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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 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 M z y I z b 28.7° ; b a tan a I z I y tan( 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 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 d h 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 M z y I z b 38.5 deg ; b a tan a I z I y tan( 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
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