Activities that are allowed on Shabbos but cause a melacha to possibly result on the side, are permitted as long as you don't have kavana for the melacha. Dovor sheayn miskavin mutar. (ShA 1)
If the resulting melacha is inevitable the activity is ossur. It's called psik raysha. If you don't care about the result, then it is at most an issur d’rabbonon.(ShA 1 – ShaH 2)
You are allowed to drag furniture over ground not intending to make a scratch. If the furniture is heavy and will inevitably create a scratch, it is forbidden because of psik raysha.(ShA 1 – MB 4)
The Rama (316:3) holds that a double d’rabbonon (i.e. an activity forbidden only d’rabbonon for two reasons) is permitted with p’sik raysha. However, the Bais Yosef (here) brings poskim who are machmir in the case of dragging a heavy bench over ground. It is forbidden only d’rabbonon for two reasons: 1)digging with a shinui – 2)destructive ; yet because it is a p’sik raysha they still forbid it.(ShaH 2)
You are allowed to instruct a gentile to do a permitted action that inevitably will result in a melacha.(MB 10)
Do not sweep an earthen floor on Shabbos – it will inevitably level the ground which is the melacha of Choresh.(ShA 2 – MB intro.)
You are allowed to sweep a tiled floor (or floorboards). Since most of the houses in the city are tiled no one will come to allow sweeping on an earthen floor.(BeH “v’yaysh”)
Sweeping causes you to move muktza. However, this is allowed for two reasons.: First of all the garbage that you were sweeping is categorized as graaf shel r’ee – and secondly you are pushing the garbage by means of a broom (indirectly) for the sake of Shabbos.(BeH ibid.)
It is forbidden to use a stiff bristle broom which breaks all the time because of Sosayr Kli. Even if it is not a psik raysha when sweeping, it's still not worth being lenient because it looks like uvdin d’chol.(MB 14 – BeH “shelo”)
You are not permitted to wash any kind of floor on Shabbos.(ShA 3)
This entire siman applies to Yom Tov just as to Shabbos.(MB 20)