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It is anchored at each end but the span is over open water.

So if we are walking across it, or making a bridge with two of them spaced 24" apart, when we are at center, I need to know how much weight it will hold.

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It depends on the wood you choose, and the quality (number) of that wood. Pine can only support about 70% of Douglas Fir for example, and engineered wood can support 50%-100% more than that.

Worst case, if you're using number 2 2x12x14 pressure treated pine, and 2x beams with 24" of space between them, you can support over 7,500lbs, so if you're making a bridge with that, it will even handle motorcycles and 4 wheelers. If you made it wider and kept adding beams every 24" it would even support a small car.

Keep in mind there are other structural considerations to make, but if you're just making this bridge for humans to walk across, you are TOTALLY going to be fine.

To address the other answer here, you don't need 100psf unless you want to support an absolutely huge amount of weight. Psf means pounds per square foot of the entire span, not just average per foot. For example in the US, most homes are built to 40psf. I worked for a general contractor and we built homes with Jacuzzis on the top floor with 40psf rated beams (12 inch tall, 12 inch on center Douglas Fir, with a 20 foot span, i.e. unsupported for 20 feet of length). The tub with people and water in it weighed 3,500lbs, and this is on top of the tile and supporting wood frame. The floors also had beds, dressers, toilets, showers, you name it. Those homes have been around for 20+ years and I lived in one for 10 years with zero issues or cracks of any kind. This is standard.

The "psf" rating is overall, i.e. evenly distributed weight across the entire span. No normal home in the US would ever be built to 100psf. That is extreme overkill and for industrial and commercial use.

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TL;DR: Zero

According to this joist span table the absolute maximum span you can get with a 2x12 is 13'10" assuming a 100PSF live load. (I went with that because an average adult human is going to weigh at least that much.)

span table with max span highlighted

The footnotes for this table indicate that this is for "dry service conditions", and I'd think that your span over open water and outside is probably not considered "dry service". This will likely reduce the span.

They have additional tables so you can look up other situations if I haven't picked the proper one for you.

If you will reduce your spacing to 16" you can easily span more than 15' so you should be able to build your bridge that way. If you want the bridge to be 24" wide, simply add a third joist in the middle, reducing the spacing to 12" OC, and you can span more than 17 feet. This would make your 14 foot span comfortably within the the specs for a 2x12" and you can happily move on from there.

NOTE: I am NOT a structural engineer, so I have not "calculated" the live load, but have gone with what I believe to be a "common sense" approach to selecting a reference table to look at. I will happily accept correction on the loading to use. That's why I've also provided the link to other tables to make it easy to look up other load factors.

Note, this website was selected as it was the first result for a web search for "floor span table". I have no association with that site and cannot vouch for the accuracy of the information.
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    Well, "just two joists" is an array of two, making a very narrow floor carrying an average load per square foot. Also, my recommendation was to add a 3rd joist, spreading the load further and making it safer. It is, of course, up to the OP to decide how to build his bridge, but this would be my recommendation.
    – FreeMan
    Oct 7, 2022 at 15:35
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    @WeatherVane: if two people can fit side by side on this bridge, two people will eventually stand side by side. If you make the bridge wider, you need to increase the load capacity than if it was narrower.
    – whatsisname
    Oct 7, 2022 at 17:00
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    A 100 lb woman, @RobertChapin, wearing high heels with a 1/4" square heel exerts 400 psi when she steps down on it...
    – FreeMan
    Oct 7, 2022 at 17:03
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    @FreeMan Other than being an absurd example, a 1/4" square is 1/16 of a square inch and at 50 lb per heel would result in 50 x 16 = 800 psi, which of course has absolutely nothing to do with structural loading.
    – Robert Chapin
    Oct 7, 2022 at 17:18
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    That’s not how psf works in structural contexts. The International Residential Code requires bedroom floors to be built to 30 psf live load, and other residential floors to 40 psf live load. That’s a much closer benchmark for what OP is trying to achieve—less, if they’re willing to live with some bounciness.
    – Mitch
    Feb 1 at 0:42

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