Timber Framers Guild Forums Tools Timberframe Design Purlin into valley Beam?

I am in the process of cutting a vaulted oak framed gable which cuts in at 90 degrees to the main roof of a new extension to my property. The two valleys are to be constructed with oak beams which run from the wallplate (building plate) of a conventional block cavity wall (U.K. build) up to a steel “I” beam which is used as a side purlin in the main roof .

The two oak valley beams have been sized by an engineer at 10” x 5” timbers. Note. The ridge purlin of the vaulted gable will also meet the two valley purlins at the steel beam. (I imagine I will have to fabricate some sort of steel hanger at this point, however that is another problem). Back to the vaulted gable, there are three purlins on this gable all sized at 7” x 5” – one at the ridge, mentioned before and one either side of the ridge, halfway between ridge and wallplate. One end of the side purlins is built into the block gable end and the other end is to be framed halfway up the valley beam. My question is what would be a suitable joint at the point where the side purlin meets the valley beam (the side purlins are to be at 90 degrees to the rafters of the vaulted gable and rafters will be peg jointed) I hope I have painted a clear enough picture of the roof !
Originally posted in general qestions by mistake I hope I get some replies this time.
Any ideas would be greatly appreciated.

Under the "learn more" menu in the tools category you will find a angle calculator and schematics for the purlin valley case.

http://www.tfguild.org/tools/tool2.html

One concern one my part is that you might need to increase the section of the raw timber to retain strength after making the backing cut (valley profile) and housings.

Any miter and bevel angles may be solved by extracting and developing the tetrahedron of the compound angle . The process is exactly the same as the development of a Hip roof, here's a comparison of the mathematical models .

This is one method of analysing the geometry of the Purlin meets Valley Rafter Intersection .
Translation so you can cross reference with the diagrams in the "Tools" link:
"Sheathing Angle" or "Angle of Saw Travel" is 90° – P2
"Backing Angle" is C5
"Angle on Adjoining Face" is 90° – P1
"Mortise Layout Angle on Hip Rafter" is 90° – R2
"Saw Blade Bevel along angle on face perpendicular to surface of Roof" is C1

The lengths of the sides of the tetrahedron may be expressed in terms of trig functions of the angles to find formulas. If you aren't comfortable with trigonometry the Pythagorean Theorem will work fine, or just pull the measurements of the angles directly from the development.

Another related method:
Development of Purlin Compound Angle on the Stick .

Can you post a picture of what you are making? I'm assuming that the joint in question is similar to those in the image above. If your "Valley beam" is a layover then the compound angles at the purlin to Valley intersection will be different.

Joe, thanks for posting this info.

I don't know if that's the kind of info greener wanted ...
If the tenons on both ends of the purlins are cut as per the drawings in the "Tools" link they can't be flown in from above with a crane. We do what we call a "step cut"; the housing is cut as detailed but imagine the tenon sliding up so that it's upper face is lying in the plane of the roof. (Actually, if it was up to me I would prefer cutting the tenons as shown in those drawings and there is a way of getting everything together but it's time consuming).
When I get back online tomorrow I can post some simple graphics (if requested) of chamfering or square cutting; the principle behind the housing and tenon cuts.

Thanks to everyone who have taken the time to reply, this is very much appreciated, I am sorry I have taken so long to get back, the reason being I have been trying to get my head around your replies. The housed Tenon joint described could be fitted with ease in my situation as the other end of the purlin is to be built into a masonary wall and therefore could be slid from this end. Any more information/drawings on this joint would be great.

This may seem like a basic question but I think I will ask it anyway (you never Know there
may be lots of people out there dying to know the answer to this, but are too scared to ask in this risk of looking stupid!)

When the wood is cut out of a structural timber (beam) as in the joint described above,
in replacing the lost wood with the other half of the joint on the end of the adjoining
timber do you retain all the strength and load carrying capabilities the main timber first
posessed?

Thanks again Greener (hopefully not so green soon)

As Roger noted in terms of backing the Valley, I would assume that any material removed will weaken the beam even if it's filled by the purlin tenon. This is more of an engineering issue and I'm curious myself as to the how much of an effect mortising has (there likely isn't a simple catch-all answer to this).

Here's an animation showing the principle behind the housing chamfer . The images show a rafter rather than a purlin and for the sake of clarity the cut along the plumb line has been omitted. Nevertheless, the idea is always the same: remove the acute angle . The cut is square to the reference face and follows a line parallel to the edge. The planes created by making both square cuts intersect to form a line perpedicular to the reference plane; this plane also represents the inside face of the housing on the Valley. Furthermore, regardless of whether this line formed by the intersecting chamfer cuts is viewed in plumb section, cross section, or plan, it's always at right angles to the side (plumb) face of the Valley.

With log work the mortise or housing depth and tenon dimensions may vary. What I do is assign the line created by the intersecting square cuts a unit value. As the square cuts pass through the purlin (or whatever we are cutting) they form scalene triangles on the outer faces. I make a 3D cardboard model of the purlin showing the lengths of the sides of these triangles calculated with respect to the unit housing depth. In the field, the distance in cross section from the inner face of the housing to the point on the log Valley where it is intersected by the purlin is measured. The figures on the model are multiplied by the actual measurements ... and there's the numbers for the housing and tenon layouts.

Greener you asked "When the wood is cut out of a structural timber (beam) as in the joint described above, in replacing the lost wood with the other half of the joint on the end of the adjoining timber do you retain all the strength and load carrying capabilities the main timber first posessed?"

Simply put, no. A common beam can have material removed from the center portion without great loss because the fiber is not highly stressed. The lower portion is under high tension so any cut fiber can not be replaced by simple plugging. The upper portion of the beam is under compression and plugging may seem to be a solution but you should realize that with a very long load duration and many moisture cycles the plug can expand and contract against the end grain of the timber creating a compression set in the plug and an increasing sag in the beam.

So I would draw a cross section of the finished beam and size the beam so I would have the required 5 x 10 between the housings and under the backing cut.

That's not a bad "catch-all" answer. Also a good reason to cut the tenons and mortises as detailed in the "Tools" illustrations.

Joe:

The animation rocks! This stuff is so hard to draw and explain, and seeing all the steps really clarifies it. Your previous posts explaining the dihedral angle were also useful. I really like your whole site, and I greatly appreciate you sharing your expertise publicly. Keep up the great work. CB.