Transit visa exemption

I am travelling from USA (LA) to Bangladesh. I have a layover at Shanghai for 3 hours and 35 minutes and then a flight from Shanghai to Beijing (flight duration 3 hours) and then another layover of 8 hours 20 minutes (at Beijing) before my flight to Dhaka, Bangladesh. Do i qualify for the 24 hour TWOV? Do i need to get an entry permit or any other documentation? I hold a bangladeshi passport and my nationality is bengladeshi.