It's one of the timber bamboos but need more detail to determine which. This might help to narrow it down - timber bamboo. IME, Bambusa or Phyllostachys are most commonly grown species.

Unless there is containment that I can't see, that looks like a clumping bamboo, rather than a running bamboo, like a Phyllostachys.

I'd like the OP to tell us what part of the country this is growing in, and to reconfirm the dimensions, as those culms don't look 4"-6" wide to me...maybe in circumference, but not diameter.

Kudzu9, you were right. I had just guessed on the size, and not actually measured them. I went out and measured them. The majority of them are around 3 1/2" wide. The smallest I could find was 1" wide, and yes it's clumping bamboo. This is in Tampa, FL and it's around 10 years old.

Ok, I'm not an expert on clumpers; I grow mainly runners because most clumpers don't do well in my area (Pacific NW), so this is just a guess, but I'm thinking a Bambusa. Given your dimensions and the stub of a thick-walled culm I see in your third picture, it could be B. beecheyana, which grows to 50', has culms up to 5" in diameter, has thick walls, a weeping habit, and relatively short internodes. This is just one possibility. I suggest you check out bambooweb.info, which has photos of almost every species grown in the U.S. Here is a link to the photo page for B. beecheyana: B. beecheyana

You should look at photos of other bamboos there, too. When you click on a thumbnail of any photo, it will list the maximum height and diameter of that species.

I'm almost positive it is a Bambusa, but there is a slight possibility it is a Dendrocalamus, and I think of Dendrocalamus because of the older culms that have the grayish dirty look to them. Most Bambusas stay green or 'clean' looking even as they age. Dendros generally have larger leaves then most Bambusas.

What size are the leaves?

It has a growth habit like Bambusa CloneX or Bambusa dissimulator. It does not grow like my Beechyana since it leans outward too much and has longer lower internodes.

hard to tell. searching online, in some pictures it looks like beecheyana bambusa, others dendrocalamus, and even bambusa blumeana because it has some branches (lack of better word). It's growing in Tampa FL. I'm not home, but I'll add more pictures tomorrow.