How long will the span be? Stretching the RR ties across the creek and fastening them to the posts will maximize the amount of stress you put on the posts. I'd say it's the very worse way to go about it unless it's a very short span.
I don't think I'd be comfortable driving a tractor over anything more than 4 feet max with that design. Walking would be fine, but no weight at all.
Your tires will concentrate the weight of the tractor to the RR ties it's riding on. It will have to absord 100% of the weight, multiplied by the distance from its' mounting position.
This means that when the heaviest part of the tractor is dead center of the span, you are putting your tractor and yourself in danger.
If you put two beams across the creek that can handle the load and the span, then put the RR ties across the beams so the are in perpendicular to the beams, you will be tying everything together.
As for putting the RR ties in the ground, I'd also reconsider that too. I've bought, remodeleld and workd on quite a few homes that have used RR ties for landscaping. In every case, they are rotted out where they touch the dirt.
Don't the railroads put their ties on a bed or rock?
With them planted in the moist soil around the creek, your just a matter of time until they rot out. How long depends on your area, and the individual RR tie.
Save yourself allot of work, money and heartache and buy a culvert large enough for your creek, then cover it with dirt and be done with it. Bridges are very complicated and even the experts get it wrong.
Good luck,
Eddie