CANADA NATIONAL BUILDING CODE 2010 TABLE CHECK WITH YOUR BUILDING INSPECTOR FOR YOUR AREA
ROOF
EXTERIOR DETAIL
ROOF
INTERIOR DETAIL
ROOF
SIDE VIEW DETAIL
Roy’s
theorem
every triangle has a rise, a run, and
a rake
so: for every simlar triangle unknown over known times known equals unknown
rise/run =
% or tan * any run = rise
(the rise = a percentage of any run ...run = 1)
and rise /
% = run
rise/rake=%
or sin x any rake = rise
run/rake
=% or cos x any rake = run
rake/rise=%or
cosecant x any rise = rake
rake/run=%
or sec x any run = rake
hint :
draw out and label every triangle
note: the top
number is a
percentage of the bottom number which becomes the number 1
line length is marked out on top of rafter with working points being the plumb lines
rake 
rise
or tan 
run
of 1 
rise/run 
plumb
cut 
1.054093 
0.3333333 
1 
pitch4/12 
18.4 
1.083333 
0.4166667 
1 
pitch5/12 
22.82 
1.118034 
0.5 
1 
pitch6/12 
28.57 
1.157704 
0.5833333 
1 
pitch7/12 
50.26 
1.20185 
0.6666667 
1 
pitch8/12 
33.69 
1.301708 
0.8333333 
1 
pitch10/12 
39.81 





with run
reduced to one the above chart gives rise and rake per one of run and
the plumb cut for some common pitches.. below is dgree to tan table for angles when cutting
Deg 
Tan 
Deg 
Tan 
0 
0 


1 
0.0175 
24 
0.4452 
2 
0.0349 
25 
0.4663 
3 
0.0524 
26 
0.4877 
4 
0.0699 
27 
0.5095 
5 
0.0875 
28 
0.5317 
6 
0.1051 
29 
0.5543 
7 
0.1228 
30 
0.5774 
8 
0.1405 
31 
0.6009 
9 
0.1584 
32 
0.6249 
10 
0.1763 
33 
0.6494 
11 
0.1944 
34 
0.6745 
12 
0.2126 
35 
0.7002 
13 
0.2309 
36 
0.7265 
14 
0.2493 
37 
0.7536 
15 
0.2679 
38 
0.7813 
16 
0.2867 
39 
0.8098 
17 
0.3057 
40 
0.8391 
18 
0.3249 
41 
0.8693 
19 
0.3443 
42 
0.9004 
20 
0.364 
43 
0.9325 
21 
0.3839 
44 
0.9657 
22 
0.404 
45 
1 
23 
0.4245 


Rafters
common
rise
squared plus run squared equals rake squared... (example a
rise of
2 squared plus a run of 4 squared would equal 20 the square root of 20
equals 4.47 the line length of the rafter from centre of ridge to
outside of plate)
take
the square root of rake =( theoretical line length) using
your
simlar triangle ratios... add on your projection for eaves layout your
three working points on top of your rafter
the
working point #1 line
length is from the centre of the ridge board so you must mark
your first plumb line at working point one then
PLUMB
CUTS AND LEVEL LINES
shorten
1/2 thickness of ridge at 90 degrees
from plumb line and mark your actual cut line
regular
birdsmouth is
(90 degrees from plumb is level) working point #2
working point #3 is the
overhang or eves plumb cut
because these are simlar
triangles the ratios of rise to run to rake are the same
I find it simplest to reduce
the run to 1 example a 4/12 roof =.33/1
Any run of 1 equals a rise of
.33 ....
A run of ten feet would equal a
rise of 3.3 ft (10x.33= 3.3)
A run of ten metres would equal
a rise of 3.3 metres (10x.33=3.3)
An overhang of 2 ft would have
a rise of .66 ft (2x.33=.66)
An overhang of 24 inches would
have a rise of 7.92 inches (24x.33=7.92)
using
your square, you mark out
your plumb cut using a rise of.33 and a run of one.. or any multiple of
don't have a builders square
use a tape measure... measure from a squared line at wp1, wp2, wp3 measure down stock from bottom of squared line
Rafters
common,
hip, and valley birdsmouth
 start at
WP2 (working point 2)  plump down
and measure 2/3rds of stock thickness then mark a level saw cut line
drop hip
rafter at birdsmouth by
plumbing second line 20 mils up from
the WP2
(working point 2) plumb
line then mark a level seat cut line extending back through to WP2
plumb ( note new level seat cut line is less than 2/3 of stock... hip
must be dropped for plywood sheathing to lie flat

raise valley rafter at birdsmouth by plumbing second line 20
mils
down from
WP2 (working point 2) plumb line, then a level seat cut line
extending
back through to WP2 plumb (note new level seat cut
line is more than
2/3 of stock) valley must be raised so that the sheathing lies flat
Rafters
common
ridge
length of
house
if house
has
over hanging gables then add to length
the
width of gables
joints
are centered on rafters
plumb end rafters when raising
collar ties
are the
horizontal joists tying the rafters together
dwarf
or pony walls often used
instead or with collar ties
Rafters or
trusses
framing a
dormer
height of
ceiling in a dormer bedroom at least
50% has to be 2300 and 50% or the rest
has to be 2100
double
header framed across the top and the
bottom of the opening
edge
rafters doubled
roof end
of dormer rafters are cut to slope of
the roof
above seat cut for valley dormer jack...to plywood sheathing or a 2 by plate
side
studs for dormer.. they are the rise for
a proportional triangle.. rise of roof 200 rise of dormer roof 50 rise
(20050=150) of unit rise of dormer stud =150
Roy’s
theorem
every triangle has a rise, a run, and
a rake
so: for every simlar triangle unknown over known times known equals unknown hint :
draw out and label every triangle
rise/run =
% or tan x any run = rise
(the rise = a percentage of any run ...run = 1)
and rise /
% = run
rise/rake=%
or sin x any rake = rise
run/rake
=% or cos x any rake = run
rake/rise=%or
cosecant x any rise = rake
rake/run=%
or sec x any run = rake
note: the top
number is a
percentage of the bottom number which becomes the number 1
take a 4:12 roof ...4/12 =.33 for a rise and 1 for a run
example:
a run of 5 times the percentage .33 of rise will give you the rise for a run of 5 is1.65
Rafters
dormer
gable
small
intersecting roof:
Parts:
valley jack rafter, valley rafter, minor
common rafter.. major common rafter.. . double headers top and bottom.. double rafters
common
rafters run =1/2 the span of dormer
valley
rafter squared = rise (1/2 the span)
squared + run (length of common rafter)squared
Rafters
gable end
gable
studs laid out from each side of centre
from ridge
 mark
out plate 16 inch centres
plumb up
from marks to inside face of end
rafters
 stand
gable stud plumb at marks and scribe at
top and bottom of rafter
 notch
out for
rafter
attach end
ceiling joists to the gable studs
 common difference can be used
to cut studs on the ground
common difference means that for every equal gable end stud
space the stud size always changes an equal amount
Rafters
gambrel
radius
scribes the arc in which the gambrel is
built the radius is
the run and the rise of the roof
the rise
to run combination of the bottom
slope is the opposite of the rise to run configuration of the top slope
a good example is bottom slope has a run of 104 and a rise of 250 the
top slope has a rise of 104 and a run of 250 the total run of the roof
in this case is the radius of 3600 the unit rake = 271 x 2 = 542
Roy’s
theorem
every triangle has a rise, a run, and
a rake
so: for every simlar triangle unknown over known times known equals unknown
rise/run =
% or tan x any run = rise
rise/rake=%
or sin x any rake = rise
run/rake
=% or cos x any rake = run
rake/rise=%or
cosecant x any rise = rake
rake/run=%
or sec x any run = rake
hint :
draw out and label every triangle
hint: the
top number is a percentage of the
bottom number which becomes the number 1
542
is the rake
354 is the
run
= 1.53 x the run of 3600=5511.8 /
2=2756 which
is the rake (rafter length)for each slope
tan angle top
104/250 tan angle bottom 250/104
Rafters
hip jack
rafter
run same
as distance from corner,
note
common
differences can be used to compute all hip jack line lengths
 rake/run
x length of run = line length of rake
of the hip jack rafter
example
using a 5/12 roof... 5/12 = a rise of .416 for every run of 1
.416 squared plus1 squared=1.173 square root of=1.083 your rake
 rake(1.083)/run(1)
x length of run(24centres) = line length of rake(25.99)
plus overhang for soffit
Rafters
hip rafter
unequal pitch roof
rise same
as common
run of
common run squared plus the run of the
end common squared = the square of the hips run
rise
squared plus run squared = line length
squared
shorten
hip by drawing a full size of the
ridge and measuring the appropriate shortenings
#1 cheek
cut .
#2 double
cheek
tail cut
same process as #2 above
drop hip at birdsmouth by
measuring up the line length 1/2 the width of the stock
SAMPLE
OF 5/12 ROOF for a run of 1
5:12 
ROOF
SLOPE 

RISE 
RISE
OVER RUN =5/12 ALSO EQUALS TAN 
0.416667 
RUN 
RUN =1 
1 
RAKE 
=SQRT((0.416*0.416)+(1)) 
1.083077 
HIP 


RISE 
RISE SAME FOR HIP OR COMMON 0.41667 
0.41667 
RUN 
HIP
STANDARD SQUARE ROOT OF 1+1 = 1.41 
1.41 
RAKE 
=SQRT((0.41667*0.41667)+(1.41*1.41)) 
1.470277 
PLUMB 
=DEGREES(ATAN(0.41667/1.41)) 
16.46297 
HIP PLUMB
CUT IS 16.46 DEGREES AND A 45 MITRE CUT
Rafters
hip valley
cripple
these
rafters are all the same length
the run is
equal to the distance from the
corner of the hip to
the corner of the valley
top
end cut and bottom end cuts are simple cheek cuts the shortening on
both ends is 1/2 the 45° thickness of the respective
rafters (38)
knee wall
gambrel
are often supported on a knee
wall, maximum lean 45°

knee wall runs from lower
ceiling joists to intersection of upper and lower
rafter
Rafters
line
lengths
all line
lengths are mathematical centre to centre measurements

when cutting lengthen or shorten exact centre of ridge to outside edge
of plate
Rafters
lookouts
soffit ladder
on a gable roof the lookout is
the ladder that holds the soffit and fly rafter
Rafters
major ridge
Adjust line length by adding
1/2 width of common rafter to each end
Rafters
minor
on intersecting roofs the minor
span
Rafters
minor ridge
length of
ridge is 1/2 minor span plus length
of minor span
simple square cut ends
Rafters
octagon
metric sample
octagon
roof: common rafters octagon hip
rafters, octagon hip jack rafters (this is a shortened common rafter)
2.414
octagon
hip rafter has a run of 271 this
compares to a standard common rafter with a run of 250 and hip rafter
with a run of 354 Note: the run for an octagon hip is 1.082 for each 1
of a regular run
the plumb
cut is rise/run example 150 over 271
gives a pitch of 29°
so plumb cut would be 61°
birdsmouth moves forward
104/250 of 19 =8 mm
Rafters
projection
over hang
at eaves same ratio and proportion as
roof
for valley and hip of unequal
pitch roofs use the percentage of the common .. line length. eaves/line
length common times the line length of the valley equals line length
valley projection
Rafters
proportion
rise over
unit rise = run over unit run = rake
over unit rake = the number of units
Roy’s
theorem
every triangle has a rise, a run, and
a rake
so: for every simlar triangle unknown over known times known equals unknown
rise/run =
% or tan x any run = rise
rise/rake=%
or sin x any rake = rise
run/rake
=% or cos x any rake = run
rake/rise=%or
cosecant x any rise = rake
rake/run=%
or sec x any run = rake
hint :
draw out and label every triangle
FACT: the
top number is a percentage the bottom
number is the number 1
EXAMPLE: 150
is the rise
250 is the
run
= tan .6 x the run of 400 =240 which
is the
rise (height)IN THIS CASE of first dormer stud
sin angle
top 50/250
sin angle bottom 200/250
tan =
rise/run
sin =
rise/rake
cos =
run/rake
cosecant =
rake/rise
sec = rake/run
Rafters
purlin
on a
gambrel roof the purlin is the mid ridge
board
the
lower rafter the upper
rafter and the ceiling joist all meet at the purlin a purlin is any hirizontal support perpendicular to rafters
Rafters
rake rafter
lookouts supported by lowered
or notched gable end
Rafters
ratio and
proportion
Coefficient
factor equals
unknown divided by known/ example rise divided by run gives
the factor for rises for all similar triangles /use the factor times
the new run gives new rise (rise/run.. .run/rise .. .rake/rise etc.)
Rafters
ridge of a
hip roof
the ridge
theoretical line length of an equal
span hip is length minus
span
there are
two methods of cutting the hip
rafters Method #1, and Method #2
...method #1
lengthen
ridge 1# when cutting by width of one
common (1/2 each end)
 lengthen #2 when cutting by
1/2 45 degree thickness of hip and 1/2
thickness of ridge
The hip is all about the isoceles triangle
The rise of the hip rafter is the same as used to cut the common rafter
The run of the hip rafter is the run of the common rafter times 1.41
The rake line length of the hip rafter is the square root of
the run squared plus the rise squared
Hip jack rafters run decreases by the distance it moves away from common
Rafters
shortening
... the rafter has to be shortened from the theorietical line length to
the actual line length ...this is 1/2 the thickness of the
ridge
board
always
shorten at right angles to the plumb
line
always
shorten 1/2 the
angle at which the rafter meets the ridge
Rafters
the
proportion of rise to run of a rafter equals
pitch, slope or cut
Rafters
span is
width of building when measuring for rafters measure from outside edge to outside edge ...do not ssume both ends will be the same measure at both ends and mid span
make sure the walls have been straightened use a stringline first
mid point is centre of ridge and your rafter span in this case 9'7" your collar ties can reduce the unsupported span and thus the rafter size example from 2x8 lumber to 2x6 lumber
pony
walls or dwarf walls and struts also can reduce unsupported span
but may increase ceiling joist dimension look up your local span tables
Rafters
tail cuts
plumb,
straight,
cheek cut
at tail of hip 45 degrees
 reverse cheek cut at tail of
valley 45 degreesIii
Rafters
trigonometry
arc/ ?°
= circumference/360°
the
angle that the tangent of
a circle meets an adjoining chord is equal to 1/2 the angle of the
chord’s two radiuses at the circle’s centre
Rafters
truss
lower and
upper chords and diagonal webs
19x89
web
bracing
diaganol braces nailed to first four webs and repeated every 6meters
Rafters
units of
proportion
run, rise, or rake
run
standard unit equals 250 millimeters,
similar
triangles number of units time size of unit equals line length
similar
triangles are in proportion to each
other
Rafters
valley hip
cripple jack
runs
between hip and valley rafters
 they are
all equal length
run is
equal to the plate distance from hip
seat to valley seat
single
cheek cuts each end
shorten both ends by 1/2 45
degree thickness of common
Rafters
valley
cripple jack
runs
between the shortened valley rafter and
the supporting valley rafter
 the run
is always 2 times the horizontal
distance from the intersection of the two valley rafters
shorten
each end 1/2 45 degree thickness of
rafter stock
single
cheek cuts each end on the same side of
the board
Rafters
valley jack
runs from
the ridge to the valley rafter
the run
is equal to the common rafter minus
the distance in from the corner meeting point of the plate and the
valley rafter
shorten
1/2 stock at top and 1/2 45 degree
stock at bottom
plumb cut
at ridge
 cheek cut at valley
Rafters
valley
rafter
runs from
the plate to the ridges of the
intersecting roofs
run same
as common times 1.41 or 1.41 times
unit of run
shorten
at ridge 1/2 the 45°
thickness of the ridge at 90°
to plumb cut
a double
cheek cut at the ridge
 at
WP2 plumb a line down for a birdsmouth
 from
this line raise the birdsmouth by
measuring down the line
length 1/2 the thickness of the rafter
plumb a
second line down this point
measure
down this line the same depth as the
common rafter usually
80 to 90 mark
at the
mark bring in a seat cut line at 90°
and cut out on this
line the birdsmouth seat back
to the plumb line at WP2
reverse cheek cut at tail
shorten tail for rough fascia
Rafters
valley
rafters shortened
runs from
the plate to the supporting valley
rafter
run same
as minor common
rafter times 1.41 or 1.41 times unit
of run
 raise birdsmouth
Rafters
valley
rafters
supporting
runs from
the plate to the major ridge
run same as common times 1.41
or 1.41 times unit of run

raise birdsmouth
Rafters
working
points
line length of
rake broken into working points  working point one WP1 is the
ridge  WP2 is the birdsmouth WP3 is the tail
Roofing
asphalt
shingles
square of
shingles is enough to cover 100 sq
ft.
slopes
greater than or equal to 1:3 have
double coverage
1:3 low
slope shingles less than 1:3 must have
triple coverage greater than 1:3 double coverage
less than
1:3 starter strip cemented to
sheathing 200 wide cement
first
layer 100 band of cement to starter
strip
next shingle layers cement
band equal to exposure plus 50
wood
shingles
laid on
sheathing or on spaced boards
spaced
boards centre to centre is same as
shingle exposure
first
shingle course laid double with a 25
over hang
 eaves
protection 900 .. 300 inside wall
wood
shingles:
400 min
length
 6 apart
350 max
width
75 min
width
staggered
joints at least 40 not to line up
for at least two previous courses
fasteners
40 above butts 20 from sides 2 per
shingle hot dipped galvinized nails
shakes:
wind
driven snow areas closed sheathing
recommended
lapped
sheating set at widths equal to the
weather exposure
starter
row doubled or trippled
froe end
or smooth end towards ridge
450 min
length
 6 apart
350 max
width
100 min
width
staggered
joints at least 40
fasteners
40 above butts 20 from sides
 450
breather type underlay under each row
overlaps = to twice the exposure covers the top 100 of the shake
ridge and hips finished butts
away from the wind
Roofing
sheet metal
comes in
762 to 914 widths
nailed to
19 by 89 furring strips at 400 C
thickness depends on snowloads
supplied from manufacturer
Roofing
built up
roofing
built up
roofing:
cant
strip, metal gravel stop
dry laid
felt over lapped 50 #15 tar saturated
rag felt four to five layers
225, 450,
675, 900, 900 exposure of 215
100 then
200 then 300 then 300 each mopped
with 1 kg asphalt per metre squared
covered
with a flood coat 3 kg per metre
squared
covered
with aggregate .15 kg per metre
squared or 10 kg slag per metre squared
roof edge
cant strip with roofing felts mopped
up
1:50
minimum roof without ponding
1:25
minimum slope for built up roofs without
gravel
1:25 is
the maximum built up roof with coal
tar and gravel , coal tar will run when heated by the sun
1:6
minimum roof slope for low slope asphalt
shingles
meeting
of a masonry
wall and a built up roof . cant strip
with
roofing felts mopped up 150 above cant ..metal flashing embedded in
masonry 25 and metal flashing overlaps felt by 100
single
ply roof membranes poly vinyl chloride
membranes , concrete, membrane, insulation, stone ballast or bearing
pads and patio blocks
liquid
envelope roof vinl base compound
sprayed on built up
applications to .4 to 1 mm applied to most decks can be carried over
parapets to reinforce flashing
space age fabrics
are
applied all over the world on large roofes (air supported)
Sheathing
eaves
protection
ice
damming
 most
common protection is rolled roofing
 or two
layers of asphalt paper cemented
together with lap cement
modified
bituminous membranes
polyethylene films can no
longer be used on roofs .. cause sheathing rot
Sheathing
numbers
walls and
chimney flashing
step
flashing:
layered
like shingles bottom of slope to top
of slope minimum 75 head
lap
minimum
75 horizontal lap
sheathing
paper laps flashing by 75, siding
over sheathing paper, 50 between deck and siding (sheathing paper)
 flashing
embedded in masonry by 25
skylights
or roof openings
flashing extends up the roof 1/6 the
opening
or minimum of 150
skylight
opening have double headers around
opening
chimney
wider than 750 use either a chimney
saddle or flashing
flashing
up chimney 1/6 of chimney width or
150 what ever is greater and up the roof to the same elevation as
chimney
Sheathing
valley
flashing
metal
flashing a 600 strip
centered
rolled roofing
bottom
layer mineral surface down 457 wide nailed 25 from edge 450 on centre
top layer no less than type “M” 914 wide nailed to hold in place until
shingles are applied
Trusses
insulation
space
for extra
insulation space use:
raised
heel, dropped chord, scissors, parallel
chord.. trusses
or larger
ceiling joists and larger rafters
cross
purlins give better air circulation
attic
access hatch size 500 to
900 dwelling other 550 t0 900
