I talked to Rob and we sorted out this mezzanine.
This thread has been a great opportunity to point out a couple of structural things that are of use to anyone doing wood framing of a mezzanine.
First thing to check. What materials are being used? In this case, the framing is doug-fir. That has much different structural properties than hem-fir. Better properties, as a matter of fact.
Second thing to check is how loads are transferred. In this case the floor loads are transferred through the floor joists into beams on each end of the joists. In the back of the mezzanine, these beams are called ledgers as they are against the wall of the pole barn. In most cases, ledgers are fastened into a wall structure often so that they don't act like an independent beam spanning their entire length. In this case they weren't fastened so well. They were fastened to the a 2x6 on edge that was a girt. So they were acting as more of a beam. The ledger/beams here are just 2x8's. Not adequate for the load and span.
That gives us the second thing to think about. The design load. It can be anything you desire. In this case, I looked at the joist span tables to see what the structure that was already there, would support. The 2x6 joists at 16"o.c. with a span just under 10' would support a live load of 40#/SF and a dead load of 10#/SF, for a total load of #50/SF. So if we make sure that all the other members will match this, then we have an economical system, where all the member are sized to match the loads and this makes it the most economical setup.
You see, engineering is simply making all the structural members closely match the loads in the most economical way possible to accommodate the intended uses.
I personally think all structures should have placards that say, for example, "This floor rated for #40/SF uniform load, point loads should follow the following chart".
So let's get back to those beam/ledgers. If you cut the span in half, they are adequate. So the answer is to support each of them at midspan with a column. Much easier than replacing them with something bigger.
The ledgers at the 10' ends of the mezzanine are 2x8's here. They needn't be. Just a regular 2x6 joist will do since they support no additional loads besides the floor sheathing.
The 30' long front of the mezzanine is a different matter than the above 2 cases. These 3 beams do support joists, like the ledger/beams at the back, and you can't just put columns under their midpoints. These beams need reinforcing. They are 2x8's. and luckily, since they are doug-fir, adding another 2x8 will make an adequate beam of each of them.
Finally, the thing that caught my attention here, is the way these front beams were fastened. NAILS! Nails in shear are not adequate to support the #1,250 load on the end of each of these beams. And the piece of 2x6 nailed onto the face of the column does little more. In fact, those columns are not able to carry the mezzanine load because of the connections. The easiest solution to this is to put a 4x4 column under each of the revised 2 2x8's beam ends.
So 3 2x4's, 3 2x8's and 4 4x4's solve all the problems here. Easy peasy.
But you need to be able to look at a structure and analyze what the loads are, where the loads transfer and look at how members are supported and connected. It also matters what the properties of the materials are.
One other thing of interest. The builders of the pole barn offered Rob the option of doubling up the trusses, which he accepted. This makes the doubled up truss assembly stronger, for whatever purposes that will allow, but if you wanted to be able to hang a ceiling, adding a few trusses and spacing them equally would meet your needs better. When building a structure, you need to think of all the possible future uses to make sure the structure will accommodate them.
A last word. This structure was self supporting as the photos show, and supported the people building it. And would likely have held up some unspecified additional load placed up on the mezzanine. The trouble is, you don't know how much, without doing the calculations.
That is what engineering does. It tells you how much. So you know, and can count on it.
Now back to hoist talk...