15_ch 07 Mechanical Design budynas_SM_ch07

# 15_ch 07 Mechanical Design budynas_SM_ch07 -...

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192 Solutions Manual • Instructor’s Solution Manual to Accompany Mechanical Engineering Design Plot M / I as a function of x . x ( m ) M / I ( 10 9 N/m 3 ) Step Slope ± Slope 00 52.8 0.04 2.112 0.04 1.2375 0.8745 30.942 21.86 0.1 3.094 0.1 1.932 1.162 19.325 11.617 0.14 2.705 0.14 2.705 0 15.457 34.78 0.21 1.623 0.21 2.6 0.977 24.769 9.312 0.275 0.99 0.275 1.6894 0.6994 42.235 17.47 0.315 0 The steps and the change of slopes are evaluated in the table. From these, the function M / I can be generated: M / I = ± 52 . 8 x 0 . 8745 ± x 0 . 04 ² 0 21 . 86 ± x 0 . 04 ² 1 1 . 162 ± x 0 . 1 ² 0 11 . 617 ± x 0 . 1 ² 1 34 . 78 ± x 0 . 14 ² 1 + 0 . 977 ± x 0 . 21 ² 0 9 . 312 ± x 0 . 21 ² 1 + 0 . 6994 ± x 0 . 275 ² 0 17 . 47 ± x 0 . 275 ² 1 ² 10 9 Integrate twice: E dy dx = ± 26 . 4 x 2 0 . 8745 ± x 0 . 04 ² 1 10 . 93 ± x 0 . 04 ² 2 1 . 162 ± x 0 . 1 ² 1 5 . 81 ± x 0 . 1 ² 2 17 . 39 ± x 0 . 14 ² 2 + 0 . 977 ± x 0 . 21 ² 1 4 . 655 ± x 0 . 21 ² 2 + 0 . 6994 ± x 0 . 275 ² 1 8 . 735 ± x 0 . 275 ² 2 + C 1 ² 10 9 (1) Ey = ± 8 . 8 x 3 0 . 4373 ± x 0 . 04 ² 2 3 . 643 ± x 0 . 04 ² 3 0 . 581 ± x 0 . 1 ² 2 1 . 937 ± x 0 . 1 ² 3 5 . 797 ± x 0 . 14 ² 3 + 0 . 4885 ± x 0 . 21 ² 2 1 . 552 ± x 0 . 21 ² 3 + 0 . 3497 ± x 0 . 275
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