How do I calculate the weight capacity of my one side supported bookshelf (Spine Booshelf?)

Question

I am planning on building a bookshelf as shown below. Each shelf (maple plywood) will only be supported via a dado cut into the 2x4 (SPF pine), and glued. I am currently planning on cutting 3/4" deep dados.

How do I go about figuring out how much weight each shelf can support? I am hoping to use it as an home entertainment unit, so it needs to hold up to 30 lbs per shelf for consoles and audit receivers.

I tried the Sagulator, but it apparently is for shelves supported on both ends.

Also, what are some better ways then dado + glue? I am thinking one or all of the following:

1. Screws from the back of the spine into the back side of the shelfs
2. adding L brackets underneath each shelf (I am hoping not to do this for aesthetic reasons)

Would these measures be overkill?

Edit: On a separate note, does anyone has any ideas how can I mount this to the wall as clean as possible? I mean clean as showing little hardware, and flush to the wall. I was thinking doing French cleat cutout on the spine, but I don't know if I can given I only have a circular saw.

Answer 1

How do I go about figuring out how much weight each shelf can support?

Based on what follows this becomes sort of irrelevant, but if you did want actual numbers the only way I can think of realistically is to make sample shelves (note, not just one) and test them, see how much weight they can take before A) bending too much to be acceptable, B) fracturing or C) somehow falling out of the dado. Empirical numbers are the only real way to know for sure, especially with plywood.

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Also, what are some better ways then dado + glue? I am thinking one or all of the following:

Both your 1 and 2 would add strength and security here, with obviously 2 being the superior option in a couple of ways. But like you say, brackets under the shelves spoil the aesthetics here and it would be nice to maintain the clean, uncluttered look.

So, based on this, other design details and given the material of the shelves is intended to be plywood, I would recommend using either two long bolts or lag screws per shelf, approximately 3" apart. Or even better, steel rod/threaded rod since either might be cheaper if you want to go, say, a full 6" into the edge of each shelf (although then drilling the holes becomes more of a technical hurdle).

This mimics to some extent the way that floating shelves have long been installed so it's a sort of proven technology, and what's more it may then be possible to make this a knockdown piece so if/when you move you don't have to try to transport it as one awkwardly shaped item.

Answer 2

Your design raises some interesting issues and requires additional consideration for connections. Each shelf is supported at only one location and the actual load on each shelf is not the only consideration. The only way I can thin k of to evaluate the design is to actual test the assembly. You may want to make a mockup of a single shelf and test it before proceeding with the entire assembly.

Here are several things to consider as you work out the design:

1. The shelf will have a tendency to rotate out of its connection point. Imagine pulling down at the center front. The shelf will want to rotate up at the vertical connection. The joint between shelf and column must be tight to prevent this rotation. In addition, if the depth of the shelf extending into the column is too shallow, then it will be easier for the shelf to rotate out.
2. The two side edges of the shelf are unsupported and the entire shelf will want to curve down at the sides from loads. (a similar tendency will exist at the front edge) For this reason plywood is better than wood solid wood panels since it can better resist this curving to both the sides and the front where wood planks will be weaker across the grain than with it.
3. Your design is a cantilever and the further the weight is from the bearing point the more it will tend to curve the flat shelf profiles. This affect will be more noticeable over time.
4. You could reinforce the shelf by using a pair of long screws (say 1/4" x 6") countersunk into the 2x4 from the rear. In that case I would minimize the dado depth and maximize the depth of solid column wood the screws engage before entering the shelf panel. Make the holes in the column very snug to prevent any rotational movement of the screws.
5. Steel 'L' brackets might work if the steel is thick enough (1/8" thick or more). I would mount the vertical leg of the angle to the rear side of the column and pass the horizontal through a slot opening . You could cut a rabbet in the bottom of the shelf to make the underside of the steel and shelf flush. I would make the legs on the steel as long as possible.
6. My instincts tell me that a denser hardwood would do better on the column than pine.

Whatever design you finally work out I would love if you would follow up with a post after it is completed and tested to show us what you actually did and how well it works.

Answer 3

Your question mentions that you only have a circular saw. This makes me question what other tools you might have access to. Be aware, though, that you can make jigs to help you with some tasks.

This suggestion would require the following tools:

• A hammer
• A bench vise
• A drill
• A looooong drill bit
• A hacksaw or angle grinder with cutting wheel

I would suggest you make some internal reinforcement. Several people have suggested long screws or threaded rods. Have you considered installing a "hidden" support?

Imagine you purchase some 1/4" steel round bar. Now cut it to length and bend a right angle into it, making an ell shape of rounded rod. Make two of these per shelf, times however-many shelves.

Now, using your circ saw (and a narrow chisel, if you have one), make two grooves in the back (wall-facing side) of the spine. The grooves should be 1/2-3/4 inch apart, centered left-to-right. The grooves should be the width of the rod, and the depth of the rod. They should run from the bottom of the spine to the height of the top shelf.

At each shelf, drill a hole inside each groove. The hole should be just slightly bigger than the rod. The hole should extend through the spine, into the shelves as far as you can possible make it reach. (For 12 inch deep shelves, see if you can make a 10" or more deep hole- they sell long drill bits.) The holes should be parallel to the shelves (obviously! otherwise the holes will come out the top/bottom) and at an appropriate angle to point at the front corners of the shelf. I believe this is about 55 degrees from the centerline of the shelf.

The idea is to insert the bent ell shapes into the groove in the spine, and into the hole in the shelf. You can then secure the bottom end of the ell shapes using epoxy or just screws and metal tabs or just screws carefully placed. The ell shapes are totally invisible from every direction except when the shelf is pulled away from the wall. They're customizable to the specifics of your shelf, and they should be something you can make with a few tools.

My local orange box sells 1/4" x 72 round rod for $5.87 (USD). Your drawing suggest a small distance between shelves - maybe 6"? So 18" of rod would bend into a 12" leg and a 6" leg nicely. Thus, you could get 4 ells, or 2 shelves, per unit. 5 shelves would cost < $20 to reinforce, plus any screws, drill bits, and other tools.