505_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

505_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 6.2 Composite Beams 499 M AXIMUM MOMENT BASED UPON THE WOOD M max_w 119.9 kN # m M max_w s allow_w J E w I w + E s I s a b 2 b E w K M AXIMUM MOMENT BASED UPON THE STEEL S TEEL G OVERNS . M max 90.9 kN # m ; M max min ( M max_w , M max_s ) M max_s 90.9 kN # m ; M max_s s allow_s J E w I w + E s I s a b 2 + t b E s K Problem 6.2-3 A hollow box beam is constructed with webs of Douglas-fir plywood and flanges of pine, as shown in the figure in a cross-sectional view. The plywood is 1 in. thick and 12 in. wide; the flanges are 2 in. 4 in. (nominal size). The modulus of elasticity for the plywood is 1,800,000 psi and for the pine is 1,400,000 psi. (a) If the allowable stresses are 2000 psi for the plywood and 1750 psi for the pine, find the allowable bending moment M max when the beam is bent about the z axis. (b) Repeat part a if the b.eam is now bent about its
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Unformatted text preview: (b) (a) z y C 1.5 in. 1.5 in. 1 in. 1 in. 3.5 in. 12 in. z y C 1 in. 1 in. 1.5 in. 1.5 in. 3.5 in. 12 in. Solution 6.2-3 (a) B ENT ABOUT THE Z AXIS M AXIMUM MOMENT BASED UPON THE WOOD M AXIMUM MOMENT BASED UPON THE PLYWOOD M max_2 ± 172 k # in. ; M max_2 ± s allow_2 J E 1 I 1 + E 2 I 2 a h 2 b E 2 K M max_1 ± 193 k # in. ; M max_1 ± s allow_1 J E 1 I 1 + E 2 I 2 a h 2 b E 1 K E 1 I 1 + E 2 I 2 ± 9.26 * 10 8 lb # in. 2 I 2 ± 2 th 3 12 I 2 ± 288 in. 4 I 1 ± b ( h 3 ³ h 3 1 ) 12 I 1 ± 291 in. 4 t b t h h 1 2 2 1 1 s allow_1 ± 1750 psi s allow_2 ± 2000 psi E 1 ± 1.4 * 10 6 psi E 2 ± 1.8 * 10 6 psi b ± 3.5 in. t ± 1 in. h ± 12 in. h 1 ± 9 in. 06Ch06.qxd 9/24/08 5:32 AM Page 499...
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