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There is an epoxy made for this very purpose. I used such an epoxy to anchor my shed. The strength is rated greater than the concrete. Just look for concrete anchor epoxy (or something like that). Then fill the hole with the epoxy and then you can push a bolt into the hole and wait for it to cure. Then you can use a nut on top of the bolt. You may need to actually make the hole even larger and find an appropriate bolt.

 

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I have had the exact opposite experiences.

I stay away from Tapcon made bits.
...

Mostly Agreed. Tapcons are great for light anchoring like a stud wall baseplate into concrete, but I wouldn't trust them for anything that needs real strength. They're brittle and the threads have relatively limited grip strength in the concrete. IMHO.