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525_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 525_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 5:34 AM Page 519 519 SECTION 6.3 Transformed-Section Method Problem 6.3-12 A wood beam reinforced by an aluminum channel section is 150 mm shown in the figure. The beam has a cross section of dimensions 150 mm by 250 mm, and the channel has a uniform thickness of 6 mm. If the allowable stresses in the wood and aluminum are 8.0 MPa and 38 MPa, respectively, and if their moduli of elasticity are in the ratio 1 to 6, what is the maximum allowable bending moment for the beam? y 216 mm 250 mm z O 40 mm 6 mm 162 mm Solution 6.3-12 Wood beam and aluminum channel (1) Wood beam: bw 150 mm (sw)allow 8.0 MPa (2) Aluminum channel: t ha (sa)allow hw 6 mm 250 mm Use the base of the cross section as a reference line. h2 ba 40 mm 162 mm © yiAi © Ai Area A1: y1 3 23 A2 (36)(34) 1224 28,152 mm3 y2A2 Area A3: y3 131 A3 (150)(250) 37,500 4,912,500 mm3 y3A3 h2 5832 17,496 mm Area A2: y2 TRANSFORMED SECTION (WOOD) (972)(6) 3 y1A1 38 MPa A1 y1A1 + 2y2A2 + y3A3 A1 + 2A2 + A3 4,986,300 mm3 45,780 mm2 108.92 mm h1 256 h2 147.08 mm MOMENT OF INERTIA Area A1: I1 1 (972)(6)3 + (972)(6)(h2 12 65,445,000 mm4 Wood beam is not changed. n Ea Ew Area A2: I2 6 Width of aluminum channel is increased. nb (6)(162 mm) nt (6)(6 mm) 972 mm 36 mm All dimensions in millimeters. 1 (36)(34)3 12 + (36)(34)(h2 9,153,500 mm4 6 17)2 3)2 ...
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