6_ch 03 Mechanical Design budynas_SM_ch03

6_ch 03 Mechanical Design budynas_SM_ch03 -...

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Unformatted text preview: budynas_SM_ch03.qxd 11/28/2006 21:21 FIRST PAGES Page 19 19 Chapter 3 3-4 (a) q = R1 x −1 − 40 x − 4 −1 + 30 x − 8 −1 + R2 x − 14 −1 − 60 x − 18 −1 V = R1 − 40 x − 4 0 + 30 x − 8 0 + R2 x − 14 0 − 60 x − 18 0 M = R1 x − 40 x − 4 1 + 30 x − 8 1 + R2 x − 14 1 − 60 x − 18 1 for x = 18+ V =0 and M = 0 0 = R1 − 40 + 30 + R2 − 60 (1) (2) Eqs. (1) and (2) give ⇒ R1 + R2 = 70 0 = R1 (18) − 40(14) + 30(10) + 4 R2 ⇒ (3) 9 R1 + 2 R2 = 130 Solve (3) and (4) simultaneously to get R1 = −1.43 lbf, R2 = 71.43 lbf. (4) Ans. + From Eqs. (1) and (2), at x = 0 , V = R1 = −1.43 lbf, M = 0 x = 4+ : x = 8+ : V V M x = 14+ : V M + x = 18 : V (b) q = R0 x −1 = −1.43 − 40 = −41.43, M = −1.43x = −1.43 − 40 + 30 = −11.43 = −1.43(8) − 40(8 − 4) 1 = −171.44 = −1.43 − 40 + 30 + 71.43 = 60 = −1.43(14) − 40(14 − 4) + 30(14 − 8) = −240 . = 0, M = 0 See curves of V and M in Prob. 3-3 solution. − M0 x −2 − 2000 x − 0.2 −1 − 4000 x − 0.35 0 + 4000 x − 0.5 V = R0 − M0 x −1 − 2000 x − 0.2 0 − 4000 x − 0.35 1 + 4000 x − 0.5 M = R0 x − M0 − 2000 x − 0.2 1 − 2000 x − 0.35 2 + 2000 x − 0.5 2 0 1 (1) (2) at x = 0.5+ m, V = M = 0, Eqs. (1) and (2) give R0 − 2000 − 4000(0.5 − 0.35) = 0 ⇒ R1 = 2600 N = 2.6 kN R0 (0.5) − M0 − 2000(0.5 − 0.2) − 2000(0.5 − 0.35) 2 = 0 Ans. with R0 = 2600 N, M0 = 655 N · m Ans. With R0 and M0, Eqs. (1) and (2) give the same V and M curves as Prob. 3-3 (note for V, M0 x −1 has no physical meaning). q = R1 x −1 − 1000 x − 6 −1 + R2 x − 10 V = R1 − 1000 x − 6 0 + R2 x − 10 0 M = R1 x − 1000 x − 6 1 + R2 x − 10 1 (c) −1 (1) (2) at x = 10+ ft, V = M = 0, Eqs. (1) and (2) give R1 − 1000 + R2 = 0 10 R1 − 1000(10 − 6) = 0 0 ≤ x ≤ 6: 6 ≤ x ≤ 10: ⇒ ⇒ R1 + R2 = 1000 R1 = 400 lbf , R2 = 1000 − 400 = 600 lbf V = 400 lbf, M = 400x V = 400 − 1000( x − 6) 0 = 600 lbf M = 400x − 1000( x − 6) = 6000 − 600x See curves of Prob. 3-3 solution. (d) q = R1 x −1 − 1000 x − 2 −1 − 2000 x − 8 −1 + R2 x − 10 V = R1 − 1000 x − 2 0 − 2000 x − 8 0 + R2 x − 10 0 M = R1 x − 1000 x − 2 1 − 2000 x − 8 1 + R2 x − 10 1 −1 (1) (2) ...
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This note was uploaded on 12/13/2011 for the course EML 3013 taught by Professor Shingley during the Fall '11 term at UNF.

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