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ROOF RAFTERS



CON-TEC VENTURES LTD.
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 CANADA NATIONAL BUILDING CODE 2010 TABLE
CHECK WITH YOUR BUILDING INSPECTOR FOR YOUR AREA

ROOF NAILING TABLE NATIONAL BUILDING CODE 2010


ROOF EXTERIOR DETAIL
ROOFING ANATOMY

ROOF INTERIOR DETAIL
ROOF VIEW FROM INTERIOR

ROOF SIDE VIEW DETAIL
ROOF VIEW FROM SIDE


attic access



common roof


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

similar triangles

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

rise, run, rake

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

ridge

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

birdsmouth

-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)

plumb cut

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 

plumb cut wp1, wp2,wp3

shortening the rafter


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

dropping hip rafter

- 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

raise valley birdsmouth


Rafters

common ridge

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

collartie

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

framing in your dormer

-roof end of dormer rafters are cut to slope of the roof

dormer framing

dormer opening

dormer double rafter each side

frame dormer walls to deck

dormer header

dormer roof

laying out seat cut for dormer valley jack

above seat cut for valley dormer jack...to plywood sheathing or a 2 by plate

dormer or other rafter to roof cuts

-side studs for dormer.. they are the rise for a proportional triangle.. rise of roof 200 rise of dormer roof 50 rise (200-50=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

sketch out similar triangles

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

soffit in front of dormer


Rafters

dormer gable 

gable dormer

small intersecting roof:

intersectting gable 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 endgablestuds

-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

gambrel roof

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









knee wall

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
lookout

dropped gable


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 rafter runs

octagon 

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.)

hip












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


Raftersrafter span

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


RaftersRAFTER TAIL CUTS

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

TANGENT TO CHORD


Rafters

truss

lower and upper chords and diagonal webs
-19x89 web bracing
-diaganol braces nailed to first four webs and repeated every 6meters

truss wall attachment


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

valley


Rafters

hip valley cripple jack

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

VALLEY HIP


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
valley flashing
valley duroid shingles
step flashing

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