# Cutting diagonal braces in rectangular frames



## Markymark (21 Oct 2012)

Hi

This may be an easy one. I have built a frame with 4" square timber and I am wanting to make it more rigid by adding diagonal bracing. My question is for the mathematicians, I have calculated using pythag the length of the diagonal brace corner to corner but I want to know how to cut the angles on the ends of these braces to fit in the frame. 


Any help gratefully received.

Mark


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## BRYAN (21 Oct 2012)

Hi Mark.
I can't remember much about Pythagaurus(spelling) it was a long time ago.
Measure diagonals to ensure frame is square. Lay the brace material over where required and mark from below to give position of cut. DO NOT remove pencil line.
If needs be,insert a small piece of pencil in a small batten to allow markig from underside without disturbing brace piece. Good luck.

Bryan.


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## Markymark (21 Oct 2012)

Thanks Bryan. 

So easy when you know how. I think I was overcomplicating it by trying to use Trigonometry sin/cos/tan.

Mark


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## AndyT (21 Oct 2012)

One more point - you'd normally position your struts so that their ends get two cuts, meeting in a right angle. That avoids short grain on a sharp corner which would have no strength.


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## Jacob (21 Oct 2012)

Cut the brace over size and lay it on the frame and take the marks off direct. Couldn't be simpler.


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## JakeS (22 Oct 2012)

While I'd agree with the previous replies - lay the brace against the frame and mark off the actual space it's going in - for reference, the maths to work out the angles is as follows:







The hypotenuse measurement you've already come up with, via Pythagoras: H = the square root of (a squared + b squared). This should be the centre line of the brace, with two angles cut at each end.

All the blue angles are the same angle as each other, and all the green angles are the same angle as each other, so to work out all of them we'll take the top-right triangle, formed by a right-angle in the top corner, and the angles marked 1 and 2.

The three basic trigonometric formulae are:

sin(angle) = opposite/hypotenuse
tan(angle) = adjacent/opposite
cos(angle) = adjacent/hypotenuse
where the adjacent side is the one of side A or B which meets the angle we're calculating at the time, and the opposite is the other one.

You can set the Windows calc to scientific mode by going into the View menu and selecting 'Scientific'; from here you can use the 'inverse' of the sin, cos or tan functions to work out the angle required by clicking 'Inv' and then the button that used to say 'sin', 'cos' or 'tan' but now says 'sin-1', 'cos-1' or 'tan-1'. (It's actually written as "tan raised to the power of negative 1", but really it's just the inverse-tan function. Be careful not to get confused between tan and tanh, which are different functions.)

So to work out the angle 1 (and all other blue angles) from the length of sides A and B:

- you have the adjacent and the opposite, so we can use tan. You can usually get away with just using tan all the time, when you have measurements for all three sides of the triangle you can just use the right-angled ones.
- divide the adjacent by the opposite; A is the adjacent side, B is the opposite side, so divide length A by length B. This gets us the value of tan(angle), so now we need to reverse the tan function.
- do the inverse-tan, by hitting 'Inv' on Windows Calc and then hitting 'tan-1'
- the answer is the number of degrees for angle 1.

Working out angle 2 (and all other green angles) would be just the same, just dividing B by A instead of the other way around.


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## AndyT (22 Oct 2012)

If you couldn't just mark the brace from the frame directly, isn't this the sort of problem that a roofing square is designed for? You would know measurements A and B, so you would lay the square across the brace with those same numbers along the legs touching the long edge of the brace. It would give you a smaller triangle the same shape as half of your rectangular frame, so the legs of the square would be at the correct angles for the cuts.


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## bugbear (23 Oct 2012)

AndyT":1ouu04rh said:


> If you couldn't just mark the brace from the frame directly, isn't this the sort of problem that a roofing square is designed for? You would know measurements A and B, so you would lay the square across the brace with those same numbers along the legs touching the long edge of the brace. It would give you a smaller triangle the same shape as half of your rectangular frame, so the legs of the square would be at the correct angles for the cuts.



Yes - a roofing square is a just a (very handy) scale diagram of a right angle. Since right angles are (rather) common, this is (rather) useful.

BugBear


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## Markymark (25 Nov 2012)

Thanks for all the replies. I went for the first option. The old ways seem the best. 

Thanks for all the advice. This site is great!!!

Mark


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