I wonder, he thought out loud, whether it makes any difference in fixing an angle piece to the edge of a shelf, whether the vertical is above or below the horizontal element. To my simple mind the torsional benefit is the same irrespective, although I suppose it will take more force in compression and probably well beyond a load of books. Cleverer folk than I will I hope point out if my thinking is awry.
Martin
I’ll not claim “cleverer”, but the issue is bending, not torsion.
Angle is about as stiff in torsion as flat bar of the same total width and thickness, which is generally counter-intuitive, but still the case!
The bending is resisted best by a deep section (think twanging a ruler over the desk edge, compared to bending it when it’s upright) and so fixing the angle to the shelf so the height of the flange is added to the thickness of the shelf will be the stiffest. The flange below, is in tension so won’t buckle. If you put the flange above, obviously it would be in the way, but the failure would eventually be the flange buckling as the shelf collapsed. Putting the flange in line with the shelf, like the middle diagram, will add the stiffness of the angle to that of the shelf, for negligible weight, and the shelf itself will tend to prevent buckling. This might be a worthwhile addition to the front of the shelves.
alternatively, an extruded aluminium tube say 15mm square, might be screwed below the shelf, if there’s space. That’ll be stiffer still.
if you go down the ally angle / tube route, there are lots of on-line metal resellers who have a better range and better prices than the DIY sheds.
Brian’s dividers are a very effective solution.