imac running sierra cannot boot up using disk utility

Most likely the hard drive on the iMac is beginning to fail. If you use Verbose Mode look to see if there are any "I/O errors" listed on the screen.

Can you boot into Safe Mode?

Try running the Apple Diagnostics.

Restart your mac.

Press Command (⌘) – V as soon your computer starts. Before the apple logo. While the Mac OS is loading it is paramount that it identifies that you had Command (⌘) – V  pressed.

This will bring the Verbose mode. It will show all the commands executed while the Mac OS is starting-up. Normally it will show Apple logo and the horizontal bar.

Anyway, very likely it will hang somewhere doing something and some point. Take a screenshot and post it here.

xh0sa wrote:

Could not boot up in safe mode. Disk utility gave ok results for my hard drive

Disk Utility only checks the file system and does not check the health of the hard drive (technically it does check, but only reports when the drive is almost dead so not much use). If you are using Disk Utility does this mean you are booting into Recovery or Internet Recovery Mode? If you are booting to the internal drive normally, then run DriveDx and EtreCheck and post the reports here using the "Additional Text" icon which looks like a piece of paper.

Sometimes the Apple Diagnostics will detect a failing drive. Did you try Verbose Mode as the other user suggested and look to see if any "I/O Errors" were listed which would indicate a failing drive?

OK many thanks but I ended up reformatting the drive and reinstalling Yosemite

Could not boot up in safe mode. Disk utility gave ok results for my hard drive