Sile base shears and overturning.

Also,
where does the lateral force act along the height of the silo?

Assuming this is a granular/powder product, see 15.7.9 of ASCE 7-05, if you haven't found that section.

Generally, ASCE-7 tries to treat different tanks by referring to the standards governing design and making modifications as required. With something like a steel silo, where there is no standard, it becomes more of a problem. The non-building parts of ASCE 7 seem to be poorly written, and at some point you just have to make your best guess at what they mean and go on.

It looks like you could go to the API specs in chapter 23. They have something on tanks and silos. What we would probably do is go to the ACI guide on liquid containing structures and utilize the commentary for calculating the sloshing forces. your not designing the steel silo itself, you just need the foundation forces.

if it were me, i would use the vertical distribution equation F=wh/Swh for buildings from ASCE 7-02 (dont have the code in front of me). if your silo period is low enough, k in the exponent becomes 1 and it turns into a triangular distribution along the height of the silo. in other words, the base shear acts at a point 2/3 up the silo.

perhaps you have already discounted this method.