541_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

541_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 6.5 Bending of Unsymmetric Beams 535 Problem 6.5-8 The cross section of a steel beam is shown in the figure. This beam is subjected to a bending moment M having its vector at an angle u to the z axis. Determine the orientation of the neutral axis and calculate the maximum tensile stress s t and maximum compressive stress s c in the beam. Assume that u ± 22.5° and M ± 4.5 kN m. Use cross sectional properties I x 1 ± 93.14 ² 10 6 mm 4 , I y 1 ± 152.7 ² 10 6 mm 4 , and u p ± 27.3°. # y z y = 52.5 mm 30 mm 30 mm 15 mm 30 mm 90 mm 90 mm 30 mm 120 mm 180mm 180 mm 105 mm O C M u y 1 x 1 u p Solution 6.5-7 M ± 75 k in. u ± 30° P LATE : h p ± 6 in. W SECTION : h w ± 18.47 in. b w ± 7.635 in. I wy ± 60.3 in. 4 C SECTION : h c ± 10.0 in. b c ± 3.033 in. I cz ± 103 in. 4 B UILT - UP SECTION : c bar ± 1.80 in. I z ± 2200 in.
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Unformatted text preview: 4 I y I wy I cz I plate I y 172.3 in. 4 B ENDING MOMENTS M y M sin( u ) M y 3.125 k ft M z M cos( u ) M z 5.413 k ft # # I plate b p h 3 p 12 I plate 9.00 in. 4 b p 1 2 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 1157 psi ; z B b w 2 y B h w 2 + c bar s t s x ( z A , y A ) s t 1397 psi ; z A h c 2 y A h w 2 b c + c bar s x ( z , y ) M y z I y M z y I z b a tan a I z I y tan( u ) b b 82.3 ; 06Ch06.qxd 9/24/08 5:54 AM Page 535...
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