467_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

467_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 5.10 Shear Stresses in Beams with Flanges 461 Solution 5.10-8 R A ± R B ± q 2 L 2 + q 4 L 2 ± 3 8 qL S ± 2 I h S ± 3.427 * 10 7 mm 3 I ± 3.194 * 10 10 mm 4 I ± 1 12 1 bh 3 ² bh 1 3 + t w h 1 3 2 b ± 450 mm t f ± 32 mm t w ± 16 mm h ± 1864 mm h 1 ± 1800 mm L ± 14 m (a) M AXIMUM LOAD BASED UPON BENDING STRESS q max ± 184.7 kN m ; q max ± s allow S 5 48 L 2 ; s ± M max S ± 5 48 qL 2 S ± 5 48 qL 2 M max ± 3 8 qL L 2 ² q 2 L 2 L 4 ² q 2 L 4 L 6 s allow ± 110 MPa (a) M AXIMUM LOAD BASED UPON BENDING STRESS (b) M AXIMUM LOAD UPON SHEAR STRESS t max ± V max 8 It 1 bh 2 ² bh 1 2 + th 1 2 2 q ± 1270 lb/ft s ± M S ± 5 12 qL 2 S q ± 12 S s allow 5 L 2 ; Shear stress governs q ± 1270 lb/ft q ± 3210 lb ft q ± t allow 32 It 3 L 1 bh 2 ² bh 1 2 + th 1 2 2 ± 3 qL 32 It 1 bh 2 ² bh 1 2 + th 1 2 2 Problem 5.10-8 A bridge girder AB on a simple span of length L ± 14 m supports a distributed load of maximum
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Unformatted text preview: intensity q at midspan and minimum intensity q /2 at supports A and B that includes the weight of the girder (see figure). The girder is constructed of three plates welded to form the cross section shown. Determine the maximum permissible load q based upon (a) an allowable bending stress s allow 110 MPa and (b) an allowable shear stress t allow 50 MPa. q 2 q 2 A B L = 14 m q 450 mm 450 mm 1800 mm 16 mm 32 mm 32 mm 05Ch05.qxd 9/25/08 2:29 PM Page 461...
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