The ladder won't be fun for long, I would plan to be able to add a stairs later anyhow, sometimes its so easy to add a couple bits now and save a lot of retrofitting later.....
So, the beams under the floor will be 30 foot, split in half with the post so they will span 15 feet. So you will be having a 15 x 8 floor supported by 4 2x10. Likely the back beam will be anchored to a couple of poles, but the other 3 will be clear 15 foot span.
That would seem light to me, but I'm only a simple dirt farmer.
I'd think you need more on that front free beam at least. Taller, or doubled, or something. I'd think your loft would sag and want to bow down and out into the shed.
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