453_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

453_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 5.8 Shear Stresses in Rectangular Beams 447 Solution 5.8-8 (a) F IND M BASED ON ALLOWABLE SHEAR STRESS IN GLUED JOINT M AX . SHEAR ST LEFT SUPPORT t a ± V m Q Ib I ± b h 3 12 Ib ± b 2 h 3 12 V m ± qL 2 + M L and V m ± t a a Ib Q b q ± 10 N m beam distributed weight q ± W L W ± 3.6 N L ± 360 mm b ± 30 mm h ± 30 mm t a ± 0.3 MPa M max ± 72.2 N # M ; M ± L c t a a 3 bh 4 b ² qL 2 d M ± L c t a a I b Q b ² q L 2 d Q I b ± 4 3 bh Q ± b h 3 h 3 Q ± b h 2 9 Q Ib ± b h 2 9 b 2 h 3 12 P max ± 2.03 k (governs) P max ± A t allow ² 3 qL 4 P ± a A t max ² 3 qL 4 b t max ± 3 V 2 A ± 3 2 A a P 2 3 + qL 2 b V ± P 2 3 + qL 2 A LLOWABLE LOAD BASED UPON BENDING STRESS ; P allow ± 2.03 k P max ± 3.165 k P max ± s allow S 3 (3 ft) 2 ² 3 2 a qL 2 ² q 2 (3ft) b s max ± M S ± P 2 3 3 ft + qL 2 3 ft ² q 2 (3 ft) 2 S S ± b h 2 6 M ± P 2 3 3 ft + qL 2 3 ft ² q 2 (3 ft) 2 Problem 5.8-8 A laminated plastic beam of square cross section is built up by gluing together three strips, each
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Unformatted text preview: 10 mm 30 mm in cross section (see figure). The beam has a total weight of 3.6 N and is simply supported with span length L 360 mm. Considering the weight of the beam ( q) calculate the maximum permissible CCW moment M that may be placed at the right support. (a) If the allowable shear stress in the glued joints is 0.3 MPa. (b) If the allowable bending stress in the plastic is 8 MPa. M 30 mm 30 mm 10 mm 10 mm 10 mm q L 05Ch05.qxd 9/25/08 2:29 PM Page 447...
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