A 1000 x 750 shelf whit is to carry 40kg, constructed from 18mm chipboard with a 35 x 35 with white wood edging will sage 68mm. I you are happy with your shelf sagging this amount then fine.
If the shelf is 12mm chipboard then the sag will be 116mm
I didn’t see chipboard so I used OSB it as the same strength as chipboard.
If you used joinery grade timber with a 18mm plywood shelf then the sag would be 46mm.
To have no sag or very little then the self supports will need to be 120 x 25
BTW if you want to check my calculations then all you need to do is visit this site.
I Must be doing something wrong, i get 15.67 mm total sag using the dimensions stated, and a point load of 40kgs?!?!? thats using 12mm OSB(min stiff), floating, and no stiffner.
35x35 on it's own gives 2.15 mm?!?
Also? 120x25?? are you sure? two of those side by side is nearly a floor joist!!!
If you have the wood already, and you've got enough.... instead if putting in the 'green' uprights, double up the stiles, and make them 70x35.
You could make the frame as previously discussed, cut the stiffners to length, then glue'n'screw them straight to the side (might want to plane them smooth first, glue'em clamp, 'n' screw together....You could [probably] stand on that!!!
put a couple strips along the front to stiffen the shelf..