Calculation of roof members
It is important to calculate the dimension
of the true length of a roof member. These dimensions are essential to
determine the accurate span of rafter, overhang, underpurlins, fan struts
etc.
Click here if you have
forgotten the trigonometry functions.
You can also use the Roof Multiplier
Table, which you can print from the web page.
Example
Find the span of a rafter.
The AS 1684.2 – 2006 Residential timberframing construction clearly differentiate
between spacing and span (see Fig. 2.18 and Paragraph 2.7.5.
2.7.5.2 Spacing the centretocentre distance between
structural members, unless otherwise indicated.
2.7.5.3 Span the facetoface distance between
points capable of giving full support to structural members or assemblies.
In particular, rafter spans are measured as the distance between points
of support along the length of the rafter and not as the horizontal projection
of this distance.
2.7.5.5 Single span the span of a member supported
at or near both ends with no intermediate supports.
2.7.5.5 Continuous span the term applied to members
supported at or near both ends and at one or more intermediate points
such that no span is greater than twice another.
Span/length calculation for roof members.
As can be seen the span of the rafter in the figure below is not quite
in agreement with the Code but we will use the figures for the rafter
span as calculated below.
We use trigonometric functions for the calculation
The angle will be the roof
pitch
The opposite site is the rise of the roof
The adjacent side is the rafter run
The hypotenuse is the true length of the rafter
The example shows brick veneer construction (see Figure 1) the roof pitch
is 20°, the rafter run is 3.340 metres and for an eaves width of 0.6 metres, the actual measurement to calculate
the overhang is in this case 0.76 metres (0.60 + 0.16 face brick + cavity).
Therefore the span of the rafter is 3.554 metre.
Please remember that the rafter span according to the Code is the facetoface
distance and that our calculated distance is 96 mm longer in this
case (see Figure 2). This provides a safety margin, and in a border case,
where the span is just a couple of mm too short, you may use the facetoface
distance for the span.
Calculation of roof overhang
You need to distinguish between clad timber framing and a brickveneer construction
calculate the eaves overhang. Look also at Figure 2.18 (b) in Section 2
of the code regarding the length of the overhang.
Let's assume an eaves width of 600 mm. The
horizontal dimension for the overhang is then 600 mm plus the 110 mm brick
wall plus the 50 mm cavity, which equals 760 mm.
Now do the same as for the rafter (the overhang is in this case the Hypotenuse).
_{
}
The eaves overhang for the brick veneer building with 600 mm eaves width
is 0.809 metre
Find the length of a strut
If a rafter is supported on to points only (single span)
and an appropriate size cannot be found in the tables then an additional
support (underpurlin) is needed. Underpurlin
must be supported by struts.
Struts may be arranged vertically as shown in Figure 4 (a) or perpendicular
to the rafter (b).
The position of the underpurlin must be determined before you can calculate
the length of the strut. To utilise the continuous span of a rafter the
position of the underpulin must be in the middle onethird of the rafter
as shown in the Figure 5. Remember that continuous span member is a member
whereby no span is greater than twice another (Section 2, Paragraph 2.7.5.5).
As soon as you have determined the position of the underpurlin you can
calculate the length of the vertical strut using sin, cos
or tan. However, the underpurlin in class examples is usually placed
at midspan, because that simplifies the calculation for all roofmembers
of the Roof Framing Section.
Strutting
Roof struts can be applied
in various ways, some examples are:
Verticle struts Perpendicular to the roof
Roof struts 7.2.15.1
Where necessary, struts shall be provided to support roof members, such
as underpurlins, ridgeboards and hip and valley rafters.
Ridge strut
This strut support the ridge down the center of the
roof. If a ridge is strutted, then you need to find the length of
the ridge strut.
The length of the strut is found by using the opposite calculation:


Vertical strut
If the underpurlin is positioned at midspan, then the vertical underpurlin
strut length equals half of the length of the ridge strut (½ x 1216 = 608). Alternatively,by
calculation ½ of the rafter run (½ x 3340 = 1670) multiplied by the tangent of the
roof pitch.
Therefore the length of the vertical strut is:
_{
}
Perpendicular strut
To calculate the length of a strut perpendicular
to the rafter you need to calculate the rafter span (Hypotenuse)
first. The rafter span (strut at midspan) is
is half of the rafter run (3340/2) divided by cos 20°.
Now you can use the tanfunction again to calculate the strut perpendicular
to the rafter._{}
The length of the perpendicular strut is therefore


Fan strut
The span of an underurlin can be reduced if a fanstrut is used instead of a single
strut. Paragraph 7.2.15.3 in AS 1684.2  2006 stipulates that the angle
of a fanstrut should not exceed 45°.
(A single strut should not be less than 30° from the vertical.)
Fan struts are more effective with steeper roof pitches where the length of
the strut is notable.
To reduce the span of an underpurlin effectively the fan strut should have an
angle of 45° because this results in a maximum spread of the fan strut.
Find the spread of a fan strut.
Geometrically the fan strut should consists of two isosceles right angle
triangles as shown in Figure 6. As both angles are the same therefore both
sides must be the same. Check on your calculator the sin of 45° (=
0,707) and cos 45° (= 0.707) and you will see that you will get equal
figure for both (sin and cos).
In the previous calculation the length of the
vertical strut is 0.608 m (at midspan)
and the length of the perpendicular strut 0.647 m (at midspan)
The spread of a vertical fan
strut is therefore 0.608 x 2 = 1.216 m
and
the spread of a strut perpendicular to the rafter fan
strut is therefore
0.647 x 2 = 1.294 m
The calculation of load width and roof area supported is easily understood
if you consider the load on a structural member. Ask yourself what load
is going onto a member. Study Section 2 of the code and look at the Figure
2.10 & 2.11 Floor Load Width (FLW), Figure 2.12 Ceiling Load Width
(CLW) and Figure 2.13  2.16 Roof Load Width (RWL) and make sure you understand
the significance of the load width.
Roof area supported (RAS)
For dimensioning of strutting beams (7.3.11), combined counterstrutting
beams (7.3.10) or combined strutting/hanging beams (7.3.9) you need to know
the roof area supported. The area can be easily found by be multiplying
the RLW with the length of the underpurlin (˝ x span 1 + ˝ x span 2) that the strut supports. Usually
we select only one size for the underpurlin and therefore only the worst
case need to be considered. Find out how many strutting beams are needed.
As soon you have determined how many strutting beams are required identify
the worst case. This situation will be used for the size selection of the
underpurlin.
Figure 7 below is an example that illustrate the process to find RAS. RAS equals
the RLW of the underpurlin multiplied by the longest span of the underpurlin.
Refer to Figure 7 to find the worst case in the roof structure (longest
underpurlin span). The strut on the left is vertical because the span on
the left side of the strut is less then the reduced span 1. The span between
the struts supported on walls is excessive and a strutting beam or combined
counterstrutting beam is required. A fan struts have been chosen (see Figure
7) to reduce the span of the underpurlin even more (span u/p 1 and span
u/p 2). As can be seen span u/p 1 has been reduced by ½ spread of
the fan strut resulting in a reduce span 1. Span u/p 2 is reduced by the
spread of the fan struts (left and right side) i.e. reduce span = span u/p
2 minus strut height ×2 ).
Figure 7
Alternative strutting system
Where it is not possible to support underpurlins off walls or struts some alternatives can be applied as shown in Figure 8. Often underpurlins are projected (cantilevered) more than 25% of the maximum allowable span then you may reinforce the hiprafter with a tiebolt truss system. The hiprafter in this case will support the underpurlin.
Figure 8
Span and spacing
The Figure 8 shows you the difference between span and spacing of members
and the load width (e.g. FLW in this case) for the middle bearer. The
load area supported by the middle stump would be the floor load width
(L1/2+L2 /2) × Bearer
span (i.e. half of the bearer span to the left and half of the bearer
span to the right, as indicated by the blue area).
Figure 9
Calculation set out
All calculations should be done on a separate A4 sheet . Make sure it's
logical set out because you may need to refer to previous calculation figures.
Write all dimensions down as well as you calculated figures. Follow a similar
procedure as shown below:
 Rafter run = external width between the wall plates divided by two.
 Rafter span = rafter run divided by cos °.
 Overhang = eaves width divided by cos °
(add dimensions for brick veneer).
 Ridge strut = rafter run times tan °.
 Decide whether an underpurlin is needed; if it is place it at midspan.
 New rafter span = rafter span found in 2) divided by two.
 Vertical strut to underpurlin = ridge strut length divided by 2 (if
u/p positioned at midspan).
 Strut perpendicular to rafter = rafter span time tan °.
 Determine the position of struts (usually on supporting walls).
 If the distance between supporting walls is excessive a strutting
beam may be needed.
 Span of underpurlin can also be reduced if fanstrut is used.
 Determine the length of the strut and the dimensions between the struts
(or fanstruts).
 Roof load width (RLW) = rafter span (if placed at midspan) otherwise
˝ span1 + ˝ span2.
 Roof load area = RLW × (˝ u/p
span left + ˝ u/p span right) or with fan struts
RLW × (˝ u/p span left + ˝ u/p span right + spread of fan strut).
 Hanging beams are required if ceiling joist span is excessive.
 Place hanging beams in center of room or if needed divide room length/width
by 3 (4) and space them equally.
Click
here for a Calculation Template
that you can print and use

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