Model the truck as a moving load on a simply supported bridge
Let the truck axle loads be (P_1, P_2, dots, P_n)
Let the axle spacings from the front axle be (a_1=0, a_2, dots, a_n)
Let the bridge span be (L)
Choose the section where the bending moment is required
Write the influence line ordinate for bending moment at that section
Compute the moment at the section as the sum of axle load times influence ordinate
Express the moment as a function of truck position (x)
Find the truck position that maximizes the moment
Differentiate the moment function with respect to (x)
Set (frac{dM}{dx}=0) and solve for critical positions
Check positions where axles enter or leave the bridge
Evaluate the moment at all critical and boundary positions
Select the largest value as the maximum moment
For maximum midspan moment in a simply supported bridge, place the truck so the resultant load is near midspan
For a single point load (P) at distance (x) from the left support, use (M=xP(L-x)/L)
Maximize by setting (dM/dx=0), giving (x=L/2)
For multiple axle loads, use the same influence-line method with all axle positions included
Verify the governing case by comparing all possible truck placements
Use the same procedure for shear if needed, but with the shear influence line instead of the moment influence line