the answer to question is no. the way you plan on doing it.

now go back and read either the 1981 version or all new version either will cure you of your delusions.

All that will be too heavy for a single trellis. I had two cucumbers and 1 tomato on a single trellis last year and even that was too much. After just a couple of months, the weight of the plants and fruit had the whole thing severely leaning. In fact if it hadn't fallen back against the house it would have completely collapsed. haha Good luck!

Agree with carrotcate. A string trellis will be much too flimsy. If you had something sturdier like a cattle panel it could probably be done. This is assuming the bed runs north to south. If the bed is east to west then you would put the trellis on the north side of the bed and you'd only be able to plant on one side.

Also, zucchini are mostly all bush type plants. Trying to trellis them would be a major pain in the rear.

Rodney

I think beans and cucumbers would be fine together on the same trellis, but yeah, the heavier fruit/veg would be too much for it. You might get something like this (trellis wire) for the heavier stuff.

The zucchini will need to be staked individually, as they grow quite large. I see no problem with the cucumbers and beans being on the same trellis. The tomatoes will also be fine as long as you plant one per square foot and prune them heavily to only one, possibly two, stems per plant. As well as staying diligent about pruning off the suckers. The success of your trellis will greatly depend on the material used, string is not a sturdy as steel remesh. I hope this helped!