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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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510 CHAPTER 6 Stresses in Beams (Advanced Topics) Solution 6.3-2 Box beam S IMPLE BEAM : L 3.2 m q 48 kN/m (1) Wood flanges: b 100 mm h 300 mm h 1 150 mm ( s 1 ) allow 6.5 MPa E w 10 GPa (2) Steel plates: t thickness h 300 mm ( s 2 ) allow 120 MPa E s 210 GPa T RANSFORMED SECTION ( WOOD ) M max qL 2 8 61.44 kN # m Width of steel plates nt 21 t All dimensions in millimeters. R EQUIRED THICKNESS BASED UPON THE WOOD (1) (E Q . 6-15) Equate I T and ( I T ) 1 and solve for t : t 1 12.92 mm R EQUIRED THICKNESS BASED UPON THE STEEL (2) (E Q . 6-17) Equate I T and ( I T ) 2 and solve for t : t 2 14.97 mm S TEEL GOVERNS . t min 15.0 mm ; 1.612 * 10 9 mm 4 s 2 M ( h /2) n I T ( I T ) 2 M max ( h /2) n ( s 2 ) allow 1.418 * 10 9 mm 4 s 1 M ( h /2) I T ( I T ) 1 M max ( h /2) ( s 1 ) allow 196.9 * 10 6 mm 4 + 94.5 t * 10 6 mm 4 I T 1 12 (100 + 42 t )(300) 3 1 12 (100)(150) 3 Wood flanges are not changed n E s E w 21 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
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