I am installing a 5' x 3' kitchen island consisting of two base cabinets. Once I've installed the two base cabinets, SilestoneUSA will install a quartz counter top.
My plan is to screw two parallel 2x4 blocks/cleats to the floor, then screw the cabinets to the cleats, as pictured here:
source: Step #6, photo #11 of Installing Kitchen Cabinets
Given the layout of our kitchen, the cleats will run parallel and in-between joists. This way the screws I drive through the cabinet into the cleats will be hidden by the toe kick. These cleats will be screwed 8" to either side of one joist. Once everything is finished, I think most of the load be distributed on a portion of the hardwood floor ultimately supported by three joists... although full weight of the cabinet & counter will mostly be distributed in-between one joist!
The kitchen has a hardwood floor supported by 2x8 with 16" centering. The 2x8's span 11'6". The 5'x3' (15 sq ft) quartz countertop weighs about 18 lbs/sq ft. Can my floor support the weight of the counters?
Here's a picture of my plan:
2x4 cleats will be drilled into floor. Masking tape marks approximate location of 2x8 joists spaced 16" apart.

2x4 cleats will be drilled into floor. Masking tape marks approximate location of 2x8 joists spaced 16" apart.