I recently purchased Granhult from IKEA for my wall shelf. The problem is that my wall stud do not align with the brackets because of the size of my shelf. Can I simply screw the bottom screws into the noggins and use wall anchors for the top screws? The shelf is going to hold books and some legos. Thanks in advance!
No.
First off, the top screws take up most of the load. The weight of the shelf + stuff will try to pull the top screws out of the wall, the bottom screws comparatively hold very little actual load.
Secondly, why are your studs not vertical? I'm having trouble picturing why the bottom holes hit a stud but the top screws do not.
Books are very heavy and a shelf needs to be well built to hold them up. Your best bet is to get different brackets with larger vertical members, which reduces the bending torque the screws have to withstand.
Floating or floating-ish shelves are challenging because their fasteners are extremely highly loaded compared to traditional shelves.
It sounds like you've found some horizontal blocking (nogging) typically designed to slow down the spread of fire.
At minimum attach the top of the bracket to the blocking since those will experience the greatest stress; Option 1 in attached image.
Even better would be to find a stud and get two screws into it and one into the blocking; Option 2.
Best yet would be to get a shelf which is as wide as your stud spacing and hit all four screws into a stud.
The bottom screws are there more to keep things aligned. The top screws carry the load, where the weight on the shelf gets amplified because of the short distance from the top screw down to the very bottom of the bracket. The worst case load amplification looks to be about 300% at one top screw (when all of the load is located at the tip of a single bracket). For something small like this, I would take 300% of the weight you expect and multiply it by a safety factor. I would shop for drywall fasteners that claim to hold this load in tension. It's a pullout load, not a shear load.
Often times when I design something, I'll imagine what would happen if some idiot decided to climb up and jump on, say, my arched trellis, and I'll treat that idiot as the expected load instead of climbing roses. Those brackets look flimsy enough that somebody probably won't try sitting on your shelf, but if you have a pet chimp, then consider anchoring to support the chimp weight instead of the weight of your books.
* For comparison, the AWC connection calculator outputs the withdrawal strength of a #8 screw with 1-1/2" embedment (2" minus a half inch of drywall) at 117 pounds for Doug Fir studs. For 1" embedment (1-1/2" minus a half inch of drywall), it's 78 pounds.
Another option would be to find two verticals, and cut the shelf width so that the brackets aligned with them. Or at least use one upright for one top fixing, and an expanding plasterboard fixing for the other, which will spread out behind the plasterboard. They actually use a setscrew rather than a 'woodscrew', so present a much larger support area behind.
As already mentioned, the top fixings are the weight bearers, so they need to be the stronger ones, but without knowing exactly where the fixings will be compared with the noggins, it's difficult to give a more helpful answer.
