There are a couple of different ways to approach the design of this structure depending upon the governing code. One way is to design it is with the ACI code load factors and the AASHTO loads. Another way is to design it all by the AASHTO (loads and load factors). I do not have the current AASHTO but would be surprise if this section has changed much. Another is to use Westegaard's method with either ACI or ASSHTO load factors.
I agree with JAE that the 640 plf and 18 kip concentrated load is to be distributed over the full lane width of 10 feet. According to AASHTO for this span the live load should have an impact factor of 1.3.
By various design methods, the area of main (bottom) steel that I calculate (assuming no mistakes) is (based upon
F'c =6000 psi and Fy = 60 ksi):
AASHTO Loads with
ACI load factors 0.89 sq. in. per foot of width
AASHTO Loads with
AASHTO load factors 1.14 sq. in. per foot of width
Westegaard method with
ACI load factors 0.83 sq. in. per foot of width
Westegaard method with
AASHTO load factors 1.06 sq. in. per foot of width
Please note that with the Westergaard method, I have only used the concentrated wheel loads and have not included any uniform lane load.
By various design methods, the area of distribution (bottom) steel is:
AASHTO Loads with
ACI load factors 0.20 sq. in. per foot of width
AASHTO Loads with
AASHTO load factors 0.26 sq. in. per foot of width
Westegaard method with
ACI load factors 0.37 sq. in. per foot of width
Westegaard method with
AASHTO load factors 0.46 sq. in. per foot of width
The distribution steel for the 20 foot span by AASHTO is 22% of the total main reinforcement (DL + LL). The distribution steel by the Westegaard method (for this particular problem) is 67% of the steel required for the main bending moment due to the concentrated loads (only) or 44% of the total main reinforcement (DL + LL). Please note that the distribution steel will vary with span.
I understand that the modern AASHTO code was based upon the information that came out of Westegaard's report for the U.S. Bureau of Public Roads in the early 30's. I do not know why the difference in distribution steel.
Westegaard's report is an excellent reference for anyone designing for concentrated wheel loads on one way slabs, whether it is for buildings or bridges. It's title is "Computation of Stresses in Bridge Slabs Due to Wheel Loads" by H. M. Westegaard, Professor of Theoretical and Applied Mechanics, University of Illinois, Urbana, Il. Your local library should be able to order a copy for you.
I hope this helps!