Janet, I make lots of tote bags and use the poly webbing for handles. (My handles go under the tote-so form one giant loop). The frayed ends are easily sealed with a butane lighter (same one I use for the gas grill). You can also use a lit match. If the bag is close to the frayed edge, I'd loosen a section so there is no chance of burning the basse fabric. You might want to hold the webbing with a forceps for safety.Trim the frayed edges first, otherwise the sealed edges can be rough. Maybe you could turn the sealed end under and then do the X box to secure. If you have a std home machine, a denim needle may be the best. I have two commercial machines that sew through upholstery, leather, even some heavy plastics.
Good luck.

Thanks, Blueberrier, the straps frayed and came off the tote bag. I used a candle to seal the straps and sewed them back on. It twas pretty easy. Thank you for you quick response.

Janet