Q: My MacBook pro frozen after installing updates

Howdy NigelM100,

Thank you for visiting Apple Support Communities.

You state the computer stops at about 40% of the boot progress bar.  Does than mean you are not getting to the login screen?

There are a few more troubleshooting steps and articles to check out.

Try booting to safe mode.  OS X Yosemite: safe mode

When you start up in safe mode, your Mac prevents some software, such as startup items, from loading, and it performs a check of your startup disk. Your Mac may take longer to start up because of the check.

(So be patient with that.)

OS X Yosemite: Start up in safe mode

2. After your Mac shuts down, wait 10 seconds, then press the power button.

 

3. Immediately after you hear the startup tone, hold down the Shift key.

 

You should press the Shift key as soon as possible after you hear the startup tone, but not before.

 

4. Release the Shift key when you see the gray Apple logo and progress indicator.

 

To leave safe mode, restart your Mac again, but don’t hold down any keys during startup.

There's also things you can try here:

OS X Yosemite: If your Mac stops or delays while starting up

And to get a better idea of what's happening when it stops, see:

Mac OS X: How to start up in single-user or verbose mode - Apple Support

That may seem like a lot, but it's worth checking out.

Nubz

Hi Nigel,

Glad you are getting help.

Take care,

Nubz