493_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

493_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 5.12 Beams with Axial Loads 487 Solution 5.12-14 Bar with reduced cross section (a) S QUARE BAR Cross section is a rectangle. S TRESSES s c ± P A ² Mc I ± 2 P b 2 ² 6 P b 2 ±² 4 P b 2 ; s t ± P A + Mc I ± 2 P b 2 + 6 P b 2 ± 8 P b 2 ; M ± P a b 4 b c ± b 4 A ± ( b ) a b 2 b ± b 2 2 I ± 1 12 ( b ) a b 2 b 3 ± b 4 96 mn (b) C IRCULAR BAR Cross section is a semicircle From Appendix D, Case 10: M ± P a 2 b 3 p b ± 0.2122 Pb I ± 0.1098 a b 2 b 4 ± 0.006860 b 4 A ± 1 2 a p b 2 4 b ± p b 2 8 ± 0.3927 b 2 mn C ROSS SECTION OF BLOCK (a) M AMIMUM TENSILE STRESS ( AT TOP OF BLOCK ) ± 400 psi + 1500 psi ± 1900 psi ; ± 1200 lb 3 in. 2 + (1200 lb)(0.625 in.)(0.5 in.) 0.25 in. 4 s t ± P A + Pey I y ± t 2 ± 0.5 in. A ± bt ± 30 in. 2 I ± 1 12 bt 3 ± 0.25 in. 4 M AXIMUM COMPRESSIVE STRESS ( AT BOTTOM OF BLOCK ) (b) I F IS INCREASED , increase the eccentricity increases and both stresses in magnitude. e d ± 400 psi ² 1500 psi 1100 psi ; ± 1200 lb 3 in. 2 + (1200 lb)(0.625 in.)( ² 0.5 in.) 0.25 in. 4 s c ± P A + Pey I y t 2 0.5 in. Problem 5.12-14
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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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