445_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

445_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 4:59 AM Page 439 439 SECTION 5.7 Nonprismatic Beams d c dx 288 1 L * 2 pbAhA2 (3L + x)3 d s (x) dx c (864 PL d 9PL2 2880 P x) p bA hA2 (3 L L2 + x)4 d 9M0L 0 0.105m solution agrees with plot above, evaluate using numerical data L2 x)3 smax s(xmax) sA s(0) sB s(L) 1440Px22 864 M0 L pbAhA2 (3L 36PxL + 5Px2 Solving for x max: xmax 0 3 1864 P x L * OR 3 M0 L + 5 P x22 3 Px L 0 smax 214 MPa ; sA 210 MPa ; sB 0 MPa ; OR simplifying 2 (288 L ) Problem 5.7-5 c 9PL2 36PxL + 5Px2 9M0L d c pbAhA2 (3L + x)4 d 0 Refer to the tapered cantilever beam of solid circular cross section shown in Fig. 5-24 of Example 5-9. (a) Considering only the bending stresses due to the load P, determine the range of values of the ratio dB/dA for which the maximum normal stress occurs at the support. (b) What is the maximum stress for this range of values? Solution 5.7-5 Tapered cantilever beam FROM EQ. (5-32), EXAMPLE 5-9 s1 32Px p c dA + (dB [32Px][p] [3] c dA + (dB Eq. (1) x3 dA) a b d L 32pP c dA + (dB D p 2 c dA + (dB FIND THE VALUE OF x THAT MAKES s1 A MAXIMUM Let s1 N u v ds1 dx p c dA + (dB du b dx dA) d After simplification: N va x 21 dA) a b d c (dB L L ua dv b dx 2 v x3 dA) a b d [32P] L N D ds1 dx x2 dA) a b d c dA L 2(dB x dA) d L x6 dA) d L N D 32P c dA 2(dB p c dA + (dB x dA) d L x4 dA) a b d L ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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