A bridge of length L 5 48 ft is to be built on a secondary

Chapter 5, Problem 5.96

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A bridge of length L = 48 ft 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 \(\sigma_U = 60 \text{ ksi}\). The combined weight of the slab and beams can be approximated by a uniformly distributed load w = 0.75 kips/ft on each beam. For the purpose of the design, it is assumed that a truck with axles located at a distance a = 14 ft from each other will be driven across the bridge and that the resulting concentrated loads \(\mathbf P_1\) and \(\mathbf P_2\) exerted on each beam could be as large as 24 kips and 6 kips, respectively. Determine the most economical wide-flange shape for the beams, using LRFD with the load factors \(\gamma_D = 1.25\), \(\gamma_L = 1.75\) and the resistance factor \(\phi = 0.9\). [Hint: It can be shown that the maximum value of \(|M_L|\) occurs under the larger load when that load is located to the left of the center of the beam at a distance equal to \(aP_2/2(P_1 + P_2)\).]