Hip and Valley Framing I

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OST timber framers learned their roof main common, adjacent common and hip rafters, Mframing using the steel square. This is and whose interior angles are the level and plumb adequate for stick-built hips and valleys with Hip and cuts of these three slopes. their thin butted members set plumb and level, To obtain the main backing angle for the but timber-framed roofs use thick stock, often hip rafter, draw a line from the foot of the cut into non-rectangular shapes and set in a Vallev main common perpendicular to the run of the variety of orientations to the roof plane. To hip. Continue on from there with a perpen- make things worse, timber framers don’t sim- dicular to the hip itself. With the center at the ply butt pieces together, but connect them Frarmng beginning of this second line, swing an arc with mortise and tenon joints. These multiple from its end back to the hip run and draw a compound intersections result in angles which third line from this last point back to the ori- cannot be obtained with the steel square in meet at the eaves to form a level line called the ginal starting point. The angle between the any straightforward way. gutter track (Fig. 1). The extension of this plane first and third lines is the main backing angle. Help does sometimes arrive from an unex- throughout the building is the ground line. The Repeat the operation starting with the adja- pected quarter. In the decades near the turn of roof surface as defined by the tops of the rafters cent common for the adjacent backing. this century, fashions in architecture ran to and purlins is called the lattice. Once you have Top Cuts (Fig. 4). With the center at the styles often requiring elaborate hip and valley laid out ground line and lattice, you can create foot MF of the main common, swing an arc roofs, and often enough these were framed in a developed drawing that will generate all the down from the peak P to meet the rise of the steel. Builders had to find ways to lay out and framing angles. adjacent pitch and draw a line connecting this cut compound intersections of I-beams, chan- point with the foot HF of the hip rafter. nels, angles and tees. Roof framers’ handbooks Repeat, beginning at AF, for the adja- appeared, some produced in-house for a lim- cent pitch. The triangles formed by these ited audience. Most of these are gone now two lines and the sides of the kernel rectangle except for a few copies kept by steel detailers, yield the top cuts for jacks and purlins. the specialists who design the connections for Purlin Track (Fig. 5). Unlike the commons, steel-framed buildings. One of these hand- jacks and hip, the sides of the purlins do not lie books, known famllirly as Martinddle ’s, has in the vertical plane, as is plain from Fig. 1. In come to light and proved most helpful to order to determine the purlin side angles, you .. r timber framers. must first draw the plane in which they fall. FIG.1. THEG~ER TRACK. Martindale’s presents us with two power- This is done by locating where the face of the ful tools as alternatives to the square for deriv- Our model is a hip roof with both purlins purlin intersects the lattice and ground. A word ing lengths and angles in hip and valley roofs: and jack rafters. You can tell from the roof about the notion of thepurlin track: assume for geometry and math. Nowadays most framers plan (Fig. 2) that this is an irregular pitch roof the purposes of the model that the purlin is take a mathematical approac h-t abu 1ate d in which the adjacent pitch on the ends is laid out from the corner where its front face trigonometric formulas are worked out with steeper than the main pitch on the sides of the (the long or downslope side) and top edge the aid of electronic calculator or personal building. One advantage of geometric meth- (roof surface) meet. The face of the purlin computer. In the most highly evolved applica- ods is that supposedly complicated roofs (ir- defines a plane-the purlin track-at right tions, entire joint layouts are produced para- regular pitch, irregular plan) are no more chal- angles to the roof surface that cuts all the rafters metrically by special-purpose software. But lenging to deal with than simple ones. Eaves at the same height. To fully develop this sur- all this high-tech wizardry is based on ancient and ridges which don’t meet at 90 degrees, or face, the purlin track must be found both in techniques of geometry. The formulas for hips or valleys that don’t join them at 45 in plan and elevation. Remember that the major angles are derived from drawings which can plan are no more difficult to draw than ones rectangle in Fig. 5 is a plan view of the kernel, be produced with simple draftsmen’s tools that do. In addition, all drawing procedures while the three large triangles represent the (dividers, straightedge, square). With its are identical for main and adjacent pitches. vertical sections taken at the main, adjacent complementary presentation of both geomet- One problem that is worth mentioning: in and hip rafters. ric drawing and derived trigonometry, Mar- order to maintain a level gutter line all around, Start with the elevations. The single circles tindale’s serves as a convenient point of depar- builders of irregular pitch hips must vary ei- show where the upper (lattice) end of the pur- ture for the development of both systems. ther plate heights or overhang widths on main lin track hits the rafters. To locate these points Speaking of development, the essence of the and adjacent eaves. in plan, drop plumb (dotted) lines down to the geometric method is a technique called devel- runs and continue straight on in plan until the oped drawing. In this technical sense, a devel- three lines intersect the hip run. As you would opment is the unfolding of a three-dimen- expect, they all converge on the same point sional object so that all of its surfaces lie in a (double circle). The plan of the lower (ground) single plane. In other words, developed draw- end of the purlin track is found by dropping ing is a way of reproducing the parts of a perpendiculars (dashed) from the same start- complex shape on a piece of paper. This is ing points on the commons down to the com- useful when searching for angles in hip and mon runs. From there extend the lines at right valley roofs since the same three points which angles from the common runs until they strike determine an angle also define a plane, and, the run of the hip (triangles). typically, once you have developed the surface Purlin on Hip (Fig. 6). To find the projec- on which an angle falls, finding the angle itself tion of the faces of the purlins on the sides of is a simple matter. the hip, connect the hip-purlin intersection (single circle) with the hip run-purlin ground HIS article is the first of a series covering intersections (triangles). The angles between T applications of geometric and mathemati- these two lines and the hip mark the downslope cal methods to the design, layout and cutting ends of the mortises for the main and adjacent of hip and valley roofs. Our introduction to purlins in the side of the hip. the subject is a geometric one, drawing on the Purlin Side Cuts and Lip Cuts (Fig. 7).To presentation made at the 1990 conference by FIG.2. THEROOF KERNEL. find the side cuts, need some additional Frederic Brillant of Celtic Construction, construction lines. Extend the purlin lattice Vashon Island, Washington. Frederic received All the information needed for framing is (dotted) lines from Fig. 5 beyond their inter- his carpentry training in southern France as contained in the roof kernel delineated by the section with the hip run (double circle). Arc apprentice and journeyman in the unbroken heavy dashed rectangle in the roof plan. This is the common-purlin intersection points (single tradition of the Compagnons du Devoir, the the starting point for the drawing. The long circles) down to the common runs and drop French trade guild. As he points out, the sys- sides of the rectangle represent the run of the perpendiculars from there to meet the dotted tem presented here was “developed and re- main roof slope, tLe skort sides the adjacent lines. Connect these two points (pentagons) fined by skilled journeymen at a time of gen- run, and the diagonal the run of the hip. The with the hip run-purlin ground intersections eral illiteracy. The approach does not use drawings which follow (Figs. 3-7) are (triangles). The angle between the two (solid) numbers or mathematics and the amount of Frederic’s, recast and translated for a North lines is the purlin side cut. abstraction is minimal.” American audience. The lip cut is needed only in those instances The core of Frederic’s workshop was a Pitches, Plumb Cuts and Backing (Fig. 3). where the purlin is deep enough that part of it simple geometric construction which gener- For the sake of simplicity and clarity, the lay- passes under the hip. The lip cut is the angle on ates the data needed to frame a hip. This roof out is broken up into several drawings. Begin the side of the purh between the bottom of the layout can be lofted full-size on the shop floor the first by reproducing the plan of the kernel. purh and the bottom of the hip. Raise a perpen- in order to obtain stock lengths and joint loca- While the various runs differ in length, the dicular from the lower end of the hip run. Extend tions as well as angles, or it can be drawn to rise, a given, is common to all three, so you can it and the purh ground tracks until they meet scale at the drawing board, yielding angles only. add elevations to the drawing by erecting the rise and connect these intersections (diamonds) with To perform the latter exercise, all you need perpendicular to each of the three runs, and con- the pentagon points (see above). The lip cuts are to start is the ground line and the lattice. Some necting foot to peak. You now have three triangles the angles between the ground tracks and these definitions: the tops of the rafters and fascia whose sides are the run, rise and length of the last two hes. -ED LEVIN

6 FIG.3. PITCHES,PLUMB CUTS, BACKING. FIG.4. Tor Curs.

/ I/I / / +.I /,I I/ p’ 1.1 +- +- +-+- + + FIG.5. THEPURLIN TRACK. FIG.6. PURLINFACE ON HIP.

I-/ / 1 1 I / +t--t---- I I

KEY

GUTTERTRACK- +- 4- - GROUNDLINE -- -- - LA~ICE _.-.-.-.-

PURLIN TRACKS AT LA~ICE ...... AT GROUND ------

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