How to build shelf brace from 2x4's (as pictured)

Question

Pictured below is my second attempt at this. The first time I used a table saw to cut the slots, and this time I used a band saw. I liked using the bandsaw for this a lot better, but I don't know how to properly measure my cuts.

Here's was my process:

1. Cut two 14" pieces of 2x4

2. Use my miter saw to angle the ends to 45 degrees. After applying a corner clamp, it became clear that it wasn't a perfect 45 degrees, but it was pretty close.

3. I had the 9" (on the long side) cross brace from my previous attempt, and I had a right angle triangle block that was conveniently the perfect size to help me align it such that it would go into the other 2x4's about half way. Using the right angle triangle block, I positioned the cross brace by hand such that it was going into both the other 2x4's equally and then traced around it in pencil.

4. Sadly, my new bandsaw saw was missing the miter slide (I've emailed the manufacturer and hope to receive it soon), so I had to make the cuts freehand.

As you can see, the bubble on the level is all the way to the right. I'm not necessarily looking for perfection, but I would like to at least get the bubble in the center section on the level.

I wish I still had enough math skills to draw this on paper and determine where my cuts should be, but sadly I don't so that's why I just tried to position pieces and trace around them. And to be honest, the fact I even made it all fit together is encouraging to me. But there are two things I need to improve on:

1. How to make more accurate measurements
2. How to accurately cut said measurements

Hopefully when I get my miter slide (or whatever it's called) that will help with 2). But I'm open to any suggestions. I think one issue is that I have trouble holding the pieces straight when cutting because 2x4's are curved around the edges. I do have a planer, so perhaps if I used it (or even my table saw) to make the wood more square this would be less of a problem.

On 1), I know there are often many ways to accomplish the same thing. So my hope is that someone can suggest a simpler method, but if the best path is simply to improve my math skills, then it is what it is and I will accept that.

@Graphus, thank you in advance :). And thanks to everyone who answers helping me in my journey to be a real woodworker!

And yes, I know what some of you are thinking, "that guy would make a fantastic hand model". I just don't have the time right now though, so please no solicitations!

Answer 1

There's a few things going on here; I don't claim this is a full answer, but simply a bit of the puzzle.

You're doing a lot of math here, which isn't in and of itself a bad thing, but it's unnecessary. Instead of painstakingly calculating where the cross brace goes, just build the "L", lay a hunk of wood across it at 45 degrees, mark the cuts, then go for it. Once you've cut the mortise, you can sneak up on the length of the brace and get a perfect fit. You'll probably even have a chance to tweak the angle to 45.5 degrees if the cutting didn't go exactly as planned. (Note that I didn't suggest cutting the bracket first and trying to make the mortise work. Mortise first is generally good advice.)

Plus, you're making joints that are more complicated than needed. The miter at the corner of the "L" is probably weaker than a simple butt joint with a couple of nice long screws sunk downward.

The mortise is also more complicated than needed. I'd build it like this:

Whether you're doing the roughing of the mortise with a circular saw, table saw, or bandsaw, it's easier to finish the edges with a chisel when it's either an easy 45 or a straight 90. Finishing an undercut 45 with a chisel is a curse, and forces your bracket to be more perfect than perfect. In pergola scale joinery, the straight 90 is almost certainly stronger (because your surfaces mate better), though it wouldn't matter in this application.

Other minor comments: adjust your miter saw, at least to the point where 90 degrees is absolutely positively dead square. 45 will probably be pretty darn good after that.

Your life will be better during assembly if you put the bracket on after you've mounted the "L" on the wall.