How can I attach wood to concrete in this bench?
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Bolts going into a slieve like RedGrittyBrick suggested is the best answer for appearance and strength. Another option for speed and simplicity are Tapcon screws:
No affiliation, and no direct experience, I'm just aware of the existence of this product.
I'll second BMitch's TapCon screws. They work great.
If you want to have some fun, you could also go with a powder actuated hammer:
It's essentially a gun that will shoot a nail into the concrete. Works great. Would be super-fast (no pre-drilling). But likely the least accurate option. You'd also be left with the nail heads/washers to deal with.
Style/aesthetic-wise, however, I'd probably consider some epoxy options. I'd epoxy a washer or nut to the underside of the wood (to give it a spacer between the concrete to avoid wicking water) and then epoxy that to the concrete.
A final thought...don't permanently attach it at all. Instead create 3 or 4 sleepers that would run under and perpendicular to the slats. Have the sleepers attached at the corner. Then attach the slats to that. The entire thing could then just sit on top of the concrete without needing any attachment hardware at all. Bonus is that if/when the wood ever becomes weathered to much, it'll be super easy to replace.