7_ch 03 Mechanical Design budynas_SM_ch03

7_ch 03 Mechanical Design budynas_SM_ch03 - 3 ± x − 20...

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20 Solutions Manual • Instructor’s Solution Manual to Accompany Mechanical Engineering Design At x = 10 + , V = M = 0 from Eqs. (1) and (2) R 1 1000 2000 + R 2 = 0 R 1 + R 2 = 3000 10 R 1 1000 ( 10 2 ) 2000 ( 10 8 ) = 0 R 1 = 1200 lbf, R 2 = 3000 1200 = 1800 lbf 0 x 2: V = 1200 lbf, M = 1200 x lbf · ft 2 x 8: V = 1200 1000 = 200 lbf M = 1200 x 1000( x 2) = 200 x + 2000 lbf · ft 8 x 10: V = 1200 1000 2000 =− 1800 lbf M = 1200 x 1000( x 2) 2000( x 8) =− 1800 x + 18 000 lbf · ft Plots are the same as in Prob. 3-3. (e) q = R 1 ± x ² 1 400 ± x 4 ² 1 + R 2 ± x 7 ² 1 800 ± x 10 ² 1 V = R 1 400 ± x 4 ² 0 + R 2 ± x 7 ² 0 800 ± x 10 ² 0 (1) M = R 1 x 400 ± x 4 ² 1 + R 2 ± x 7 ² 1 800 ± x 10 ² 1 (2) at x = 10 + , V = M = 0 R 1 400 + R 2 800 = 0 R 1 + R 2 = 1200 (3) 10 R 1 400(6) + R 2 (3) = 0 10 R 1 + 3 R 2 = 2400 (4) Solve Eqs. (3) and (4) simultaneously: R 1 =− 171 . 4 lbf, R 2 = 1371 . 4 lbf 0 x 4: V =− 171 . 4 lbf, M =− 171 . 4 x lbf · ft 4 x 7: V =− 171 . 4 400 =− 571 . 4 lbf M =− 171.4 x 400( x 4) lbf · ft =− 571.4 x + 1600 7 x 10: V =− 171 . 4 400 + 1371 . 4 = 800 lbf M =− 171.4 x 400( x 4) + 1371.4( x 7) = 800 x 8000 lbf · ft Plots are the same as in Prob. 3-3. (f) q = R 1 ± x ² 1 40 ± x ² 0 + 40 ± x 8 ² 0 + R 2 ± x 10 ² 1 320 ± x 15 ² 1 + R 3 ± x 20 ² V = R 1 40 x + 40 ± x 8 ² 1 + R 2 ± x 10 ² 0 320 ± x 15 ² 0 + R
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Unformatted text preview: 3 ± x − 20 ² (1) M = R 1 x − 20 x 2 + 20 ± x − 8 ² 2 + R 2 ± x − 10 ² 1 − 320 ± x − 15 ² 1 + R 3 ± x − 20 ² 1 (2) M = 0 at x = 8 in ∴ 8 R 1 − 20(8) 2 = ⇒ R 1 = 160 lbf at x = 20 + , V and M = 160 − 40(20) + 40(12) + R 2 − 320 + R 3 = ⇒ R 2 + R 3 = 480 160(20) − 20(20) 2 + 20(12) 2 + 10 R 2 − 320(5) = ⇒ R 2 = 352 lbf R 3 = 480 − 352 = 128 lbf ≤ x ≤ 8: V = 160 − 40 x lbf, M = 160 x − 20 x 2 lbf · in 8 ≤ x ≤ 10: V = 160 − 40 x + 40( x − 8) = − 160 lbf, M = 160 x − 20 x 2 + 20( x − 8) 2 = 1280 − 160 x lbf · in 10 ≤ x ≤ 15: V = 160 − 40 x + 40( x − 8) + 352 = 192 lbf M = 160 x − 20 x 2 + 20( x − 8) + 352( x − 10) = 192 x − 2240...
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