I thought right off the bat that the round stuff was Swamp White Oak (Quercus bicolor, which we have all over our farm as a preferred species in the program in which that the government pays us to take our river bottom out of production).
But the endgrain color stranding is so striking and broad that I think it may be a Swamp Chestnut Oak (Quercus michauxii). I have tried to plant some of these up around me, as the plumb-sized acorns are supposed to be the ultimate deer candy, but it hasn't done very well (we're too far north). There are also some Bur oak/swamp oak hybrids that can happen, but I'm not really sure what they look like in endgrain.
If you paint the end with a 10% solution of sodium nitrate, and it's part of the White Oak family, it will turn a deep purple color within an hour or so. If it's a red oak, not much happens.
If you know where the tree is, get a leaf or two, a picture of the bark from the bole, (that "beechy" salt and pepper flat bark is uncommon, but the bark lower down may be very different) and, even better, an acorn and I'm pretty sure I can tell you what you've got.
