Here at the Library, we tend to frown upon unfinished work. Namely, because many of our current users came from writing wikis where works were allowed to be unfinished - and they never got finished.
You can see why this a problem, and the Library is an archival-structured site. We want finished quality work.
You do not have to post immediately after getting an idea. Writing a decent story takes time - Dawkson's Cave, for example, took almost 3 months to complete. You don't want to write something of bad quality - you want to strive for quality similar to True Tales of Terror from the Peace Corps or Dogscape, and unless your talent at writing is so good that you could write a full-blown novel in less than a week, it takes time to achieve that kind of quality. We aren't expecting you to rush and post chapter by chapter.
Therefore, we kindly ask that you don't post unfinished stories or chapter works. If you honestly need to post unfinished stories, there are other sites which will accept it.