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458_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

458_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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452 CHAPTER 5 Stresses in Beams (Basic Topics) Problem 5.8-12 A wood beam ABC with simple supports at A and B and an overhang BC has height h 300 mm (see figure). The length of the main span of the beam is L 3.6 m and the length of the overhang is L /3 1.2 m. The beam supports a concentrated load 3 P 18 kN at the midpoint of the main span and a moment PL /2 10.8 kN . m at the free end of the overhang. The wood has weight density g 5.5 kN/m 3 . (a) Determine the required width b of the beam based upon an allowable bending stress of 8.2 MPa. (b) Determine the required width based upon an allowable shear stress of 0.7 MPa. Solution 5.8-12 Numerical data: Reactions, max. shear and moment equations (a) R EQUIRED WIDTH b BASED UPON BENDING STRESS
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Unformatted text preview: L 2 ² q beam L 2 2 ± PL 2 ² 17 18 q beam L 2 V max ± R B ± 2 P + 8 9 q beam L R B ± 3 P 2 + M L + 8 9 q beam L ± 2 P + 8 9 q beam L R A ± 3 P 2 ² M L + 4 9 q beam L ± P ² 4 9 q beam L g ± 5.5 kN m 3 q beam ± g A M ± PL 2 A ± bh P ± 6 kN L ± 3.6 m h ± 300 mm (b) R EQUIRED WIDTH b BASED UPON SHEAR STRESS Shear stress governs b ± 89.1 mm ; (governs) b ± 3 P h a t allow ² 4 3 g L b b ± 89.074 mm ± 3 2 bh a 2 P + 8 9 q beam L b ± 3 P bh + 4 3 g L t ± 3 V max 2 A ± 3 V max 2 bh V max ± 2 P + 8 9 q beam L t allow ± 0.7 MPa ; b ± 3 PL s allow h 2 b ± 87.8 mm s ± M max S ± 6 M max bh 2 A C B b h = 300 mm 3 P L L 2 — L 3 — M = PL 2 ––– 05Ch05.qxd 9/25/08 2:29 PM Page 452...
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