I have a foot bridge I wish to plank with 1x4 or 1x6 material. The bridge is 3' wide. The planks will be simply supported at each end by 4" beams. Will a 1x4 or a 1x6 3' long support a 200 pound load?
The boards will flex something awful, which makes for an unpleasant walking experience. Tying them together with an unsupported stringer in the middle will make things quite a bit less wobbly. If the bridge is short then an X-shaped brace between the beams will give you much better support with the same look.
I personally would opt for the 1x4 if all other things were equal. Three feet is a really wide span for rotten or insect-damaged boards. Falling through a floor all the way to your hip is hilarious for everyone who sees it, but not an experience I'd be keen to repeat. With a 4" board any way you stand you're spanning two of them.
This all seems like “opinion-based” answers.
Okay, I’ll give one more “opinion-based” answer. The op’s question is, “...will 1x4 or 1x6 that is 3’ long support 200 lbs.?”
Structural calculations are based on “ultimate design” or “working stress design”.
When using ultimate design (or failure) we then calculate a “safety factor” into the calculations. Depending on the structural element we’ll use a higher or lower factor, (say:1.5 for common area floors and 2.2 for critical beams.)
Working stress design has a safety factor already calculated into the equations.
Unfortunately, I don’t know of a safety factor for “bridges”. (FIU bridge designers evidently don’t either.)
Hmmm...so, based on experience, I wouldn’t use anything less than a 2x material. If the material is cedar or redwood, which is good for exterior use, (but weaker than other species,) or if it’s pressure treated material (which looses its strength when pumped full of pressure treatment liquid), only 2x material will support 200 lbs. (BTW, the op didn’t say 200 lbs. per square foot...just 200 lbs. for a 1x4 or 1x6. )
Also, all grading rules allow some “non-compliant” material to be included. So, if you choose one of those boards, they will fail.
1x4's will flex more than 1x6 material. As to whether it can support a 200 pound load is up in the air because we have no idea what type of material you are using. Oak boards would hold more than fir boards which in turn will be able to support more than soft pine boards.
Another thing to consider is that often time a bridge structure is built with the support beams closer together than the full width of the bridge tread boards. This has the decided advantage of letting the boards support more because the span between the beams is less. The boards overhang some but can still support the load near the ends. For say a 3 foot wide tread let them overhang the beams by 3.5 inches on each end. If you have 4x4 posts bolted to the side of the beam that extend up for a safety/hand rail just notch the boards around the posts.
Five-quarter decking is much more appropriate for that span, and even that is still a bit light. Two-by decking is much better.
Regardless, run a floating rail down the center and screw each deck board to it with two screws. This will spread the load to adjacent deck boards and prevent most of your flex.
The bottom line is that pressure-treated one-by boards are probably more expensive than PT 5/4 decking anyway. I would certainly not use untreated one-by boards. They'll be rotting and (more) dangerous within a few years.