4_ch 04 Mechanical Design budynas_SM_ch04

4_ch 04 Mechanical Design budynas_SM_ch04 -...

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Unformatted text preview: budynas_SM_ch04.qxd 11/28/2006 20:50 FIRST PAGES Page 73 73 Chapter 4 4-8 M = M1 = M B EI dy = M B x + C1 , dx EIy = y= dy = 0 at x = 0, dx C1 = 0 y = 0 at x = 0, C2 = 0 MB x 2 + C2 , 2 MB x 2 2E I Ans. 4-9 y ds = ds dy dx2 + dy 2 dx dy = dx 1 + dx 2 Expand right-hand term by Binomial theorem 2 1/2 dy 1+ dx =1+ 2 dy dx 1 2 + ··· Since d y /dx is small compared to 1, use only the first two terms, d λ = ds − dx 1 dy = dx 1 + 2 dx = λ= 1 dy 2 dx 1 2 l 0 2 − dx 2 dx dy dx 2 dx Ans. This contraction becomes important in a nonlinear, non-breaking extension spring. 4-10 w y = C x 2 (4lx − x 2 − 6l 2 ) where C = 24 E I dy 2 2 = C x (12lx − 4x − 12l ) = 4C x (3lx − x 2 − 3l 2 ) dx dy dx 2 = 16C 2 (15l 2 x 4 − 6lx 5 − 18x 3l 3 + x 6 + 9l 4 x 2 ) l dy dx 1 λ= 2 0 = 8C 2 l 2 dx = 8C (15l 2 x 4 − 6lx 5 − 18x 3l 3 + x 6 + 9l 4 x 2 ) dx 2 0 w 97 l =8 14 24 E I 2 w 97 1 l= 14 112 E I 2 l7 Ans. ...
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