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491_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 491_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 5.12 Beams with Axial Loads 485 Solution 5.12-12 (a) E QUAL MAXIMUM TENSILE STRESSES C IRCULAR POST Tension s t P A + M S 4 P p d 2 + 16 P p d 2 12 P p d 2 A p 4 d 2 S p 32 d 3 M Pd 2 C OMPRESSION R ECT ANGULAR POST T ENSION s t P A + M S P bd 3 P bd 2 P bd A bd S bd 2 6 M Pd 2 4 P p d 2 16 P p d 2 20 P p d 2 s c P A M S Substitute numerical values into Eqs. (1) and (2): (b) M AXIMUM DEPTH FOR NO TENSION Set = 0 in Eq. (1): h g c + d 3 g w t 2 0 d 3 ht 2 a g c g w b s t s c 6.042 psi 93.600 psi 99.6 psi ; s t 6.042 psi + 93.600 psi 87.6 psi ; d max 28.9 in. ; d 3 (72 in.)(12 in.) 2 a 145 62.4 b 24,092 in. 3 Problem 5.12-12 A circular post, a rectangular post, and a post of cruciform cross section are each compressed by loads that produce a resultant force P acting at the edge of the cross section (see figure). The diameter of the circular post and the
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Unformatted text preview: at the edge of the cross section (see figure). The diameter of the circular post and the depths of the rectangular and cruciform posts are the same. (a) For what width b of the rectangular post will the maximum tensile stresses be the same in the circular and rectangular posts? (b) Repeat (a) for the post with cruciform cross section. (c) Under the conditions described in parts (a) and (b), which post has the largest compressive stress? 4 ´ = d d 4 — 4 ´ = b b 4 — Load P here P P P b d d d x 05Ch05.qxd 9/25/08 2:29 PM Page 485...
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