You shouldn't have strapping that stops in the middle of the joist cavity. You would want to cut them so they share space on a joist. In other words, they would "butt" together on the same joist. If that's not possible, you would need to put up some 2 x 4 nailers between the joists so the strapping has something solid on which to be nailed. If you just leave them floating, then when you install your ceiling drywall, you will have a weak spot that could sag, etc.

 

Joist put a 2x4 above them and screw into it.

 

The Gypsum Construction Handbook has a section on adhesive application it states that the adhesive should meet ASTM C557 this section covers wall & ceiling adhesive methods. You need to follow the guide lines in this section.
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