Do I need header support for tail-joists?

[Pennsyltucky]

Hi all,

I'm trying to figure out how I need to frame out the opening for my basement stairs.

I'm planning on moving them and the new location will put them perpendicular to the joists. I'll end up with, I think, seven tail-joists. The stairs will be up against (and parallel to) the center girder. The existing span is 15' 2x10s 16" OC. Once the stairs are moved the tail-joists will be about 12'. The tails support my dining room floor.

Now, some things I'm reading are saying that a triple header and doubled or tripled trimmers are enough support with maybe a support wall underneath the header. Another source says that the header needs to be supported by footers in the floor and columns.

If I'm correct in thinking that the footing idea is probably right, what size footings? 24"x24"x24"? Do the columns need to be in the footing or can they sit on top? Would two Home Depot lolly columns set on top of two 24"x24"x24" footings be adequate.

I'm really trying to avoid bringing in a structural engineer as it will probably put the job beyond my budget.

Thanks!