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588_Mechanics Homework Mechanics of Materials Solution

588_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: PROBLEM 5.105 l'.‘l.llll.'5 A bridge oflengthL = 48 fl is to be built on a secondary road whose access to trucks is limited to two-axle vehicles of medium weight. It will consist of a concrete slab and of simply supported steel beams with an ultimate strength q, = 60 ksi. The combined weight of the slab and beams can be approximated by a uniformly distributed load is = 0.75 kip/ft on each beam For the purpose ofthe design, it is assumed that a MWithaxleslocatedatadistanoea= l4 fifiomeachofllerwillbedriven across the bridge and that the resulting concentrated loads P, and P, exerted on each beam could be as large as 24 kips and 6 tips, respectively. Determine the most economical wide- flsnge shape for the beams, usingLRFD with the load factors r0 = 1.25, n = 1.75 and the resistance factor ¢ = 0.9. [Hint It can be shown that the maximum value of {Mil occurs under the larger load when that load is located to the left of the center of the beamatadistanceequaltoaP,I2(P1+P2).] SOLUTION Decal Poul : 'R, E R3 = (fi-ltmxms) = t8 kip: Area. A455 of shear 01.1»er (Hams).- 2|; kip-H Mm = 214 lap—H = 2592 k.-,.;... J Paid 5 Live ”and: U = -U= 24—1.? + = 2161-14 - -G-= “lg-36$ x X L 2 M. = o -43 R. +(2S4X1Hi-(HJJHG) = O P. = H.125 ta... A in, C V ‘1' l‘i. lZS. kilos C- +0 0' V= '4.l1$’- 1‘! : ~9.37$‘ in}?! D +3 B V '-‘ * 15.875 115.95 Ana A lo C (21.004.125) r 3H.22$’ lap-H Benita: mane-d5 MC: 317.223— k.‘,.--H .- 333: kw... _3_Desi n= Tm» 7: Mt = (PHI: = 906.33“. S..- : “Vino +YLML _ (l.2$')(25"72)+(l.7$}(3831) <9 62:: tostteo) = IB‘L 2 ...
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