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Scenario : shop is at 65 degrees, humidity 45%, the glue is titebond original, a fresh bottle.

Gluing on the top braces using clamps.

Will it dry in 30 minutes? Or will it actually be ANY better of a glue joint letting it set longer?

Clamp as long as you can . I allow at least 1 hr for tite bond 8 to 12 for HHG or Fish

A little longer dry time certainly will not hurt -- our large shop is about 70 degrees all the time during the summer a little cooler in the winter -- if I want a little "gitty up!" I use an electric heater with a fan -- we have a couple of the $17 units from the big box store.