I think you'd be better off putting your trellis at the north end of your garden and running it east to west, though maybe that's what you meant. If you run it north-south, you'll shade everything east and west of it as the sun passes overhead.

I plant my trellised beans on both sides and haven't had any problems with their growth!

I plant on both sides of all trellises (have some running north-south and some east-west, some others in between). Sometimes with peas, if some shading occurs, this actually extends your pea growing period a bit, it protects the shaded ones from the hot sun in the late spring. Of course, I have a lot of sunny days, but in z8 Texas I bet you do too.

I've planted on both sides of the trellis running North/South using concrete reinforcing wire trellis, and as long as the rows are at least 3 feet apart so that sun can fall in between them, got good results. Those years that the rows were closer, and more shaded, some vines failed to produce as much. The tops were in full sun all day, of course.

So yes, plant on both sides at least 3 feet apart, and each side will get at least half a day of full sun. Even if you ran East/West you could plant on the North side too, maybe with favas or peas like Cabrita said. The plants on the North will reach for whatever sun they can get. Indirect light is still light. If you happened to have a wall painted white to the North of an East/West row, it would bounce reflected light back on to shaded plants there.

Next year I'm planning to plant them in more isolated, smaller stands running East/West so that the entire body of the plants on the South side will get full sun all day. Will plant on the North side too and see if it makes a difference. A six foot row planted every six inches is 12 beans planted. As long as I get at least 12 beans back, I lost nothing.

Ahh, the joys of being sleep deprived. I did mean running the trellis east to west at the northern part of my garden. It would be perfect if the sun went right overhead, but it does not...

But now I am thinking it might be beneficial for me to put the trellis on the west side of the garden, so that the beans provide some afternoon shade, which tends to be the hottest...

Or maybe I am overthking the whole thing :)

We're going to put in an overhead trellis, since our beans completely overgrew the six foot poles I had them on. This is only our second year gardening so we're still learning, but I think we'd have gotten more beans if we'd had overhead area for them to grow. We don't have a lot of space where we plant them so I'm hoping this will work well. We'll see! :)