if the crane starts out at ground level and the skyscraper is being built next to it, how does the crane get moved to the top of the building once the skyscraper has been built to the level of the top of the crane? (eg: the crane can reach a height of 30 stories but the building being const. is 100 stories)
It is usually self-hoisting. There is motor and gear assenbly that lifts the crane within the tube (usually a future elevator shaft) the is constructed around it. Then it is bolted down and goes back to work.