Sample
Rafters
■
Chapter 6
65
■
EXAMPLE 6.5
The common rafters on a hip roof have a pitch of 9
⬙
, and a run of 16
⬘
-4
⬙
.
Find the lengths, plumb cuts, and level cuts for the common rafters and hip
rafters, as well as the cheek angle for the hip rafters.
Solution:
KEYSTROKE
DISPLAY
For the common rafters, use the same key sequence demonstrated in our
previous examples:
9 i p
PTCH 9 INCH
1 6 f 4 i R
RUN 16 FEET 4 INCH
d
DIAG 20 FEET 5 INCH
d
PLMB 36.87°
d
LEVL 53.13°
Corresponding values for the hip rafter are obtained by successively press-
ing the
H
key:
H
H/V 26 FEET 1-3/4 INCH
H
PLMB 27.94°
H
LEVL 62.06°
H
CHK 1 45.00°
In the preceding example, notice that the plumb cut for the hip rafter
is significantly different from that of the common rafter. This phenomenon
seems to violate all rules of common sense, and is one which perplexes
many builders. (This is especially true if the common rafters are cut at an
angle of 45°!) Using our definition of pitch, however, it is fairly easy to see
why the hip rafter’s plumb cut angle is always
less than
the plumb cut an-
gle for its adjoining common rafters.
Figure 6-5
shows a typical corner for a regular roof, where the com-
mon rafters have a run of Rc and both the common and hip rafters have an
identical rise, Ri. Triangle A-B-C in the horizontal plane is a 45° right tri-
angle having two sides of length Rc as shown in
Figure 6-6(a).
Side length
“d” opposite the right angle, then, is greater than Rc; in fact, it may be
shown using trigonometry that this side has a length of d
⫽
1.414
⫻
Rc.
Figure 6-6(b)
and
(c)
show the pitch triangles for the hip and common
rafters respectively. The hip’s pitch angle (and therefore its plumb cut an-
gle) is Ph
⫽
Ri / 1.414 Rc, while that of the common rafter is Pc
⫽
Ri / Rc.
Since the hip rafter has the same rise but a longer run than the common
rafter, its pitch will always be less than that of its adjacent common rafters.
The framing members required to make the hip-plate and valley-ridge
connections have varying lengths as shown for the hip rafter in
Figure 6-7.
Notes
Copyright © 2007 by Calculated Industries, Inc.
and Thomson Delmar Learning
Construction Master® Pro Workbook and Study Guide
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