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corner summerhouse with cathedral rafter question

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corner summerhouse with cathedral rafter question

Postby oddsocks » 31 May 2016, 21:45

Hopefully I'll have time next weekend to create a WIP post for the summerhouse I've finally designed in Sketchup and started to build (sneak preview of sketchup file here https://drive.google.com/open?id=0B23Hn ... HhMTFBaZ1k and video of layers building up here https://drive.google.com/open?id=0B23Hn ... HlxdHRnOE0).

I'm currentlly at rafter level...
Image


and have spent the past week researching into the sawtable angles to cut the jack rafter that joins the hip rafter and got completely confused by trapeziodal diagrams etc. I have actually worked out the angle by a simple jig, a manual saw cut in the correct plane then used that to set the saw table up. However I still would like to know what the maths are that converts the plan angles into sawtable compound angles. Everything I've found has assumed a ridge angle of 90 degrees, but this being a corner summer house the pitch of the hip rafter is 15.7 degrees (3.37:12) and the common /jack rafters are 21.7 degrees (4.78:12), so the relevant ridge angle is 180-15.7-15.7 = 148.6 degrees (this is actually to keep the max height to 2.49m due to planning permission).
From sketchup the hip rafter compound angles are 42.9degrees and 68.3 degrees, yet the saw table to achieve this is approx 47 degrees and 70.7 degrees (the 47 was achieved by using a wedge as the table only tips to 45). I understand why they are different from plan and elevation angles, but would like to understand the calculation.

Heres some images from sketchup (I had to save the design in sketchup 8 format and move to an old laptop that has the roof framing geometry plugin that gives angle dimensions)

the jack rafters joining the hip rafter (kingpin also shown)
Image

A close up of the hip rafter to kingpin (90-74.27 = 15.73 degree pitch)
Image

and the angles of the jack rafter where they meet the hip rafter (key angles are 42.9 and 68.3 - these are the ones that 'adjust' when put on a compound angle mitre saw)
Image

Image
Finally the plan view that shows the jackrafter is 90 to the wallplate and the hip rafter is 45.

Any help in understanding the maths gratefully received (just in case I ever need to build another one!). i have some other rafters on the door section that are at a different pitch again (23.5) as they travel a shorter distance to get from wall plate to kingpin height.

Thanks
Dave
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Re: corner summerhouse with cathedral rafter question

Postby Pinch » 01 Jun 2016, 19:59

Tricky project Dave. :eusa-think:

I certainly couldn't help you with the geometry as I can't remember the good old college days - too many liquid lunches. But you could work out all the cuts another way, by physically scaling a drawing and using that as your workshop rod.
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Re: corner summerhouse with cathedral rafter question

Postby oddsocks » 01 Jun 2016, 21:42

thanks -its certainly been a challenge! When I looked at 'standard' summerhouses the window walls are half the length of the other two walls, which means hip rafters are at 90 to each other and the kingpin is a simple octagon....but my wife wanted longer walls and a smaller door so that added complexity.

It's the 'mathematician' in me that wants to know the calculation, I only have 6 of each handed jack rafter to cut and I proved to myself last night I can mark that from the jig I made and cut it accurately in less than 2 minutes....its just a case of marking all the lines and keeping the saw cut parallel to the top plane all the way through the cut, as the cut is compound. Now I know the actual sawtable settings I might 'in slow time' research for the formula.

Work schedule permitting I'll cut the remaining jack rafters on Friday night and fit them on Sunday. Heres a sketchup plan view image of the roof (rafters at 40cm/16" center spacing):
Image
Rafters the same colour are the same size and hand. Once I've done the 12 main jack rafters I then need to do the remaining 4 unique ones that touch the door hip rafters (these are different angles due to pitches but the same principle). My aim is to have them all fitted on Sunday.

And the 3D view:

Image

The inner black line that follows the shape of the wallplate is a design aid - all the hip, common and jack rafters touch it - they start at the same kingpin height and touch at this point; that's what results in the various pitch angles to ensure a flat roof on each side. The outer black line was just to ensure as I drew each rafter it extended far enough. I'll cut when fitted so that the ends are vertical and aligned.

I'll add more detail and installation photos when I create the WIP thread.
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Re: corner summerhouse with cathedral rafter question

Postby meccarroll » 09 Jun 2016, 08:50

oddsocks wrote:Any help in understanding the maths gratefully received (just in case I ever need to build another one!). i have some other rafters on the door section that are at a different pitch again (23.5) as they travel a shorter distance to get from wall plate to kingpin height.

Thanks
Dave


It looks like you don't really need any help here as you have already done it. :eusa-clap:

I have worked on a few roofs over the years and most cippies just use a string line taken from the ridge to the corner of the wall plate and set it at the right height then use a bevel to obtain the angles between the wall plate and string line. Simple but it works (80% of roofs will have been put up using a string line to obtain the bevels).

I use Trigonometry and geometry for bevels and lengths of rafters etc.

For the top angle just use the right angle triangle formula: all angles in a right angle triangle add up to 180 deg.

Hence if your pitch is 15 deg . From above, 180 - (15+90 deg) = 75 deg. 75 deg is your top cut. I think you are already aware of this but it's that simple, no complicated maths involved.

Simple maths

Trigonometry will give the lengths of the rafters. Use the cosine.

Formula: 1/2 span divided by the Cosine of the Pitch of the roof = length of Rafter or Hip.

Cosine 15 deg = 0.965
1/2 span Roof = 150

Eg: 150/0.965 = 155.291 (length of rafter)

Please a look at the drawing below which may help.

I have given the pitch to be 15 deg (not hip pitch), total span to be 300 and half span to be 150.
Image

If you look at the section drawing of the roof (top triangle) you can see the dimentions and look back at the cosine formula will see it works for the length of the rafter.

Geometry
Developing the roof surface area will give you the edge angle for the jack rafter.

It's quite simple to do, if you look at the drawing the developed area of the roof is simply obtained by using the true length of the rafter (obtained by Cosine formula above).

Just draw a perpendicular line from the midpoint of the roof (dotted line, purple drawing) and extend at 90 deg the length of the rafter (155.291). Then draw two lines to intersect from the corners of the base to the tip of the line. This forms the purple triangle which is the developed roof surface. The jack rafter edge bevel is taken from the developed roof as shown in the drawing. If you develop the front roof surface where the door is it will work for the too, just use the height of the roof and relative span for each individual roof development.

There are numerous ways to make things simple for onsite angle development but it would take all day to go through them.

Hope some of this makes sense, Mark

PS there is a really simple method for obtaining the edge angle of a jack rafter, I'll post the link to where someone has explained it.
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Re: corner summerhouse with cathedral rafter question

Postby oddsocks » 09 Jun 2016, 08:59

Thanks Mark, that was really useful and easy to follow (unlike some of the others sites I've read in recent weeks!).
I did get my jack rafters cut and fitted on Sunday, but did it by hand as I only had 6 left to do. I've not started the WIP thread yet due to being ill since Sunday, but on the mend now so will do it soon.

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