On The Job Mathematics For Floor Framing

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Nov 25, 2013 (3 years and 8 months ago)

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On The Job Mathematics

For Floor 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 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
-
wor
k
close to problem you are working on, save it, do not erase, this will help if you need to make corrections later.
All work will need to be 100% correct before you will be given credit for this math unit.


When constructing the floor frame of a typical
ranch style
house one of the first things you need to do is construct the
beam (called a girder) that runs down the center of the
basement. If the beam is 56' long and is made up of 3 layers of
2"x10" boards
,

how many L.F. of boards will you need to buy
f
or the beam? Note: Round your answer up to the next full
foot.


_________ L.F. of 2"x10"









If you order16' long boards for the girder in the problem above, how many boards will you need to order? Note:
Round your answer up to the next full
-
length b
oard.


_________ Number of 2"x10"x16'








Sometimes the house plans
specify

a single steel I
-
beam girder to be used. If you use a steel I
-
beam for the
girder above and it weighs 18
L
bs. per L.F. how much will the 56' long girder weigh? Note: Round you
r answer
up to the next full
L
b.


_________ Lbs.

2"x10"
Girder

2

Columns (commonly adjustable steel posts) are placed under the girder to support it. In the house drawing
below
,

fill in the missing dimensions
A
and

B.
Note: t
he 3 columns are evenly spaced, and centered
.
Measurements are from inside the 8" thick basement walls to the centers of the columns.


A. = _____'
-

_____"




B. = _____'
-

_____"




















After the girder is in place, the next step is to bolt
down the sill plate. The sill plate (a 2
" x 6" board)
goes around the entire top perimeter of your basement
walls. How many L.F. of sill plate will you need for
these houses? Note: The sill does not overlap at
corners but estimate L.F. of sill as though they did.


26' wide by 40' long
-


L.F
. of 2"x6" = _______










24' wide by 36' long
-


L.F. of 2"x6" = _______


28' wide by 48' long
-


L.F. of 2"x6" = _______


26' wide by 56' long
-


L.F. of 2"x6" = _______





House Foundation Plan
4"
Columns
26'
8"
38'8
8"
40'
A.
A
.
A
.
A
.
B.
B.
Basement
Wall
Anchor
Bolts
Sill
Plate

3

When ordering the sill plate boards from the lumber company you

find out they only have 12' lengths in stock. How many boards
will you need to buy for sill plates for the houses in the previous
problem? Note: Round up your answer to the next full board.



26' wide by 40' long
-

Number of 2"x6" = ______









24'

wide by 36' long
-

Number of 2"x6" = ______


28' wide by 48' long
-

Number of 2"x6" = ______


26' wide by 56' long
-

Number of 2"x6" = ______



















To install the sill plate you need to drill holes through it
for the anchor bolts. If the anchor

bolts are located in
the center of the sill plate, how far in from the edge of
the 2"x6" will you need to drill the holes?

Note: A 2"x6" is actually 5 ½" wide.


________" from the edge














2"x6"x12'
Anchor
Bolt
Hole
5 1/2"
?

4

After you drill holes for the anchor bolts and check

for fit, you place sill sealer under the sill. If the sill sealer
comes in 25' rolls, how many rolls will you need for each of these houses? You can use the L.F. figures already
determined in a previous problem. Note: Round your answers up to the next
full roll.


26' wide by 40' long
-

Number of rolls = ______









24' wide by 36' long
-

Number of rolls = ______


28' wide by 48' long
-

Number of rolls = ______


26' wide by 56' long
-

Number of rolls = ______











Floor joists are framing members
that carry the load of the floor between the sill and girder. They are usually
laid out 12", 16", or 24" O.C. To determine how many joists you need for a 16" O.C. layout, simply multiply
the length of the house by 3/4 and add one for the end joist. For

a 16” O.C. layout, how many floor joists will
you need for half of the house shown below?

For a 16” O.C. layout, how many floor joists will you need for the whole floor?


________ Number of Joists for half of the floor


________ Number of Joists for
the whole floor





















40’
Girder
Joists
16” O.C.
Header
Joist

5

Using the drawing in the previous problem, how many joists are needed for a floor layout of 24" O.C. and then
for 12" O.C.?


________ Number of Joists for half of the floor 24" O.C.


________ Number of Joists for the

whole floor 24" O.C.





________ Number of Joists for half of the floor 12" O.C.


________ Number of Joists for the whole floor 12" O.C.






Header joists are nailed to the ends of floor joists. They keep the
floor joists in a vertical position.
How many 16' long boards will
you need to buy for the header joists in the previous problem?
Add 10% for waste and round up your answer to the next full
-
length board.


________ Number of boards for Header Joists










When laying out floor joists o
n the header you can't just mark
the centers. If you did, the floor joists would cover up the
mark and you couldn't be sure of the correct placement. You
need to mark lines for the edges of the joists. If the joists are
1 ½" thick, what is half the jois
t thickness?

This is the
measurement from the center of the joist to the edge of the
joist.


________" = half of the joist thickness








Floor Joists
Header
Joist

6



Some construction jobs call for rough sawn lumber and it is somewhat thicker than surfaced lumber. A deck
you
are making specifies joists that are made of rough sawn 1 7/8" thick lumber, how far from center should you
mark to locate the joist edge?


________" Back from center











When floor joists are in place and a normal load is on the
floor the joists
will deflect (bend down at the center). The
deflection should not be more than 1/360th of the joist
span. How much allowable deflection would there be for a
joist spanning 16 feet? Note: Round answer off to the
closest 1/16"


________" Deflection














When nailing a 1 ½" thick header joist to the floor joists, how far will the 3 ¼ " nail penetrate into the floor
joist?


________"










Floor Joists
Header Joist
Nail
Joist
Deflection

7

Sometimes to give a basement more headroom, the girder is
raised up and the floor joists are butte
d to it (shown at right).
Joist hangers are then commonly used to attach the floor joists to
the side of the girder. How many joist hangers are needed for the
floor system if the girder is 56' long and the joists are laid out 16"
O.C.? For 24" O.C.?

For 12" O.C.?

Note: No hangers are needed for end joists resting on sill plate.



_______ Number of Hangers for 16" O.C.


_______ Number of Hangers for 24" O.C.


_______ Number of Hangers for 12" O.C.














If it takes five 16d nails to a
ttach the 2"x12" joist header to each joist, how many nails are needed to nail the
header to 62 joists?


_______ Number of Nails Needed








If there are 49 nails per Lb., how many pounds of nails are needed for the problem above? Add 5% for waste.

N
ote: Round answers up to the next half pound.


______ Lbs. Needed


______ Lbs. Needed For Waste


______ Total Lbs. Needed







8

To pull two joists tightly together we nail a few nails
straight through them. The nails are then clinched over
on the
back and the remaining nails are driven in at an
angle so they'll not protrude out the backside. If we use a

3 ¼" long nail driven straight through, how much of the
nail will stick out on the backside?

Note: The joists are each 1 ½" thick.



_____
___" Sticking Out the Back Side

















When constructing a stair opening,
double headers are cut and nailed to
the trimmer and tail joists as shown in
the picture. If the R.O. (rough
opening) for the stair width is 37"
what is the total L.F.
of all cut header
boards added together?

Note: Remember each header is made
of two boards.


_______'
-

______"








2"x10"
Joists
3 1/4” Nail
1 1/2”

9

This house measures 26' wide from outside

of joist header to outside of other joist
header. If the girder is 4 ½" thick (it is
centere
d in the house) and the joist
headers are 1 ½" thick, what is the length
of the floor joists?


Joist length =______'
-

______"

















Using the joist length determined in the previous problem, figure the length for the tail joist dimension
A.

in the
drawing on the final page of this math unit?

Note: Headers are made up of two 1 ½" thick boards.


Tail Joists Length
A.

=______'
-

______"









If the house plans on the final page show 21'
-
3" from the end of the house to the center of the
floor opening,
what is the distance from the center of the opening to the inside edge of the trimmer joist, dimension
B.
?


Dimension

B.
=______'
-

______"









26'


10

Most building codes require bridging installed in the floor system. Bridging runs perpendic
ular to the joists and
transfers the load from one joist to another, thus stiffening the floor system. If your house plans specify bridging

placed down the center of the joists, what is dimension
C.

shown in the drawing on the final page of this math
unit
? Note: Dimension
C.

is from the outside edge of the 1 ½" thick joist header.


Dimension

C.
=______'
-

______"







Most carpenters estimate the 1"x3" wood needed for bridging by multiplying the total length of each double run

of cross bridging by 3. Ho
w many L.F. of 1"x3" are needed for the house on the final page? Note: Do not
deduct for floor opening.


L.F. of 1"x3" = _______








If the 1"x3" came in 8' lengths how many lengths would you need to buy?


Number of 1"x3"x8' = ________








8d na
ils are commonly used to secure 1"x3" cross bridging. If it takes one pound of 8d nails to install 12 sets of
cross bridging, how many Lbs. of 8d nails will it take to install bridging for the house on the final page?

Note: Figure the joists 16" O.C.


________ Lbs. of 8d nails needed








11

If it takes one hour to install 10 sets of cross bridging, how many hours will it take to install the cross bridging
for the house on the final page?


________ Hours of labor



Sub
-
flooring is appli
ed over the joist system and is
nailed or screwed in place. There are many different
types of subflooring, but most come in 4'x8' size sheets.
In the drawing on the final page you see the 1
st

row of
plywood starting to be laid. How many sheets will it
t
ake for the 1
st

row? Note: The 8' length of the plywood
is laid perpendicular to the floor joists.


Number of 4'x8'sheets for 1
st

row = _______






The joints are staggered when laying subfloor as seen in the 2
nd

row of subflooring in the drawing on

the final
page. How many full and half sheets will the 2
nd

row of subfloor have in the plan shown on the final page?


Number of full sheets for 2nd row = _______






Number of half sheets for 2nd row = _______



How many 4'x8' sheets of subfloor will yo
u need to buy for the entire house shown on the final page?

Note: Round up your answer to the next full sheet.


Number of 4'x8'sheets = ______




How many 4'x8' sheets will you need to buy for the subfloor in the following houses?

Note: Round up your
answer to the next full sheet.


28' wide by 42' long house
-

_______4'x8'sheets


24' wide by 36' long house
-

_______4'x8'sheets


28' wide by 48' long house
-

_______4'x8'sheets


26' wide by 56' long house
-

_______4'x8'sheets

12

For 3/4" plywood s
ubfloor, some contractors use 2" long #8 square head screws 8" O.C. along the edges and in
the field. Using this screw pattern it takes about 42 screws to lay one sheet (joists 16" O.C.). If there are about
145 screws per Lb., how many Lbs. of screws wil
l you need to lay the subfloor for the house on the final page?
Note: Round up your answer to the next full Lb.


________ Lbs. of screws needed







If you use 8d nails as fasteners for the subfloor and if it takes about 20 Lbs. per 1000 Sq.

Ft. of subflooring, how
many Lbs. of 8d nails would be needed for the houses below? Note: Round up your answers to the next full Lb.


26' wide by 40' long
-

Lb. of nails = ______


24' wide by 36' long
-

Lb. of nails = ______


28' wide by 48' long
-


Lb. of nails = ______


26' wide by 56' long
-

Lb. of nails = ______











If it takes about 12 ½ labor hours to install a 1000 Sq. Ft. of subflooring, estimate how many labor hours it will
take to install the sub
-
floor for the houses below? Note: R
ound your answer off to the closest ¼ hour.


26' wide by 40' long = _________ Labor hours


24' wide by 36' long = _________ Labor hours


28' wide by 48' long = _________ Labor hours


26' wide by 56' long = _________ Labor hours











13


Note: Drawing is not to scale.