I am trying to find the right board combination for a bridge. Need to build a 20’ bridge across a ditch for Kawasaki mule or atv ; example will 4 2x12’s support 1500 pound load
I am also exploring building an ATV bridge.
If you are at all uncertain, it is worth consulting an engineer about these things and/or drastically over-engineering for safety. And beware of trusting random people (like me!) on the internet. That being said, a few comments:
It is easy to find calculations/examples online of the "weight that can be borne by a 2x something beam". Many of these are focused however on an evenly distributed load, e.g. snow on a deck or many people having a party above. That is different from the situation of weight supported by a single point.
The crucial element is the maximum bending moment your beams can support versus the bending moment induced by your proposed load. For a beam fixed at both ends, the bending moment is
P x L / 4for a single weight
Pat the middle, and
P x L / 8for an evenly distributed weight load, across a beam of length
Lattached at both ends. So it's proportional to the length, and a point mass of 1/2 of the evenly distributed load can be supported. More details can be found at https://www.awc.org/pdf/codes-standards/publications/wsdd/AWC-WSDD1986-ViewOnly-0301.pdf
The actual "strength" of the wood is determined by the allowable fiber stress, in psi. There's a range of figures out there for that. I would expect it depends on the specific material, e.g. SPF vs PT vs whatever you have on hand. The calculation at https://www.hunker.com/12484662/how-to-calculate-load-bearing-beams , which I have not verified, gives a ballpark allowable stress of 1132 psi. For a single 12' 2x12 (which is actually 1.5 x 11.25 inches) this comes out to a maximum allowable point weight of ~1000 lbs (at the midpoint).
If it's 1000 lbs for a 12' 2x12, it would be (12/20) times that for a 20', so about 600 lbs. Four of those would then carry 2400 lbs. I would find this inadequate in your situation, first because I'd want more of a safety margin (not sure how much to trust the 1132!), but also since you want to carry not only the 1500 lb UTV, but also likely 2-4 people, maybe a cargo in the back, and/or pulling a (full) ATV trailer...
If 20' is your span, to get the above capacities you need to attach the beams on solid bridge abutments on either side. The capacity of boards just lying there will be less, not only since they could slip, but because the forces are different (if the end is not attached, your ATV in the middle is not benefitting from longitudinally stretching the wood). In particular, is this covered in your 20', or does it mean you actually need, say, 28'?
Are 2x12s of the needed length available, and at a tolerable price, where you are? Where I am, up to 16' is easy, beyond that is much trickier. If you need to construct a beam from shorter boards, you're in a whole new ballgame (doable, by doubling up, glueing and nailing/screwing, and staggering the joins, but a much bigger project.)
With all this in mind, in my own slightly worse situation (I need to span 25' bank-to-bank, plus abutments) I've decided to hold out until I find a pair of used steel beams the right length; which is why also why I haven't fully verified the above numbers (but sharing in case useful to you and/or others.)