Brace Pocket Height calculation?

[Lennyzx11]

How do I figure the total height of the mortise pocket mathematically? I know I can cut and measure and have done so. But I can't quite figure out how to do it with math and now it's became a puzzle.

Jim has a very good thread titled Brace layout questions and answers but this didn't come up in it.
EDIT Jim also has a thread titled Brace Pocket Measurement that I just found and going back to digest. At first glance, it didn't seem to help me with a way to figure it but using a rule of thumb.

And it's not as simple as Pythagorean formula or right triangle's 1/2 of base x height. Or law of cosines and sines.
I've managed to prove that!

See photo below. If picture is fuzzy, the green line is the measurement I want to be able to figure out.

Assume a 1/2" mortise housing depth, 4 inch tenon, 8" vertical post. I forgot to add those measurements on the drawing.

Thanks,
Lenny

[beenthere]

What is your angle shown in red?
And what is your width of the brace (red line)?  
And you want to know the length of the green line, right?

Tell us about what you have proved that Pythagorean doesn't work. Interested.

[Lennyzx11]

What is your angle shown in red?
And what is your width of the brace (red line)?  
And you want to know the length of the green line, right?

Tell us about what you have proved that Pythagorean doesn't work. Interested.

Angle shown in Red at the top of the brace leaving the post is 45 degrees. (across the brace is a 90 degree angle)
Width of the brace (Red Line) is 8 inches.
Yes. I want to know the length of the green line.
The theorem doesn't work alone.I do believe it's part of the solution though.
A (squared) plus b (squared) equals c (squared) doesn't work by itself because we don't know what that bottom line of the brace sticking out of the post length is.
Because the bottom of brace isn't actually sticking "out" of the post 8". The 8" corner is theoretically deeper inside the post. but that portion is removed from the brace to shape the tenon. The shaping of the tenon being cut off at its angle to fit the pocket influences that.
I think it may be to do with having to figure in the top side of the brace total length of the tenon but that's didn't come out right either when I just did it.

[beenthere]

If the red line is 8", and that angle is 45° (looks to be drawn less than 45°), then the length of the green line should be 11.313708499"

You are saying the pocket cut to that size doesn't work?

[Lennyzx11]

Yes. I see where your 11.3 would be similar to my 11.5 on the scrap I'm working with.
The actual measurement to fit is roughly 9 5/8" as shown.
That 4" tenon plus the 2" step cuts that 11.5 down to my 9 3/4".
That "step" may be what is messing me up.  

 

 

 

[Don P]

for 45's the rule of thumb numbers to burn in your brain are 1.414 and .707. Multiply 8 by one and divide 8 by the other and you will get Beenthere's numbers or close enough for framing. The rest of the issue looks like visualizing. When my brain isn't wrapping around it, its time to find some scraps and mock stuff up.

[Jim_Rogers]

When we layout a brace pocket/mortise and it's housing or where the post is reduced to the 1/2" smaller size, the dimension for the green line is always longer on the post than the line on the brace.
That is because the brace stock is or can be a variable sized timber. What I mean is that if the brace is larger than 8" that line is longer. So, you have to compensate for the longer line.
We do that by automatically making the mortise and housing longer than the shoulder of the brace by at least 1/4".

If you try and make each brace pocket exactly the same size at the brace, then you are going to have to custom fit each brace end to each brace pocket. Label that brace on both ends to both pockets and keep track of that so you can put them back together correctly later on. Too much extra work for nothing. We don't do that.

Making the housing shoulder line longer automatically makes it so that any brace can fit in any pocket/location in the frame. No need for labels or keeping track of where each brace goes. Much easier.

This is standard practice.

In timber framing there are rules. And there are exceptions to those rules. One exception is that the tenon on a brace or the brace itself is not reduced to 1/2" lower in size, on the opposite adjacent side.

The hypotenuse of the right triangle is the 3/8" layout line drawn on the brace. That corner of the right triangle is where you measure your leg of the triangle back to the 90° corner.

The right triangle and the hypotenuse line are fixed and can't be wrong or you won't have 45 degrees ends on the brace.

To find the actual length of that line, just draw a 45 degree line on the brace through the 3/8" layout line and measure it. Then make your housing 1/4" longer than that distance.

Jim Rogers

PS. I tried to find a picture of this but I haven't found it yet.
PPS: found it:



 

Here you can see the shoulder/housing line is cut longer that the shoulder of the brace.
You can also see the 3/8" layout line pointing to the corner of the housing where the leg of the right triangle connects.

[Lennyzx11]

I think I got it. Thanks to all.
Related question. (And I know this has been answered but I can't find the thread again)

What's done about any extra width of the brace stock ?

The brace is 4 inches across nominally. (4x6) 
I layout 2" from the reference face of the post/beam, then cut a 2" wide mortise. 2+2=4. Then the remainder across the 8x8 is left untouched &  unhoused. 
I cut an 1/2" housing across the first 2" of the post/beam from the reference face but none on the remainder of the 8x8 post/beam past the 2" mortise hole.

But if the 4" width of the brace is actually rough cut 4 1/4", then what's done with the 1/4" extra?
I know not to cut on the side to the reference face or the alignment of the outside edges is messed up.

Do I trim the brace down to exact 4", widen the mortise to 2 1/4" (custom fitting)?

What's the standard practice?

[Jim_Rogers]

Plane off the back side to 4" thick with a hand plane or power hand plane or bench top planer after you establish the 2" thick tenon.
That's what we do, because I intentionally mill my brace stock 1/8" over thickness so that if it sits for a while and shrinks, we'll still have 2" of wood to make the tenon the right thickness.

Jim Rogers

[Lennyzx11]

Plane off the back side to 4" thick with a hand plane or power hand plane or bench top planer after you establish the 2" thick tenon.
That's what we do, because I intentionally mill my brace stock 1/8" over thickness so that if it sits for a while and shrinks, we'll still have 2" of wood to make the tenon the right thickness.

Jim Rogers

Perfect. 
Thanks Jim for all the help you give us newbies.
Lenny

[Don P]

for 45's the rule of thumb numbers to burn in your brain are 1.414 and .707. Multiply 8 by one and divide 8 by the other and you will get Beenthere's numbers or close enough for framing.

Off on a cosine;

From an old book on roof framing, the 1.414 is what is known as a line length ratio. It is Pythagoras reduced to 1 to give a ratio you can multiply by to get the hypotenuse (the line length) rather than having to do square roots in the field.

A 45 is the simplest case so maybe a good example of the idea.
Pythagoras says; A²+B²=C²
With a 45 degree brace or a 12/12 roof the length of each side is the same so I'll call each side 1 unit in length.

So 1²+1²⁼2
And the square root of 2 is... 1.414. If each side is 1, the hypotenuse is 1.414
On a brace, if it is laid out 36" both out and down from a corner;
36 x 1.414=50.904" is the length of the line that connects those 2 points, 50-7/8 and a red one.

Let's use that to burn another common number, go 12" each way, 12 x 1.414=16.968" or... a regular hip or valley travels 17" per foot of common travel.

Some more common LLR's
10/12= 1.302
8/12= 1.202
6/12= 1.118
4/12= 1.054