Floor Trusses

Hello. I have a set of basement stairs that follows an exterior wall until the landing, then turns inward. The trusses used are supported on the inner stair wall so they do not extend all the way to the foundation wall. So, between the two full length trusses on either side of the stairs, there is no structure other than the rim board that spans the entire length of the house along the cutout of the trusses. What is the best way to support the load above that gap? Will 2x4 (same length and doubled up like the floor trusses - i think the trusses are about 22" tall) be sufficient? Or is there a preferred method to set this gap up.

Thanks!