MDX, Merlin-Dash, Lusas, Influence lines, moment distribution, etc.
If you can a copy of the old AISC Moment Shear Tables tables it won't be too difficult to solve by hand. You'll just have to combine the lane load with the HS-20 load.
Here's an old California DOH example. It should give you an idea where to start. I have another example - also CDOH -that I'll try to post. I have to reduce the file size.