Hip and Valley

This can be complicated. Is the common practice a butt joint with big screws or housings with clip angles and such. How do you all find the neccessary information to lay-out a hip or valley (especially with purlins with housings)? AutoCad, paper, pencil, triangles, etc?

Plan views?




It seems that when you want to timber frame hip and valley it gets more complicated. I am wondering how you all approach it?

Wow, huge topic. This is a great example of why one should join the Guild. There was a recent series of articles in the Journal on compound joinery. There are many layout systems, some using trig, some using developed drawings. All of these have been discussed in the guild's pubs. The red book even has a pullout centerfold with provocative drawings :-) There are also classes available specific to the topic. Will Beemer teaches one at heartwood. I'll be demonstrating how to use Sketchup to develop compound joinery in situ without trig at the Western Conference in Coeur d'Alene this spring. CB.

Mo, the best answer is … do the math. It looks like you are on the right track. Start with a sketch of the geometry like you have on the plywood in the background, then scale the lengths in terms of trig functions of the angles. Make models out of bristol board and wood (like in your photos).

You need not do the trig - every angle in a Hip/Valley roof may be developed with nothing more than a compass and straightedge. I prefer to make a worksheet or program to solve all the angles:
Hip and Valley Roof Framing and Joinery Angle Calculators ... print the list, and final dimensioning is done in the field with a scientific calculator (the programmable graphing type preferred). If you understand how to derive a formula from the geometry then by default you will know how to apply the trigomometry to dimensioning the roof components.

I only have a few minutes of time online today so for now here are links to a couple of roof framing math discussions:

Roof Math
Hip and Valley Roof Compound Angle Formulas and Geometry

Once you get the hang of it there isn't much to "complex" roof joinery. It's just a bunch of right triangles. See you all next year!

Make models out of Bristol Board? Any links to photos of that? I know BB is used for drawing on but I don't think I've ever seen TF's modeled from it. Just curious.
IS the BB just to use as sheathing?
thanks
andy

The angles on the developed faces of the rafter or purlin are laid out to scale using a blend of geometry and trigonometry. The dihedral angles may be double checked after the model is constructed.

When I first studied compound joinery geometry I made simple models of the triangles and tetrahedra. Sorry, no pics of these ... I outgrew them and passed them along to other folks who are just starting to learn the math.

The models in the pages below are "working models" for use in the field. They take no longer to make than orthographic, isometric or perspective drawings and have the advantage of not suffering from the angles and planes being distorted. It's nice to see exactly what you are shooting for in 3D when doing the layout on a log or timber.

Models of Roof Member Intersections
Models of Square Hung Fascia intersects foot of Hip Rafter
Model of Three-Branch Compound Joint ... scroll down the page

Curved intersections can be developed and modeled as well ...

Barrel Arch intersects Conical Roof
Barrel Arch intersects Barrel Arch
Flashing intersects slope of Roof

I don't have any photos of the models in their developed (laid out flat) form but there is a sketch drawn to scale near the bottom of this page. Just lay out the angles and dimensions on the faces, cut, fold, and tape and/or glue ...

Square Hung Fascia at an Irregular Plan Angle

Hey Joe, awesome stuff as usual.

"You need not do the trig - every angle in a Hip/Valley roof may be developed with nothing more than a compass and straightedge"

That is how I have learned to do this. We just use centerlines of each piece and represent a corner of the roof in plan view. From there with the rise, angle of plates, spacing, backing cut, and hip offset one can calculate everything. By laying certain triangles down in plan view and knowing which points to connect the angles can be found. If you are very precise with this you can then use a bevel to transfer the angles on the plywood or paper to the timber for lay-out, probably some of the most challenging geometry I have attempted, but once it clicks it clicks.

"This can be complicated. Is the common practice a butt joint with big screws or housings with clip angles and such. How do you all find the neccessary information to lay-out a hip or valley (especially with purlins with housings)? AutoCad, paper, pencil, triangles, etc?"

This isn't really complicated but it's harder to describe than it is to actually do. All the final dimensioning is done on-site with a calculator (usually trigonometry), with a printout of the angles and models of the joints for reference.

The first step is to find the dimensions between the working points at the intersections of the unadjusted rafter lengths. On a log Valley the ends are squared off. Then the compound angles at the peak and foot, and the backing trough, are cut.

The distances between purlins are laid out along the Valley trough line and the adjusted centerlines of the purlins are marked on the planes of trough. The traces of the pockets for the housings are projected to the irregular round on the Valley with jigs.

I have never seen an intersection simply butted and lagged. All roof members are housed, tenoned or step cut and the joints joints are supplemented with through bolts, knife plates or plates lagged from the surface of the roof.

at least two bevels with this one. (6/12 purlin side, 10/12 rafter side)
where the hip meets the plates unbacked was a little tricky (housed).
This stuff is way fun though.

On to valleys next. As far as finding the angles (for example, where the jack hits the hip unbacked) will it be simular to finding the valley rafter intersecting with the valley (without the trough)?

mo,

it looks like the hips are all offset. I reckon that's to keep the backing cut the same height on each side?
I would love to know an easy way to figure that offset. Actually, I would love to know both a graphical and a formulaic way to figure that offset. Can you help me out?

Gabel, this is the "natural", proportional or geometric offset. The Hip/Valley rafter crosses the intersection of the eave lines. Although the eave lines in the animation are shown meeting at a right angle this corner angle can be any value.

Development of the Backing Angle ... or C5 in the Hawkindale angle nomenclature used here.

This is looking at the same offest viewed in plumb section through the Hip rafter. The blue line being rotated is what many framers call the "Hip" drop on an unbacked Hip rafter. The offset produces equal shoulder heights on both sides of the Hip and determines the correct "plane in" point for the jack rafters on a backed or unbacked Hip rafter.

Development of the Plumb Backing Angle ... Hawkindale angle A7

The offset formulas derived from the geometry are given on the last page of Hip Shift/Drop Analysis. A similar formula may be derived from the side cut angles on the upper shoulder of the unbacked Hip/Valley. And here are some example Hip Shift/Drop Calculations and Diagrams

There are other offsets. The Hip/Valley can be shifted laterally or radially to produce equal overhangs ... but that's another story.

Gabel, Yes they are offset for that reason. If you did not offset them your stick dimensions would be odd with trying to leave enough face for intersecting purlins or rafters.

Here is a photo of a simple way to find the offset.
All you need to do is represent the two plates (at any angle you wish to build with) the two common rafters, and the hip centerline in plan (which is actually the top of your backing, due to the offset). I used a 3" hip in this one because of sheet paper size.

All you really need is the angles between plate, hip, plate in plan view.

I know someone who found the reasoning for this with formulas and such. It was about two pages long when the variables were introduced. I'll see if I can post it sometime soon.

If there any questions about the illustration, feel free.

mo

"I know someone who found the reasoning for this with formulas and such. It was about two pages long when the variables were introduced. I'll see if I can post it sometime soon."

Two pages!!!

The ratio for the offset is the Major (or Minor) Plan Angle rise divided by the sum of both Plan Angle rises.

Produce the lines at a right angle to the Hip run until they intersect the eave lines.

thanks mo and Joe,

I'll have to look at this for a few minutes when my head's in the game.

mymymy...
Ya, this is the way I figured it out, when I finally did. And I'm sure that next time it comes up, I'll have to re-figure it out again.

I find it quite difficult to wrap my brain around something on the written page, but in the shop with the plans and the timbers in front of me, well that's a whole different scene!
And somehow, I found the valleys easier to work with than the hips....either way, both are a great challenge!
And yes, they gotta have housings or something...don't just be lagging those jacks!

Good luck, buddy