120kg load shelf - awkward fixing situation

[sandyman44]

need some materials advice for a specific problem. need to put a shelf across a 700mm span , 600mm deep alcove, to support 120kg uniform load. solid internal house breeze block wall on 2 sides and back

sound trivial, ... but, there is an immovable object below the shelf that means I cannot drill for fixing any lower than the height that the shelf actually needs to go at, and I need a way to mount the fixings to the wall , and the spans to the fixings, with minimal access from underneath.
furthermore, I cannot go up by much in terms of the height of the supports for the shelf / the shelf itself , between the immovable object below, and the height I need the shelf's level to be at.. I've only got about 60mm of height to play with between the below object and the shelf finished height. the fixings can go higher.

I was thinking of using these something like these angle brackets (facing outwards and upwards so they can be fixed from above) to get onto the wall and then smallest timber I can get away with to span the width, screwed to the brackets before the brackets are screwed to the wall (can't do after... can't get from underneath). however I'm struggling to find a load rating vs span for smaller size timber e.g. 38x38 rather than the larger ones used for joists, studwork etc - any pointers please? there's space to put in multiple fixings and spans, 3 or 4 or 5 is fine... doesn't have to be just 2. then just say 12mm ply for the shelf (appearance is unimportant).

have also considered possibly using the metal support beams that used as spans in much industrial shelving but not clear how such would be wall-fixed in this situation or where to source as a standalone item that'd need to be cut to size / not spend a fortune.

thanks in advance

 

[Justin Passing]

There are deflection tables about - here's a something - https://joneakes.com/jons-fixit-database/652-Pro-Shelving-that-does-not-Sag

WHat's worth bearing in mind from the calculation side, is that it turns out that the stiffness of a beam (or table) is proportional to the cube of its thickness. (second moment of area it was called in my day, but they changed it to something else). Have you tried to bend 3/4" ply? If you doubled up (you HAVE to glue the sheets together ) then I don't think you'd see a bend if a bloke like me sat on it, You'd only need small battens on the walls. It would be interesting to try a sheet of 38mm ktchen worktop, I expect it would be fine if it's a dry area.
I wanted to span an alcove about 900mm in a kitchen, for an old style heavy (barely liftable) TV, so I glued two sheets of cheap melamine faced chipboard together. Batten each end and I (129kg back then) jumped on it. I didn't measure the deflection but it wasn't much. Remarkable.
The calculations from first principles aren't complicated if you can find a figure for plywood strength.

 

[sandyman44]

thanks for those tables. that suggestion makes a lot of sense. I'll get 18mm ply and glue it doubled to make 36mm should be more than enough.

 

[big-all]

have a look at scaffold boards they come in 38mmx 225mmx 3m/3.9m