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Question 2.20: An application requires the support of an axial load of 100 ...

An application requires the support of an axial load of 100 kips with a round rod without exceeding

the yield strength of the material. Assume the current cost per pound for round stock is given

in the table below for several materials that are being considered. Material properties are available

in Tables A–5, A–20, A–21, and A–24. Select one of the materials for each of the following

additional design goals.

(a) Minimize diameter.

(b) Minimize weight.

(c) Minimize cost.

(d) Minimize axial deflection.

Material  Cost/lbf
1020 HR $0.27
1020 CD $0.30
1040 Q&T @800°F $0.35
4140 Q&T  @800°F $0.80
Wrought Al 2024 T3 $1.10
Titanium alloy (Ti-6Al-4V) $7.00

 

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Appropriate tables: Young’s modulus and Density (Table A-5)1020 HR and CD (Table A20), 1040 and 4140 (Table A-21), Aluminum (Table A-24), Titanium (Table A-24c)

Appropriate equations:

For diameter, \sigma=\frac{F}{A}=\frac{F}{(\pi / 4) d^{2}}=S_{y} \quad \Rightarrow \quad d=\sqrt{\frac{4 F}{\pi S_{y}}}

Weight/length =\rho A, Cost/length = $ /in=($  / \mathrm{lbf} )Weight/length,

Deflection/length =\delta / L=F /(A E))

With F=100 kips =100\left(10^{3}\right) \mathrm{lbf}

 

 

 

(Table A-5)

Material Modulus of Elasticity E Modulus of Elasticity G Poisson’s Ratio Unit Weight w
Mpsi Gpa Mpsi GPa lbf/in^{3} lbf/ft^{3} kN/m^{3}
Aluminum(all alloys) 10.4 71.7 3.9 26.9 0.333 0.098 169 26.6
Beryllium copper 18 124 7 48.3 0.285 0.297 513 80.6
Brass 15.4 106 5.82 40.1 0.324 0.309 534 83.8
Carbon steel 30 207 11.5 79.3 0.292 0.282 487 76.5
Cast iron(gray) 14.5 100 6 41.4 0.211 0.26 450 70.6
Copper 17.2 119 6.49 44.7 0.326 0.322 556 87.3
Douglas fir 1.6 11 0.6 4.1 0.33 0.016 28 4.3
Glass 6.7 46.2 2.7 18.6 0.245 0.094 162 25.4
Inconel 31 214 11 75.8 0.29 0.307 530 83.3
Lead 5.3 36.5 1.9 13.1 0.425 0.411 710 111.5
Magnesium 6.5 44.8 2.4 16.5 0.35 0.065 112 17.6
Molybdenum 48 331 17 117 0.307 0.368 636 100
Monel metal 26 179 9.5 65.5 0.32 0.319 551 86.6
Nickel silver 18.5 127 7 48.3 0.322 0.316 546 85.8
Nickel steel 30 207 11.5 79.3 0.291 0.28 484 76
Phosphor bronze 16.1 111 6 41.4 0.349 0.295 510 80.1
Stainless steel(18-8) 27.6 190 10.6 73.1 0.305 0.28 484 76
Titanium alloys 16.5 114 6.2 42.4 0.34 0.16 276 43.4

 

(Table A20)

1 2 3 4 5 6 7 8
AISI No. Treatment Temperture °C (°F) Tensile Strength,Mpa (kpsi) Yield Strength,Mpa (kpsi) Elongation,% Reducation in Area , % Brinell Hardness
1030 Q&T* 205(400) 848(123) 648(94) 17 47 495
Q&T* 315(600) 800(116) 621(90) 19 53 401
Q&T* 425(800) 731(106) 579(84) 23 60 302
Q&T* 540(1000) 669(97) 517(75) 28 65 255
Q&T* 650(1200) 586(85) 441(64) 32 70 207
Normalized 925(1700) 521(75) 345(50) 32 61 149
Annealed 870(1600) 430(62) 317(46) 35 64 137
1040 Q&T 205(400) 779(113) 593(86) 19 48 262
Q&T 425(800) 758(110) 552(80) 21 54 241
Q&T 650(1200) 634(92) 434(63) 29 65 192
Normalized 900(1650) 590(86) 374(54) 28 55 170
Annealed 790(1450) 519(75) 353(51) 30 57 149
1050 Q&T* 205(400) 1120(163) 807(117) 9 27 514
Q&T* 425(800) 1090(158) 793(115) 13 36 444
Q&T* 650(1200) 717(104) 538(78) 28 65 235
Normalized 900(1650) 748(108) 427(62) 20 39 217
Annealed 790(1450) 636(92) 365(53) 24 40 187
1060 Q&T 425(800) 1080(156) 765(111) 14 41 311
Q&T 540(1000) 965(140) 669(97) 17 45 277
Q&T 650(1200) 800(116) 524(76) 23 54 229
Normalized 900(1650) 776(112) 421(61) 18 37 229
Annealed 790(1450) 626(91) 372(54) 22 38 179
1095 Q&T 315(600) 1260(183) 813(118) 10 30 375
Q&T 425(800) 1210(176) 772(112) 12 32 363
Q&T 540(1000) 1090(158) 676(98) 15 37 321
Q&T 650(1200) 896(130) 552(80) 21 47 269
Normalized 900(1650) 1010(147) 500(72) 9 13 293
Annealed 790(1450) 658(95) 380(55) 13 21 192
1141 Q&T 315(600) 1460(212) 1280(186) 9 32 415
Q&T 540(1000) 896(130) 765(111) 18 57 262
Q&T* 205(400) 1630(236) 1460(212) 10 41 467
Q&T* 315(600) 1500(217) 1380(200) 11 43 435
Q&T* 425(800) 1280(186) 1190(173) 13 49 380
Q&T* 540(1000) 1030(150) 910(132) 17 57 315
Q&T* 650(1200) 814(118) 703(102) 22 64 245
Normalized 870(1600) 670(97) 436(63) 25 59 197
Annealed 865(1585) 560(81) 361(52) 28 56 156
Q&T 205(400) 1770(257) 1640(238) 8 38 510
4140 Q&T 315(600) 1550(225) 1430(208) 9 43 445
Q&T 425(800) 1250(181) 1140(165) 13 49 370
Q&T 540(1000) 951(138) 834(121) 18 58 285
Q&T 650(1200) 758(110) 655(95) 22 63 230
Normalized 870(1600) 1020(148) 655(95) 18 47 302
Annealed 815(1500) 655(95) 417(61) 26 57 197
4340 Q&T 315(600) 1720(250) 1590(230) 10 40 486
Q&T 425(800) 1470(213) 1360(198) 10 44 430
Q&T 540(1000) 1170(170) 1080(156) 13 51 360
Q&T 650(1200) 965(140) 855(124) 19 60 280

(Table A-21)

1 2 3 4 5 6 7 8
AISI No. Treatment Temperture °C (°F) Tensile Strength,Mpa (kpsi) Yield Strength,Mpa (kpsi) Elongation,% Reducation in Area , % Brinell Hardness
1030 Q&T* 205(400) 848(123) 648(94) 17 47 495
Q&T* 315(600) 800(116) 621(90) 19 53 401
Q&T* 425(800) 731(106) 579(84) 23 60 302
Q&T* 540(1000) 669(97) 517(75) 28 65 255
Q&T* 650(1200) 586(85) 441(64) 32 70 207
Normalized 925(1700) 521(75) 345(50) 32 61 149
Annealed 870(1600) 430(62) 317(46) 35 64 137
1040 Q&T 205(400) 779(113) 593(86) 19 48 262
Q&T 425(800) 758(110) 552(80) 21 54 241
Q&T 650(1200) 634(92) 434(63) 29 65 192
Normalized 900(1650) 590(86) 374(54) 28 55 170
Annealed 790(1450) 519(75) 353(51) 30 57 149
1050 Q&T* 205(400) 1120(163) 807(117) 9 27 514
Q&T* 425(800) 1090(158) 793(115) 13 36 444
Q&T* 650(1200) 717(104) 538(78) 28 65 235
Normalized 900(1650) 748(108) 427(62) 20 39 217
Annealed 790(1450) 636(92) 365(53) 24 40 187
1060 Q&T 425(800) 1080(156) 765(111) 14 41 311
Q&T 540(1000) 965(140) 669(97) 17 45 277
Q&T 650(1200) 800(116) 524(76) 23 54 229
Normalized 900(1650) 776(112) 421(61) 18 37 229
Annealed 790(1450) 626(91) 372(54) 22 38 179
1095 Q&T 315(600) 1260(183) 813(118) 10 30 375
Q&T 425(800) 1210(176) 772(112) 12 32 363
Q&T 540(1000) 1090(158) 676(98) 15 37 321
Q&T 650(1200) 896(130) 552(80) 21 47 269
Normalized 900(1650) 1010(147) 500(72) 9 13 293
Annealed 790(1450) 658(95) 380(55) 13 21 192
1141 Q&T 315(600) 1460(212) 1280(186) 9 32 415
Q&T 540(1000) 896(130) 765(111) 18 57 262
Q&T* 205(400) 1630(236) 1460(212) 10 41 467
Q&T* 315(600) 1500(217) 1380(200) 11 43 435
Q&T* 425(800) 1280(186) 1190(173) 13 49 380
Q&T* 540(1000) 1030(150) 910(132) 17 57 315
Q&T* 650(1200) 814(118) 703(102) 22 64 245
Normalized 870(1600) 670(97) 436(63) 25 59 197
Annealed 865(1585) 560(81) 361(52) 28 56 156
Q&T 205(400) 1770(257) 1640(238) 8 38 510
4140 Q&T 315(600) 1550(225) 1430(208) 9 43 445
Q&T 425(800) 1250(181) 1140(165) 13 49 370
Q&T 540(1000) 951(138) 834(121) 18 58 285
Q&T 650(1200) 758(110) 655(95) 22 63 230
Normalized 870(1600) 1020(148) 655(95) 18 47 302
Annealed 815(1500) 655(95) 417(61) 26 57 197
4340 Q&T 315(600) 1720(250) 1590(230) 10 40 486
Q&T 425(800) 1470(213) 1360(198) 10 44 430
Q&T 540(1000) 1170(170) 1080(156) 13 51 360
Q&T 650(1200) 965(140) 855(124) 19 60 280

 

(Table A-24)

ASTM Number Tensile Strength  S_{ut} , kpsi Compressive Strength  S_{uc}, kpsi Shear Modulus  of Rupture S_{cu}, kpsi Modulus of Elasticity, Mpsi Endurance Limit*  S_{e}, kpsi Brinell Hardness H_{B} Fatigue Stress- Concentration Factor k_{f}
Tension†  Torsion
20 22 83 26 9.6–14 3.9–5.6 10 156 1
25 26 97 32 11.5–14.8 4.6–6.0 11.5 174 1.05
30 31 109 40 13–16.4 5.2–6.6 14 201 1.1
35 36.5 124 48.5 14.5–17.2 5.8–6.9 16 212 1.15
40 42.5 140 57 16–20 6.4–7.8 18.5 235 1.25
50 52.5 164 73 18.8–22.8 7.2–8.0 21.5 262 1.35
60 62.5 187.5 88.5 20.4–23.5 7.8–8.5 24.5 302 1.5

(Table A-24c)

Titanium Alloy Condition Yield, S_{y} (0.2% offset) MPa (kpsi) Strength  Tensile, S_{ut} MPa (kpsi) Elongation in 2 in, % Hardness (Brinell or Rockwell)
Ti-35A^{†} Annealed 210(30) 275(40) 30 135 HB
Ti-50A^{†} Annealed 310(45) 380(55) 25 215 HB
Ti-0.2Pd Annealed 280(40) 340(50) 28 200 HB
Ti-5Al-2.5 Sn Annealed 760(110) 790(115) 16 36 HRC
Ti-8 Al-1 Mo-1 V Annealed 900(130) 965(140) 15 39 HRC
Ti-6 Al-6 V-2 Sn Annealed 970(140) 1030(150) 14 38 HRC
SNAG-21100305020000

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