Sagulator doesn't calculate sag when using both front and rear shelf edge stripping

I've used Sagulator many times over the years, it's a helpful tool. I've always wondered, however, why it doesn't allow for both front AND read shelf edging instead of just front edge in calculating sag. I've built many wide floating shelves where the recommended edge stiffener is too tall, reducing vertical shelf access. To mitigate this, instead of of a single tall shelf edge I've applied shorter strips to both front and rear edges. However, it's always a guess and it would be great if Sagulator were to add this calculation to their on-line tool.

Also, unless I've overlooked it they don't specify whether the shelf edge stiffener is intended to be attached to the side edge of the shelf or to the shelf underside. This matters since adding the stiffener to the front edge would typically require a narrower shelf, whereas placing the stiffener on the underside wouldn't affect shelf width. For example, if my shelf is 18" deep and I intend to add a 3/4 x 1.5" stiffener to the shelf edge, I would have to rip 3/4" off the shelf to arrive at the desired 18" width with the edging added....17 3/4 + 3/4 edging. Some time ago I was discussing this with a friend and his approach was to first determine the desired edging width using Sagulator and then dividing that in 2 to determine the front and rear edging strip widths. I have no idea if that makes sense from an engineering standpoint but it seems to work. Anyone have insight on this?

I’d expect having half-height edge stiffeners front and back will be less stiff than a single stiffener at the front. You would want to calculate the second moment of the area to determine the stiffness in bending. Here is an online calculator that has formulas for both L-shape sections and C-shape sections. Bigger numbers are stiffer. Total deflection is inversely proportional to the stiffness.

it looks like the sagulator uses standard engineering load calculations to estimate deflections. Since I haven’t done those in 20 years, I’ll let someone else chime in on the specifics.

https://amesweb.info/section/section...alculator.aspx

Adding edge stiffeners does make the shelves less useful. My choice is usually to just add thickness to the whole shelf. But if you are locked into say 3/4" MDF with an edge stiffener then face mounted hardwood with a little rabbit is the way to go. And 2 x 2 is as good as 4 x 1/2

Putting the reinforcing strip on the bottom of the shelf adds more than on the front of the shelf but it looks bad. Cutting the height of the strip in half cuts the strength to 1/4. Doubling the thickness doubles the strength.

Adding to the back edge is as important as to the front, probably more if it is for books or something that gets bushed to the back. And since it is out of the way, make it a little taller. A full back is even better.

From an engineering standpoint, the second moment of area (as Ben mentioned) is the double integral of the y axis over the cross sectional area - in effect the only thing that matters is you're counting the offset from the centroid, not the position of the offset.

In short, that means your approach to calculate the shelf with an edgeband as thick as the front plus the rear will give the same results. The math that's being done will still come to the same results as if you were able to add a front and a rear stiffener.