CHAPTER LEVELLINGConstRUCT AND SETTINGadvanCed OUT RooFS 31 DR Glenn P. Costin This chapter focuses on the construction of five common roof forms that fall within the very broad advanced roofing category: • Gambrel (Dutch gable) • 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 Framing (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: Cheetham 03.indd 73 13/11/12 1:16:32 PM 74 ADVANCED BUILDING AND JOINERY SKILLS 1. Roofs are made up of right angled triangles 1. Common rafter rise per metre run (CR rise/m and are set out to centre lines (including hip run) and valley rafters, 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 Cheetham 03.indd 74 13/11/12 1:16:34 PM CHAPTER 3 construct advanced roofs 75 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 Allowance needed = 5.079 + 0.125 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. Cheetham 03.indd 75 13/11/12 1:16:37 PM 76 ADVANCED BUILDING AND JOINERY SKILLS 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 purlin 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 Cheetham 03.indd 76 13/11/12 1:16:39 PM CHAPTER 3 construct advanced roofs 77 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.