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Magnets...
It's built into an "alcove" and the two side walls are load bearing, so there is a length of 5x2 bolted into each those walls. At the rear corners (now hidden behind wardrobes) there are vertical 5x2 lengths also bolted into the side walls sitting underneath the horizontal timber lengths and also underneath a length of 5x2 that runs across the back wall (but not bolted in as it's a stud wall). Near the front of the side horizontal timbers are two more vertical 5x2 lengths bolted to the wall and supporting them (you can see one, painted white to the left of the desk). Across the front is another piece of 5x2 screwed in and bracketed to the end of the side pieces completing the rectangular frame, but not really bearing much weight.
Running across the frame, from one load-bearing wall to the other, are three 5x2 joists on joist hangers anchored to the frame and cut into the wall. What you can see from the front in the photo is just the ply that I've cut and screwed to the front of the frame to tidy it up and stop anything from falling off the front of the mezzanine. The ply extends below the frame to hide the joists unless you're underneath it, just to make it neater. The height of the underside is 6'9".
I'll take a couple of photos to help explain.
Finally finished my project. Changes to arrangements for my kids staying with me and my son deferring his university place for a year meant the bedroom I had eyed for my office is no longer available. Sick of working at the kitchen table I decided to build a mezzanine for a double mattress in my bedroom and free up all of the floorspace, creating an area to work. Need to sort out the rugs and buy a two-seater sofa and I'll be happy.
The mezzanine was built on a 5x2 frame on two load-bearing walls with 5x2 upright supports in the corners. I put three 5x2 joists across the frame, sitting on joist hangers that sit on the frame and are cut an inch into the walls. I then boarded it 18mm ply, cut holes to allow the mattress to breathe and varnished. The mattress sits on top of a sheet of dry-mat to allow more air circulation. There's an extension lead attached to the hidden side of the ladder and recessed into the board along the wall.
Really pleased with it - a lot of headroom at the head of the bed, hardly any ambient light gets in so I'm sleeping really well, and I managed to negotiate getting in and out without incident after 4 pints.