Do I need to apply for a visa for a short stopover in Shanghai

I am an American Citizen and I am traveling to Shanghai twice as a side trip to Singapore from Seoul, South Korea. So before my trip to Singapore I am planning on staying at Shanghai for 1 night 2 days. And after my trip from Singapore, planning on staying another 1 night 2 days in Shanghai before going to Korea. Do I need an entry permit for the two times I will be staying in Shanghai? or Do I qualify for the free transit? By the way I am riding China Eastern Airline.