HP has been using elastomeric isolation drive guides for sliding HDDs into slots in the SFF workstations for some time, and adding these to the 4 corner threaded screw holes of a HDD results in the need for the metal support they slide in to being wider than a 3.5" drive by almost exactly 1/2 inch when you take both sides into account. If you go to eBay and look up 450712-001 you will see a bunch of these. The 3.5" form factor HDDs always use the #6-32 UNC (coarse thread) screws, and that is what the ones with silver screws and blue elastomer vibration isolators are, from HP.
The 2.5" HDDs, SSDs, and optical drives use M3 metric fine thread screws instead, and HP colors the screws for those as black. Those are much harder to find.... note the finer metric threads that you can see on the bottom one:
There is a HP kit I came across that appears to fit into your 3.5" form factor in/out bay that includes a receiver which accepts slide-in frames that one can screw a 2.5" form factor SATA HDD or SSD into. That can be a nice way to create backups for off site storage, or just to have removable storage. I use an Icy Dock device like that, and HP has used Icy Dock products too. This is what I'm using, and it slips perfectly into the HP 3.5" form factor floppy bay on older workstations and also fits perfectly in the HP 5.25-to-3.5" form factor converters for newer HP workstations... HERE.
http://www.icydock.com/goods.php?id=162 I'd guess you'd still need 4 of those slider mounts for this to work, too. However, you may only really want a single big storage HDD in there hidden behind the front plastic.
Included with your SFF Z240 there may be spare #6-32 isolation drive guides screwed into the metal frame hidden beneath the front bezel of the workstation.... HP has stored spares there for other SFF workstations. Take a look.....