516_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

516_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 510 5:32 AM Page 510 CHAPTER 6 Stresses in Beams (Advanced Topics) Solution 6.3-2 Mmax qL2 8 Box beam Width of steel plates 61.44 kN # m SIMPLE BEAM: L nt 3.2 m q 48 kN/m (1) Wood flanges: b 100 mm h 300 mm h1 150 mm (s1)allow 6.5 MPa Ew (2) Steel plates: 21t All dimensions in millimeters. IT 1 (100 + 42t)(300)3 12 1 (100)(150)3 12 196.9 * 106 mm4 + 94.5t * 106 mm4 10 GPa t thickness (s2)allow 300 mm 210 GPa REQUIRED THICKNESS BASED UPON THE WOOD (1) (EQ. 6-15) 120 MPa Es h s1 M(h/2) IT (IT)1 Mmax(h/2) (s1)allow 1.418 * 109 mm4 TRANSFORMED SECTION (WOOD) Equate IT and (IT)1 and solve for t : t1 12.92 mm REQUIRED THICKNESS BASED UPON THE STEEL (2) (EQ. 6-17) s2 M(h/2)n IT (IT)2 Mmax(h/2)n (s2)allow 1.612 * 109 mm4 Equate IT and (IT)2 and solve for t : t2 STEEL GOVERNS. tmin 15.0 mm 14.97 mm ; Wood flanges are not changed n Es Ew 21 y Problem 6.3-3 A simple beam that is 18 ft long supports a uniform load of intensity q. The beam is constructed of two C 8 11.5 sections (channel sections or C shapes) on either side of a 4 8 (actual dimensions) wood beam (see the cross section shown in the figure part a). The modulus of elasticity of the steel (Es 30,000 ksi) is 20 times that of the wood (Ew). z C8 C 11.5 z y (a) If the allowable stresses in the steel and wood are 12,000 C psi and 900 psi, respectively, what is the allowable load Wood beam C 8 11.5 Wood beam qallow? (Note: Disregard the weight of the beam, and see Table E-3a of Appendix E for the dimensions and proper(a) (b) ties of the C-shape beam.) (b) If the beam is rotated 90° to bend about its y axis (see figure part b), and uniform load q 250 lb/ft is applied, find the maximum stresses ss and sw in the steel and wood, respectively. Include the weight of the beam. (Assume weight densities of 35 lb/ft3 and 490 lb/ft3 for the wood and steel, respectively.) ...
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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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