CHAPTER LEVELLINGconstruct AND SETTINGadvanced OUT roofs 31 Dr Glenn P. Costin

This chapter focuses on the construction of five common forms that fall within the very broad advanced roofing category: • (Dutch ) • Jerkin head • Skewed gable • Oblique hip • Unequal pitch. For each of these, the mathematical, geometric and construction techniques are described in detail, which will give you the ability to explore other advanced roof types, such as octagonal ends, tapering spans and the comparatively simple Mansard. This chapter expands on—and at times challenges—the basic principles developed in Chapter 5 of Site Establishment, Formwork and (Laws 2009), which covered the setting out and construction of basic roofs, such as the gable, broken hip, valley and Scotch valley. We Samplewill start with a brief revision of pagesthese roofing basics.

advanced roofing, particularly by BASIC roofs with unequal pitches or tapering PRINCIPLES OF spans. We suggest that you revisit Chapter 5 of Site Establishment, ROOFING Formwork and Framing (Laws 2009) The purpose of this revision is twofold. and the PowerPoint slide show, ‘The First, it is to re-acquaint you with the Seven Pillars of Roof’ (Costin 2009), basic principles of roofing, including available with that text. the underpinning mathematics and Having developed an understanding geometry; and second, it is to highlight of basic roofing, it is reasonable for key assumptions within these basic you to have formed the belief that the principles that are challenged in following points hold true for all roofs:

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1. Roofs are made up of right angled triangles 1. Common rise per metre run (CR rise/m and are set out to centre lines (including hip run) and valley , centring rafters and

ridges). 0.466 m 2. Ridges run parallel and level to wall plates. 3. Regardless of the roof shape, rafters run at 90° to 1.0 00 m the wall plates. CR rise/m run = tan  4. Hips and valleys bisect internal and external Rise corners regardless of the angles of those corners. tan 25° = 1.000 With the exception of point 3, all of the above will 0.466 = rise be challenged at some point in the following pages. 2. Common rafter length per metre run (CR factor) And point 3, while not directly challenged here, can­ not be viewed as a given in all roofing, for there are 1.103 m 0.466 m occasions in some more complex architecture where it may be rational to forgo this ‘rule’ also (though 1.0 00 m generally in small areas where only light loads CR/m run2 = 12 + 0.4662 apply). CR/m run2 = 1 + 0.217 CR/m run = √1.217 The mathematics: the ‘Seven Pillars’ CR/m run = 1.103 m revisited 3. Common rafter set-out length (CR set-out length) From the two texts referred to earlier (Laws 2009; Costin 2009), the following is the basis of mathematics 4.419 m underpinning roofing. While there are some notable changes with regards to hip and valley length

calculations, these basic principles still hold, as does 1.103 m 0.466 m the geometry that they are derived from. 1.000 m 4.005 m This sample calculation for a basic hipped (Half span) roof is based upon a building with the following CR set-out length = CR factor 3 half span characteristics: CR set-out length = 1.103 3 4.005 Pitch = 25° Sample pages CR set-out length = 4.419 m Span = 8010 mm 4. Common rafter order length (CR order length) Eave width = 600 mm Rafter sectional size = 125 3 45 mm

Hip sectional size = 175 3 35 mm 5.204 m It is important that you develop a clear understanding of this system of calculations and, 1.103 m 0.466 m most importantly, the application of the common rafter length per metre run (CR factor) and, similarly, 1.000 m 4.605 m the hip length per metre run of common rafter (hip (Half span  eave width) factor). It is by using these factors that lengths of some of the seemingly more difficult components are most CR order length = [CR factor 3 (half span + eave easily found. width)] + rafter depth

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CR order length = [1.103 3 (4.005 + 0.600)] 7. Hip order length + 0.125

= [1.103 3 4.605] + 0.125 7 m 6.85 = 5.079 + 0.125 Allowance needed for bevel cut = 5.204 1.489 m CR order length = > 5.4 m Remember to add the depth of the rafter 5 m material (in this case 125 mm) to allow for the With allowance 4.60 for bevel cut, order 7. 2 m hip 5 m bevel cut (see the ‘Seven Pillars’ PowerPoint for 4.00 0 m clarification if you are unclear on this issue). 0.60 5. Hip length per metre run of common rafter (hip factor) Hip order length = [hip factor 3 (half span + eave Hip width)] + hip depth 0.466 m

1.414 m hip order length = [1.489 3 (4.005 + 0.600)]

1.0 00 m + 0.175 1.0 00 m = [1.489 3 4.605] + 0.175 = 6.857 + 0.175

89 m = 7.032 1.4 0.466 m hip order length = > 7.2 m

1.414 m Basic roofing geometry Hip factor = hip run2 + rise2 √ From Chapter 5 of Constructing a Pitched Roof (Laws hip factor2 = 1.4142 + 0.4662 2009), you will be aware that for basic roofing eight hip factor2 = 2 + 0.217 hip factor = √2.217 bevels are required. The development shown in hip factor = 1.489 m Figure 3.1 has been taken directly from that text. 6. Hip set-out length SampleThese pages eight bevels remain all that are required for our first two roofs (gambrel and jerkin head), and the basic principles hold for all the others. You need 5.963 m to focus particular attention on the development of the hip edge bevel. This is based upon the level line Hip factor 1.489 m (LL) principle (see Figures 3.2 and 3.3). This principle Rise 1.414 m works on the basis that any line running at 90° to the 1.0 00 m component being considered is level. And as long as 4.005 m the top edge of that component is square to a line

Hip set-out length = hip factor 3 half span running plumb or vertically through it (generally the hip length = 1.489 3 4.005 case with square or rectangular rafters, etc.), then this hip length = 5.963 m line is also running along that surface.

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90° angle PBCR Figure 3.1 One approach to the development LBCR Rise of roof bevels

Elevation view Start near here or on centre The skill in developing roof bevels is always in determining where to find the relevant right angled triangle, i.e. where to place the level line, and where to PB hip EB hip find the true length of the other side of that triangle. After that it is ‘just’ (teachers love that word!) a matter e is R of putting the two lengths together as a right angled FB triangle to form the ‘true’ bevel. In Figures 3.2 and 3.3 the component we are dealing with is a hip. Given that a level line in the plan view is a true length, it is the side running up the hip that is Start here LB hip These two lines raking and so is actually longer than it appears. The and extend same length up true length of this side is found in the side elevation

EB creeper EP purlin Plan view of the hip. Using a layout similar to that modelled in Eight roof bevels: 1 Plumb bevel common rafter  PBCR Figure 3.1, we can see one way of graphically putting 2 Level bevel common rafter  LBCR this into practice (see Figure 3.2). 3 Plumb bevel hip  PB hip 4 Level bevel hip  LB hip 5 Edge bevel hip  EB hip 6 Edge bevel creeper  EB creeper 7 Face bevel purlin  FBP 8 Edge bevel purlin  EBP

True bevel Figure 3.2 Bevel is clearly not 45° as LL1 and the true length The level line of X are not the same. principle ‘fold out’

True Rise length of X

Sample pagesRidge centre line LL1

Bevel we are looking for. X In plan appears as a 45° angle as both X and LL1 are the same length.

LL1 Hip centre line Crown end centre line

Hip centre line

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Figure 3.3 Centre lines The level line principle— pictorial view Ridge (top) and plan view (bottom) (reproduced in colour in the Appendix)

Hip Centring rafter

Hip

Crown end rafter

These lines are level as long as they run ‘square’ to the component (at 90º). In bringing the line ‘over’ the centre line of the component beside it, the resultant triangle provides the edge bevel sought. It is not the ‘true’ angle, however, until the true length of the other side is found.

Sample pages

Study this concept carefully until you can fully However, each is working on the same principle visualise what is being done. This concept will of recognising when a line is being seen in its true occur repeatedly in developing the bevels for each length, and knowing how or where to find the true of the roofs that follow. It is also important for length of those lines that are raking towards or you to realise that there are many ways that the away from us. development of the above bevel may be laid out.

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In a gambrel roof, the ridge is extended as shown GAMBREL (DUTCH in Figures 3.4 and 3.5. This means extra rafters are GABLE) ROOF installed and the hips shortened. The result is a vertical gable in the hip end, located wherever the The gambrel or Dutch is basically a hipped builder, client or architect desires: usually at the most roof with an extended ridge forming small convenient common rafter position. A waling plate is at each end, i.e. the hips start from the plates at the fixed to the last set of common rafters to pick up the corners but don’t reach the apex. Sometimes the gable ends of the jack rafters that fill out the end of the roof end is built as a vent or has vents let into it. This is a (see Figure 3.6). Then the hips and any creepers are cut style that continues to be popular in contemporary in to finish the framing. home design.

Figure 3.4 Extended ridge Gambrel roof frame Waling piece

Figure 3.5 Plan of typical Jack rafters gambrel roof framing (reproduced in Shortened hip colour in the Last common rafter Appendix)

Extension of ridge

SampleCommon rafters pages

Jack rafters

A normal hip end Centring rafters Centring

Shortened hip

Last common rafter

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Extension of ridge on the end wall plate; then all other rafter positions moving away from these centre line marks at the normal rafter spacings. At this point you should do the development of all your basic bevels (the eight bevels shown in Figure 3.1) and the calculation of the first five of the ‘Seven Pillars’, as shown in the following table.

First five roofing pillars In this case Normal hip travel (see pages 74 & 75 for calculations) Figure 3.6 Typical Dutch 1 Rise/m run of CR 0.466 m gable showing the 2 CR length/m run (CR factor) 1.103 m ridge extension 3 Set-out length of CR 2.482 m 4 Order length of CR 3.144 m 5 Hip length/m run of CR (hip 1.489 m Setting out and constructing the factor) gambrel roof From this information, you should create a pattern For simplicity, the roof being considered will have rafter as per normal (see Laws 2009, pp. 141–145), but similar characteristics to that used in the revision exclude the creeper rafter lengths for now. exercises, but a narrower span i.e.: Pitch = 25° Setting out the ridge Span = 4500 mm Ridge set-out is done by marking it off the wall plate, Eave width = 600 mm as you would in normal roofing practice, the only Rafter sectional size = 125 3 45 mm difference being the allowance for the extension. This Hip sectional size = 175 3 35 mm is simply a matter of determining which rafter is going Begin by marking out the top plates as you would a to be the last common one. normal hipped roof: i.e. the centre line of the centring rafters set back from the end of the build by the half Figure 3.7 span; centre line of the crown end at the half span Gambrel roof with Sample pages extended ridge Ridge is extended past original centring rafters as required Set out all other rafter positions as normal: i.e. working away from centring and crown end towards corners

Normal centring rafter location

Centre line of crown end as per normal Centre line of centring rafter Half span

Half span

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Figure 3.8 Ridge set-out

CL of centring rafter

Half span

Top plate

Ridge

Extension of ridge: in this case Cut-off point for extended 3  450 mm rafter spacings, or 1350 mm ridge. Mark but do not cut until roof is up.

967 mm

Figure 3.10 Figure 3.9 Jack rafter set-out Main roof section erected and braced The jack rafters and location of waling piece In this case, the plan calls for an extension of To find the location of the waling piece, we will three rafters spaced at 450 mm centre to centre (see need to set out and cut one of the jack rafters (see Figure 3.8). If in your plan no dimension is given, you Figure 3.10). This will then be used to mark where the will have to scale the length and then check with the top edge of the jacks will finish on the common rafters client or architect. (see Figure 3.11). SampleThe pages jack rafter is simply a shortened common Standing the main roof section rafter (hence the name ‘jack’). To calculate the length of Having marked out the ridge and pattern rafter, the first part of the roof may be cut out and assembled. Plumb line marked Be sure to install a temporary brace from jack rafter at this point in case of unexpected plumb cut high wind gusts (see Figure 3.9).

Top edge of waling piece Figure 3.11 Locating the Jack rafter cut to length and waling piece positioned for marking

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Line of plumb cut Figure 3.12 Locating waling Position of top piece detail edge of waling piece Jack rafter held in position for marking

Waling piece

any component that has the same pitch as a common In this case: rafter, you need two easily found pieces of information: cut-off length = 877 3 1.103 the run, or plan length, of the component; and the CR cut-off length = 967 mm length/m run, or rafter factor. Having cut at least one jack rafter as a pattern, The run of the jack is found by: place the rafter as shown above and mark down the Half span – (ridge extension + half the thickness of plumb cut (see Figure 3.12). Do this on both sides of a common rafter*) the roof. Where this plumb line meets the bottom In this case: edge of the common rafters is where you will position jack run = 2250 – (1350 + 23*) the top edge of the waling piece. jack run = 877 mm The cut-off length of the jack rafter is then simply: *Note: This reduction can be done later, as you would for a crown end rafter. In taking this alternative Cut-off length = component run 3 CR length/m approach, you will be finding the ‘set-out’ length of the run jack rafter. You must then be sure to take off the half thickness of CR (horizontally, and not down the length of the rafter).

Figure 3.13 Alternative waling 967 mm Sample967 mm pages piece positions

Option A: Notched rafters Option B: Rafters shortened by thickness of waler; waler positioned in line with top of jack rafter

967 mm Line of plumb cut Thickness of waling piece Lower waler Normal position position (Option A) Jack rafter held in Option C: Waler lowered to suit underside of position for marking jack rafter; achieved by marking the thickness of the waler back towards the wall plates from the plumb line (see explanatory figure at right)

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Alternatives for locating waling piece In this case: Locating the waling piece as described above requires hip set-out length = 0.877 3 1.489 that you notch the underside of each jack rafter as hip set-out length = 1.306 m shown on the previous page (Option A). Options B and As we are using a jack run that already allows for C offer alternatives to this approach (see Figure 3.13). the half thickness of a common rafter, no further Figure 3.14 shows the waling piece installed. reductions are required when setting out the hip. The The jack rafters can now be installed. Note that the hip set-out is shown in Figure 3.16. top outer edge of the two outer rafters should meet the edge of the common rafters as shown in Figure 3.15. Finishing the framing Installation of the hips is much the same as normal, Hip rafters though you will need to notch the top end of the hip To calculate the length of hips we use, as with basic over the waling piece. This is easiest done by direct hipped roofing, the run of the common rafter that is measurement and use of the normal hip plumb and required to obtain the same height. In basic hipped level bevels. As with the jack rafters, be sure that roofing this is simply the half span. In this case, as is the top edge of the hip aligns correctly with the clearly evident in Figure 3.16, the jack rafter obtains edges of the jack and common rafters (see detail in the height we require. So it is the run of the jack rafter Figure 3.17). that we require. We then simply multiply this length Set-out, cutting and installation of the creepers by the hip length/m run of CR (the hip factor). is now done, as for a standard hipped roof (see Hip set-out length = run of jack rafter 3 hip Figure 3.18). As always, take care that all surfaces are length/m run of CR true (in wind and straight).

Figure 3.14 Installing the waling piece

Waling piece set level and bolted or otherwise Figure 3.15 fixed as per AS 1864 Jack rafters Sample pages installed

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Figure 3.16 Hip edge bevel Hip set-out (see pages 76–77) X

1.306 m

Hip plumb bevel (see page 76) X is the plumb height taken from above the X common rafter bird’s mouth.

Figure 3.17 Hip position and detail

Sample pages

Figure 3.18 Completed framing for gambrel roof

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Extended ridge

Soldier wall

Figure 3.20 Pictorial view of jerkin head roof framing

Figure 3.19 rafter components will be familiar to those with an Ways of visualising the jerkin head understanding of basic hipped roofing. roof (reproduced The skill that you need to develop in the case of in colour in the the jerkin head roof is how to determine the height Appendix) and width of the soldier wall. Figure 3.21 offers a comparison between the framing of a ‘normal’ hip JERKIN HEAD ROOF end and the jerkin head. The length and position of the soldier wall is shown as a pink line. A jerkin head roof, like the gambrel, is an adaptation of the hipped roof. This roof form is useful where Calculating the height and width of the or roof space of a house is required as the the soldier wall living area, or where the architect desires to reduce the imposing nature of a large gable. While an interesting This is a very simple calculation once you understand and pleasing roof from a construction point of view, the basic geometry from which it derives. For this it is not much used in contemporary architecture. discussion we will use the same characteristics as in Its inclusion in this chapter is Samplebased on its value in the gambrel pages roof example: developing skills useful for more advanced forms. Pitch = 25° Like the gambrel, in constructing a jerkin head roof Span = 4500 mm the ridge is extended past the half span point where Eave width = 600 mm the centring rafters would n