With the help of the folks who own the lot above us, we first dug a trench and lined it with rebar. About half of the rebar is shown in this picture ... you can never have too much of it, you know.
We put in the concrete in three stages ... first the floor of the trench, then the wider sidewalls that support a cattle grate, then the outside walls. As usual, we mixed the concrete ourselves (six cu yds). The walls and floor were 6-8 inches thick.
A nearby landowner gave me a massive old cattle guard and I cut it up into 3 sections, each two feet wide and just under eight feet long. They sit end to end on the ledge we built into the walls of the culvert, shown here where the water enters.
Here's a view of the completed culvert looking down toward our lot. We found a nice big rock to cover the entrance so errant vehicles wouldn't drop a wheel into it. Plus it made nice landscaping.
And here's what it looks like from below. The total length is 34 feet, 23 of which is covered by the cattle guard sections. No, those aren't illegals sitting by the road, although these ones work pretty cheaply. That's my wife and the owner of the adjacent lot. His wife also worked with us almost every day, especially the hard ones (digging dirt and mixing concrete), but she wasn't here when I took this picture.