544_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

544_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 538 5:54 AM Page 538 CHAPTER 6 Stresses in Beams (Advanced Topics) Problem 6.5-10 A built-up beam supporting a condominium balcony is made up of a structural T (one half of a W 200 31.3) for the top flange and web and two angles (2L 102 76 6.4, long legs back-to-back) for the bottom flange and web, as shown. The beam 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 st and maximum compressive stress sc in the beam. Assume that u 30° and M 15 kN # m. Use the following numerical properties: c1 4.111 mm, c2 4.169 mm, bf 134 mm, Ls 76 mm, A 4144 mm2, Iy 3.88 106 mm4, and Iz 34.18 106 mm4. y u, bf /2 b bf /2 c1 C z u c2 M Ls Ls Solution 6.5-10 M 15 kN # m u MAXIMUM TENSILE STRESS (AT POINT A) 30° zA BUILT-UP SECTION: c1 4.111 mm Ls 76 mm Iy 3.88 c2 4.169 mm bf 134 mm st 2 A 4144 mm 106 mm4 Iz 34.18 106 mm4 BENDING MOMENTS st Msin(180° u) My Mz Mcos(180° u) Mz 7500 N # m zB 12990 N # m sc NEUTRAL AXIS nn b Iz atan a tan(180° Iy 78.9° yA 2 c1 My(zA) Mz(yA) Iy Iz ; 131.1 MPa MAXIMUM COMPRESSIVE STRESS (AT POINT B) My b bf ; u) b sc Ls yB c2 My(zB) Mz(yB) Iy Iz 148.5 MPa ; ...
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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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