How to calculate tenon angle for kneebrace that is not equilateral triangle?

[Yokosukadweller]

Hello forumites,

I've been lurking and reading here for a while. I now have a question I cannot really find a straight answer to and I also cannot visualise how to solve it no my own.  Basically I need to make two knee braces of same/mirror image layout. The lay out is that the brace "C" in the triangle is calculated by "A" and "B" not being equally long, in fact the vertical is longer than the horizontal side, like this:




 

I have the length of the sides and I know that the brace outer length (post to beam) is 72.46cm and the inner length is 57.78cm.  Laying out those two different measures gives me of course an angle cut. I can understand that.  But the angle of the upper end will be different than the angle of the lower. How do I go about identifying that? What is more, also I cannot visualise and figure out how I then calculate and lay out the correct angle of the tenons. 


Needless to say, I am very much a beginner. I have laid out and cut most of my mini frame already, and this is one of the last things for me to lay out and cut before I need to test fit and drill peg holes.

Any advice would be much appreciated!


Simon 

[doc henderson]

well all the angles need to add up to 180°  trigonometry is designed for this kind of problem.  I am not a timber frame guy, but would think it could be laid out and scribed.  what is dictating the angles.  is it just the "look"?  and of course A2 + B2 = C2  or the classic 3,4,5 rule to make a right triangle.  and it proves the first equation since 3 squared is 9, and 4 squared is 16,  added together is 25, and the square root of 25 is 5.  if the one angle is 90°, then you could use a framing square and put it on the brace at the points of length for A & B intersecting at the ends of the brace length.  like is done with rafters ect.  if the corner angle remains 90°, then each degree subtracted from one angle get added to the other.  I hope this helps, and I apologize if I stated information that is already known by you.

[Don P]

It looks like you are using sketchup. The quick and dirty way is to put the rotate icon on the intersection point of brace to post or brace to beam, line up on the post or beam and swing to the brace angle. The readout box will be giving the angle you have swung. 

Method 2 is to scribe it or measure with a T bevel or framing square.

If all else fails, like Doc said, back to trig. Uhh yeah, it took me 2 tries to make it through that class a long time ago so from foggy memory  : arctan of opposite over adjacent, so if it is 3' from corner post/beam corner down to brace and 2' from corner over to brace you'll end up with ~56.3° and ~33.7°. About the only thing I remember from that class is SOHCAHTOA, then I have to sit there and spin gears  :D.

[doc henderson]

If nothing else is determining the angles, and it is otherwise arbitrary, then pick a set of angles and go for it.

[Jim_Rogers]

If you layout your brace to be a 3-4-5 then the angles are 30° and 60°.

The angle that needs to be cut is along the shoulder. The tenon should be straight into the pocket.

Jim Rogers

[SwampDonkey]

If you layout your brace to be a 3-4-5 then the angles are 30° and 60°.

The angle that needs to be cut is along the shoulder. The tenon should be straight into the pocket.

Jim Rogers

I was thinking the same way on how the tenon fits. It is logical or it would require a lot more work in making it all fit. But I'm no timber framer, so best to say nothing. The angles are not that hard with the tools and the markings scribed. Transfer the angles to the tenons once measured.

[Jim_Rogers]

If you layout your brace to be a 3-4-5 then the angles are 30° and 60°.

The angle that needs to be cut is along the shoulder. The tenon should be straight into the pocket.

Jim Rogers

Ok, so I wanted to make sure my comments were correct. So, I drew a 3-4-5 brace and put it into my 2d drawing program to measure the angles.
I was surprised at the out come:


 
As you can see the angles are not simply 30° and 60°.
But I also wanted to show the shape of the tenon on the ends. This is what I meant by that they need to go in straight.
Jim Rogers

[SwampDonkey]

But I also wanted to show the shape of the tenon on the ends. This is what I meant by that they need to go in straight.
Jim Rogers

Yep, same here. Pictures certainly clear things up. I drew that out on paper this morning and figured I'd let someone in the biz step forward. ;D I never calculated angles, just marked what I was calling inner angle and outter angle at each joint.

[doc henderson]

@Jim_Rogers I wonder if it is because you are referencing the inside or the post and beam, and the outside of the brace.  seems to me the non timber frame guy, to use all inside or outside lines.  thanks and I apologize as I have not done a timber frame.

[doc henderson]

well now I take that back, if I may, as a triangle is a triangle, and it does look as if all the points of the lines meet up.  hmmm.  

3 4 5 Triangle (Angles, Sides, & How to Solve) | Full Lesson (voovers.com)

looks like they agree @Jim_Rogers and in construction we use it to check square of the 90° corner.

[doc henderson]

@Jim_Rogers as they say in construction, you hit the nail on the head!

[btulloh]

Don't need to know the angle anyway. A ruler and a square is all you need. Trying to use a protractor is just a place for errors to creep in. 

[doc henderson]

does it need to be a 3 4 5 proportion.  Unless I am missing something, he could choose any 2 outside angles he wants within reason if they add up to the remaining 90° of the triangle (in addition to the 90° corner).

[Yokosukadweller]

Good morning Gents,

I didn't realise that over night so many valuable contributions to my question would come. Thank you very much!

Also, it has been decades since my trigonometry classes. I really did not remember, duh!  

So all your inputs here are really jogging my memory and of course I think as several people here have advised, it would be relatively straightforward to just use Sketchup or another drawing programme to model the triangle. I have lengths of A and B (to get to C). Based on that, the angles would reveal themselves. Then the only thing I still need to think about (after some coffee) is how these angles will determine by layout and cut, because the brace in itself is 105mm thick, so I still need to jog brain and memory to figure our how the identified angle would determine the cut line in the brace...

I found a page online that lets me calculate angle of the corners, and I'm getting this for the inside triangle: 

Given a=33.6 and b=47,
c = 57.77508
∠α = 35.561° = 35°33'39"
∠β = 54.439° = 54°26'21"

Now I need a little more slow gentle Sunday thinking hat to conclude what those angles mean for the angled cut on a brace that is 100mm thick.

It is NOT a 3-4-5 triangle, I mean the length of the sides was arbitrary and determined by space constraints and aesthetics. That is because the braces will be on either side of a wood fired oven entrance, sort of framing it but not too tightly so.

And now I also realise that the tenons then would go 90degrees FROM the angle identified, so once I got the angles scribed the tenons should be easy.  Now the other thing that will be somewhat challenging is - I want to use recycled old Hinoki (Japanese cypress) posts to make the braces. They do not consistently have a square edge, but rather you can still see the tree (if that makes sense), so I will have to improvise there.

Cheers from Yokosuka- Japan,

Simon

[doc henderson]

I believe there are scribing techniques to use a consistent face and make rougher stuff fit.  

[Old Greenhorn]

I can add nothing to the framing guys who have very well covered your geometry question. I am not a framer, but with regard to working with the irregular surface on the material perhaps you might consider using a laser line level to shoot a line across the surface once you get it at the desired angled? Then you can just scribe that line and follow it with whatever cutting tools you are using? I used this to shoot lines on tree trunks I was using for bar legs and got them dang level on the first cut and the two trunks were even height. (Surprised myself actually.)

[Mad Professor]

You can layout a perfect 3 4 5 right triangle just using a straightedge or chalk lines , and a divider/compass.

That is how they used to check that posts and beams/ties were square to each other.  

You can layout 3 4 5 braces too, but it's a PITA compared to 1 1 root 2 triangle brace.

 

 

Note: the 1 1 root 2 triangle on the brace is laid out with the divider. The scribed circle is the unit of measure for the brace .

 As are the "stars of David" on the posts/beams.   Drawing in all the scribes (circles) to make them would make the drawings confusing.  Note the connecting the points on the stars gives a perfect 90 degrees from the centerlines, and also 180 degree reference parallel to the centerline.

On old frames these circles would be scribed on a large timber as a reference.

[Mad Professor]

It's too bad Marc, the French Scriber's website is no longer active.   If it has been moved, please post a link.  It was a wonderful resource which I learned a lot of layout.  

I spent a LOT of time there just learning more.   I had a drafting table and just did layout on paper with a compass/divider until I could do most layouts/joints.    Some I've forgotten, but I have all my work/learning saved on paper.  None is digital.

I went through TFG "Historic Timber Framing Joinery" and learned layout for most joints on paper, using a compass.  You can do most all with a little thought.  You'll note many of Jack's illustrations have a point(s), that is/are marked by the intersection of two circles/arcs.  That could be using a compass to locate the precise point.

The person who got me started learning this, was Richard "Dick" Babcock, on a bar stool over a/many beers.....

Years ago, my first "project" was a simple woodrack.  On the base, a shouldered M/T laid out just using a compass, plumb bob, and chalk line. I was still learning the cutting of the wood/chisels. And scribes were using a pencil compass and lines w/chalk lines.  See the intersecting circles/arcs to locate things

 



On this the large circle was the reference to the "beam within a beam"/ 4 X 4", and spacing joinery on the posts/ties   The small circle for tenons, half of that circle for the shoulder on the bottom tie mortices.

Besides the chalk line just a straightedge, no rulers/squares needed

[Yokosukadweller]

@Mad Professor  thanks for your posts. I have to admit this looks daunting -  almost like secret mason (carpenter!) code to me. I really need to look into that more to let it sink in and see how I can use stars and compasses to find the lines I need. Do you have a link to a PDF or somesuch with some more background explanation?  Cheers!

[Yokosukadweller]

It looks like you are using sketchup. The quick and dirty way is to put the rotate icon on the intersection point of brace to post or brace to beam, line up on the post or beam and swing to the brace angle. The readout box will be giving the angle you have swung.

Method 2 is to scribe it or measure with a T bevel or framing square.

If all else fails, like Doc said, back to trig. Uhh yeah, it took me 2 tries to make it through that class a long time ago so from foggy memory  : arctan of opposite over adjacent, so if it is 3' from corner post/beam corner down to brace and 2' from corner over to brace you'll end up with ~56.3° and ~33.7°. About the only thing I remember from that class is SOHCAHTOA, then I have to sit there and spin gears  :D.

Hi Don P. Thank you for this. I used Sketchup and got the angles slightly (but not much) different than calculating it (54.5 and 35.5). I suspect these braces here will provide me with a good challenge and a chance to revisit trigonometry after too many years haha!

[Mad Professor]

The "Star of David"

1) Scribe a line, chalkline or centerline.   From a point of reference on this line, using the compass scribe a circle of desired radius.  This could be timber within a timber.

2) Where this 1st circle radius/arc intersects centerline, use these points as a center, to scribe two more circles of same radius.

3) Note that each of these circles intersect original circle, twice.  Where the arcs intersect, on each pair of circles, connect the points.  These lines will be perfectly square to the centerline, and the intersect the arc of the first circle and centerline.

4) From the intersection of the circle arcs in 3, Draw lines to the center of the 2nd or 3rd circle/intersection of first circle radius/arc at centerline, giving two 1 1 1 equilateral triangles.  You should now have two "Stars of David".

5) Connecting the intersection of the points of the star/original circle, on either side of the centerline, gives a perfectly parallel lines to the centerline.    

This method of making 90o and 180o to centerline is more accurate than using modern tools.

If you just need a 90o to centerline this can be done much quicker.   From the first point, only intersecting arcs need be drawn. Set your compass, draw two points both sides of reference centerline point.  Open compass for bigger circle. From outer points scribe two arcs from each side of center point.  The arcs will cross from each side, a when connected form a 90o line to centerline

I spent a whole summer just drawing and re-learning geometry/analytic geometry.  This is the most basic where you never need trig/tables/calcs/rulers/squares

or

[Yokosukadweller]

Thank you for adding a big task for me here. I have to admit I need it. It has been too long since I learnt trigonometry. And as excuse I might say, back then it was all just on paper and never applied. I will carefully try to visualise and practice it when the winter comes.

For now, and because I need those two braces cut, I basically had to find another way out. Assemble and trace a jig to get the right angles. I had already cut one brace with wrong angles, I dont know if it was because the wood was not entirely straight, or my speed square is off, or a combination. But luckily there was enough wood left over to adjust the angle and cut again. Such heavy, beautiful and fragrant timber hinoki is. I did not want to waste it.