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05-02ChapGere.0001 - 304 A-PDF Stresses in Beams(Basic...

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Design of Beams Problem 5.6-1 The cross section of a narrow-gage railway bridge is shown in part (a) of the figure. The bridge is constructed with longitudinal steel girders that support the wood cross ties. The girders are restrained against lateral buckling by diagonal bracing, as indicated by the dashed lines. The spacing of the girders is s 1 50 in. and the spacing of the rails is s 2 30 in. The load transmitted by each rail to a single tie is P 1500 lb. The cross section of a tie, shown in part (b) of the figure, has width b 5.0 in. and depth d . Determine the minimum value of d based upon an allowable bending stress of 1125 psi in the wood tie. (Disregard the weight of the tie itself.) Solution 5.6-1 Railway cross tie 304 CHAPTER 5 Stresses in Beams (Basic Topics) s 1 d s 2 P P Wood tie Steel girder Steel rail (a) (b) b s 1 50 in. b 5.0 in. s 2 30 in. d depth of tie P 1500 lb allow 1125 psi S bd 2 6 1 6 (50 in.)( d 2 ) 5 d 2 6 d inches M max P ( s 1 s 2 ) 2 15,000 lb-in. Solving, d 2 16.0 in. d min 4.0 in. Note: Symbolic solution:
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