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572_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 572_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 566 6:05 AM Page 566 CHAPTER 6 Stresses in Beams (Advanced Topics) Problem 6.10-15 The hollow box beam shown in the figure is subjected to a bending moment M of such magnitude that the flanges yield but the webs remain linearly elastic. (a) Calculate the magnitude of the moment M if the dimensions of the cross section are h b 9 in., and b1 7.5 in. Also, the yield stress is sY 33 ksi. 15 in., h1 12.75 in., Solution 6.10-15 h b1 15 in. b 9 in. sy 7.5 in. h1 12.75 in. 33 ksi 1 (b 6 M1 syS1 h + h1 b 2 M2 4636 k-in. M 5977 k-in. (a) BENDING MOMENT ELASTIC CORE S1 Fa M2 b1)h2 1 M1 M 40.64 in.3 S1 M1 + M2 (b) PERCENT DUE TO ELASTIC CORE 1341 k-in. M1 M PLASTIC FLANGES F 1 syb a b (h 2 ; 22.4% force in one flange F ; h1) F 334.1 k Problem 6.10-16 Solve the preceding problem for a box beam with dimensions h and b1 160 mm, and with yield stress sY Solution 6.10-16 h h1 400 mm b (a) BENDING MOMENT 200 mm b1 sY 160 mm (see Figure 6-47, Example 6-9) M1 sYS1 b1)h2 1 3 190.1 kN # m force in one flange F 1 sYb a b (h 2 h + h1 b 2 h1) 3 864 * 10 mm F Fa M M1 Percent PLASTIC FLANGES M2 220 MPa M2 ; 524 kN m (b) PERCENT DUE TO ELASTIC CORE ELASTIC CORE S1 360 mm, b Hollow box beam 360 mm 1 (b 6 400 mm, h1 220 MPa. 880.0 kN 334.4 kN # m M1 (100) M 36% ; 200 mm, ...
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