On The Job Mathematics
For Roof Framing
By Steven W. Anderson
AM or PM Class
Name:__________________________
School:____________ Grade:_____
Date Started:_________ Age:_____
Directions: Read each of the problems carefully and answer them in order. Refer to the pictures and
Reference Guide as needed for extra help working out the problems. Do your own work and don't distract other
students from their work by asking them questions. For additional help ask your teacher. Write down all
scratch-work close to problem you are working on, save it, do not erase, as this will help if you need to make
corrections later. All work will need to be 100% correct before you will receive credit for this math unit.
After the wall framing is complete, next comes roof framing.
First, on top of the walls, you need to layout where roof
framing members are located. These are laid out similar to
floor joists and wall studs. The roof framing members may
be rafters or trusses, both are laid out in similar fashion. To
layout 16" O.C., simply start from the outside edge of the
house (the first rafter will be placed here) and measure in
16" to the center of the second rafter, 32" for the third rafter,
48" for the forth rafter, and so on. As you mark each center,
measure back from the center half the rafter thickness and
mark rafter edge. (See drawing)
If you continue the 16" O.C. layout, fill-in the following
answers.
The measurement from the outside edge of the house to the center of the fifth rafter is ________".
If the rafter is 1 ½" thick, half of the rafter thickness is _________".
With 1 ½" rafter thickness, the distance from the outside edge of the house to the edges of the fifth rafter
is_________" and _________"
The measurement from the outside edge of house to the edges of the sixth rafter is _________" and _________"
What is the distance from the outside edge of the house to the center of the 2nd through the 5th rafters if the rafter
layout is 24" O.C.?
2nd
__________"
3rd
__________"
4th
__________"
5st
__________"
2
To determine the number of roof framing members you need for your house (similar formulas used for floor
and wall framing), multiply the roof length times ¾ for 16" O.C. or ½ for 24 O.C. then add one more member
for the end. How many 16" O.C. roof framing members will be laid out on the red wall in the drawing below?
Number of roof-framing members needed for 16" O.C. layout = __________
How many roof-framing members will you need for a 24" O.C. layout?
Number of roof-framing members needed for 24" O.C. layout = __________
42’
3
If the roof framing members are trusses (shown at right), how many roof
trusses will you need for the house shown at the bottom of this page?
Number of roof trusses needed for 16" O.C. layout = __________
Number of trusses needed for 24" O.C. layout = __________
If the roof framing members for the house below are rafters (shown at
left), how many will you need for the whole house?
Number of roof rafters needed for 16" O.C. layout = __________
Number of rafters needed for 24" O.C. layout = __________
4
Because you buy large quantities, your lumber company gives you a 10% discount on your purchases. If the
24" O.C. trusses on Page 3 cost $43.50 each, and you have to pay 6% sales tax, how much will the trusses cost?
Note: Add sales tax after you figure the discount.
Cost for trusses
= $ ________
Amount of Discount = $ ________
Amount of tax
= $ ________
Total costs for trusses = $ ________
If each 16" O.C. rafter on Page 3 cost $12.35, and you get a 10% discount, and you pay 6% sales tax, what will
be the total cost for all the rafters needed to frame the roof? Note: Add sales tax after you figure the discount.
Cost for Rafter
= $ ________
Amount of Discount
= $ ________
Amount of tax
= $ ________
Total costs for Rafters = $ ________
5
There are a number of different ways to estimate the length of common roof rafters. One way is to think of a
roof section as a triangle (see drawing at bottom of this page), then use the Pythagorean Theorem as shown.
Rafter Length =
Run
2
+
Rise
2
Estimate the length of the common rafters for the houses listed below. Note: Round off answer to nearest 1/4".
Run = 12'
Rise = 4'
Rafter Length = ______' - ______"
Run = 16'
Rise = 9'
Rafter Length = ______' - _______"
6
In the same way we estimate the length of a rafter, we can also estimate the top chord length of a roof truss
(see drawing at bottom of this page).
Top Chord Length =
Run
2
+ Rise
2
Estimate the length of the top chords for the houses with the roof trusses listed below:
Note: Round answer off to the nearest 1/8".
Run = 13'
Rise = 5'
Top Chord Length = ______' - ______"
Run = 15'
Rise = 7'- 6"
Top Chord Length = ______' - _______"
7
The people who manufacture the framing square have made it easier for you to estimate rafter and top chord
lengths. Stamped on the blade of the framing square is a table that can aid you in this work (see partial picture
of the framing square below). Simply select the number in the first row that is under the number for the roof
slope. Multiply this number times the run of the roof will give you the length of rafter or top chord in inches.
Example A:
A slope of 9" rise per ft. run has a 15 multiplier.
Multiplying 15 times the Run will equal the Common Rafter Length.
Example B:
A slope of 8" rise per ft. run has a 14.42 multiplier.
Multiplying 14.42 time the Run will equal the Common Rafter Length.
Using the table on the framing square above (or ask your teacher if you may get a framing square from the tool
crib), estimate the length of the common rafters below. Note: Round off answers to the nearest 1/16".
Run = 13'
Slope = 4" rise/ per Ft. run
Rafter Length = ______' - ______"
Run = 15'
Slope = 5" rise/ per Ft. run
Rafter Length = ______' - _______"
8
Using the same framing square table as you used to figure the length of the common rafters in the previous
problems, estimate the top chord length of the trusses below. Note: Include the over hang as part of the run and
then round answers off to nearest 1/4".
Top chord Length = ______' - ______"
Top chord Length = ______' – _______"
Top chord Length = ______' - _____"
9
Determining the length of hip rafters (see
drawing at right) is similar to common rafters,
except you use the multiplier in the 2nd row on
the framing square table. Using the table on the
framing square, determine the hip rafter lengths
below. Note: Round answers off to nearest 1/8".
Run = 13'
Slope = 4" rise/ per Ft. run
Hip Rafter Length = ______' - _______"
Run = 15'
Slope = 5" rise/ per Ft. run
Hip Rafter Length = ______' - __________"
Run = 16'
Slope = 6" rise/ per Ft. run
Hip Rafter Length = ______' - ___________"
10
On some construction projects you may want to build your own trusses. Below is a common layout for Fink
trusses. What are the measurements for the following site-made trusses?
Truss span of 12' –6"
1/3 span = ______' -_________"
1/4 span = ______' -_________"
Truss span of 14' -9"
Note: Round answer off to nearest 1/4".
1/3 span = ______' -_________"
1/4 span = ______' -_________"
Truss span of 18' – 4"
Note: Round answer off to nearest 1/16".
1/3 span = ______' -_______"
1/4 span = ______' -________"
11
Roof sheathing is attached to the roof framing members and gives a base to nail shingles. Determine the
number of Sq. Ft. of sheathing needed for the following houses with gable roofs. Note: Use rafter square tables
to calculate roof rafter length when needed (round rafter length off to nearest 1/8") and round up sheathing to
the next full Sq. Ft.
Sq. Ft. of sheathing needed = _________
Sq. Ft. of sheathing needed = _________
Sq. Ft. of sheathing needed = ________
12
After determining the Sq. Ft. of sheathing needed for the houses on Page 11, add 10% for waste and
determine how many 4'x8' sheets you will need to buy for each house. Note: Round answers up to the next full
unit.
House A.
Amount for waste = __________Sq. Ft.
Total Sq. Ft. =___________
4'x8' Sheets =___________
House B.
Amount for waste = __________Sq. Ft.
Total Sq. Ft. =___________
4'x8' Sheets =___________
House C.
Amount for waste = __________Sq. Ft.
Total Sq. Ft. =___________
4'x8' Sheets =___________
13
If the sheathing costs $10.35 per 4'x8' sheet, and you get a 10% contractors discount, and pay 6% tax, how
much will the sheathing cost for houses A., B. and C. on Page 11?
House A.
Cost of sheathing
= $________
Amount of Discount = $________
Amount of tax
= $_________
Total Cost
= $________
House B.
Cost of sheathing
= $________
Amount of Discount = $_________
Amount of tax
= $_________
Total Cost
= $_________
House C.
Cost of sheathing
= $_________
Amount of Discount
= $_________
Amount of tax
= $_________
Total Cost
= $_________
14
If when applying roof sheathing you use 8d nails (2 ½" long), how deep will they penetrate into the roof
framing member using the following sheathing?
7/16" Sheathing ___________"
1/2" Sheathing ____________"
5/8" Sheathing ____________"
3/4" Sheathing ____________"
If you apply 42 nails per sheet of roof sheathing, and there are 145 nails per Lb., how many Lbs. of nails are
needed to install sheathing on houses A., B. and C. on Page 11? Note: Round up answers to the next full Lb.
House A
LBS. of nails
= _________
House B
LBS. of nails
= _________
House C
LBS. of nails
= ________