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**INTRO TO ROOFING and PRELIMINARY CALCULATIONS**

Timber Framing Code. INTRO TO ROOFING and PRELIMINARY CALCULATIONS

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**Previously. We looked at the subject in general**

Discussed assessment criteria Section 1. Scope & General Section 2. Terminology & definitions. Section 7. Roof Framing

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Flowchart It is recommended that design starts at the roof and works down to the foundation. Although the flowchart on page 17 tells us to- Determine wind classification. Consider the bracing and tie-down details. We will leave wind classification to the structures teachers Consider bracing details after roof and wall design.

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Revision Quiz 1. AS 1684 specifies the requirements for building practices for what classes of building?

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**2. List 5 limitations on building design using AS 1684**

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**4. Why is it necessary to determine**

4. Why is it necessary to determine the wind classification of a site prior to using AS 1684 to select section sizes of members?

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**5. A site may be classified as N1, N2, N3, N4, C1, C2, C3 or C4.**

a. What do the letters N and C indicate? b. True or false : The higher the number the greater the wind risk

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**6. What are racking forces and how are they resisted?**

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**7. How are overturning forces resisted?**

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**10. The amount of ‘bearing’ of a member is…….?**

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**11. What is stress grading and how is it achieved?**

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Let’s start. Remember- throughout this module we will consider Coupled roofs With single row of underpurlin. Without ridge struts

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**Roof (and ceiling) Members**

Ceiling joists Hanging beams Counter beams Strutting beams Combined strutting/hanging beams Combined counter/hanging beams Underpurlin

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Roof Members cont’d Rafters Hips Ridges Valleys

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Calculations If you look at the supplement tables you see that you need to determine Spacing of members Spans- single or continuous Ceiling load widths CLW Roof area supported Roof load widths RLW Rafter span Rafter overhang

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Calculations Spacing of members such as ceiling joists are measured centre to centre or “in to over"

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**Member sizes Remember: The flow chart dictates that we first-**

Determine the wind classification Consider position and extent of wind bracing and tie downs Let us assume- That wind classification for all our exercises is N3 There is sufficient room for bracing and tie-downs

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**Preliminary calculations**

Some calculations are required before we have sufficient data to use the span tables

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**Preliminary calculations**

You MUST have a scientific calculator. You only need to be able to do very basic trigonometry. You must be able to use Pythagoras theorem. You need to be able to perform basic algebra

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**Preliminary calculations**

What do we mean by the term ‘true length of rafter’? We need to be able to calculate the true length of the rafter so that we can determine such things as- The span of the common rafter RLW Rafter overhangs Areas supported

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Trigonometry Comes from the Greek words ‘Trigon’ meaning triangle and ‘metre’ meaning to measure. Trigonometry is based on right angled (900 ) triangles. It involves finding an unknown length or angle, given that we know a length or an angle or various combination of known and unknown data. We will also use the “Pythagoras” theorem

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**Trig ratios The 3 basic trig ratios are Sine (sin) Cosine (cos)**

Tangent (tan)

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Trigonometry The ratios are related to parts of the right angled triangle The ‘Hypotenuse’ is always the longest side and is opposite the right angle. The other two sides are either the ‘opposite’ or the ‘adjacent’ depending on which angle is being considered.

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**Trigonometry Sin =opposite ÷ hypotenuse Cos = adjacent ÷ hypotenuse**

Tan = opposite ÷ adjacent OR S= O÷H C= A÷H T= O÷A

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**Trigonometry Some Old Hounds Can’t Always Hide Their Old Age**

Some students remember this by forming the words- SOH CAH TOA Or by remembering Some Old Hounds Can’t Always Hide Their Old Age

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**The Pythagoras theorem**

The square on the hypotenuse equals the sum of the squares on the other two sides. Or A2 = b2 + c2

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**Roofing calculations. If we know the roof pitch.**

And the run of the rafter. We will use the term RUN of rafter rather than half span. We can use trigonometry and Pythagoras to find the true length of the rafter And it’s overhang.

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**True length of the common Rafter**

Centre of ridge Outside edge of top plate Rafter length underpurlin Rise of roof overhang Run of rafter

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**NOTE! We are not calculating an ordering length.**

We require the length from ridge to birdsmouth. You may know this as the set out length We need to find the Eaves overhang separately

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**Problem Calculate the true length of the rafter Pitch is 270**

Run of rafter is 4000

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**Example: Method 1. (using Tan)**

Trade students may be more comfortable with this method Find the Rise per metre of C.Raft Find the True length per metre of C.Raft Multiply TLPM x Run= True length of rafter.

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**Method 1. (using Tan) Rise per metre run = Tan 270 = 0.5095 = 0.510**

T.L. per metre CR = √ R2 + 12 = √ = √ 1.260 = 1.122m T.L.C.R. = T.L per metre X run = 1.122x 4.0 = 4.489m

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**Method 2. Using Cosine (Cos)**

Pitch is 270 The run is 4.0m Cos = adjacent ÷ hypotenuse = run ÷ rafter length Rafter length = run ÷ cos 270 = 4.0 ÷ = 4.489m

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Exercises Calculate the following rafter lengths. (choose either method) Pitch 370 , Run 3.750m 4.696m Pitch 230 , Run 4.670m 5.073m Pitch , Run 2.550m 2.705m

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**True length of eaves overhang.**

Firstly you must be aware of the difference between eave width and eaves overhang. For a brick veneer building with an eaves width of 450mm; the actual width to the timber frame is mm for brick and cavity = 600mm

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**True length of eaves overhang.**

The true length of the eaves overhang is the measurement ‘on the rake’ from the ‘x y’ line to the back of the fascia along the top edge of the rafter. It can be calculated the same way you calculate you calculated the rafter length

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**True length of the common Rafter**

Centre of ridge Outside edge of top plate Rafter length underpurlin Rise of roof overhang Run of rafter

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Student exercises 2. Calculate the true length of eaves overhang for each of the following (all brick veneer) Pitch 270, eaves width 450mm .673m Pitch 370 , eaves width 500mm .814m Pitch 230 , eaves width 480mm .684m

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**Span of the common rafter.**

The ‘Span of the rafter’ is the actual distance on the rake between points of support.

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**Span of the common Rafter**

Centre of underpurlin span Outside edge of top plate span overhang

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**Span of the common rafter.**

Span of rafter is the true length of the rafter divided by 2 That is:- from our previous example = ÷ 2 = m

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Student exercises 3. Calculate the span of the common rafter for the 3 roof pitches from previous exercise.

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**Exercises (calculate span)**

Pitch 370 , Run 3.750m 4.696m / 2 = 2.348m Pitch 230 , Run 4.670m 5.073m / 2 = 2.537m Pitch , Run 2.550m 2.705m / 2 = 1.353m

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Fan struts We can make more economical use of underpurlin by using fan struts. The fan strut does not increase the allowable span of the underpurlin. It enables the points of support (walls or strutting beams) to be further apart

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Fan struts To estimate the spread of the fan strut we make 3 assumptions The underpurlin is in the centre of the rafter length. The plane of the fan strut is fixed perpendicular to the rafter. The fans are at 450

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Fan Struts

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**Fan struts (use Tan) The formula is- ½ spread of the fan struts=**

Span of rafter x tan angle of pitch For our previous example = x (tan 27 deg.) = 1.142m

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Fan struts Therefore distance apart of strutting points for a given u/purlin can be increased by 1.142m using a fan strut at one end of the underpurlin span. Distance apart of strutting points can be increased by 2.284m using a fan strut at both ends of the underpurlin span.

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Supplement Tables Once the preliminary calculations have been done we can start to use the span tables in the supplement But which supplement????

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**Using supplement tables**

Firstly you must choose the correct supplement (see page 3 of the standard) Depends on wind classification, stress grade and species of timber Then choose the applicable table within the supplement (see list of tables page 3 of the supplement)

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**Class Exercise - N3 wind classification Using MGP 15 seasoned softwood**

Single storey building Tile roof Roof load width 3.000m Rafter spacing 600mm Select a lintel size to span 2100m

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Class Exercise- Which supplement? 6 Which table? 18

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**Class Exercise- Choose one of these 2/120x45 ? 2/140x35 170x35 ?**

Which one is the smallest cross section? But is this section commercially available?

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Class Exercise- Notice that in the last exercise the RLW, Rafter spacing and required span of lintel were all values included in the table. What if the RLW is 3300 or the rafters are spaced at 500mm or the lintel needs to span 2.250m? WE need to INTERPOLATE

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Interpolation Simply put, to interpolate is ‘To estimate a value between known values’. It is not possible to show every span or spacing related to member sizes. Convenient regular increments are used. Linear interpolation is allowed for calculation of intermediate values.

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**Cross multiplication Before we start doing interpolation calcs.**

You need to be conversant with a mathematical procedure called cross multiplication.

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**Cross multiplication In an “equation” such as A = C B D**

we can cross multiply so that A x D = B x C Same as the ration A:B::C:D

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**Class Exercise If RLW is now 3.300 Rafters still at 600**

Required span 2.100 We need to interpolate between two columns to find the most economical section size.

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Class Exercise Run your fingers down the 3000m column and the 4500m column for 600 spacing. We can tell that 2/140x35 will probably span.

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Class Exercise RLW RLW RLW ?

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Class Exercise RLW RLW RLW

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**Class exercise Using Table 18 of supplement 6**

Interpolate to find the maximum allowable span for a 290x45 lintel RLW 5300 Spacing of rafters 1200mm

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Class Exercise RLW RLW RLW ?

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Class Exercise RLW RLW RLW

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Next week We will start work on selecting suitable roofing members from a given plan and specification

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