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566_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 566_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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560 CHAPTER 6 Stresses in Beams (Advanced Topics) Problem 6.10-3 A propped cantilever beam of length L 54 in. with a sliding support supports a uniform load of intensity q (see figure). The beam is made of steel ( s Y 36 ksi) and has a rectan- gular cross section of width b 4.5 in. and height h 6.0 in. What load intensity q will produce a fully plastic condition in the beam? L = 54 in. q z y C Sliding support h = 6.0 in. b = 4.5 in. Solution 6.10-3 L 54 in. s y 36 ksi b 4.5 in. h 6.0 in. M AXIMUM BENDING MOMENT : P LASTIC M OMENT : M P s y bh 2 4 M max qL 2 2 Let M max M P gives Therefore q 1000 lb/in. ; q s y bh 2 2 L 2 Problem 6.10-4 A steel beam of rectangular cross section is 40 mm wide and 80 mm high (see figure). The yield stress of the steel is 210 MPa. (a) What percent of the cross-sectional area is occupied by the elastic core if the beam is
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Unformatted text preview: subjected to a bending moment of 12.0 kN ² m acting about the z axis? (b) What is the magnitude of the bending moment that will cause 50% of the cross section to yield? z y C 40 mm 80 mm Solution 6.10-4 s y ± 210 MPa b ± 40 mm h ± 80 mm (a) E LASTIC CORE M is between M y and M P e ± h A 1 2 a 3 2 ³ M M y b e ± 22.678 mm M P ± s y bh 2 4 M P ± 13.4 kN # m M y ± 9.0 kN # m M ± 12.0 kN # m M y ± s y bh 2 6 Percent of cross-sectional area is (b) E LASTIC CORE e ± 20 mm M ± 12.3 kN # m ; M ± M y a 3 2 ³ 2 e 2 h 2 b e ± h 4 2 e h ± 56.7% ; 06Ch06.qxd 9/24/08 5:59 AM Page 560...
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