1 Timber Framing Code. INTRO TO ROOFING and PRELIMINARY CALCULATIONS

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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-

1. Determine wind classification.2. 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 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

RaftersHipsRidges Valleys

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CalculationsIf 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-1. That wind classification for all our exercises

is N32. 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 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.

True length of the common Rafter

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overhang

underpurlinOutside edge of top plate Rafte

r length

Run of rafter

Centre of ridge

Rise of roof

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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

= √ 0.5102 + 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 270 = adjacent ÷ hypotenuse= run ÷ rafter length

Rafter length = run ÷ cos 270

= 4.0 ÷ 0.8910

= 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 19.50 , 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 450 + 150mm 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

True length of the common Rafter

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overhang

underpurlinOutside edge of top plate Rafte

r length

Run of rafter

Centre of ridge

Rise of roof

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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.

Span of the common Rafter

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overhang

span

span

Centre of underpurlin

Outside edge of top plate

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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= 4.489 ÷ 2

= 2.245m

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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 19.50 , 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

1. The underpurlin is in the centre of the rafter length.

2. The plane of the fan strut is fixed perpendicular to the rafter.

3. The fans are at 450

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U n d e r p u r l i n

M i n . a n g l e 6 0t o h o r iz o n t a l

o

E a c h s t r u t 3 0 m m m i n .b e a r in g to t o p p l a te S t i f f e n e r

C h o c k n a i l e d t o p l a te

E q u a l a n g le s n o tle s s th a n 4 5 o

9 0 x 3 5 m m s p r e a d e r c le a t s e i th e r s id e o f s t r u t s f i x e d w i th M 1 2 t h r o u g h b e l t

S t ru t n a i le d to u n d e r p u r l in w i t h 4 / 7 5 m m n a i ls

S t r u t s ( s e e Ta b le 7 .5 )

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Fan Struts

45O max.45O max.

EQUAL

60O max. 45O max.45O max.

EQUAL

60O max.

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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 = 2.245 x 0.510 (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

3000 3300 4500

2300 ? 2000

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Class Exercise

RLW RLW RLW

3000 3300 4500

2300 2240 2000

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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

4500 5300 6000

3400 ? 3100

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Class Exercise

RLW RLW RLW

4500 5300 6000

3400 3240 3100

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Next week

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