Confusion on Visa information

Hello,

I am traveling from the U.S. (US citizen and passport holder) and arriving in Beijing, China on December 29th 2017 and then departing on December 31st, 2017 for Thailand. But during this short stay I plan to visit the Great Wall. However, I will be returning to Beijing, China on the 16th or 17th of January (haven't decided yet and might plan on flying directly into Shanghai for a day and then back to Beijing or directly into Beijing) for my departure from Beijing airport on January 18th. Do I need a visa? Or do I fall under the 72 hour rule for both times that I enter China?

Thank you!