british columbia carpenter apprenticeship program joists to tie the ends of the rafters together,...

British Columbia Carpenter Apprenticeship Program

Level 3 Line H

7960003573

Build Intersecting RoofsCompetency H-7

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BC CARPEnTER APPREnTICESHIP PRogRAM—LEvEL 3 1

Competency H-7Build Intersecting Roofs

ContentsObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Learning Task 1: Describe an Equal-slope Intersecting Roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Self Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Learning Task 2: Build an Equal-slope Intersecting Roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Self Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Learning Task 3: Material Calculations for Ceilings and Roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Self Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2 BC CARPEnTER APPREnTICESHIP PRogRAM—LEvEL 3

Competency H-7Build Intersecting Roofs

Roof construction is a major part of wood-frame construction. Whether the roof is a truss roof or a rafter-framed roof, knowledge of roof framing is an important skill for carpenters.

ObjectivesWhen you have completed the Learning Tasks in this Competency, you will be able to:

• name the components of an equal-slope intersecting roof

• calculate the length of rafters for intersecting roofs

• determine the adjustments for valley and valley jack rafters

• lay out a valley rafter

• lay out a valley jack rafter

• lay out a valley cripple rafter

• lay out a hip valley cripple rafter

• calculate ceiling frame materials

• calculate roof framing materials

Competencies Written: “Frame equal-slope intersecting roofs”

You will be tested on your knowledge of intersecting roof terminology, layout methods, adjustments, calculations, and the use of rafter tables and framing squares. You will also be tested on your ability to calculate the materials required for roof construction.

You must achieve at least 70% on this Written Competency.

Practical: You will be required to calculate, lay out, cut, and erect an intersecting roof.

You must achieve at least 70% on this Practical Competency.


CoMPETEnCy H-7 LEARnIng TASk 1

Learning Task 1Describe an Equal-slope Intersecting Roof

An equal-slope intersecting roof has two or more roof lines meeting each other to form valleys between the roofs. The roofs have the same rise/run slope, and typically, intersect at 90 degrees. This style of roof also requires two or more ridge boards.

The design of the roof may include hip or gable ends. Refer to Level 1 Learning Tasks H-4 and H-5 for more information regarding gable and hip ended roofs.

Rise

Overhang

Projection

Line length

Ridge board

Common rafter

RunSpan

Figure 1. Roof framing terms (section view)

Sizes of rafters for all roofs require reference to the BC Building Code. This is covered in Learning Task 2 – Build an Equal-slope Intersecting Roof.

A rafter-framed roof allows the interior roof space to be used as living space (as opposed to a truss roof which does not). The ceiling lines formed by the roof slope and (underside of) valleys add architectural interest. In these building designs, the rafters are tied together at the bottom by floor joists, instead of ceiling joists. The rafters become “roof joists” because they now carry the interior finish as well as the live and dead load.


LEARnIng TASk 1 CoMPETEnCy H-7

Ceiling or Floor JoistsThe ceiling is constructed before the roof framing is assembled. Hand-cut, or rafter-framed roofs require ceiling joists to tie the ends of the rafters together, laterally brace exterior walls, and support the ceiling finish. In roofs built without ridge support (unsupported ridge), the fastening of the ceiling joists to the rafters, and at interior bearing walls or beams, is extremely important. The ceiling joists are under tension. The fasteners that hold them are withstanding a shearing force. The fastener requirements for ceiling joists to top plates, and rafters to ceiling joists are in the BC Building Code tables 9.23.3.4 and 9.23.13.8.(6).

Roofs built with a supported ridge, with a ridge beam, or bearing wall supporting the tops of the rafters, are referred to as vaulted ceilings or cathedral ceilings. They do not require ceiling joists. Table A-12 in the BC Building Code gives spans for ridge beams.

Equal-slope, Intersecting Roof Framing Terms

Hip jack

Majorcommon

Major ridgeCommon overhang

(rafter tail)

Shortest majorvalley jack

Major end common

Valley-valleycripple jack

Major hip

Supported(short) valley

Shortest minorvalley jackMinor ridge

Longest minor valley jack

Minor common

1st minorhip jack

Hip overhang(rafter tail)

Minor endcommon

Minor hip

Supporting(long) valley

Longest majorvalley jack

Hip-valleycripple

Figure 2. Roof framing terms (plan view)


Notes


Major RoofWhen two roofs intersect, the major roof is the roof with the wider span. The major roof is where the major ridge and the major hips are located.

Minor RoofWhen two roofs intersect, the minor roof is the roof with the smaller span. The minor roof is where the minor ridge and minor hips are located.

When both roofs have the same span, they will have the same total rise and the ridges for both roofs will intersect at the same height. In this case, the major roof is the larger of the two (covering more square footage). Some buildings will have more than one minor roof, in which case the minor roofs will be numbered. i.e., minor roof 1, minor roof 2, etc.

RidgesThe major ridge is the same as the ridge for a simple gable or hip roof. The minor ridge runs into the intersection of the valley rafters, with a double cheek cut.

HipThe hip rafter extends from the ridge to the outside corner of the wall plate. In plan view, it runs at a 45° angle to the ridge, the common rafters, and the plates. In an intersecting roof, it’s parallel to the valley rafter.

Hip JackThe hip jack rafter is a shortened common rafter that extends from the hip to the plate. It’s laid out using the same slope as the common rafter and has the same on-centre spacing, bird’s mouth, and overhang as the common. It joins the hip with a single cheek cut. In plan view, it runs at 90° to the plate, 45° to the hip, and parallel to the common rafters.

Supporting valleyThe supporting valley rafter, sometimes referred to as the long valley, extends from the major ridge to the wall plate at the inside corner. In plan view, it runs at a 45° angle to the ridge. If the major roof has a hip end, the supporting valley rafter has the same line length as the major hip rafter.

Notes



Supported valleyThe supported valley rafter, sometimes referred to as the short valley, extends from the supporting valley to the wall plate. In plan view, it runs at 90° to the supporting valley, and 45° to the plate. If the minor roof has a hip end, the supported valley rafter has the same line length as the minor hip rafter.

valley JackValley jack rafters are common rafters that are cut off to meet the valley rafter. They don’t cross the wall plate. Jack rafters have the same slope and same ridge cut as the common rafter. The on-centre spacing is laid out with the common rafters. The valley jack rafter extends from the ridge to the valley. In plan view, it runs 90° to the ridge (like a common), and 45° to the valley. It has the same plumb cut as the common at the top and a single cheek cut at the bottom where it meets the valley. Installed, the top edge of the valley jack should be slightly above the edge of the valley to allow the roof sheathing to meet at the centre of the valley rafter.

Hip-valley CrippleThe hip-valley cripple extends from the hip rafter on the major roof to the valley. It touches neither the wall plate nor the ridge. It has a single cheek cut at each end. In plan view, it looks like a parallelogram.

valley-valley CrippleThe valley-valley cripple extends from the supporting valley at the top to the supported valley at the bottom. It has a single cheek cut at each end. The long point on both ends is on the same side of the rafter.

Cheek CutsCheek cuts are angled cuts used to fit hip, valley, jacks, and cripple rafters to other rafters. The supporting valley, jacks, and cripples have a single cheek cuts. The hip rafters, where they fit into the tripod, have double cheek cuts. Valley jack and hip jack rafters are often installed as pairs on either side of the valley or hip rafters and have opposing right- and left-hand single cheek cuts.


Notes


Single cheek cut Double cheek cut

Figure 3. Cheek cuts

PurlinPurlins are used to provide cross ventilation in vaulted ceilings. Purlins are also used for roof coverings that require support across the roof such as metal roofs or tile and slate roofs. Purlins are also referred to as strapping.

Roof JoistsThe rafters in a vaulted ceiling are called “roof joists”. They support both the roof and the ceiling finish. In the BC Building Code, Span Tables A4 and A5 are used for these framing members.

Working PointsWorking points are created by the intersections of the theory lines of the rafters. Often the working point for one rafter is the working point for other rafters. The working point is always located at the centre line of the rafter.

TripodThe “tripod connection” method of connecting the common rafters to the hip, end common, and ridge is shown in Figure 4. The two commons and the end common form the three-legged tripod. Figure 4 shows the adjustments for the commons and the ridge.

Notes



Working point

Half the thickness of the common

Half the thickness of the ridge

End common

Figure 4. “Tripod connection” method

Now complete Self Test 1 and check your answers.



Self Test 1

1. Identify each roof component in Figure 1.

t

s

ba

d

c

q

r

n

p

o

k

l

i

m

j

h

g

f

e

Figure 1.



Identify each roof component by writing its name beside the number:

a. k.

b. l.

c. m.

d. n.

e. o.

f. p.

g. q.

h. r.

i. s.

j. t.

2. Describe the difference between a “major roof” and a “minor roof”.

3. What type of cheek cut is used for a supporting valley rafter?

4. What type of cheek cut is used for a valley jack rafter?

5. Which rafter has a cheek cut at both ends?

6. What is the purpose of a “purlin”?


Notes


Learning Task 2Build an Equal-slope Intersecting Roof

An intersecting roof consists of two or more roofs meeting at an angle. In this Learning Task, you’ll study roofs that intersect at right angles. On an equal-slope intersecting roof, the slope is the same for all roof surfaces. These can be hip roofs, gable roofs, or a combination.

Major roofMinor roof

Figure 1. Isometric drawing of an intersecting hip roof

The hip and valley rafters support the join between the roof slopes.

Planning for the construction of an intersecting roof begins with the blueprints. The rafter locations are not often shown on the blueprints, so the framer will draw the roof based on the floor plan.

45°45°

The supporting and the supported valley rafters are exactly the same theory lengths and slope as the corresponding major and minor hip rafters.

Supporting valley rafter

Supported valley rafter

Figure 2. The angle formed by the hip and valley rafter (plan view)

Notes



To draw the plan view location of a valley rafter on a rectangular building, draw a line from the inside corner of the building intersection toward the centre of the building at exactly 45° to the outside wall. Use a set square to lay out this angle. Draw the other valleys and hips towards the centre as well. Where these lines meet is the location of the ridge board.

Even the most complicated equal slope intersecting roof can be drawn using this simple principle (Figure 3).

Figure 3. Complicated intersecting hip roof

The following principles will help when drawing rafter locations:

• All hips and valleys are at 45° to the wall plates and ridges.

• The widest span produces the highest ridge and is the major roof.

• The ridge boards are always centered between the walls.

• The ridge board is always parallel to the walls.


Notes


Rafter Length Calculations

Ridge Theory LengthThe theory length of the major ridge board for a hip roof is equal to the length of the building minus the run of the end common at each end, or the length of the building minus the span of the building. The hip roof shown in Figure 4 has a length of 40' and the run of each end common is 12'6". This means that the theory length of the major ridge board is 40' – 12'6" – 12'6" = 15'.

The theory length of the major ridge board on a gable end roof is equal to the length of the building. In some designs, the ridge may project beyond the gable end to support the barge rafters.

The theory length of the minor ridge on a hip roof is the same as the length of the minor wall plate it parallels. The length of this wall is referred to as the jog. The minor ridge forms a parallelogram with the wall.

The theory length of the minor ridge on a gable end is equal to the jog plus the run of the minor common.

Common RaftersThe common rafter is the basis for much of the rest of the roof. The correct calculation and layout of this rafter is used in several ways:

• The roof slope given on the plans refers to the slope of the common rafter.

• The jacks and cripples have the same slope as the commons.

• The hip and valley rafters have the same number of units of run as the common.

• The hip and valley rafters use the same rise as the common (but a different run).

• The amount of the rafter that is left above the plate once the bird’s mouth is cut is the same for all rafters on the roof. This is often referred to as the “Wood Above Plate” or WAP.

The theory length of the common rafter for an intersecting roof is calculated in the same way as a common rafter on a gable end roof. (This is also described in Level 1, H-4 Learning Task 3.)

Find the run of the common rafter by dividing the span (width) of the building by two. Expressed as a decimal, this will determine the number of units of run.

Notes



18'

40'2' o.c.

14'

12'

8'

25'

1'8" TYP

Figure 4. Intersecting hip roof with Imperial dimensions



Name Run # UnitsLength/Unit of

Run

Theory Length Adjustments Amount Cut Layout #

Major Common 12'6" 12.5 14.42 180�⁄�" – �⁄� thickness of ridge ¾" square/

plumb 8 and 12

Common Overhang 1'8" 1.667 14.42 24�⁄��" – full fascia 1½" square/

plumb 8 and 12

Major Ridge 40' − 12'6" − 12'6" = 15' 15'+ �⁄� thickness of common at each end

1½" square

Major Hip X 12.5 18.76 234½"– �⁄� 45° thickness of common

1�⁄��" double cheek 8 and 17

Hip Overhang X 1.667 18.76 31¼" – full 45° of fascia 2�⁄�" double

cheek 8 and 17

Major 1st Hip Jack 10'6" 10.5 14.42 151�⁄��" – �⁄� 45° of hip 1�⁄��" single

cheek 8 and 12

Common Diff in Jacks 2' 2 14.42 28��⁄��"

Supporting Valley X 12.5 18.76 234�⁄�" – �⁄� 45° of ridge 1�⁄��" single

cheek 8 and 17

Minor Common 9' 9 14.42 129�⁄�" – �⁄� thickness of ridge ¾" square

plumb 8 and 12

Minor Hip X 9 18.76 168��⁄��"– �⁄� 45° thickness of common

1�⁄��" double cheek 8 and 17

Supported Valley X 9 18.76 168��⁄��" – �⁄� thickness of valley ¾" square

plumb 8 and 17

Minor Ridge equal to jog; 12'

Minor 1st Hip Jack 7 7 14.42 100��⁄��" – �⁄� 45° of hip 1�⁄��" single

cheek 8 and 12

Shortest Major Valley Jack 1' 1 14.42 14�⁄��" – �⁄� of ridge; −�⁄�

45° of valley 1�⁄��" single cheek 8 and 12

Shortest Valley Valley Cripple 1' 1 14.42 14�⁄��" – �⁄� 45° of valley

at each end 2�⁄�" single cheek 8 and 12

Hip Valley Cripple 8" 8 14.42 115�⁄�"

– �⁄� 45° of hip; �⁄� 45° valley

2�⁄�" single cheek 8 and 12

Shortest Minor Valley Jack 2' 2 14.42 28��⁄��" – �⁄� of ridge; −�⁄�


Longest Minor Valley Jack 8' 8 14.42 115�⁄�" – �⁄� of ridge; −�⁄�


Table 1. Imperial measurements for intersecting hip roof

The information shown in Table 1 is presented in the typical order used to calculate the rafter lengths. This table is the basis both for estimating and building the roof.

Notes



For example:

25

212 5

12 5

'. '

.

=

= units of run

For a metric roof, the unit of run is typically 250 mm. Divide the span (width) of the building by two and then divide this value by 250 to determine the number of units of run:

7600

23800

3800

25015 2

mmmm

mm

mmunits of ru

=

= . nn

The concept of units of run is useful when calculating the hip and valley rafter lengths.

The slope of the roof is shown on the building plans by a rise/run triangle and expressed as the rise in inches to the run in inches. (e.g., an “8 and 12 slope” has a rise of 8 inches for each run of 12 inches.)

The hypotenuse of this rise/run triangle is the Length of the Common Per Unit of Run (LCPUR). By using the Pythagorean Theorem (a2 + b2 = c2) with “a” as the rise and “b” as the run, “c” is the hypotenuse or the LCPUR.

Determine the LCPUR for a roof with an “8 and 12 slope”.

a b c

c

c

c

2 2 2

2 2 2

2 2

8 12

8 12

14 42

+ =

+ =

+ =

= . "

Determine the LCPUR for a metric roof with a rise of 150 mm and a run of 250 mm.

a b c

c

c mm

c

2 2 2

2 2 2

2 2

150 250

150 250

291 5

2

+ =

+ =

+

=

=

.


Notes


A framing square is stamped with tables. The rafter table is useful because it has the length per unit of run on the table for both common rafters and hip or valley rafters. Instead of calculating these numbers as described above, you can use the numbers on the framing square to calculate the theory lengths of all rafters.

12181

23

192021222321 6324 74

28 7/843 1/46 11/168 1/8

12 1717 09

16 1/424 5/1611 3/1611 15/16

COMMON RAFTER LENGTH PER FOOT OF RUNHIP OR VALLEY RAFTER LENGTHDIF F IN L E NG T H OF J A C K S 16 INC H C E NT R E SDIF F IN L E NG T H OF J A C K S 24 INC H C E NT R E SSIDE CUT OF JACKSSIDE CUT OF HIP OR VALLEY

Figure 5. Framing square

The theory length of the common rafter (also known as the Line Length) is the product of the number of units of run in the common rafter times the LCPUR. As per Table 1:

Major common: 12.5 × 14.42 = 180¼"

Minor common: 9 × 14.42 = 129¾"

This is the theory length of the common rafter, down the slope, from the centre of the ridge to the outside of the plate.

An intersecting roof will have major commons and minor commons. These rafters have the same slope, but because the buildings have different widths, the rafters have different runs and therefore have different line lengths.

Both major and minor end common rafters are calculated the same way as the major and minor commons. The end commons differ from the commons by the adjustments discussed in the Rafter Layout section later in this Learning Task.

overhang of the Common RafterThe overhang of the common rafter is the length down the slope based on the projection. The projection is the horizontal distance that the roof extends beyond the side of the building. A 20" projection has a run of 1'8" = 1.667 units of run. A 500 mm projection has 500/250 = 2 units of run. The overhang is calculated in the same way as the theory length of the common: units of run × LCPUR:

1.667 × 14.42 = 24�⁄��"

Notes



This is the same overhang for all common and hip jack rafters over the entire roof.

Hip and valley RaftersThe hip and valley rafters run at 45° to the ridge, plates, and commons.

It is useful here to consider a 45° triangle.

45° Right-angle TriangleOn an equal slope intersecting roof, the hip and valley rafters run (horizontally, in plan view) at 45° to all the other rafters.

The 45° right angle triangle is a special triangle formed by drawing the diagonal across a square (Figure 6). The hypotenuse of the 45° triangle with sides of 12" (the unit of run in an imperial roof) is 16.97". Therefore, 17" is used as the run layout number on an imperial framing square for hips and valleys.

Diagonal = 16.97"

45º

12"

12"

Figure 6. 45° right angle triangle

When framing in metric, the hypotenuse of the unit of run for the roof, typically 250 mm, results in a run of the hip and valley as 353.6 mm. 354 mm is used as the run layout number on metric framing square for hips and valleys.

8"8"

12"17"

Common Hip or valley

Figure 7. Units of run for commons and hips or valleys


Notes


For each unit of run in the common rafter, there is a unit of run in the hip rafter. The size of the unit is larger, but there are an equal number of units of run in the hip rafter as there are in the common rafter. The run of the hip (or valley) rarely needs to be computed—simply use the numbers of units from the common.

Hip and valley Line Length and overhang CalculationsThe length of the hip (or valley) per unit of run (LHPUR) is the hypotenuse of the unit rise of the roof and the unit run of the hip. On an 8 and 12 slope roof, the LHPUR is the product of 8 16 97 18 762 2+ =. . ". This is also found on the second line of the rafter table on the framing square.

The theory length of the hip is the number of units of run in the common times the LHPUR:

12.5 × 18.76 = 234½"

This is the length, down the slope, of the hip from the working point at the tripod connection to the outside corner of the plates.

The theory length of the minor hip is based on the number of units of run in the minor common:

9 × 18.76 = 168��⁄��"

The overhang of the hip or the valley is calculated the same way. Number of units of run in the common projection times the LHPUR:

1.667 × 18.76 = 31¼"

valley Rafter Line Length CalculationThe calculation for the theory length of the supporting (long) valley is the same as for the major hip rafter. In fact, because they form a parallelogram, the length does not need to be calculated, simply use the length of the major hip. The difference between these rafters is in the shortenings to their length and the layout of the cuts, both of which are described in the Rafter Layout section later in this Learning Task.

On a gable end roof, the theory length of the valley is calculated in the same way as the major hip: the number of units of run in the major common times the LVPUR.

The theory length of the supported (short) valley is the same as the theory length of the minor hip. These rafters form a parallelogram.

On a gable end minor roof, the theory length of the supported valley is calculated by the number of units of run in the minor common times the LVPUR.

Notes



valley Jack CalculationValley jack rafters are common rafters that are cut to meet the valley rafter.

The length of the first valley jack rafter is often easy to measure. From the on-centre layout on the ridge board, use a framing square to measure the length of the first valley jack rafter (Figure 8).

Length ofthe first

valley jack

Ridge

Valley rafter

Figure 8. Length of the first valley jack rafter

Make the measurement to the long point of the valley jack.

It’s not difficult to calculate the length of this rafter. Notice that, in plan view, the run of the valley jack is equal to the horizontal distance between the on-centre layout of the jack and the working point where the valley meets the ridge. Multiply the number of units of run by the LCPUR to get the line length.

As per Figure 4, the shortest valley jack rafter is one foot away from where the long valley hits the ridge. Find this by noting that the valley hits the ridge 8 feet over from the tripod (a parallelogram with the jog in the wall). The on-centre spacing of the commons and jacks, starting from the left end of the ridge, puts the valley jack 1' over from the valley.

1' = 1 unit × 14.42 = 14�⁄��"

After the first valley jack is measured or calculated, the lengths of the next rafters are found by adding the difference in lengths of jacks (from the rafter table on the framing square) to the length of the first valley jack rafter (Figure 9). This is the difference in length on the slope and is referred to as the common difference.


Notes


1218

12

3

192021222321 6324 74

28 7/843 1/46 11/168 1/8

12 1717 09

16 1/424 5/1611 3/1611 15/16

COMMON RAFTER LENGTH PER FOOT OF RUNHIP OR VALLEY RAFTER LENGTHDIF F IN L E NG T H OF J A C K S 16 INC H C E NT R E SDIF F IN L E NG T H OF J A C K S 24 INC H C E NT R E SSIDE CUT OF JACKSSIDE CUT OF HIP OR VALLEY

Figure 9. The difference in length of jack rafters

The common difference in all the jacks and cripples is based on the rafter spacing. Rafters spaced 2 feet apart run 2 feet less (or more) than the next rafter.

On an 8 and 12 roof, 2 feet = 2 units × 14.42 = 28��⁄��" = common difference.

valley valley Cripple Rafter CalculationThe valley valley cripple is often easy to measure. Measure the length of the shortest valley cripple from the layout of the corresponding valley jack. It’s worth setting a quick string line to line up the valley jack above the cripple. Measure on the same side of the rafter, from long point to long point.

The run of the valley valley cripple is twice the distance it is from the intersection of the valleys. From the run, get the number of units × LCPUR = line length of valley cripple.

Subsequent valley cripple rafters are longer by twice the common difference.

Notes



Hip valley Cripple CalculationThe hip valley cripple rafter runs between the valley rafter and the hip rafter (Figure 10).

Jog in the building

Hip jack

Hip valley cripple

Valley jack

Figure 10. Plan view of a hip valley cripple jack rafter

The calculation of the hip valley cripple is simple. The wall plate on the major roof forms a 45° right angle triangle with the run of the hip valley cripple. The jog in the building is the same as the run of the rafter.

On the roof from Figure 4, the jog is 8 feet:

8' = 8 units

8 × 14.42 = 115�⁄�" (line length of hip valley cripple)

Rafter LayoutThe theory lengths are calculated and measured from working point to working point. These working points are theoretical points. If a fishing line were stretched from point to point, the actual lengths would be the same as the theory lengths. However, since the roof is built with lumber, the lengths must be adjusted to make room for the other rafters. These are called “shortenings” or “adjustments”. Building is typically done with 2× dimension lumber (e.g., 2×4, 2×6, etc.) which has an actual thickness of 1½". Larger dimension lumber may also be used, such as in timber-frame construction.


Notes


All these shortenings and the layout of the cut lines are based on the plan view. Full-scale drawings of the connections between rafters assist in visualizing the adjustments.

The adjustment and layout line measurements are always made square from the plumb lines.

Ridge LayoutLooking at the tripod connection, notice that if the ridge is cut to its working point theory length, it would only support half the thickness of the common. Half the thickness of the common needs to be added to the length at each end of the ridge. Because the ridge is level, it gets square cuts at each end.

End common

½ the thickness of the common

½ the thickness of the ridge

Working point

Figure 11. Tripod connection

The minor ridge gets an adjustment of plus half the thickness of the common at the tripod and minus half the diagonal thickness of the valley at the other end. Because this is a double cheek cut, lay out for 45° cut lines off the shortening line. Since the lines are laid out on the side of the rafter, rather than in the centre where the theory points are, lay out and cut on lines half the thickness of the ridge on either side of the shortening. Cut the long point first.

Layout of Rafters Installed into the RidgeFor all roof framing members other than the ridge, the plumb lines at the working points are laid out using the framing square and roof slope numbers and marking on the rise.

Notes



After laying out the plumb lines at the working points, lay out the shortenings for length. It’s important that the measurements for the shortenings are made square to the plumb lines.

For the common rafters and valley jacks that hit the ridge at the top, the adjustment at the ridge is minus half the thickness of the ridge. If the ridge is 1½", this shortening is ¾".

At the tripod, the shortening for the end common is minus half the thickness of the common.

Bird’s MouthThe bird’s mouth is the shaping of the rafter to fit tightly on the wall plate. It’s formed by a plumb (vertical) cut and a seat (horizontal) cut. The BC Building Code requires a minimum bearing (seat cut) dimension of 38 mm (1½"). This is a minimum and is rarely used as it does not allow for adequate nailing. A rule of thumb for laying out the bird’s mouth is to lay out the plumb line across the whole rafter and mark the seat cut so that ⅔ of the plumb cut is above the plate (sometimes referred to as “wood above plate” or WAP) and ⅓ is below the plate. This typically ensures a bearing dimension larger than the Code requirement and is adequate for nailing.

Depending on the climate zone, the wood above plate may not be large enough to meet the Code requirement for insulation and ventilation of the attic space. In this case, it’s possible to sit the rafter on a rafter plate fastened to the top of the ceiling joists and run the ceiling joist into the soffit space where the rafter connects to the ceiling joist.

To lay out the bird’s mouth, use the roof slope numbers, mark on the rise for the plumb cut, and the run for the seat cut.

The WAP for every rafter on the roof comes from the WAP on the common rafter.

OverhangThe common and hip jacks get shortenings at the overhang. Starting from the plumb line at the working point, measure square back the full thickness of the sub fascia to the cut line.

Hip Rafter LayoutHip and valley rafter layout uses the same rise as the common, but 17" or 354 mm as the run.


Notes


End common

Hip

Working point

Half of the diagonal of the common rafter

Half the thickness of the common

Figure 12. Tripod connection showing shortening for the hip

At the tripod, the hip gets shortened by ½ the diagonal thickness of the common.

To get the diagonal thickness of any board, lay out a 45° angle on the edge of stock and measure the length of the line. For 2× dimension lumber, the full diagonal will be 2�⁄�" (54 mm), and half that diagonal thickness is 1�⁄��" (27 mm). For timbers of any stock other than dimension lumber, it’s most accurate to lay out the 45° line and measure the length of the line.

An alternate to measuring is to calculate the thickness mathematically:

1 5 1 5 2 121

2 121 2 1 061 1

2 2

116

. . . "

. . "

+ =

÷ = =

Working point4"

17"

11⁄16"

Figure 13. Shortening the hip for half the diagonal thickness of the common

Lay out the working point plumb line of the hip, measure square back half the diagonal thickness, and mark a second line. This is the shortening for length.

Notes



From this shortening line, measure and lay out half the thickness of the hip on either side. Once again, these cut lines for a double cheek cut come from the fact that the layout is on the side of the rafter, which is ¾" (19 mm) from the centre of 2× stock. Set the saw to 45° and cut the long point first. Be sure to cut on the waste side of the line.

1 1⁄16"¾"

Working point

2 × 6 hip rafter

Figure 14. Lay out the double cheek cut using half the thickness of 2× stock

The bird’s mouth of the hip rafter is a tricky layout. Looking at a plan view drawing of the hip at the corner of the plates, notice that the hip has to be cut at the working point line for the rafter to clear the corner of the building. However, to get the tops of the rafters to line up and ensure the sheathing lays flat, the Wood Above Plate (WAP) needs to be the same as the common rafter. This cut needs to be made at the place where these plumb WAP lines line up: at the edge of the plate. For the hip rafter, the side of the hip (where the layout is made) crosses the plate half the thickness of the hip towards the ridge from the working point line. Using 2× dimension lumber, this is ¾" (19 mm) up the hip. The WAP is marked on the line closest to the ridge and the cut is made on the line closest to the fascia.

Half of the thickness of the hip

Building lineWorking point

Working point

Point where the hip meets the building line

Figure 15. Bird’s mouth on the hip rafter (plan view)


Notes


Depth of the common rafter’s

bird’s mouth

Half of the thicknessof the valley

Working point

Figure 16. Bird’s mouth on the hip rafter (elevation view)

The shortening at the overhang of the hip is the full diagonal thickness of the fascia, 2�⁄�" (54 mm) when using 2× dimension lumber. From the working point line, measure up for the shortening. Then lay out a double cheek cut similar to the one at the tripod.

3"

3"

Hip rafter

Hip jack rafter

Figure 17. Wood Above Plate (WAP)

Notes



Building line

Outside of rough fascia

Working point

Projection

Full diagonal thickness ofthe rough fascia

Figure 18. Double cheek cut at the overhang of the hip rafter

valley Rafter LayoutThe supporting valley connects to the ridge at a point along the ridge equal to the jog in the building. This point in the centre of the ridge will align with the centre line of the valley. These are the working points.

The shortening of the valley is half the diagonal thickness of the ridge. Lay out the long point cut line of the single cheek cut half the thickness of the valley towards the ridge, set the saw to 45° and cut on the long point on the waste side of the line. Install this rafter so that the centre of the valley is flush with the top of the ridge. The corner of the valley that sticks above the ridge is trimmed off later.

Working point

Half the diagonal thickness of the

ridge board

Ridge

Supporting valley

Figure 19. Plan view of long valley at ridge


Notes


Working point4"

17"

½"

Figure 20. Lay out single cheek cut of valley

At the plate, the sides of the valley cross the plate ¾" (19 mm) down the valley from the working point.

The wood above plate is laid out at the working point line (the line closest to the ridge), but the cut is on the line closest to the fascia.

Rough fascia

Working pointBuilding line

Valley rafter

Figure 21. The centre of the valley meets the building line at the working point

Depth of the common rafter’s

bird’s mouth

Half of the thicknessof the valley

Working point

Figure 22. Lay out the valley bird’s mouth

The overhang of the valley rafter gets an inside double cheek cut. The shortening is the full diagonal thickness of the rough fascia, with cut lines half the thickness of the

Notes



valley away from the building. In this case, lay out on both sides of the rafter. Set the saw at 45° and set the depth to half the diagonal thickness of the valley. Cut half-way through on one side, flip the board and cut half-way through.

In a case where the soffit covers the end cuts of the rafters, a single cheek cut on the valley will be adequate.

Rough fascia

Working point

Working point

Building line

Valley rafter

Full diagonal of the rough fascia board

Figure 23. Inside double cheek cut at valley tail

One way to remember the differences and similarities of the hip and valley rafters is: the WAP is on the line closest to the ridge on both rafters, and the cut line is on the line closest to the fascia on both rafters. This is true even though the WAP is laid out up the hip, and the cut line is laid out down the valley.

Supported valley LayoutOn a building where the minor roof has a smaller span than the major, the supported valley rafter hits the supporting valley at a 90° angle part-way down the supporting valley. The line length of the supported valley is measured to the working point, which is at the centre of the supporting valley. The supported valley must be shortened by half the thickness of the supporting valley (Figure 24).


Notes


Ridge

Half of the thickness of the supporting valley

Supported valley

Supporting valley

Figure 24. Shortening of the supported valley

The measurement of the shortening is made square to the plumb cut. The saw is set square.

Jack and Cripple Rafter LayoutHip jacks, valley jacks, and cripples all get single cheek cuts. The shortening adjustments for these rafters are half the diagonal thickness of the hip or valley they connect with.

Working point

Hip jack

Hip

Half of the diagonal thickness of the hip rafter (1 1⁄16" for a 2 × 6 hip)

Figure 25. Shortening of the hip jack

It’s usually easiest to cut on the long point line of the rafter (a typical right-handed circular saw will have the large side of its base supported by the board). Lay out the long point by measuring square to the shortening adjustment line half the thickness of the rafter.

Notes



The valley jack has a common plumb cut layout at the ridge and a single cheek cut at the lower end at the valley.

The hip jack has a single cheek cut at the hip at the top and a common bird’s mouth and overhang.

The valley valley cripple has a single cheek cut at both ends, long point on the same side.

The hip valley cripple has a single cheek cut at both ends, long point on opposite sides.

When cutti ng jacks in pairs, be sure to lay out the long point cut on the opposite sides of each raft er.

Ridge board Valley jackrafters

Working point

Position of end of ridge against valleys

Back o� this portionof long valley rafter

Centre line oflong valley rafter toupper edge of ridge

Valley cripple jack rafterSupportin

g or long valley rafte

r

Supported or short valley rafter

Working point

Working point

Working point

Figure 26. Valley, valley jack, and valley cripple jack

vaulted CeilingsVaulted ceilings oft en use heavy valley raft ers to carry the load of the valley jacks. The layout and cutti ng of the laminated veneer beams shown in Figure 27 is criti cal. If they’re cut short, new beams have to be ordered, delaying the constructi on schedule.


Notes


Figure 27. Valley construction of a vaulted ceiling

The valley jack rafters shown in Figure 27 are nailed to the side of the valley beam with seven 3¼" nails. The structural engineer often requires angled joist hangers at this location.

Tail CutThe inside double cheek cut is made by cutting each lamination at a 45° bevel (Figure 28).

Figure 28. Valley beam tail cut

Notes



Figure 29 and Table 2 are an example of a similar roof with metric dimensions.

5500

12000600 o.c.

4300

3650

2200

7600

500 TYP

Figure 29. Intersecting hip roof with metric dimensions



Name Run # UnitsLength/Unit of

Run

Theory Length Adjustments Amount Cut Layout #

Major Common 3800 15.2 291.5 4431– �⁄� thickness of ridge

–10square/plumb

150–250

Common Overhang

500 2 291.5 583 – full fascia –38square/plumb

150–354

Major Ridge 12000 – 3800 – 3800 = 4400 4400+ �⁄� thickness of common @ each end

+38square/plumb

square

Major Hip X 15.2 384 5837 – �⁄� 45° thickness of common

–54double cheek

150–354

Hip Overhang X 2 384 768– full 45° of fascia

–38double cheek

150–354

Major 1st Hip Jack

3200 12.8 291.5 3731 – �⁄� 45° of hip –27single cheek

150–354

Common Diff in Jacks

600 2.4 291.5 700

Supporting Valley

X 15.2 384 5837– �⁄� 45° of ridge

–13square plumb

150–354

Minor Common 2750 11 291.5 3207‘�⁄� thickness of ridge

–10square/plumb

150–250

Minor Hip X 11 384 4224– �⁄� 45° thickness of common’

–27double cheek

150–354

Supported Valley

X 11 384 4224– �⁄� thickness of valley

–19square/plumb

150–354

Minor 1st Hip Jack

2150 8.6 291.5 2507 – �⁄� 45° of hip –27single cheek

150–250

Shortest Major Valley Jack

240 0.96 291.5 2507�⁄� of ridge;- �⁄� 45° of valley

–10, –27single cheek

150–250

Shortest Valley Valley Cripple

500 2 291.5 280 – �⁄� 45° of valley at each end


150–250

Hip-Valley Cripple

2200 8.8 291.5 2565– �⁄� 45° of hip; – �⁄� 45° valley


150–250

Shortest Minor Valley Jack

648 2.59 291.5 756�⁄� of ridge; – �⁄� 45° of valley


150–250

Longest Minor Valley Jack

2448 9.79 291.5 2854 – �⁄� of ridge; – �⁄� 45° of valley


150–250

Table 2. Metric measurements for intersecting hip roof

Notes



Putting it All TogetherOnce the ceiling joists are in place, the construction of the roof usually starts with making a walk-way on top of the joists directly under the ridges and scaffolding at the plate, either inside or outside the building.

Typically the major ridge goes up first, supported by pairs of major common rafters and braced by the end commons on a hip roof or by a sway brace on a gable end roof. Major hips and valleys follow, with jacks and cripples filled in. It’s important to keep the ridge, hips, and valleys straight by installing commons and jacks in opposite pairs. It’s good practice to place a string line along these rafters to ensure their straightness.

The minor roof follows with the short valley first and the minor ridge, with its double cheek cut at the intersection of the two valleys, supported by a pair of minor commons.

Sheathing or strapping the roof typically begins at the bottom of the roof. The fascia has been straightened and the plywood lays out much as a floor system, keeping an eye on the rafter spacing as you nail off.

Where sheathing runs into the valley, making long point and short point measurements from the leading edge of plywood ensures a good fit. This is not a 45° cut. It’s not difficult to calculate this cut. The offset from the long point to the short point is the run of a sheet of plywood with 48" on the slope. It’s a ratio equation where, on an 8 and 12 roof:

Offset

48

12

14 42

391516

" .=

=

It’s usually easier to cut this sheet on the ground than on the roof.




Self Test 2

1. Explain how the layout numbers for a valley rafter is derived.

2. What figures on the framing square are used to lay out the seat cut at the bird’s mouth for a valley rafter?

3. Calculate the line length of a supporting valley rafter for a building that is 26' wide with a 5 in 12 slope. (Use Figure 1.)

34512 3717 2316 1/224 3/411 5/8

11 13/16

12 6517 4416 7/825 5/1611 3/8

11 11/16

13 17 69

17 5/1626

11 1/1611 1/2

Figure 1.

4. Calculate the overhang length for a valley rafter if the projection is 16" and the roof slope is 5 in 12. (Use Figure 1.)



5. Draw a sketch showing the layout of the supporting valley rafter. Show in detail, including measurements, adjustments, and cut lines. Use a roof slope of 5 in 12, a 1×8 ridge board, 2×4 common rafter, and 2×6 valley rafter.


Notes


Learning Task 3Material Calculations for Ceilings and Roofs

The ceiling is constructed before the roof framing is assembled. The material calculations include the ceiling joist and blocking quantities.

Ceiling JoistsRafter-framed roofs use ceiling joists to tie the ends of the rafters together. The ceiling joists also support the ceiling finish. In roofs built without ridge support, the fastening of the ceiling joists to the rafters is extremely important. The fastener requirements for ceiling joists to top plates, and rafters to ceiling joists, are in BCBC Table 9.23.3.4 and 9.23.13.8.(6).

The design of the building may require that the underside of the roof is finished (as opposed to being attic space). This provides interesting architectural space, with sloped ceilings and the underside of the valley visible from below. In these designs, the rafters become roof joists and the dead load of the ceiling finish and insulation is additional to the load of the roof itself. Use BCBC Tables A-4 and A-5. These roof designs may require a supported ridge and are referred to as a vaulted or cathedral ceiling. The ridge could be supported by a ridge beam designed from BCBC Table A-12 or a load-bearing wall.

The design may also specify living space in what is often considered attic space. In this case, the ceiling joists become floor joists, subject to all floor loads, as well as tying the roof joists together.

Size and SpacingThe size and spacing of ceiling joists is designed using the tables in Part 9 of the Building Code. The design process is almost exactly the same as the design of floor joists. Refer to Competency H-2: Build Foundations and Floors for instructions in designing ceiling joists.

Ceiling Joist LengthThe length of the ceiling joist is based on the design of the building. For small structures, a single joist may span the entire building so its length will be equal to the building’s width. For wider buildings, the ceiling joists are lapped over interior bearing walls or beams.

Notes



Load-bearing WallWhen lapped over a bearing wall, the joists must be nailed to each other with one more nail than required to nail the ceiling joist to the rafter (Figure 1).

6 nails

7 nails

Figure 1. Joining ceiling joists over a bearing wall

The minimum amount of lap is not clearly specified in the Building Code.

When the ceiling joists provide a tie between the ends of the roof rafters, allow for a minimum lap of 12" or butt the joists and cleat the joint with a 24" block of joist material. Whenever possible, lapping the joists is preferred. This is so that the number of nails required does not split the wood.

The nailing shown in Figure 1 is only required if the rafters are not supported at the ridge. If a ridge beam or load-bearing wall supports the ridge, only two nails are required.

Supported by a BeamIf the beam is under the ceiling joists, often referred to as a drop beam, the connection of the joists is the same as shown in Figure 1.

If the beam is made flush with the ceiling joists, often referred to as a flush beam, the joists will be attached to the beam with joist hangers. A metal strap, or tie, should be used over the beam to tie the opposing ceiling joists together (Figure 2). If the joists support a floor, the floor sheathing will tie the joists together.


Notes


Metal strap tie

Figure 2. Ceiling joists butting into a flush beam

The materials for the flush beam are considered as part of the ceiling framing.

The amount of material is equal to the length of the beam multiplied by the number of plies in the beam.

number of Ceiling JoistsThe number of ceiling joists depends upon the spacing of the joists and the size of the building.

For gable roofs, the first ceiling joist is located beside the first rafter away from the gable end (Figure 3). Backing is installed at the gable wall to support the ceiling finish. This backing is often 2×4s laid on flat.

Notes



Figure 3. Ceiling joist located beside rafter

Figure 3 shows ceiling joists located beside every rafter. This arrangement requires less nailing at the connection. Figure 4 shows rafters spaced at 24" o.c. while the ceiling joists are at 16" o.c. In this case, the rafters are only tied to every third ceiling joist.

Figure 4. Rafters tied to every third ceiling joist

The arrangement shown in Figure 4 is common because the span of the ceiling joist usually requires the ceiling joists to have a closer spacing than the rafters.


Notes


Calculate the number of ceiling joists by dividing the length of the building by the spacing of the ceiling joists. Round the result down to the nearest whole number.

Blocking

Blocking at OpeningsOpenings are required in the ceiling framing to accommodate attic access holes and chimneys. The framing for the openings is identical to the framing for openings in floors (Figure 5).

Figure 5. Opening in ceiling joists

For openings that do not require more than one ceiling joist to be cut, the construction shown in Figure 5 is adequate.

If the ceiling joists are required to tie the ends of the rafters together and the opening is large, an engineer must design the construction. Special framing is required to transfer the tension loads across the wide opening. If the rafters are supported at the ridge by a ridge beam or bearing wall, large openings in ceiling joists can be designed and built following the Building Code regulations for floor openings.

The length of the headers for the opening is included in the blocking requirements.

Blocking Between JoistsAlthough not specifically required by the Building Code, blocking should be installed at the middle of the span of the ceiling joists. The blocks should be the full depth of the ceiling joists. This blocking stiffens the ceiling framing and prevents the ceiling joists from twisting.

Notes



The number of blocks is one more than the number of joists and the length of the block is equal to the joist spacing minus the thickness of the joist.

Stub JoistsWhen the roof design has a hip roof, the ceiling joists change direction at the ends of the building (Figure 6).

The short joists at the end of the building are called “stub joists”.

Stub joist

Figure 6. Stub ceiling joists

The lumber required for the stub joists is included in the blocking requirements. The approximate number of stub joists is found by dividing the width of the building by the spacing of the ceiling joists. The length of the stub joists will be determined by the distance from the wall to the first joist.

Low slope, rafter-framed roofs require the first full ceiling joist to be kept back two spacings from the ends of the building, because the joists interfere with the bottom of the hip or valley. This requires the stub joists to be two spacings long. Note in Figure 6 that the ceiling joist carrying the stub joists is doubled.

Calculation ExampleEvery roof design is different. For rafter-framed roofs, draw a layout of the location of the rafters and ceiling joists. The drawing must be to scale and is usually done on top of the floor plan of the building.


Notes


18'

40'2' o.c.

14'

12'

8'

25'

1'8" TYP

Figure 7. Intersecting hip roof

This example is the same roof as described in Learning Task 2. The ceiling joists have the same on-centre spacing as the rafters and are tied to each set of rafters.

Locating the Rafters and Ceiling JoistsThe ceiling joist layout is dependent on the rafter location. The rafter layout begins at the tripod location. The first common rafter for each of the major and minor spans is shown in Figure 7.

Ceiling Joist LengthsThe length of the ceiling joists for the major roof will be 12'6" from outside of the plate to the centre of the building plus 6" to allow for a 12" overlap at the bearing wall. The standard joist sizes are in multiples of 2 feet. The minimum joist length for the major span will then be 13 feet, ordered as 14-foot pieces.

Notes



The design of the interior walls is not shown in this example, but the joists and beam for the minor roof may be full length from wall to wall and will be 18 feet long. As this is a very long clear span for joists or beams, it’s likely that there will be supports under the beam and joists and the actual lengths of these framing members will be estimated accordingly.

number of Ceiling JoistsIf the drawing is done to scale, the number of ceiling joists is simply counted from the drawing.

For the building shown in Figure 7, the number of ceiling joists is as follows:

• 36 @ 14' joists for the major roof (13' actual)

• 5 @ 18' joists for the minor roof

• 4 @ 18' joists for the flush beam

• 26 @ 2'6" stub joists for the minor roof (the length is approximate)

• 7 @ 3' stub joists for the minor roof (the length is approximate)

Additional framing material will be needed to support the ceiling at the corners where the span from the last stub joist is too great to support the ceiling finish.

BlockingA row of blocking is required at mid span of all of the ceiling joists. This will require 34 blocks for the major roof, and four blocks for the minor roof. Special length blocking is required for the different spacing that occurs when laying out from the tripods on the major roof and for the flush beam on the minor roof. Add two additional blocks to create the attic access opening. The total number of blocks is 40.

The blocks are all 22½" in length. A 16' piece of joist material will produce eight blocks at 22½" so five 16' pieces are needed. Off-cuts from other parts of framing can often be used to create blocks.

Roof Framing Material CalculationsRoof framing materials consist of common rafters, hip rafters, valley rafters, hip jack rafters, and valley jack rafters. The rafter length calculations are discussed in Learning Task 2. An intersecting roof will have more waste that a gable roof. It is common to add 5 – 10% waste.


Notes


Calculate number of Rafters

Commons, Jacks, and CripplesAn easy way to estimate the number of common, jack, and cripple rafters is to take the overall length of the building including the projection (as if there were a gable end roof), divide by the spacing of the rafters, and add one. This will give an estimate of enough common rafters for one side. Multiply by two to get enough for both sides. (This is possible because the off-cuts from longest jack rafters are long enough to be used as short jack rafters.) Finally, add the end commons.

Using the same roof as in Learning Task 2, the calculation for the number of commons (with jacks and cripples included) will be the length of the plate plus the projection at each end.

40' + 1'8" + 1'8" = 43'4" (43.333') (overall length of the major roof)

43.333' divided by 2' o.c. spacing = 21.7 pieces

Round up to 22 and add one = 23 per side. (Note that counting off the scale drawing, you get the same number.)

23 × 2 = 46 common rafters

5% waste + 3 rafters

2 end commons + 2 pieces

Total = 51 pieces

If the rafter is one piece (the rafter and overhang are the same piece of lumber) the overall length is the theory length and the overhang added together:

180¼" + 24�⁄��" = 204�⁄��" (17.042')

51 @ 18-foot pieces are needed for the major roof.

Similarly, for the minor roof:

12' + 1'8" = 13' 8" (13.667') (overall length of the minor roof)

13.667' divided by 2' o.c. spacing = 6.834 pieces

Round up to 7 and add one = 8 per side.

8 × 2 = 16 minor commons (includes jacks and cripples)

5% waste + 1 rafter

1 end common + 1 piece

Notes



Total = 18 pieces

The minor common is 129¾" plus a 24�⁄��" overhang = 153��⁄��" (12.8')

18 @ 14-foot pieces are needed for the minor roof.

Hip and valley RaftersCounting off the scale drawing of the roof, there are four major hips and one supporting valley. The overall length (line length plus overhang) is:

234½" + 31¼" = 265 ¾" (22.146')

5 @ 24-foot pieces are needed.

The minor roof has two hips and one supported valley. The overall length is:

168��⁄��" + 31¼" = 200�⁄��" (16.672')

3 @ 18-foot pieces are needed.

Calculating FasciaFascia is used to align the ends of the rafters and support the bottom edge of the roof sheathing. There are several ways fascia is designed. If the rafter tails are exposed, the fascia is also exposed and is considered a finished surface. If the rafter tails are covered with soffit, typically rough fascia aligns the rafter ends and a finished fascia is added to cover the edge of the roof and soffit. The finished fascia supports the eaves trough.

Fascia can be calculated by adding all of the overall dimensions of the roof. These overall dimensions are the plate lengths plus the projections:

43'4" + (2 × 28'4") + 15'8" + 9'8" + (2 × 12') + 23'4" = 172'8" (172.667')

This is an accurate dimension and does not include overlaps at the corners. For rough fascia, 5% should be added for waste:

172.667' × 1.05 = 181.3 lineal feet.

If this is for finished fascia attached to the rough, with mitred corners, add another foot per corner for an estimate of 190 lineal feet of finished fascia.


Notes


Roof Sheathing CalculationsThe surface of the roof is covered with sheathing or strapping. Roof sheathing is used when the roofing materials need continuous support. Strapping is used for sheet metal roofing and for the installation of shakes.

Roof SheathingThe amount of roof sheathing depends on the size of the building and the slope of the roof. The area of the sloping surfaces is calculated in two steps: find the area on the flat and then multiply the area on the flat by the slope factor.

Area on the FlatThe area on the flat for the roof is calculated using the building dimensions plus the roof projection (Figure 7).

The area consists of two rectangles:

• The major roof is 43.333' × 28.333' = 1228 square feet.

• The minor roof is 12' × 21.333' = 256 square feet.

The total area of the roof on the flat is 1484 square feet.

Area on the SlopeThe area on the slope is calculated by multiplying the area on the flat by the slope factor. The slope factor is equal to the length of the common per unit of run divided by the unit of run. Figure 8 shows slope factors for various roof slopes.

Slope factor: 12.65 ÷ 12 = 1.054 Slope factor: 14.42 ÷ 12 = 1.202

12 12

4

812.65

14.42

Figure 8. Slope factors

The slope of the roof for Figure 7 is 8 and 12 which has a slope factor of 1.202. Therefore, the area of the roof is 1484 × 1.202 = 1784 square feet.

Notes



Panel-type SheathingMost roof sheathing is panel-type, either plywood or OSB. For panel-type sheathing, the number of sheets is calculated by dividing the area to be covered by the area of one sheet of sheathing.

The sheathing panels are 4 feet by 8 feet and have an area of 32 square feet. The number of sheets needed for the building shown in Figure 7 is 1784 / 32 or 55.75 sheets.

WasteThe roof shown in Figure 7 is an intersecting hip roof. With this type of roof, there is considerable waste due to the cuts at the hips and valleys. Allow an additional 5% for this waste:

55.75 × 1.05 = 58.5 sheets

Round this number up to 59 sheets.

Panel sheathing requires the use of sheathing clips to align and support the edges of the plywood in between rafters. With rafter spacing of 2' o.c., there are 5 spaces between rafters on an 8' sheet of plywood. The number of sheathing clips required is:

59 sheets × 5 clips per sheet = 295 sheathing clips

Lumber SheathingLumber roof sheathing is only used when the shrinkage of the sheathing will not affect the roofing material. Sheet metal roofing and wood shingles or shakes can be installed over lumber sheathing.

For lumber sheathing, the amount of sheathing is calculated by dividing the area to be covered by the coverage per lineal foot of lumber sheathing. The coverage per lineal foot depends upon the size and type of lumber sheathing used.

For example, 1×8 shiplap sheathing will only cover 7" in width per board, whereas 1×8 resawn or S4S boards will cover 7¼" in width per board. To find the actual coverage per lineal foot, divide the coverage by 12.

If the building in Figure 7 is sheathed with 1×6 S4S boards, the coverage per lineal foot is 5.5 ÷ 12 or 0.458. The amount of sheathing required is:

1784 square feet ÷ 0.458 = 3895 lineal feet of 1×6 lumber sheathing


Notes


WasteThe amount of waste is less using lumber sheathing than using panel-type sheathing. For an intersecting hip roof, allow an additional 3% for this waste:

3895 × 1.03 = 4012 lineal feet

Accuracy of Waste FactorsThe accuracy of waste factors is dependent on the methods used by the builders, the experience of the faming crew, and on the shape of the building. Some builders are very careful with materials while others consider wasting material to be cheaper than the labour required to be more careful. Buildings with many intersecting roof shapes will require higher waste factors than those with few or no intersections.

Roof StrappingRoof strapping is used with metal roofing and with shake roofing. Buildings built in cold climates require protection from “ice dams”.

Eave ProtectionEave protection is used to make the eave of the building waterproof. It requires solid sheathing to support it.

Ice dams are created when the ceiling insulation is poor and the weather is cold. The heat that escapes from the building warms the snow on the roof. The water from the melting snow runs down the roof and then freezes on the colder eave (Figure 9).

Over time, the frozen water builds up into a large dam. The dam backs up into the warm area of the roof. If the roofing is a shingle type, the backed-up water will leak into the building.

SnowTrapped water

Thin ice slab under snow

Trapped water moves behind the shingles and leaks into thebuilding envelope

Heat from the building meltssnow where the ceiling insulationis inadequate

Ice

Figure 9. Ice dam

Notes



Calculating Strapping AmountsThe amount of strapping needed for a building is calculated in a similar manner as calculating the amount of lumber sheathing.

Eave ProtectionIf support for eave protection is required, either a full sheet of panel-type sheathing is used at the eaves or lumber sheathing is used for a distance of 3 feet up the roof slope. In either case, the area of the eave protection on the flat is multiplied by the slope factor and then the resulting square footage is divided by the area of the sheet or by the coverage of the lumber sheathing.

StrappingThe balance of the roof area (or the full area if eave protection is not required) is then used to find the amount of strapping required. The coverage of the strapping is dependent on the spacing of the strapping.

Strapping that supports sheet metal roofing is usually 2×4 lumber spaced at 16" or 24" o.c. Strapping for 18" long barn shakes is 1×4 spaced at 7½" to the weather.

For 2×4 strapping at 2' o.c., the strapping will cover 2 square feet per lineal foot of strapping. The coverage is then 2 sq. ft. per lineal foot.

For 1×4 strapping at 7½" o.c., the strapping will cover 7.5 ÷ 12 square feet per lineal foot of strapping. The coverage is then 0.625 sq. ft. per lineal foot.

In either case, the area of the roof on the flat is multiplied by the slope factor and then the resulting square footage is divided by the coverage of the strapping.

Calculating SoffitThe area of the soffit can be estimated by taking the length of the fascia and multiplying it by the projection:

172.667' × 1.667' = 288 square feet

This is slightly high because we used the outside dimension for length. This number will include a waste factor.

A more accurate method is to take the plate length plus the outside length and divide by two:

(154' + 172.667') ÷ 2 = 163.333'

163.333' × 1.667' = 272.3 square feet


Notes


272.3 + 5% waste = 286 square feet

Using a vinyl or aluminum soffit also requires estimating the length of the F or J channels. An accurate estimate will be plate length plus fascia length:

154' + 173' = 327' of channel

There is very little waste if the strips are handled carefully. These channels often come in 10-foot lengths, so 33 – 10-foot lengths will be required.

It’s not uncommon to use tongue and groove 1×4 for soffit. As with strapping or lumber sheathing, calculate the coverage of a lineal foot of soffit and divide this into the whole soffit area:

One lineal foot of 1×4 covers 3 × 12 = 36 square inches (0.25 square ft.)

286 ÷ 0.25 = 1144 lineal feet of 1×4 T&G soffit

Depending on quality, lengths, and how the corners are installed (mitred corners have more waste than running one side through), waste can be as much as 5%:

1144 × 1.05 = 1201 lineal feet

Bargeboard Calculations for gable RoofsGable roofs have both fascia and bargeboards. The fascia lengths are measured for each side across the rafter tails. Bargeboard material take-offs need to be done for each gable-end.

The length of each bargeboard is the length of the common rafter that it parallels, and includes the overhang length.

Additional length is needed for cutting the roof slope angles at both the top and bottom. The bargeboard needs to cover half the ridge board. The bargeboard often projects past the fascia and sometimes past the ends of the eavestrough (gutter) for a decorative look. Typically, the length required is the length of the common rafter including overhang, plus 2 ft.

Fastener CalculationsThe number of nails or screws required is usually roughly calculated for bidding purposes. In reality, most carpenters stock large quantities of nails and screws. Any leftover goes to the next job.

Tables 9.23.3.4 and 9.23.3.5 of the BC Building Code stipulate the minimum numbers

Notes



of nails needed for each type of application. For example, a 4' × 8' sheet of wall sheathing requires nails every 6" on the edge supports, and every 12" along the intermediate supports. Using these numbers, a minimum of 33 nails are required, but it’s not unusual to use more.

Typically, it takes about 250 pounds (lbs) of nails to frame a 1200 – 1500 sq. ft. house. A more accurate method is to use the total board feet of material to calculate the number of nails needed.

For sheathing, subflooring, and 1× material, the number of pounds of nails needed is found by multiplying the nail length by the board feet and then dividing by 400 (treat each sheet of plywood or OSB as 40 board feet).

For framing 2× material, the number of pounds of nails needed is found by multiplying the nail length by the board feet and then dividing by 600.

For specialty nailing, such as fastening fascias and bargeboards, an unusual length of galvanized casing nails might be needed that won’t be used for the next job. For these situations, a rough count can be done and then the total number can be converted to pounds.

There are many types of nails and the number per pound varies by length, type, gauge, and finish. This information is available online. Table 2 lists some examples:

Type Nail Length number of nails per lb.Hot dip galvanized casing 2" 245

2½" 146

3½" 77

Joist hanger nails (9 gauge) 1¼" 149

1½" 125

Common bright 2" 170

2¼" 140

2½" 105

3" 65

3¼" 60

Table 2. Number of nails per pound

Similar tables are available for the number of screws per pound.




Self Test 3For questions 1 – 11, use the hip roof building as shown in Figure 1.

40'

15'

13'

27'

38'

Figure 1. Building dimensions

The roof projection is 24" beyond the face of the walls. A bearing wall runs centred on the major roof and a 4-ply beam is used to support the ceiling joists between the major and minor roofs. Both the rafters and the ceiling joists are spaced at 24" on centre. The roof projection is 24" beyond the face of the walls. Both the rafters and the ceiling joists are spaced at 24" on centre. The roof slope is 4 in 12.

1. How many ceiling joists are required for the major roof?

2. How many ceiling joists are required for the minor roof?

3. How many stub joists are required for the major roof?



4. How many stub joists are required for the minor roof?

5. How many blocks are needed if two extra blocks are cut for the attic access?

6. What is the total lineal feet of ceiling joist material required? (Use only 2' increments in joist lengths.)

7. How many major common rafters are required?

8. How many hip jacks are required for the minor roof?

9. How many lineal feet of hip rafter materials are needed for the major hips?

10. How many lineal feet of valley rafter material are needed?

11. How long is the major hip rafter? Will it be able to be cut from a board that is readily available?



For questions 12 – 13, use the hip roof building as shown in Figure 2.

40'

15'

13'

27'

38'

Figure 2. Building dimensions

The roof projection is 24" beyond the face of the walls. The slope of the roof is 5 in 12.

12. How many sheets of plywood are needed to cover the roof? (Include a 5% waste factor.)

13. How many lineal feet of 1×8 resawn lumber sheathing are needed to cover the roof? (Include a 5% waste factor.)

14. Why are waste factors approximate?



15. What is an “ice dam”?

16. What is the coverage of 1×4 strapping used for 24" barn shakes spaced at 10" to the weather?

17. Using the board foot formula and Table 2, how many 2" bright common nails are needed for one 4' × 8' sheet of �⁄��" OSB wall sheathing?

british columbia carpenter apprenticeship program joists to tie the ends of the rafters together,...

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