All this is very true, and right as far as it goes, but it so happens
that many workmen do not have the necessary learning to work out these
problems in footing on the lines laid down by W. H., but, in order to
meet conditions of this kind I have prepared a series of tables which is
inserted in the larger volumes, giving the length of rafters for any
building having a width of from five to sixty feet and a rise of roof of
from one to eighteen feet to ridge. This will cover the whole ground,
and form a ready table for the estimator to take his quantities from.
I may be pardoned for again showing the common and simplest method of
laying out an ordinary rafter, for notwithstanding all I have said and
described and explained on this subject, there will always be some
persons who will not be able to grasp the method, unless it is put to
them in some other light. I am sure of this from the long experience I
have had in the answering of questions of this kind through the columns
of different building journals. This is no doubt owing to some
constitutional peculiarities of both the person who makes the inquiry
and the person who attempts to answer it. This is one of the main
reasons why I have admitted into this work various methods and
descriptions of others than myself, so that readers will have the same
methods described and explained to them in several different ways by
several writers.
[Illustration: Fig. 49.]
Let us take the diagrams shown at Fig. 49, which shows a portion of a
roof having a quarter pitch. CEB showing the height, and AB the length
and inclination of rafter. D shows the foot of the rafter on the plate,
cut “flat foot” and the line EC the plumb cut. This is quite plain. The
building may be any width, let us say in this case, that it is 30 feet
wide from A to O. That will make the distance from A to C 15 feet.
[Illustration: Fig. 50.]
A method of obtaining the bevels for this rafter is given in Fig. 50
where the steel square is shown laid on the pattern with the points 16
inches on the blade and 8 inches on the tongue applied to the edge of
the stuff. The line HO on the blade gives the bevel for the foot of the
rafter AC. The line OP, Fig. 50 gives the bevel for the top of the
rafter or the plumb cut, as most workmen call it. Now, there is nothing
in this diagram, which is from Bell’s Carpentry, an excellent work—from
which the workman can get the length of his rafter, without complicating
matters. Had the figures 12 inches and 6 inches on the square been
employed instead of 16 and 8, then the distance across the diagonal from
these two points would have equalled on the rafter, one foot on the base
line or seat of the rafter, so that 15 times that length would have been
the total length of the rafter. Better still, however, would have been
the application of the square 15 times on the edge of the rafter pattern
with the points 12 and 6 on gauge points, then both length and bevels
would have been obtained at one operation.
Of course, the expert workman will often invent, or discover, methods of
using the square in certain phases of roof framing, that can not be
found in books, or that cannot be taught because of the peculiar
circumstances of the particular case. Having a fair knowledge of the
uses of the steel, the workman will seldom be overtaken by difficulties
he cannot overcome if he studies the problems before him and then
employs his knowledge of the square to their solution, as a little
application on this line will remove all possible troubles.
Every carpenter knows, or ought to know, that the run and rise of the
rafter taken on the square will give the seat and plumb cuts, but
inasmuch as buildings are not all of the same width, it requires a
different set of figures for each run, and as it requires an extra
calculation to first find the run of the hip or valley, it is better to
use the full scale for a one-foot run of the common rafter which answers
for any run.
[Illustration: Fig. 51.]
[Illustration: Fig. 52.]
Referring to Fig. 51, we show a square bounded by A, B, C, D, the sides
of which are 12 inches. E is at a point 5 inches from B, and C 12 inches
from B. B-A represents the run of the common rafter. E-A represents the
run of the octagon hip or valley, and C-A the same for the common hip or
valley, their lengths, being 12, 13, and 17 respectively. Now since 12,
13, and 17 are fixed numbers, we take them on the tongue of the square,
as shown in Fig. 52. Now suppose we want to find the lengths and cuts of
the rafters for the ⅜ pitch. We take 9 on the blade. Why? Because the
run being 12 inches, the span must be two times 12, which equals 24, and
since the pitch is reckoned by the span, we find that ⅜ of 24 is 9,
which represents the rise of the foot run. Then 12 and 9 give the seat
and plumb cuts for the common rafter, 13 and 9 for the octagon hip or
valley, and 17 and 9 gives the same for the common hip or valley. In
Fig. 53 I show each separately.
[Illustration: Fig. 53.]
The measurement line of hips and valleys is at a line along the center
of its back, and just where to place the square on the side of the
rafter so as to make the cuts and length come right at that point is a
question that taxes the skill of most carpenters, especially so when the
rafters are so backed. In Fig. 54 I have tried to make the above points
clear.
[Illustration: Fig. 54.]
First, I show the plan of the rafter. The cross lines on same represent
an external corner for the hip and valley respectively. Above the plan
is shown the elevation. The sections 1-2-3-4 represent the position of
the rafters under the following conditions: No. 1 hip when not backed,
No. 2 hip when backed, No. 3 valley when not backed, No. 4 valley when
backed. No. 1 is outlined by heavy lines, and sets lower than the
others. By tracing the bottom line of the sections down to the seat of
No. 1, thence up to the second elevation will show just how deep the
notching should be for each rafter. No. 1 cuts into the right hand
vertical line from the plan, which would make it stand at the right
height above the plate, but in order to make the seat cut clear the
corner of plate, it is necessary to cut into the center line above the
plan. No. 2 cuts into the same points as No. 1, but owing to its being
backed, the seat cut drops accordingly. No. 3 cuts into the center
vertical line, and in order to clear the edges of the plate must cut out
at the sides to the left vertical line. No. 4 cuts in the same as the
latter, but as much lower than No. 3 as No. 2 is below No. 1.
The outer vertical lines from the plan represent the width of the
rafter. Therefore if the rafter be two inches thick, would be one inch
apart, and this amount set off along the seat line (or a line parallel
with it) will give the gauge point on the side of the rafter. To make
this clearer refer to Fig. 53; 17 and 9 gives the cuts. Now leaving the
square rest as it is, measure back from 17 one-half the thickness of the
rafter, and this will be the gauge line point from which to remove the
wood back to the center line of hip, and the measurement from the edge
of the rafter taken vertically down to the gauge point set off on the
plumb cut regulates how far apart the parallel lines of the seat cuts
will be under the above conditions. This rule applies to any roof so
long as the pitches are regular.
Proceed in like manner for the octagon hip, the variation, however, is
practically one-half of the above results for the square cornered
building.
[Illustration: Fig. 55.]
Fig. 55 illustrates side cut of the jack, 12 on the tongue, and 15
(length of the common rafter) on the blade.
[Illustration: Fig. 56.]
Fig. 56 illustrates side cut of the octagon jack, 5 on the tongue and 15
on the blade.
[Illustration: Fig. 57.]
Fig. 57 illustrates the side cut of the hip or valley, 17 on tongue, 19¼
(length of the hip) on the blade giving the cut in each case.
The latter, however, is for the unbacked rafter. If it has been
previously backed, then apply the square with the above figures on the
lower edge at bottom of the plumb cut, or apply the square as for the
jack, Fig. 56, to the backing line, which will give the same result as
17 and 19¼.
It is quite clear that when a workman cuts a common rafter, he is also
cutting a timber that would answer for a hip for a building of less span
having the same rise, only taking some adjustment of the top bevel to
fit against a ridge. This is quite plain, and if we refer to Fig. 58, we
find that the common rafter for a 1-foot run becomes a hip for an
8½-inch run, and that a hip for a 1-foot run of the building becomes a
common rafter for a 17-inch run. Therefore, the rule that applies to the
common rafter also applies to the hip rafter, _i. e._, the run and rise
taken on the square will give the seat and plumb cuts. The run and
length of the rafter taken on the square will give the side cuts, or
taking the scale for a 1-foot run, Fig. 58, it is 12 on the tongue and
the rise on the blade for the common rafter, and 17 on the tongue and
rise on the blade for the hip. The tongue giving the seat cut and the
blade the plumb cut. For the side cuts we take 12 on the tongue and 15⅝
inches on the blade, and the blade will give the side cut of the jack.
Take 17 on the tongue and the length of the hip, 19¾ inches, on the
blade and the blade will give the side cut of the hip. It would also be
the side cut of the corresponding jack if it be a common rafter.
Seventeen is used for a foot run of the hip rafter because the diagonal
of a 12-inch square is practically 17 inches.
[Illustration: Fig. 58.]
If we were to use 12 on the tongue for a foot run of the hip the rise to
the foot would necessarily be less than 10 inches. In Fig. 59 I show
what the difference is in rise to the foot.
[Illustration: Fig. 59.]
From 12 to 12 is the length of the run of the hip would only have 10-17
of an inch to one run of the common rafter, and an equal rise of the
common rafter, set off as at A, and a line from this to 12 on the tongue
passes at 7 1-17 inches on the blade, because the common rafter having a
rise of 10 inches to one foot, for one inch it would have 10-12 of an
inch, while the hip would only have 10-17 of an inch to one inch and for
12 inches it would be 12 times 10-17 equals 120-17, or 7 1-17 inches.
Therefore the figures given in the second illustration would give the
same cuts as those in the first, but as the latter necessitates a
calculation that ends in fractions—fractions not given on the square—and
for that reason 17 is generally used for a foot run for the hips and
valleys.
[Illustration: Fig. 60.]