## Wednesday 20/1/21

I did end up taking off the tent canvas last night and I got a good night’s sleep as a result despite the wind. The strong winds and rain continued today and will carry on through the night tonight. This gave me time to check the geometry of the roof and work out the point at which the principal rafters should hit the tie beam and the height of the king post.

These calculations took me a couple of hours as I needed to dredge up my O Level maths. The calculation sequence is shown below. If you want to know the actual calculations involved please ask in a comment to this blog post and I will post them. The key thing to note is that in order to achieve the 45mm gap between the underside of the softwood rafter and the top face of the green oak principal rafter, the top face of the green oak principal rafter needs to hit the top surface of the tie beam 182mm in from the outside shoulder of the cog joint.

Click image to view full size on Flickr

I used this information, together with the actual distance between the outside edges of the cog joints on the tie beam (4306mm) to calculate the height of the tie beam. The calculation sequence shown below indicate that the distance between the top of the tie beam and the top of the king post should be 1654mm.

Click image to view full size on Flickr

The next job will be to lay up all these elements of the truss using these calculated values to check it all works.

[Addendum. This is how things worked out: Shaping the Roof]

Hi Simon. I’ve just found your blog and really enjoying reading your timber frame build, especially the English tying joint. The king truss looks great. I’m late to this party but would be interested to know the actual calculations involved above as I’m planning something similar soon.

Thanks for your comment. In 2018/19 we extended our house and part of this was a two-storey oak frame. My barn is essentially a copy of the second storey of that. It has the same truss design and the softwood elements of the roof are the same size.

Regarding the oak frame, the view among engineers and building inspectors seems to be that this form of construction is older than the regulations and so they are not applied subject to the timbers being “well selected” (ie a straight grained as possible for the posts and beams and curved for the braces), “big enough” and the pegging follows “good traditional practice”. We offset all the pegging holes so that the joints pull together as the timber shrinks.

I hope this helps.

Thanks Simon, I’m planning on a truss something similar to this but I’m unclear about the king to tie and principle to tie joinery. Are these all mortise and tenon, drawbored. Are the principles to tie notched in? Apologies if this is shown elsewhere but I haven’t come across it yet. This blog is great by the way.

A search on “truss” should give you the answers you are after: http://simonberry.net/?s=truss

Sorry, I’ve just read the blog post again and realise now what calculations you are talking about! So here goes. The whole point of these calculations is to arrive at the distance to the top of the king post from the top surface of the tie beam:

Roof Geometry – 1 of 2

Level 1 (Horizontal distance between principal rafter and softwood rafter):

Space between principal rafter and softwood rafter = 45 mm

Pitch of roof = 40 degrees

Horizontal distance between principal rafter and softwood rafter = x

sin(40) = 45 / x

x = 45 / sin(40) = 70 mm

Level 1 (Depth of softwood birdsmouth):

Width of birdsmouth = 45 mm

Pitch of roof = 40 degrees

Depth of softwood birdsmouth = y

tan(90-40) = tan(50) = 45 / y

y = 45/tan(50) = 37.76, say 38mm

Level 2 (Top of tie beam to bottom edge of birdsmouth)

Depth of wall plate to tie beam joint = 35 mm

Depth of softwood birdsmouth = 38 mm

Depth of the tie beam = 200 mm

Top of tie beam to bottom edge of birdsmouth = z

z = 200 + (38-35) = 203 mm

Level 3 (Horizontal distance between outer edge of wall plate and underside of softwood rafter = a):

tan(90-40) = tan(50) = a / z = a / 203

a = tan(50) * 203 = 242

Level 4 (Horizontal distance between outer edge of wall plate and the point at which the principal rafter hits the tie beam = b)

b = x + a = 70 + 242 = 312 mm

Final level (Horizontal distance between outer edge of wall plate to tie beam joint and the point at which the principal rafter hits the tie beam = c):

Outer edge of wall plate to outer edge of wall plate joint = 130mm

c = b – 130 = 312 – 130 = 182 mm

Roof Geometry – 2 of 2

Level 1 (Outer edge of wall plate to tie joint to centre of king post = d):

Distance between outer edges of tie beam to wall plate joints = 4306 (given)

d = 4306 / 2 = 2153 mm

Level 2 (distance between the point at which outer edge of principal rafter hits the top of the tie beam and the centre of the king post = e):

e = d – c = 2153 – 182 = 1971 mm

Final calculation (the distance to the top of the king post from the top surface of the tie beam = f):

tan(40) = f / e

f = tan(40) * e = tan(40) * 1971 = 1654 mm

PHEW!

This is brilliant! Exactly what I’m after, many thanks… I might pose a question or 2 more as I read through your other posts: I hope you don’t mind! My interest in the king post relates to my intention to put some rather heavy rosemary clay tiles on the roof so the king post should minimise thrust on the plates and posts. Your design is something close to what I hope to achieve.

That truss design is very clever as weight on the principal rafters exerts an upward force on the king pin which is transferred to the tie beam.