By starting from the directions here and making a few improvements, I have been able to repair two of my chairs, and have enough materials left for a dozen more repairs, for about $60. My repair won't last as long as the original manufacture, but I can always repeat the repair after a couple of years; it only takes a few minutes.
The materials needed:
- Replacement vinyl strapping; I bought 50' of it from Patio Furniture Supplies for about $50, delivered, and that'll be enough for many repairs.
- A grommet kit, bought from a local hardware store for $4; includes grommets and the tools to install them
- Flat-head screws of the right size, cost a few bucks for way too many
- Measuring tape
- Vise grips
I used one of the torn straps to measure the length from one screw-hole, around the beam, across, and to the other screw-hole, being sure to pull as tight as I could. Note that these chairs narrow slightly so I had to re-measure for each strap to be replaced. Once I had a measurement, I measured the vinyl stripping and marked it with the Sharpie:
Then cut where marked:
Now I followed the directions in the grommet kit to install a grommet near one end of the strip. First, use the hole-punch (held in place with vice-grips) to cut the hole cleanly to the right size:
The circle of vinyl left over inside the hole punch can be tapped out with a long screw and the same hammer. Then set the grommet on the anvil:
Place the washer, rounded side up, into place on top of the grommet:
Then use the provided tool to tap the grommet closed.
The result is a nice, tight grommet that looks professionally installed:
Repeat at the other end. Then use a screw to affix one end to the frame:
This is the trickiest part. Pull as tight as you possibly can, then a little tighter, to get the other screw-hole to align. If you've cut to the right length, it should require everything you can do to just get the grommet-hole to only partially align with the screw-hole just barely enough to get the other screw to start gripping, whereupon you can tighten it, thus pulling the strap tighter as it straightens out:
Repeat for any other broken straps:
And that's all there is to it. Once I had it figured out, it took about five minutes a strap.
If you've simply lived with torn straps for a while (since the chair is probably still usable with them), it'll feel remarkably improved once you've done this. Sure, the lack of those extra windings will make it not quite as firm a support as when it was new, and while the grommets will provide some protection against tearing, the strap won't last as many years before it tears again. But you can always pop in another strap in five minutes when it does. You can make those chairs last decades instead of years if you keep it up.