Finding Maximum Moment: Determining HL-93 Truck Position on Simple Spans

In the days of the AASHTO standard bridge design specifications, engineers used simple equations for calculating the HS-20 live-load moment for a simple span bridge. Engineers computed and compared the lane load moments to the truck load moments. The larger moment controlled the design. The second axle of the design truck was not placed at midspan but rather at a 2 ft 4 in. (0.711 m) offset from midspan. The correct orientation of the offset required that the truck’s resultant force reside on the opposite side of the midspan from the second axle. As an example, for a 50 ft (15.240 m) span, this 2 ft 4 in. (0.711 m) offset yielded a $628\hspace{0.17em}\text{kip-ft}/\text{lane}$ ($851\hspace{0.17em}\text{kN-m}/\text{lane}$) truck moment compared with a $620\hspace{0.17em}\text{kip-ft}/\text{lane}$ ($841\hspace{0.17em}\text{kN-m}/\text{lane}$) truck moment without an offset. By the 1990s, a new AASHTO specification was introduced based on LRFD. The old HS-20 live-load model was modified to combine its component lane load and truck load cases into a single load case called HL-93. This combined load case impacted the traditional 2 ft 4 in. (0.711 m) offset and made it vary according to span length. This paper proposes to derive an equation for determining the correct truck offset to produce maximum moment using HL-93 loading on simple spans greater than 40 ft (12.192 m). The scope of this paper does not include the tandem vehicle, because it does not govern spans greater than 40 ft (12.192 m) in length.