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535_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 535_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 6.5 Bending of Unsymmetric Beams 529 Bending of Unsymmetric Beams When solving the problems for Section 6.5, be sure to draw a sketch of the cross section showing the orientation of the neutral axis and the locations of the points where the stresses are being found. Problem 6.5-1 A beam of channel section is subjected to a bending moment M having its vector at an angle u to the z axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress s t and maximum compressive stress s c in the beam. Use the following data: C 8 11.5 section, M 20 k-in., tan u 1/3. ( Note : See Table E-3a of Appendix E for the dimensions and properties of the channel section.) B ENDING MOMENTS
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Unformatted text preview: N EUTRAL AXIS nn M AXIMUM TENSILE STRESS P OINT A: (b) B UILT UP SECTION : I y ² I sy ´ 2 I cz I y ² 9.50 in. 4 b ² d c b ² 4.000 in. d ² d s + 2 b c d ² 9.160 in. I z ² 60.4 in. 4 I z ² I sz + 2 c I cy + A c a d s 2 + c b 2 d s A ² s x ( z A , y A ) s A ² 8469 psi ; z A ² ³ b 2 y A ² ³ d 2 s x ( z , y ) ² M y z I y ³ M z y I z b ² ³ 76.2° ; b ² a tan a I z I y tan( ³ a ) b # # N EUTRAL AXIS nn M AXIMUM TENSILE STRESS P OINT A: s A ² s x ( z A , y A ) s A ² 8704 psi ; z A ² ³ b 2 y A ² ³ d 2 s x ( z , y ) ² M y z I y ³ M z y I z b ² ³ 79.4° ; b ² a tan a I z I y tan( ³ a ) b z y C M u Probs. 6.5-1 and 6.5-2 06Ch06.qxd 9/24/08 5:54 AM Page 529...
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