Chapter 5.3, Problem 97P

Assuming that the front and rear axle loads remain in the same ratio as for the truck of Prob. 5.96, determine how much heavier a truck could safely cross the bridge designed in that problem.

5.96 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 σ_U = 60 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 P₁ and P₂ 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 γ_D = 1.25, γ_L = 1.75 and the resistance factor ϕ = 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 aP₂/2(P₁ + P₂).]

Fig. P5.96