TWOV qualifications

Hello,

I am traveling on holiday from Los Angeles to Beijing and onwards from Beijing to India. The problem is I have a 3 hour layover in Shanghai both on my incoming and outgoing flights in China (LAX>PVG>PEK...and 54hrs later PEK>PVG>DEL(India). I have looked up the Traveling Without Visa rules and it's looking like I'll have to have to have a visa solely because of the layovers. Is this correct? Many thanks!
Clarification: Flying Los Angeles to Beijing with w/ 3 hr layover in Shanghai. Will spend 2.5 days in Beijing, then fly out of Beijing to India with another 3 hr layover in between in Shanghai. Does TWOV cover this?