539_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

539_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 6.5 Bending of Unsymmetric Beams 533 Solution 6.5-5 (a) B UILT UP SECTION : I z ± 2 I L 1 I z ± 20.000 in. 4 B ENDING MOMENTS M y ±² M sin ( u ) M y 1.250 k ft M z ± M cos ( u ) M z ± 2.165 k ft N EUTRAL AXIS nn M AXIMUM TENSILE STRESS s x ( z , y ) ± M y z I y ² M z y I z b 28.7° ; b ± a tan a I z I y tan( ² u ) b # # h 1 ± d h 1 ± 1.650 in. b ± 7.750 in. h ± h L 1 h ± 5.000 in. b ± gap + 2 h L 2 I y ± 21.065 in. 4 I y ± 2 c I L2 + A L a gap 2 + c b 2 d A L ± 4 in. 2 gap ± 3 4 in. t ± 1 2 in. h L 1 ± 5 in. h L 2 ± 3.5 in. I L 2 ± 4.02 in. 4 d ± 1.65 in. c ± 0.901 in. L5 * 3 q 1/2 * 1/2 I L 1 ± 10.0 in. 4 M ± 30 k # in. u ± 30° P OINT A: M AXIMUM COMPRESSIVE STRESS P OINT B: (b) B UILT UP SECTION : I z ± 2 I L 1 I z ± 20.000 in. 4 I y ± 2( I L 2 ³ A L c 2 ) I y ± 14.534 in. 4 h ± h L 1 h ± 5.000 in. b ± 2 h L 2 b ± 7.000 in. h 1 ± h ² dh 1 ± 3.350 in. N EUTRAL AXIS nn M AXIMUM TENSILE STRESS P OINT A: M AXIMUM COMPRESSIVE STRESS P OINT B: s c ± s x ( z B , y B ) s c 4868 psi ; z B ± t y B ± h 1 s t ± s x ( z A , y A ) s t ± 5756 psi ; z A b 2 y A h + h 1 s x ( z , y ) ± M y z I y ² M z y I z b 38.5 deg ; b ± a tan a I z I y tan( ² u ) b s c ± s x ( z B , y B ) s c 4903 psi ; z B ± b 2 y B ± h 1 s t ± s x ( z A , y A ) s t ± 4263 psi ; z A gap 2 + t y A h + h 1 Problem 6.5-6 The Z-section of Example 12-7 is subjected to
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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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