÞp ð7-5Þ where ¼ efficiency (refer to Table 7-4 for ) y ¼ temperature coefficient (refer to Table 7-3 for y) C ¼ minimum allowance for the threading and structural stability, mm (in) (refer to Table 7-5 for h values and Table 7-6 for C values) 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 Grade, alloy designation and temper C C 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 S31500 S31500 TP410 TP405 TpxM-8 TpxM-8 18Cr-2Mo 18Cr-2Mo TP304L TP304H, TP304 TP304N TP304N TP316L TP316L TP316H XM-15 XM-15 TP316N TP316N XM-29 TP321 TP321H FP347H TP348 TP348H, TP347H S30815 Low Alloy Steel: SA-209g SA-213 SA-369 SA-250 (B) High Alloy Steels SA-268 SA-268 SA-268 SA-268 SA-268 SA-268 SA-249 SA-312 SA-213, SA-312 SA-213, SA-312 SA-249, SA-312 SA-213, SA-312 SA-312, SA-688 SA-452 SA-312 SA-213 SA-213 SA-312 SA-312, SA-688 SA-213, SA-312 SA-249, SA-312 SA-430 SA-213 SA-249, SA-312 SA-213, SA-312 SA-789, SA-790 SA-789, SA-790 SA-789, SA-790, SA-669 SA-789, SA-790 T1 T12 Fp11 T1 SA-210 SA-557b,f c (A) Carbon and Low Alloy Steels Carbon Steel: SA-106c A Specification number S4 000 S40500 S43035 S43035 S44400 S44400 S30403 S30409, S30400 S30451 S30451 S31603 S31603 S31609 S31800 S38100 S31651 S3i651 S24000 S32100 S32109 S34700 S34800 S34809, S34709 S30815 S32550 S32550 S31500 S31500 UNS number 13Cr 12Cr-1Al 18Cr-Ti 18Cr-Ti 18Cr-2Mo 18Cr-2Mo 18Cr-8Ni 18Cr-8Ni 18Cr-8Ni-N 18Cr-8Ni-N 16Cr-12Ni-2Mo 16Cr-12Ni-2Mo 16Cr-12Ni-2Mo 18Cr-18Ni-2Si 18Cr-18Ni-2Si 16Cr-12Ni-2Mo-N 16Cr-12Ni-2Mo-N 18Cr-3Ni-12Mn 18Cr-10Ni-Ti 18Cr-10Ni-Ti 18Cr-10Ni-Cb 18Cr-10Ni-Cb 18Cr-10Ni-Cb 21Cr-11Ni-N 25.5Cr-5.5Ni-3.5Mo-Cu 25.5Cr-5.5Ni-3.5Mo-Cu 18Cr-5Ni-3Mo 18Cr-5N-3Mo 1Cr-1Mo 11Cr-1Mo-Si C-2Mo* C-Mn-Si C-Mn C-si Nominal composition and size, mm (in) Smls.Tb Wld.Tbf Wld.Tbd;f Smls.Tbd;f Wld.Tbd;f Smls.Tbd;f Wld.Tbf & Pp Smls.Tbg,h & Pp Smls.Tb & Ppg,h Wld.Th & Ppf,g,h Smls.Tb & Pp Wld.P & Tbf Cast Ppg Wld.Tbf,g Smls.Tbg Smls.Tbg,h Wld.Ppf,g,h Wld.Ppf & Tb Smls.Tbg,h & Pp Wld.Tb & Ppf Smls.Ppg Smls.Tbg,h Wld.Tb & Ppf,g Smls.Tb & Ppf Smls.Tb & Ppd Wld.Tb & Ppd Smls.Tbd,f Wld.Tbd,f Smls.Tb Smls.Tb Smls.Pp Wld Pp & Tb Smls.Tb** Smls.Tb Smls† Pp* Product form TABLE 7-1 Maximum allowable stress values in tension of metals for tubes and pipes, sa 207 207 207 207 276 276 172 207 241 241 172 172 207 207 207 241 241 379 207 207 207 207 207 310 552 552 441 441 207 207 207 207 276 276 207 MPa 30 30 30 30 40 40 25 30 35 35 25 25 30 30 30 35 35 55 30 30 30 30 30 45 80 80 64 64 30 30 30 30 40 40 30 kpsi Specified minimum yield strength, sy 414 414 414 414 414 414 483 517 552 552 483 483 517 517 517 552 552 689 517 517 483 517 517 600 758 758 634 634 379 414 414 379 483 483 331 MPa 48 60 60 60 60 60 60 70 75 80 80 70 70 75 75 75 80 80 100 75 75 70 75 75 87 110 110 92 92 55 60 60 55 70 70 kpsi Specified minimum tensile strength, st 103 88 88 103 88 103 92 130 138 117 108 92 130 110 130 138 117 146 130 110 130 130 110 150 190 161 159 135 10 MPa 15.0 12.8 12.8 15.0 12.8 15.0 13.3 18.8 20.0 17.0 15.7 13.3 18.8 15.9 18.8 20.0 17.0 21.2 18.8 16.0 18.8 18.8 16.0 21.8 27.5 23.4 23.0 19.6 11 kpsi 38 (100) 99 84 84 98 84 99 78 123 138 117 92 78 130 104 122 138 117 143 127 93 123 123 105 149 189 161 153 130 12 MPa 14.3 12.2 12.) 14.3 12.2 14.3 11.4 17.8 131 17.0 13.3 11.3 18.8 15.1 17.7 20.0 17.0 20.8 18.4 13.5 17.9 17.9 15.2 21.6 27.4 23.3 22.2 18.9 13 kpsi 93 (200) 95 81 81 95 81 95 70 115 20.0 111 82 70 127 97 115 132 112 132 119 83 113 113 97 141 177 151 147 125 14 MPa 13.8 11.8 11.8 13.8 11.8 13.8 10.2 16.6 19.0 16.1 11.9 10.1 18.4 14.1 16.6 19.2 16.3 19.2 17.3 12.1 16.4 16.4 14.0 20.4 25.7 21.9 21.3 18.1 15 kpsi 150 (300) 92 78 78 92 78 92 64 112 126 108 75 63 125 95 111 130 110 119 118 76 107 107 91 135 170 145 146 124 16 MPa 13.3 11.3 11.3 13.3 11.3 13.3 9.3 16.2 18.3 15.6 10.8 9.2 18.1 13.7 16.1 18.8 16.0 17.3 17.1 11.0 15.5 15.3 13.2 19.6 24.7 21.0 21.2 18.0 17 kpsi 205 (400) Maximum allowable stress, sa 89 75 75 89 75 88 60 110 123 104 69 59 124 93 110 128 109 110 118 70 103 103 88 127 170 145 146 124 18 MPa 12.9 10.9 10.9 12.9 10.9 12.8 8.7 15.9 17.8 15.1 10.0 8.5 18.0 13.5 15.9 18.6 15.8 16.0 17.1 10.2 14.9 14,9 12.7 18.4 24.7 21.0 21.2 18.0 19 kpsi 260 (500) PIPES, TUBES, AND CYLINDERS 7.3 21 20 22 MPa 23 kpsi 370 (700) 7.4 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 21.2 18.0 146 124 146 124 53 105 115 98 59 50 110 89 104 127 108 97 107 63 101 101 86 116 8.0 15.9 17.1 14.6 9.0 7.6 16.3 13.5 15.9 18.6 15.8 14.7 15.8 9.3 14.7 14.7 12.5 17.3 21.2 18.0 65 65 93 99 93 84 77 10.3 10.3 13.8 15.0 14.2 12.8 12.1 64 83 70 24 MPa (B) High Alloy Steels 73 10.6 71 73 10.6 71 86 12.4 72 10.5 86 12.4 57 8.3 55 110 15.9 110 120 17.4 118 102 14.8 101 51 7.4 62 55 8.0 52 117 17.0 112 93 13.5 93 110 15.9 110 128 18.6 128 109 15.8 109 106 15.4 101 112 16.4 109 67 9.7 64 101 14.7 101 101 14.7 101 86 12.5 86 122 17.7 119 95 103 Low Alloy Steels 13.8 95 15.0 103 98 88 12.8 88 86 12.4 83 (A) Carbon and Low Alloy Steels Carbon Steel: 83 12.0 81 11.7 121 17.5 115 16.6 103 15.0 97 14.1 kpsi MPa 315 (600) 7.7 15.2 16.6 14.2 8.6 7.3 15.9 12.9 15.1 18.4 15.6 14.1 15.5 9.2 14.7 14.7 12.5 16.8 9.4 9.4 13.5 14.4 13.5 12.2 11.1 9.3 12.0 10.2 25 kpsi 427 (800) 14.7 15.9 13.5 8.2 12.7 11.0 12.5 11.0 9.7 6.5 5.0 5.5 27 kpsi 15.5 12.4 14.6 18.1 15.4 15.3 9.0 14.7 14.7 12.5 16.3 101 110 93 57 86 76 86 76 67 45 35 38 26 MPa 482 (900) 107 85 101 125 106 106 62 101 101 86 112 13.8 8.9 14.4 14.0 12.3 14.9 13.7 17.4 14.8 95 120 102 95 61 99 97 84 103 15.3 13.8 15.0 12.7 3.4 4.8 5.5 6.2 4.1 6.4 2.5 1.5 2.1 29 kpsi 106 95 103 86 23 33 38 48 98 44 17 10 15 28 MPa 538 (1000) 4.0 2.6 31 kpsi 48 52 90 63 76 62 85 72 85 6.9 7.5 13.0 9.1 11.1 9.0 12.4 10.5 12.4 9.8 9.7 8.3 20 68 67 57 2.9 27 18 30 MPa 593 (1100) 24 32 55 30 46 36 51 43 51 42 41 35 32 MPa 3.6 4.6 7.9 4.4 6.7 5,2 7.4 6.3 7.4 6.1 6.0 5.1 1.0 1.2 1.0 33 kpsi 650 (1200) for metal temperature, 8C (8F), not exceeding TABLE 7-1 Maximum allowable stress values in tension of metals for tubes and pipes, sa (Cont.) 12 19 30 15 25 21 28 25 34 MPa 1.7 2.7 4.4 2.2 3.7 3.1 4.1 3.7 35 kpsi 704 (1300) 11 17 15 13 16 16 36 MPa 0.8 1.6 2.5 1.2 2.1 1.9 2.3 2.3 37 kpsi 760 (1400) 9 10 38 MPa 0.3 1.0 1.3 0.8 1.1 1.3 1.3 1.4 39 kpsi 815 (1500) SA-268 SA-268 SA-268 SA-268 SA-268 SA-249, SA-312 SA-213, SA-312 SA-213, SA-312 SA-249, SA-312 SA-213, SA-312 SA-312, SA-688 SA-452 SA-312 SA-213 SA-213 SA-312 SA-312, SA-688 SA-213, SA-312 SA-249, SA-312 SA-430 SA-213 SA-249, SA-312 SA-312, SA-213 SA-789, SA-790 SA-789, SA-790 SA-789, SA-790, SA-669 SA-789, SA-790 SA-209g SA-213 SA-369 SA-250 SA-268 SA- 106c SA-210c SA-557b,f 40 Specification number PIPES, TUBES, AND CYLINDERS Grade, alloy designation and temper e SB-234 C700-Ann LCW*** p C71500 Ann Nickel and High Nickel Alloys: SB-161 201 Ann SB-163 800H Annk SB-163 825 Annk SB-144 625 Annp SB-468 20 cb.Wld Annk,p SB-619 C-276 Sol Annp SB-619 G Sol Annk,p SB-543 SB-467 pp C71500 Ann SB-466 p 655 Ann SB-315 g 192 Ann SB-1 1 Copper and Copper Alloys: SB-111 102, 120, 122, 142i 6061-T6 3003-H25 SB-234 e 3003-H118 5083-H111d,p 1060-H14e SB-241 SB-241 SB-234 e 6061-T6 SB-210 e (C) Non-ferrous Metals Aluminum and Aluminum Alloys: SB-210 1060-1114d Specification number N02201 N08810 N08825 N06625 N08020 N10276 N06007 UNS number Ni Low C Ni-Fe-Cr Ni-Fe-Cr-Mo-Cu Ni-Cr-Mo-Cb Cr-Ni-Fe-Mo-Cu-Cb Ni-Mo-Cr (All sizes) Ni-Cr-Fe-Mo-Cu (All sizes) (Up to 112.5 incl) (up to 41 incl) Ann LD‡ HD** Up to 125 (up to 5.00) 0.250–12.50 (0.010–0.5000) 0.625–6.225 (0.025–0.249) 0.250–12.500 (0.010–0.500) 0.625–12.50 (0.025–0.50) Under 25 (under 1) Nominal composition and size, mm (in) 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 Pp & Tb Pp & Tb Pp & Tb Pp & Tb Pp & Tb Pp & Tb Wld.Cu-Ni-90/10Tb Smls Copper, iron alloy condenser Tb Smls Cu-Si Alloy Pp and Th Smls Cu-Ni 70/30 Pp & Tb Wld Cu-Ni-70/30 Pp Smls Copper condenser, Tb Smls.Pp Smls extruded Tb Condenser and heat exchanger Tb Condenser and heat exchanger Tb Condenser and heat exchanger Tb Smls.Tb Drawn Product form 69 69 172 241 414 241 283 242 103 241 138 124 103 62 207 276 83 241 131 165 131 69 241 MPa 10 25 35 60 35 41 35 15 35 20 18 15 30 40 12 35 19 24 19 10 35 10 kpsi Specified minimum yield strength, sy TABLE 7-1 Maximum allowable stress values in tension of metals for tubes and pipes, sa (Cont.) 83 345 448 586 827 552 689 620 270 310 345 345 345 207 248 310 262 290 145 186 228 83 290 MPa 50 65 85 120 80 100 90 40 45 50 50 50 30 36 45 38 42 21 27 33 12 42 12 kpsi Specified minimum tensile strength, st 46 112 146 207 117 146 132 59 59 87 83 69 41 62 78 52 72 38 47 57 21 72 21 10 MPa 6.7 16.2 21.2 30.0 17.0 21.2 19.1 8.5 8.5 12.6 12.0 10.0 6.0 9.0 11.3 7.5 10.5 5.5 6.8 8.3 3.0 10.5 3.0 11 kpsi 38 (100) 44 112 146 207 117 146 132 56 56 61 78 69 33 62 78 46 72 38 46 57 21 72 21 12 MPa 6.4 16.2 21.2 30.0 17.0 21.2 19.1 8.1 8.1 8.9 11.3 10.0 4.8 9.0 11.3 6.7 10.5 5.5 6.7 8.3 3.0 10.5 3.0 13 kpsi 93 (200) 43 112 146 207 115 146 132 52 52 61 75 69 32 60 78 42 58 30 37 38 18 58 18 14 MPa 6.3 16.2 21.2 30.0 16.8 21.2 19.1 7.6 7.6 8.8 10.8 10.0 4.7 8.7 11.3 6.1 8.4 4.3 5.4 5.5 2.6 8.4 2.6 15 kpsi 150 (300) 43 112 146 194 110 143 128 50 50 61 71 35 21 57 30 31 17 17 21 31 16 6.2 16.2 21.2 28.2 15.9 20.7 18.6 7.2 7.2 8.8 10.3 5.0 3.0 8.2 4.3 4.5 2.4 2.5 3.0 1.2 4.5 1.2 17 kpsi 205 (400) MPa Maximum allowable stress 43 110 146 186 107 140 126 43 43 61 68 18 MPa 6.2 16.0 21.2 27.0 15.5 20.3 18.3 6.3 6.3 8.8 9.9 19 kpsi 260 (500) PIPES, TUBES, AND CYLINDERS 7.5 21 20 22 MPa 23 kpsi 370 (700) Nickel and High Nickel 6.2 43 16.0 108 21.2 145 26.4 179 15.1 101 20.0 135 17.9 123 9.6 8.8 4.3 4.3 Alloy 6.2 15.7 21.0 26.0 14.7 19.6 17.8 41 105 143 179 99 134 120 24 MPa 5.9 15.3 20.8 26.0 14.3 19.4 17.4 25 kpsi 427 (800) 4.5 14.8 20.5 26.0 27 kpsi 18.9 17.0 31 102 141 179 26 MPa 482 (900) 130 117 128 111 21 99 36 179 28 MPa 18.5 16.1 3.0 14.4 19.7 26.0 29 kpsi 538 (1000) 2.0 11.6 31 kpsi 12.7 179 88 26.0 14 80 30 MPa 593 (1100) 57 91 51 32 MPa 8.3 13.2 1.2 7.4 33 kpsi 650 (1200) 32 34 MPa 4.7 35 kpsi 704 (1300) 21 36 MPa 3.0 37 kpsi 760 (1400) 13 38 MPa 1.9 39 kpsi 815 (1500) SB-161 SB-163 SB-163 SB-444 SB-468 SB-619 SB-619 SB-111 SB-111 SB-315 SB-466 SB-467 SB-543 SB-210 SB-210 SB-241 SB-241 SB-234 SB-234 SB-234 40 Specification number Source: The American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section VIII, Division 1, July 1986 * Pp ¼ pipe; ** Tb ¼ tube; *** LCW ¼ light cold worked; Smls ¼ seamless; Wld ¼ welded; ‡ LD ¼ light drawn; HD ¼ hard drawn; Ann ¼ annealed; Soln Ann ¼ solution annealed Notes: The superscript letters a, b, c, etc., refer to notes under each category of (A) Carbon and Low Alloy Steels, (B) High Alloy Steels, and (C) Non-ferrous Metals in Tables 8-9, 8-10, and 8-11 in Chapter 43 110 146 182 104 138 123 67 61 30 30 Copper and Copper Alloys: (C) Non-ferrous Metals Aluminum and Aluminum Alloys: kpsi MPa 315 (600) for metal temperature, 8C (8F), not exceeding TABLE 7-1 Maximum allowable stress values in tension of metals for tubes and pipes, sa (Cont.) PIPES, TUBES, AND CYLINDERS 7.6 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 PIPES, TUBES, AND CYLINDERS PIPES, TUBES, AND CYLINDERS 7.7 TABLE 7-2 Thickness factor for expanded tube ends e for use in Eqs (7-3) and (7-4) Particular Value of e Over a length at least equal to the length of the seat plus 25 mm (1 in) for tubes expanded into tube seats, except 0.04 For tubes expanded into tube seats provided the thickness of the tube ends over a length of the seat plus 25 mm (1 in) is not less than the following: 2.375 mm (0.095 in) for tubes 31.25 mm (1.25 in) OD 2.625 mm (0.105 in) for tubes >31.25 mm (1.25 in) OD and 50 mm (2 in) OD, including 3.000 mm (0.120 in) for tubes >50 mm (2 in) and 75 mm (3 in) OD, including 3.375 mm (0.135 in) for tubes >75 mm (3 in) OD and 100 mm (4 in) OD, including 3.75 mm (0.150 in) for tubes >100 mm (4 in) and 125 mm (5 in) OD, including For tubes strength-welded to headers and drums Source: ASME Boiler and Pressure Vessel Code, Section 1, 1983 TABLE 7-3 Temperature coefficient y Temperature, 8C (8F)a 482 (900)a Material 510 (950) 540 (1000) 565 (1050) 595 (1100) !620 (1150) Ferrite steels 0.4 0.5 0.7 0.7 0.7 0.7 Austenitic steels 0.4 0.4 0.4 0.4 0.5 0.7 For nonferrous materials 0.4 0.4 0.4 0.4 0.4 0.4 a Temperatures in parentheses are in Fahrenheit (8F) Values of y between temperatures not listed may be determined by interpolation Source: ASME Boiler and Pressure Vessel Code, Section 1, 1983 TABLE 7-4 Efficiency of joints, Particular Efficiency, Longitudinal welded joints or of ligaments between openings, whichever is lower Seamless cylinders 1.00 For welded joints provided all weld reinforcement on the longitudinal joints is removed substantially flush with the surface of the plate 1.00 For welded joints with the reinforcement on the longitudinal joints left in place 0.90 Riveted joints Refer to Table 13-4 (Chap 13) Ligaments between openings Refer to Eqs under Ligament (Chap 8) Welded joint efficiency factor Refer to Table 8-3 (Chap 8) Source: ASME Boiler and Pressure Vessel Code, Section 1, 1983 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 PIPES, TUBES, AND CYLINDERS 7.8 CHAPTER SEVEN Particular Formula TABLE 7-5 The depth of thread h (formula h ¼ 0:8=i ) Number of threads per mm (in), i Depth of thread, h mm (in) 0.32 (8) 0.46 (11.5) 2.5 (0.100) 1.715 (0.0686) Source: ASME Boiler and Pressure Vessel Code, Section 1, 1983 The maximum allowable working pressure from Eq (7-5) as per ASME Power Boiler Code The minimum required thickness of nonferrous seamless tubes and pipes for outside diameters 12.5 mm (0.5 in) to 150 mm (6 in) inclusive and for wall thickness not less than 1.225 mm (0.049 in) as per ASME Power Boiler Code The maximum allowable working pressure as per ASME Power Boiler Code pẳ 2sa h Cị sa h Cị or p ẳ 7-6ị 2yh Cị ri ỵ yịh Cị hẳ pdo ỵC 2sa 7-7ị Refer to Table 7-6 for values of C pẳ 2sa ðh À CÞ ð7-8Þ ð7-9Þ The minimum required thickness of tubes made of steel or wrought iron subjected to internal pressure which are used in watertube and firetube boilers as per ASME Power Boiler Code h ¼ 0:0251do The minimum required thickness of tubes made of nonferrous materials such as copper, red brass, admiralty and copper-nickel alloys used in watertube and firetube boilers with a design pressure over 207 kPa (30 psi) but not greater than 414 kPa (60 psi) hẳ ỵ 0:75 30 SI 7-10aị hẳ ỵ 0:03 30 USCS 7-10bị The minimum required thickness of tubes made of nonferrous materials such as copper, red brass, admiralty and copper-nickel alloys used in steam boilers of less than 103 kPa (15 psi) and water boilers of less than 207 kPa (30 psi) hẳ ỵ 0:75 45 SI 7-11aị hẳ ỵ 0:03 45 USCS 7-11bị The minimum required thickness of tubes when made of nonferrous materials but assembled with fittings, which are based on materials used, and based on whether the pressure is over 207 kPa (30 psi), but not in excess of 1013 kPa (160 psi) or whether the pressure does not exceed 207 kPa (30 psi) hẳ ỵ 0:75 except for copper ¼ 0:027 factor The formula for permissible pressure in wrought-iron and steel tubes for watertube boilers according to ASME Power Boiler Code SI 7-12aị hẳ ỵ 0:03 USCS 7-12bị factor h À Â 10À3 À 0:32 SI 7-13aị p ẳ 125 where h, in m, and p in MPa h À 0:039 p ẳ 18000 250 USCS 7-13bị where h, in in, and p in psi 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 PIPES, TUBES, AND CYLINDERS PIPES, TUBES, AND CYLINDERS Particular 7.9 Formula h À Â 10À3 p ¼ 96:5 SI where h, in m, and p in MPa h À 0:039 USCS p ¼ 14000 where h, in in, and p in psi h À Â 10À3 p ¼ 73 SI where h, in m, and p in MPa h À 0:039 USCS p ¼ 10600 ð7-14aÞ ð7-14bÞ ð7-15aÞ ð7-15bÞ where h, in in, and p in psi Formula (7-13) applies to seamless tubes at all pressures, to welded steel tubes at pressure below MPa (875 psi), and to lap-welded wrought-iron tubes at pressures below 2.5 MPa (358 psi) Formula (7-14) applies to welded steel tubes at pressures of MPa (875 psi) and above Formula (7-15) applies to lap-welded wrought-iron tubes at pressures of 2.5 MPa (358 psi) and above ENGINES AND PRESSURE CYLINDERS The wall thickness of engines and pressure cylinders hẳ pdi ỵ 7:5 103 2sta SI 7-16aị where p, st in MPa, and di and h in m hẳ pdi ỵ 0:3 2sta USCS 7-16bị where p, t in psi, and di and h in in sta ¼ MPa (1250 psi) for ordinary grades of cast iron OPENINGS IN CYLINDRICAL DRUMS pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hð1:0 À KÞ SI ð7-17aÞ where and h in m pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d ẳ 2:75 h1:0 Kị The largest permissible diameter of opening according to D S Jacobus USCS ð7:17bÞ d ¼ 0:81 where and h in in 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 ... 81 81 95 81 95 70 11 5 20.0 11 1 82 70 12 7 97 11 5 13 2 11 2 13 2 11 9 83 11 3 11 3 97 14 1 17 7 15 1 14 7 12 5 14 MPa 13 .8 11 .8 11 .8 13 .8 11 .8 13 .8 10 .2 16 .6 19 .0 16 .1 11. 9 10 .1 18.4 14 .1 16. 6 19 .2 16 .3 19 .2... 17 .3 12 .1 16. 4 16 .4 14 .0 20.4 25.7 21. 9 21. 3 18 .1 15 kpsi 15 0 (300) 92 78 78 92 78 92 64 11 2 12 6 10 8 75 63 12 5 95 11 1 13 0 11 0 11 9 11 8 76 10 7 10 7 91 135 17 0 14 5 14 6 12 4 16 MPa 13 .3 11 .3 11 .3 13 .3... 21. 2 18 .0 14 6 12 4 14 6 12 4 53 10 5 11 5 98 59 50 11 0 89 10 4 12 7 10 8 97 10 7 63 10 1 10 1 86 11 6 8.0 15 .9 17 .1 14 .6 9.0 7 .6 16 .3 13 .5 15 .9 18 .6 15 .8 14 .7 15 .8 9.3 14 .7 14 .7 12 .5 17 .3 21. 2 18 .0 65 65