OB Engineers: Steel Beams to Make a Bridge

We have a steep, nasty creek at our farm that basically cuts off 1/4 of our place. We have a low water crossing that worked well for years. But lately has begun to be a problem. A combination of high MS Rivers and silt, and a moving bank. Basically it's time for a bridge.

From bank to bank it is about 75 feet across (and about 12-15 feet deep). I had a guy come out and quote me an 89 foot railcar bridge, installed, for $26,000.

I am looking for cheaper options. I was looking at used steel beam prices. And basically they are pretty reasonable in the 50 foot range. Any longer than this and they go way up in price, plus they become expensive to haul. I found some 50 footers for about $650 each. (12 inches and 55 pounds per foot if I remember correctly).

I am thinking about buying four of the 50 footers. And joining two of them together with some sort of fabricated jointing plate? That would give me two 100 foot beams. Dig some footings and pour some concrete to anchor them with about 10-15 feet of overhang on either side.

I would place them about 7 feet apart (about the width of tractor or pickup truck stance). And then deck the bridge with some 10 foot 3"x10" pine (treated) timbers that I would have custom cut.

I'm only looking to support pickups and ATVs. With the occasional tractor hauling a fertilizer buggy (tractor, buggy, and payload would weigh max of 20,000). So maybe something rated to 25,000 to 30,000. I do not need to support log trucks or heavy equipment.

Two basic questions:

1) will this idea work?

2) how do I make the calculations for how large of a beam I need? Is there a simple formula for this?