If I get a new PC will I still be able to access shared games?

I'll be changing my PC, if I change it will I still be able to have all of my shared games?

To have access to a steam library, both the PC you are using and the account you are using must have been given access to the library.

Taken from the Steam family guide:

Is there a limit to the number of devices or friends I can authorize to share my Library?

Yes. You may authorize Family Library Sharing on up to 10 devices at a given time, and for up to 5 accounts that may then use your game library on any of your authorized computers.

Source

So, if you get a new PC or do a significant upgrade on it (E.g. change your operating system version from Windows 8 to 10 (Thanks to Khale_Kitha for the info)), you need your device to be authorised, by the sharer account owner, before you can access those games again.

The reason I know this, I've had this issue with my friends and had to re-authorise their new PCs to access my library, whilst removing their old PC. This was even with their account already being authorised to access my games.