Re: screw down connectors
While we are waiting for a more clear question I will add that many screw down connectors are only rated for one or the other. Some are rated for both solid or stranded.
Generally speaking for stranded there is usually something to prevent the screw from destroying the strands as the screw is turned-- something like a washer or something like a mash plate.
It comes down to the listing on the connector. Post back with more details and we can give you a less generic, and a better & safer answer.