Shigleys ch20

Chapter 20
20-1 (a)
12 10 8 6 4 2 0

60

70

80

90 100 110 120 130 140 150 160 170 180 190 200 210

(b) f/(N x) = f/(69 · 10) = f/690 x 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 f 2 1 3 5 8 12 6 10 8 5 2 3 2 1 0 1 69 fx 120 70 240 450 800 1320 720 1300 1120 750 320 510 360 190 0 210 8480 f x2 7200 4900 19 200 40 500 80 000 145 200 86 400 169 000 156 800 112 500 51 200 86 700 64 800 36 100 0 44 100 1 104 600 f/(N x) 0.0029 0.0015 0.0043 0.0072 0.0116 0.0174 0.0087 0.0145 0.0116 0.0174 0.0029 0.0043 0.0029 0.0015 0 0.0015

Eq. (20-9) Eq. (20-10)

x= ¯

8480 = 122.9 kcycles 69
1/2

1 104 600 − 84802 /69 sx = 69 − 1 = 30.3 kcycles Ans.

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Solutions Manual • Instructor’s Solution Manual to Accompany Mechanical Engineering Design

20-2

Data represents a 7-class histogram with N = 197. x 174 182 190 198 206 214 220 f 6 9 44 67 53 12 6 197 x= ¯ fx 1044 1638 8360 13 266 10 918 2568 1320 39 114 Ans.
1/2

f x2 181 656 298 116 1 588 400 2 626 688 2 249 108 549 552 290 400 7 789 900

39 114 = 198.55 kpsi 197

7 783 900 − 39 1142 /197 sx = 197 − 1 = 9.55 kpsi 20-3 Form a table: x 64 68 72 76 80 84 88 92 f 2 6 6 9 19 10 4 2 58 x= ¯ sx = From Eq. (20-14) 1 1 f (x) = √ exp − 2 6.57 2π fx 128 408 432 684 1520 840 352 184 4548 Ans.

f x2 8192 27 744 31 104 51 984 121 600 70 560 30 976 16 928 359 088

4548 = 78.4 kpsi 58 359 088 − 45482 /58 58 − 1
1/2

= 6.57 kpsi

x − 78.4 6.57

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Chapter 20

3

20-4 (a) y 5.625 5.875 6.125 6.375 6.625 6.875 7.125 7.375 7.625 7.875 8.125 f 1 0 0 3 3 6 14 15 10 2 1 55 fy 5.625 0 0 19.125 19.875 41.25 99.75 110.625 76.25 15.75 8.125 396.375 f y2 31.640 63 0 0 121.9219 131.6719 283.5938 710.7188 815.8594 581.4063 124.0313 66.015 63 2866.859 y 5.625 5.875 6.125 6.375 6.625 6.875 7.125 7.375 7.625 7.875 8.125 f/(Nw) 0.072 727 0 0 0.218 182 0.218 182 0.436 364 1.018 182 1.090 909 0.727 273 0.145 455 0.072 727 f (y) 0.001 262 0.008 586 0.042 038 0.148 106 0.375 493 0.685 057 0.899 389 0.849 697 0.577 665 0.282 608 0.099 492 g(y)