Residential Structural Design Guide 2000 Edition

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Residential Structural Design Guide


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ERRATA #1:

Residential Structural Design Guide


2000 Edition

July 2000




Replace Example 5.11 with the following:


EXAMPLE 5.11

Hip Rafter

Design







Given







One
-
story building

Hip rafter and roof plan as shown below

Rafters are

2x8 No. 2 Hem
-
Fir at 16 in on center

Loading (see Chapter 3)


Dead

=

10 psf


Snow

=

10 psf


Wind (90 mph, gust)

=

4 psf (inward)



=

10 psf (uplift)


Live (roof)

=

15 psf






















Hip Rafter

Framing and Tributary Load Area







Find

1.

Hip rafter design approach for conventional rafter
-
ceiling joist roof framing.

2.

Hip rafter design approach for cathedral ceiling framing (no cross
-
ties; ridge
beam and hip rafter supported by end
-
bearing supports).

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Solution









1.


Evaluate load combinations applicable to the hip rafter design (see Chapter 3,
Table 3.1)


By inspection, the D + L
r

load combination governs the design. While the wind
uplift is sufficient to create a small upward bending load above the counter
acting
dead load of 0.6 D, it does not exceed the gravity loading condition in effect.
Since the compression edge of the hip rafter is laterally braced in both directions
of strong
-
axis bending (i.e., jack rafters frame into the side and sheathing
provides

additional support to the top), the 0.6 D + W
u

condition can be dismissed
by inspection. Likewise, the D + W inward
-
bending load is considerably smaller
than the gravity load condition. However, wind uplift should be considered in the
design of the hip ra
fter connections; refer to Chapter 7.









2.


Design the hip rafter for a rafter
-
ceiling joist roof construction (conventional
practice).


Use a double 2x10 No. 2 Hem
-
fir hip rafter (i.e., hip rafter is one
-
size larger than
rafters
-

rule of thumb).
The double 2x10 may be lap
-
spliced and vertically braced
at or near mid
-
span; otherwise, a single 2x10 could be used to span continuously.
The lap splice, when used to allow for shorter members, should be about 4 feet in
length and both members face
-
nailed

together with 2
-
10d common nails at 16
inches on center. A vertical brace to framing below (ceiling joists and walls) must
be located at or near to the lap
-
splice. Design is essentially by conventional
practice.


Note: The standard practice above applies
only when the jack rafters are tied to
the ceiling joists to resist outward thrust at the wall resulting from truss

action of
the framing system. The roof sheathing is integral to the structural capacity of the
system; therefore, heavy loads
on the roof before roof sheathing installation
should be avoided, as is common. For lower roof slopes, a structural analysis (see
next step) may be warranted because the “folded
-
plate action” of the roof
sheathing is somewhat diminished at lower slopes. Al
so, it is important to
consider connection of the hip rafter at the ridge. Usually, a standard connection
using toe
-
nails is used, but in high wind or heavy snow load conditions a suitable
connector or strapping should be considered.

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3.







Design the

hip rafter by assuming a cathedral ceiling with bearing at the exterior
wall corner and at a column at the ridge beam intersection


a.

Assume the rafter is simply supported and ignore the negligible effect of
loads on the small overhang with respect to ra
fter design.


b.

Determine the hip rafter loading based on the tributary loads from each
supported jack rafter (see figure above):



Hip rafter horizontal span* =

2
2
)
in
5
.
3
ft
14
(
)
in
5
.
3
ft
14
(





= 19.4 ft




Determine the span, L, of the tributary load (1/2 of the jack rafter span) at
the top of the rafter:



L = 1/2 (13.71 ft)* = 6.86 ft



*The clear span does not include the wall thickness of 3.5 inches.



Determine the uniform lo
ad at the top end of the hip rafter (bottom end is 0
plf):



w = 2L(uniform roof design load) = 2(6.86 ft)(25 psf)


= 343 plf



This load is ‘per linear foot’ as measured perpendicular to the jack raft
敲s=
-
=
no琠p慲慬汥氠瑯=瑨攠h楰=r慦瑥t=wh楣h=楳=慴a慮=慮g汥l of=45=d敧r敥s.=䙯r=敶敲y=
foo琠m敡sur敤=p敲p敮d楣i污l=to=瑨攠j慣k=raf瑥ts,=瑨敲攠is=1.41=f敥t=of=h楰=raf瑥t=
(1=f琯捯s=45

). Convert to a ‘per linear foot of hip rafter basis’ and determine
瑨攠maximu
m=uniform=汯慤=on=瑨攠h楰=r慦瑥t=慴ath攠瑯p=慳⁦o汬ows:
=
=
=
t
max

= 343 plf x
hip
'
41
.
1
'
1
= 243 plf


Alternatively, the loading may be more simply determined by observing that the
hip carries load from one
-
half of the corner area of the roof.



Cor
ner Area = (13.71 ft)(13.71 ft) = 188 ft
2


Horizontal Roof Area Supported by Hip Rafter = 1/2 (188 ft
2
) = 94 ft
2


Total Load, W, on Hip Rafter = (94 ft
2
)(25 psf) = 2,350 lbs




Assuming a triangular uniform load shape,



W = 1/2 w
max




w
max

=

W
2
=
ft
4
.
19
)
lbs
350
,
2
(
2
= 242 plf


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Draw an approximate free body diagram for the hip rafter as follows:



















c.

From beam equations in Appendix A, determine reactions, maximum shear,
and maximum moment on the hip rafter
:



lb
786
6
)
ft
4
.
19
)(
plf
243
(
6
l
w
R
max
1






lb
571
,
1
3
)
ft
4
.
19
)(
plf
243
(
3
l
w
R
max
2









The value of R
2
is appropriate for the determination of connection or
support loads at the end of the hip rafter. For the design of the hip rafter
itself, the load for a distance

equal to the depth of the member from its
bearing may be discounted when evaluating horizontal shear stress (see
NDS

3.4.3).Thus,ford敳楧nof瑨攠h楰r慦瑥tmemb敲(慳aum楮g愠212),
瑨攠maimumdes楧nsh敡r汯慤楳d整敲min敤慳afo汬lws:


†††
)
ft
94
.
0
ft
4
.
19
(
x
ft
4
.
19
plf
243





†††
plf
231
x


(uniform汯慤慴a愠d楳瑡tc攠ofmemb敲d数瑨fromth攠敮d)


†††
lb
348
,
1
)
ft
94
.
0
)(
plf
243
plf
231
(
2
1
lb
571
,
1
V
max






†††
Th攠maimummom敮琠tsd整敲m楮敤慳afo汬lws:


†††
lb
ft
867
,
5
3
9
)
ft
4
.
19
)(
plf
243
(
3
9
w
M
2
2
max
max







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d.

Determine the required b
ending stress value, grade, and species if a
continuous double 2x12 member (no splice) is to be used.



Section Modulus of 2
-
2x12s, S = 63.3 in
3







psi
112
,
1
in
3
.
63
12
lb
ft
867
,
5
S
M
f
3
ft
in
d
'
req
,
b







Set f
b,req’d
=
敱u慬a瑯=c
b
’ and solve for the tabula
瑥t=un慤jus瑥t=b敮d楮g=s瑲敳s=
v慬a攠(乄p

Supp汥men琩慳afo汬lws:


†††
F
b
’ = F
b
(C
D
)(C
r
)(C
F
)(C
L
)




1,112 psi = F
b
(1.0)(1.1*)(1.0)(1.0)



* C
r

= 1.1 is chosen (see Table 5.4)



F
b

= 1,011 psi


This bending stress value would

require the use of two No. 1 & BTR Hem
-
fir 2x12s (F
b

= 1,100 psi) which is not a very economical solution. A No. 1
Grade (F
b

= 975 psi) may be considered “close enough” for practical
purpos敳⸠bven=wi瑨=卯u瑨敲n=m楮攠lumb敲,=a=乯.=2=䑥nse=gr慤攠(c
b

= 1,15
0
psi) is required. Use of an engineered wood member (i.e., laminated veneer
lumber, etc.) may also be considered. The reader is alerted to the fact that
system effects from the sheathed roof assembly and the “folded
-
plate” action
慴a 瑨攠 h楰= 慲攠 no琠 捯ns楤
er敤.= 卵捨= sys瑥m= eff散瑳= may= signif楣in瑬y=
捯n瑲楢u瑥t瑯=瑨e=b敮ding=捡pa捩cy=of=the=h楰=memb敲=and=瑯=汯慤=sh慲ing=in=a=
m慮n敲=d楦f敲敮琠from=th慴a imp汩敤=by=瑨攠fr敥=body=d楡iram=us敤=for=瑨e=
purpos敳e of= 瑨楳= 楬ius瑲慴楯n.= ff= me瑨ods= 數is瑥t= 瑯= 捯ns楤敲
=
瑨敳攠敦f散ts=
慮慬y瑩捡汬y,= 楴i wou汤= b攠poss楢汥l 瑯= produ捥= much= more= 散onom楣慬i 慮d=
慣捵r慴攠d敳楧ns.
=
=
=
=


e.

Check horizontal shear:




f
v

=

A
2
V
3

=

)
in
25
.
11
)(
in
5
.
1
)(
2
(
2
)
lb
384
,
1
(
3

=

62 psi



f
v

<<

F
v
' = (75 psi)(2.0) = 150 psi (based on Hem
-
fir with C
H

= 2.0)


f.

Consider deflection:


Deflection

is considered OK by experience. No method exists to accurately
estimate deflection of a hip rafter that is subject to significant system
stiffness because of the folded
-
plate actio
n of the roof sheathing
diaphragm. The reader may, however, calculate a theoretical value using
the beam equations in Appendix A without the consideration of system
effects that may actually reduce the calculated deflection by 50 percent or
more.







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Conclusion










For the “engineered” solution, 2
-
2x12s=of=乯.=1=䡥e
-
䙩爠ar攠r敱u楲敤,=prov楤楮g=
more than twice the capacity of the “conventional” practice. Since data to
捯ns楤敲=sys瑥m=eff散ts=in=瑨攠d敳楧n=of=愠h楰=r慦瑥t=楳=no琠捵rr敮瑬y=慶慩l
慢汥l=
瑨敲攠 楳= an= unn散敳s慲楬y= 污lg攠 d楳捲数慮cy= b整we敮= th攠 so汵瑩tn= by=
“conventional” practice relative to the “engineered” solution. For traditional
r慦瑥t
-
捥楬楮g=jo楳琠捯ns瑲u捴楯n,=愠s楮g汥lh楰=raf瑥t=on攠or=t睯=s楺敳i污lg敲=th慮=瑨e=
r慦瑥ts=may=b攠
us敤.=t楴i=捥楬楮g=jo楳瑳=or=捲oss
-
瑩ts,=瑨攠r楤g攠memb敲=慮d=h楰=
r慦瑥t= memb敲= n敥d= only= s敲v攠慳a p污瑥s= or= bo慲ds= 瑨慴a prov楤攠愠捯nn散瑩tn=
楮瑥tf慣攬=no琠n散敳s慲楬y=愠beam=suppor琬tfor=th攠r慦瑥ts.=qhus,=in瑥t捯nn散瑩tn=of=
r慦瑥ts=慮d=捲oss
-
瑩敳=慲攠瑨
攠mos琠捲楴楣慬i d敳egn=捯ns楤敲慴楯ns.=䑥f汥捴楯n=was=
no琠捨散k敤=楮=瑨is=數amp汥land=楴Ⱐ瑯o,=楳=s楧nif楣in瑬y=慦fe捴敤=by=瑨攠pr敳en捥=of=
the roof sheathing and the stiffening effect of the “folded
-
plate” action not
捯ns楤敲敤=楮=瑨攠eng楮敥ring=慮慬ys楳
.
=
=
=
=
=
=
=
=
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Replace Figure A.4 of Appendix A with the following:




R
1

= V
1

=
6
L
W
max

R
2

= V
2

=
3
L
W
max

V
x

=
2
max
max
x
L
2
W
6
L
W










M
max

(at x =
3
L
) =
3
9
L
W
2
max

M
x

=
L
6
x
W
max
(L
2
-
x
2
)


max

(at x = 0.52L) = 0.0065
EI
WL
4


x

=
EIL
360
x
W
max

[3x
4
-
10x
2
L
2
+7L
4
]

Figure A.4
-

Simple Beam
-

Load Increasing Uniformly to One End