STATIC STRESSES IN MACHINE ELEMENTS STATIC STRESSES IN MACHINE ELEMENTS 2.39 TABLE 2-10 Mechanical and physical constants of some materials1;2 Modulus of elasticity, E Modulus of rigidity, G Material GPa Mpsi GPa Mpsi Aluminum Aluminum cast Aluminum (all alloys) Beryllium copper Carbon steel Cast iron, gray Malleable cast iron Inconel Magnesium alloy Molybdenum Monet metal Nickel-silver Nickel alloy Nickel steel Phosphor bronze Steel (18-8), stainless Titanium (pure) Titanium alloy Brass Bronze Bronze cast Copper Tungsten Douglas fir Glass Lead Concrete (compression) Wrought iron Zinc alloy 69 70 72 124 206 100 170 214 45 331 179 127 207 207 111 190 103 114 106 96 80 121 345 11 46 36 14–28 190 83 10.0 10.15 10.4 18.0 30.0 14.5 24.6 31.0 6.5 48.0 26.0 18.5 30 30.0 16.0 27.5 15.0 16.5 15.5 14.0 11.6 17.5 50.0 1.6 6.7 5.3 2.0–4.0 27.5 12 26 30 27 48 79 41 90 76 16 117 65 48 79 79 41 73 3.8 4.35 3.9 7.0 11.5 6.0 13.0 11.0 2.4 17.0 9.5 7.0 11.5 11.5 6.0 10.6 43 40 38 35 46 138 19 13 6.2 5.8 5.5 5.0 6.6 20.0 0.6 2.7 1.9 70 31 10.2 4.5 Poisson’s ratio, Density, a, Mg/m3 0.334 2.69 0.320 0.285 0.292 0.211 2.80 8.22 7.81 7.20 0.290 0.350 0.307 0.320 0.332 0.30 0.291 0.349 0.305 8.42 1.80 10.19 8.83 8.75 8.3 7.75 8.17 7.75 4.47 6.6 8.55 8.30 0.33 0.324 0.349 0.326 0.330 0.245 0.431 0.33 8.90 18.82 4.43 2.60 11.38 2.35 6.6 Unit weight, b kfg/m3 kN/m3 lbf/in3 lbf/ft3 2,685 2,650 2,713 8,221 7,806 7,197 7,200 8,418 1,799 10,186 8,830 8,747 26.3 26.0 27.0 80.6 76.6 70.6 0.097 0.096 0.10 0.297 0.282 0.260 167 166 173 513 487 450 83.3 17.6 100.0 86.6 85.80 7,751 8,166 7,750 4,470 76.0 80.1 76.0 43.9 0.307 0.065 0.368 0.319 0.316 0.300 0.280 0.295 0.280 0.16 530 117 636 551 546 518 484 510 484 279 8,553 8,304 8,200 8,913 18,822 443 2,602 11,377 2,353 7,700 83.9 81.4 0.309 534 87,4 184.6 4.3 25.5 111.6 23.1 0.322 556 0.016 0.094 0.411 28 162 710 147 0.24 415 ¼ mass density: ¼ weight density; w is also the symbol used for unit weight of materials Sources: K Lingaiah and B R Narayana Iyengar, Machine Design Data Handbook, Vol I (SI and Customary Metric Units), Suma Publishers, Bangalore, India, and K Lingaiah, Machine Design Data Handbook, Vol II (SI and Customary Metric Units), Suma Publishers, Bangalore, India 1986 a b 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 E E ð" "2 ị 21 ỵ ị Maximum shearing stress, max Angle from gauge axis to maximum normal stress angle, p 2"2 "1 ỵ "3 ị tan1 "1 "3 ! E 21 ỵ ị q' "1 "3 ị2 ỵ ẵ2"2 "1 þ "3 Þ2 "1 þ "3 Â À 1þ 1 q' "1 "3 ị2 ỵ ẵ2"2 "1 þ "3 Þ2 & "1 þ "3 Â þ 1ỵ 1 q' "1 "3 ị2 ỵ ẵ2"2 "1 ỵ "3 ị2 & E 1ỵ s! " ỵ "2 ỵ "3 "2 "3 p "1 ỵ 3 "1 ỵ "2 ỵ "3 1ỵ 31 ị s! " ỵ "2 ỵ "3 "2 "3 p ỵ "1 3 "1 ỵ "2 ỵ "3 ỵ 1ỵ 31 ị s! " ỵ "2 ỵ "3 "2 "3 p ỵ "1 3 pffiffiffi ð"2 À "3 Þ 7 tan1 "1 ỵ "2 ỵ "3 "1 À E E Rosette type Poisson’s ratio The author has used as symbol for Poisson’s ratio Source: Perry, C C., and H R Lissner, The Strain Gage Primer, 2nd ed., McGraw-Hill Publishing Company, New York, p 147, 1962 E "2 ỵ "1 ị 2 Minimum normal stress, min & E E ð"1 þ "2 Þ À 2 Maximum normal stress, max Required solutions TABLE 2-11 Relations between strain rosette readings and principal stresses 2ð" À "3 Þ tanÀ1 pffiffiffi 2 3"1 "4 ị E 21 ỵ ị r! "1 "4 ị2 ỵ "2 "3 ị2 E "1 ỵ "4 1 1ỵ r! "1 "4 ị2 ỵ "2 "3 ị2 E "1 ỵ "4 þ 1À 1þ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! ð"1 À "4 Þ2 þ ð"2 À "3 Þ2 STATIC STRESSES IN MACHINE ELEMENTS 2.40 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 STATIC STRESSES IN MACHINE ELEMENTS Table 2-12 Singularity functions Graph of fn xị Function Concentrated moment Meaning hx ai2 ẳ ðx À1 Concentrated force À1 Unit step Parabolic x¼a x 6¼ a x¼a x 6¼ a hx À aiÀ1 dx ¼ hx À ai0 & À1 Rump & x