05-04ChapGere.0009 - max 5 qL 2 8 s 5 M max S q 5 8 S s L 2...

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Problem 5.10-8 A bridge girder AB on a simple span of length L 5 14 m supports a uniform load of intensity q 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 5 110 MPa, and (b) an allowable shear stress t allow 5 50 MPa. Solution 5.10-8 Bridge girder (simple beam) 346 CHAPTER 5 Stresses in Beams (Basic Topics) L 5 14 m b 5 450 mm t 5 15 mm h 5 1860 mm h 1 5 1800 mm s allow 5 110 MPa t allow 5 50 MPa c 5 h /2 5 930 mm Eq. (5-47): 5 29.897 3 10 9 mm 4 S 5 I c 5 29.897 3 10 9 mm 4 930 mm 5 32.147 3 10 6 mm 3 I 5 1 12 ( bh 3 2 bh 3 1 1 th 1 3 ) (a) M AXIMUM LOAD BASED UPON BENDING STRESS 5 144.3 3 10 3 N/m 5 144 kN/m (b) M AXIMUM LOAD BASED UPON SHEAR STRESS (Eq. 5-48a) Substitute numerical values: q max 5 173.8 3 10 3 N/m 5 174 kN/m N OTE : Bending stress governs. q allow 5 144 kN/m q max 5 2 V max L 5 16 It ( t allow ) L ( bh 2 2 bh 2 1 1 th 1 2 ) V max 5 qL 2 Ê t max 5 V max 8 It ( bh 2 2 bh 1 2 1 th 1 2 ) q max 5 8 S s allow L 2 5 8(32.147 3 10 6 mm 3 )(110 MPa) (14 m) 2 M
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Unformatted text preview: max 5 qL 2 8 s 5 M max S q 5 8 S s L 2 t h 1 b h A B L = 14 m q 450 mm 450 mm 1800 mm 15 mm 30 mm 30 mm Problem 5.10-9 A simple beam with an overhang supports a uniform load of intensity q 5 1200 lb/ft and a concentrated load P 5 3000 lb (see figure). The uniform load includes an allowance for the weight of the beam. The allowable stresses in bending and shear are 18 ksi and 11 ksi, respectively. Select from Table E-2, Appendix E, the lightest I-beam ( S shape) that will support the given loads. Hint: Select a beam based upon the bending stress and then calculate the maximum shear stress. If the beam is overstressed in shear, select a heavier beam and repeat. C P = 3000 lb q = 1200 lb/ft 12 ft 4 ft 8 ft A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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