Just fit a piece of 2x4 flat between the joists. Nail or screw it through the joist to secure. Use a couple of 2" drywall screws drilled through the 2x and into the strapping from above, so you don't make holes in your ceiling. Do this before you cut the strapping if you can, to give a more solid base for when screwing down through to secure the strapping.
I'll assume you want to install a new pancake box for a fixture or fan. You could get away with doing nothing, as the strapping is pretty stiff, but if it's on a seam, or someone puts pressure on it from above, it could become an issue.
Just offset the 2x4s on each side of the joist so you're able to screw through the joist and into both at the cut spot.