Supporting Ridge Beam Post with LVL

If you are butting a rim joist into the beam, you can frame like the first photo with the beam held back 1-1/2" and the first rim joist extending to the end of the post.

Then, in the corner of the second (inner) rim joist and the beam, attach some Simpson A35's. 1 should do, but if you have enough height you could install 2. Each A35 can transfer nearly 600lb of gravity load into the beam. If this truly is a rim joist, then 1,200lb of (2) A35's + the shear on the first rim should be more than enough.

Then use (6+) 3-1/2" quality construction screws (vs cheap deck screws) end screwed through the outer rim into the end of the beam to tie the rim and the beam together.

I would not recommend a Simpson ECC style column cap; these are only needed in extreme (for DIYers) load cases.

I would consider beefing up the beams a little and going to just four posts.

Using table 14-40 in this document:

http://www.southernpine.com/app/uploads/SS_13-14L.pdf

you can use doubled No. 1 2x10's for a 10' beam supporting 10' long floor joists. Depending what's available where you shop, if it's easier to get No. 2 grade, you might want to bump up to doubled No. 2 2x12's.

For the joists - using this table

http://www.southernpine.com/app/uploads/SPtable7_060113.pdf

you see you can use No. 2 2x8's spaced 12 inches, or No. 1 2x8's spaced 16", or No. 2 2x10's spaced 16" (or even up to 19.2"), or No. 1 2x10's spaced 24".

I'd probably buy all No. 1 2x10s because I'd prefer to just use all one size and better lumber is easier to work with.

I'd use 6x6 posts without even thinking about 4x4s, even if you don't need it for the weight, it's worth it for the additional bearing surface, just makes life easier.