Shanghai to Beijing

No, unfortunately you are not allowed to do that. When you have two or more consecutive stops within different Chinese transit zones (Shanghai and Beijing in your case), you are automatically limited to just 24 hour visa free transit. If you exceed 24 hours just for a minute, you will have to obtain a Chinese visa in advance.

Of course, if you are a Japanese citizen, then you don't have to bother yourself about these rules because Japanese citizens can enter, travel and stay within China for up to 15 days visa free.