504_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

504_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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498 CHAPTER 6 Stresses in Beams (Advanced Topics) Problem 6.2-2 A wood beam with cross-sectional dimensions 200 mm ± 300 mm is reinforced on its sides by steel plates 12 mm thick (see figure). The moduli of elasticity for the steel and wood are E s ² 190 GPa and E w ² 11 GPa, respectively. Also, the corre- sponding allowable stresses are s s ² 110 MPa and s w ² 7.5 MPa. (a) Calculate the maximum permissible bending moment M max when the beam is bent about the z axis. (b) Repeat part a if the beam is now bent about its y axis. Solution 6.2-2 (a) B ENT ABOUT THE Z AXIS E w I w ³ E s I s ² 1.52 ± 10 7 N ´ m 2 I s ² 2 th 3 12 I s ² 5.40 * 10 7 mm 4 I w ² bh 3 12 I w ² 4.50 * 10 8 mm 4 s allow_w ² 7.5 MPa s allow_s ² 110 MPa E w ² 11 GPa E s ² 190 GPa b ² 200 mm t ² 12 mm h ² 300 mm M AXIMUM MOMENT BASED UPON THE WOOD
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Unformatted text preview: M AXIMUM MOMENT BASED UPON THE STEEL S TEEL G OVERNS . (b) B ENT ABOUT THE Y AXIS E w I w + E s I s 1.76 * 10 7 N # m 2 I s 8.10 * 10 7 mm 4 I s 2 c t 3 h 12 + t h a b + t 2 b 2 d I w b 3 h 12 I w 2.00 * 10 8 mm 4 M max 58.7 kN # m ; M max min ( M max_w , M max_s ) M max_s 58.7 kN # m M max_s s allow_s J E w I w + E s I s a h 2 b E s K M max_w 69.1 kN # m M max_w s allow_w J E w I w + E s I s a h 2 b E w K (a) (b) z y C 200 mm 12 mm 12 mm 300 mm z y C 200 mm 12 mm 12 mm 300 mm 300 mm 200 mm 12 mm 12 mm y z C 2 1 06Ch06.qxd 9/24/08 5:32 AM Page 498...
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