Publisher’s version / Version de l'éditeur:
Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.
Questions? Contact the NRC Publications Archive team at
PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.
https://publications-cnrc.canada.ca/fra/droits
L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.
Building Research Note, 1976-01
READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE. https://nrc-publications.canada.ca/eng/copyright
NRC Publications Archive Record / Notice des Archives des publications du CNRC :
https://nrc-publications.canada.ca/eng/view/object/?id=d99325b8-d701-4109-a519-a1f99cf5759d https://publications-cnrc.canada.ca/fra/voir/objet/?id=d99325b8-d701-4109-a519-a1f99cf5759d
NRC Publications Archive
Archives des publications du CNRC
This publication could be one of several versions: author’s original, accepted manuscript or the publisher’s version. / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur.
For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.
https://doi.org/10.4224/40000602
Access and use of this website and the material on it are subject to the Terms and Conditions set forth at
Upward deflection of wood trusses in winter
UPWARD DEFLECTION
OF WOOD TRUSSES IN
WINTERby W.G. Plehres
Within the last year the Division has received many
reports o f wooden r o o f trusses d e f l e c t i n g upwards in the winter.
This is c o n t r a r y t o t h e normal expectation that i f any s i g n i f i c a n t d e f l e c t i o n d i d occur it would b e downward because o f dead and live
l o a d s . In the r e p o r t e d cases deflection e f f e c t became n o t i c e a b l e
when l a r g e cracks opened between the ceiling and partitions which
c o u l d n o t be explained through foundation or partition settlement. It w a s suspected t h a t moisture c o n t r i b u t e d to t h e problem
and DBR was asked f o r an o p i n i o n . Probing calculations were made
which i n d i c a t e d t h a t under some c o n d i t i o n s ,
and
certainly f o r thecases reported, seasonal changes
i n
the moisture- temperature regimec o u l d cause an upward movement. VART AB LES
A f u l l y developed laboratory and f i e l d research project
i n t o t h i s phenomenon would r e q u i r e several seasons. Variables
t h a t would have to be explored would be :
I i 3
(ii] [iii) (iv3 Cv3 Ivi3(vii)
(vi
i i) I i x ) (XI
(xi3
span of trusses size o f members types of truss amountof
i n s u l a t i o ntype
of
joint connectionslocal outdoor environment
moisture c o n t e n t
of
wood when i n s t a l l e dventilation of a t t i c
effectiveness of vapour b a r r i e r
k i n d o f wood
snow loads on roofs
In t h e p r e s e n t study t h e f i r s t s i x variables were f i x e d
by selecting two s p e c i f i c designs from
those
parts o f t h e c o u n t r yin
which
the problem occurred. The remainder of the f a c t o r s were i n v e s t i g a t e d to a Limited e x t e n t by estimating a seasonable rangeTYPES OF ROOFS
INVESTIGATED
Two t y p e s
OE
r o o f s were i n v e s t i g a t e d : mobile home roofin
theL e t h b r i d g e area; and metal gusset p l a t e Hawe truss roof on a house
in t h e hiontreal area.
MOB1 LE HOME ROOF
D e s c r i p t i o n o f Roof
The shape, span and timber member sizes of the mobile
home rsaf as well as the i n s u l a t i o n are shown in F i g u r e 1. I t s
shape and construction is t h a t of a tied arch. Because of the
"foamcore" i n s u l a t i o n over the top chord it was assumed t h a t t h e
metal r o o f i n g is not a t t a c h e d r i g i d l y enough to participate in t h e arch a c t i o n .
Arch Deflection Formula
The complete derivation of formulae for moisture and t h e r m a l deflections o f a tied arch are l e n g t h y (1). For the g i v e n configuration and dimensions however they reduce t o t h e following simple expression :
y = 1032 [at + As]
where
y = the d e f l e c t i o n ( n e g a t i v e when downwards) a = the c o e f f i c i e n t
of
thermal expansiont = the difference between t h e t o p c h o r d temperature
and t h e bottom chord temperature (negative f o r temperature decrease)
A s = movement
o f
t o p chord r e l a t i v e to movement o f bottom chard due to moisture change (negative f o r shrinkage)hr;surnptions and R e s u l t s of C a l c u l a t i o ~ l s
Bccausc t h e real t h e r m a l - n ~ o i s t u r c c o n d i t i o n s within t h e roof space arc in general unknown, calculations were made f o r
Calculation A
It was first assumed t h a t the rcof space had encugh
ventilation to allow the thermal-moisture c o n d i t i o n s of t h e a i r and timber arch members to come into equilibrium w i t h o u t d o o r conditions
D a i l y f l u c t u a t i o n s were ignored s i n c e the wood moisture content
would depend on changes in the daily average temperature and r e l a - t i v e h u m i d i t y over periods of weeks or months.
P u b l i s h e d research r e s u l t s (2,3] i n d i c a t e that i n
December, January, and February both the moisture c o n t e n t o f wood
and t h e relative humidity in a l o c a t i o n exposed to outdoor tempera- t u r e s , b u t n o t to r a i n and snow, t e n d to remain f a i r l y c o n s t a n t .
D u r i n g the S p r i n g months they d r o p b u t become s t a b l e again at a
lower v a l u e during June, July and A u g u s t . In t h i s i n v e s t i g a t i o n , therefore, the o u t d o o r mean temperatures and r e l a t i v e h m i d i ty f o r J a n u a ~ y and July were used
in
t h e c a l c u l a t i o n s . I f t h e upwardd e f l e c t i o n of roofs is due to thermal-moisture movements a l o t
would depend
on
thetime of
year of construction but t h e f o r e g o i n gassumptions were expected to predict t h e maximum p o t e n t i a l range
of
possiblemovements.
From
climatolagical records (4) the following weather data was obtained f o r Lethbridge:Mean January
Temperature
-
14.5"FMean January R/H
-
71%Mean July Temperature - 65°F
Mean J u l y R/H
-
50%F u r t h e r assumptions had t o be made regarding the
a i r
temperature in t h e roof space because it is, in general, unknown. In winter the mean temperature was taken to be 0, 5, 10 or 20F
d c ~ r e e s above t h e mean o u t s i d e temperature; in summer, 0, 20 or 40F degrees.
Values for the relation between relative h u m i d i t y and
wood moisture content which
arc
p r o b a b l y averagc for t h e common species were taken from previously p u b l i s h e d data (5,6).
Moisture c o n t e n t v s shrinkage r e l a t i o n s were a l s o taken ( 7 ) . Shrinkageparallel to the
grain from
f i b r es a t u r a t i o n
to oven dry was takena s 0.2 per cent C8).
As the bottom chords of the trusses are i n s u l a t e d on
b o t h s i d e s , the mean temperature of the truss chord was estimated on the basis of a one-dimensional heat flow assumption. The
tcniperature of t h e t o p chord was t a k e n to be t h e same as that
of t h e air space because of t h e i n s u l a t i o n between it and t h e metal
roofing.
In this calculation it was a l s o assumed t h a t the vapous b a r r i e r in t h e ceiling was p e r f e c t and t h e i n t e r i o r temperature
7 2 O F .
The r e s u l t s of the calculations are shown in Figure 2 .
The predicted upward d e f l e c t i o n was found to be due to the h i g h e r moisture c o n t e n t of t h e t o p chord r e l a t i v e to t h e bottom one and
its variation w i t h seasonal temperatures and r e l a t i v e h u m i d i t y . Calculated deflections caused by temperature changes and t h e
c o e f f i c i e n t o f e xpansim were relatively m i n o r and in the o p p o s i t e
d i r e c t i o n b u t were i n c l u d e d in t h e analysis. The maximum deflec- t i o n o b t a i n e d was about 3 J 4
in.
reached when t h e roof spacetemperature was the same as outdoors. For an a t t i c temperature o f 34 -5°F (10" above outdoors) t h e c a l c u l a t e d deflection was about
75 p e r c e n t lower.
In
general, d e f l e c t i o n s are more s e n s i t i v e t o uintcr temperature assumptions than to summer attic spacetemperatures.
The r e p o r t e d d e f l e c t i o n
i n
t h e mobile home was 1 L J 2in.
or about twice t h a t calculated under the foregoing assmptians.
This may b e due to some sort o f r a t c h e t i n g action between the
trusses and the p a r t i t i o n s w i t h the trusses r i d i n g up on the
partition installation screws. It i s more l i k e l y , however, t h a t
t h e assumptions for t h e calculations were wrong.
Calculation B
As a second t r i a l it w a s assumed t h a t t h e r o o f space was
completely sealed and t h a t the wood was i n s t a l led a t a moisture
conrent of 10 per cent. With an assumed w i n t e r attic temperature
n f 2 0 O ~ and a hortom c h o r d temperature of 4 2 ' ~ , zhe r e d i s t r i b u t i o n
o f m o i s t u r c bctwcen the lower and upper chords [equalization o f
v:q>our pressures) was i n v e s t i g a t e d along w i t h an estimate of t h e
:~ccompany i n g d e f l e c t i o n s .
Por t h i s calculation it was necessary
t o
assume a linear r e l a t i o n s h i p between r e l a t i v e h u m i d i t y and wood moisture c o n t e n t .Prom i n s p e c t i o n of graphs by HedPin (63 it was taken t h a t f o r relative h u m i d i t i e s above 10 p e r cent:
m o i s t u r e content (%) =
K
(W) + 3Althongh the assumptions nere rather crude, it was found
that upward deflections of o n l y about 1 / 2 in. could be accounted
f o r by t h i s mechanism.
Calculation C
A f u r t h e r assumption to be explared w a s t h a t s m a l l brcaks or leaks
in
the c e i l i n g vapour b a r r i e r permit moisture-laden airi n t o t h e roof space which would increase the moisture content o f
the wood. This would be a f a i r l y continuous process and might
r e s u l t
i n
f r e e water or hoar f r o s t on some members. Such a situa- t i o n isnot
amenable to calculation but to explore t h e possibilitiest h e following procedure was adopted.
It was assumed t h a t enough moisture entered t h e space to
raise the
RI-3
at the top chordt o
100 per cent and the moisturecontent to the f i b r e saturation p o i n t . The system was then assumed
sealed and t h e t o p and bottom chords allowed so come to moisture
equilibrium.
On t h i s b a s i s , upward truss d e f l e c t i o n s of 1.1 to 1.4 in. were p r e d i c t e d dependidg on w h e t h e r f i b r e saturation was t a k e n as
30 or 24 p e r c e n t moisture c o n t e n t respectiveIy, This is approxi-
mately equal to t h e reported d e f l e c t i o n s .
Conclusions re Mobile Home Roofs
The calculations made are speculative and dependent on t h e assumptions made. It seems a reasonable conclusion, however, t h a t the upward deflection of the mobile
home
roofs can beaccounted EOT by moisture considerations caused p r i m a r i l y by
differences in temperature between the t a p and bottom chords. There is every possibility a l s o t h a t moisture e n t e r i n g the r o o f
space from the i n t e r i o r contributes to t h e problem.
Deflection is controlled mainly by the movements of the t o p chord and there seems to be
no
possibility o f holding the r o o fdown by screwing or nailing it onto the p a r t i t i o n s . The forces
r e q u i r e d would exceed the roof design Load by a f a c t o r
of
fouro r
more.
A solution to the problem would r e q u i r e an extensive research project to d e t e r m i n e the actual conditions and to e x p l o r e
the mechanismr; f u r t h e r . Onc s c t
of
msisture
content measurements t a k c nin
March i n a n occupied mobilehome,
for example, gaveT h i s is t h e reverse o f what was p r e d i c t e d herein f o r January.
It seems l i k e l y t h a t the s o l u t i o n to t h e problem lies in
keeping the temperatures and m o i s t u r e contents of the upper and lower chords approximately equal. One way of a c h i e v i n g this m i g h t he t o suspend the i n s u l a t i o n below the bottom c h o r d , b u t t h i s may
not be practicaI.
RESI DENTIhL METAL GUSSET PLATE TRUSS
The second roof i n v e s t i g a t e d incorporated I-lowe trusses
2 7 ft 8 in. in span having a 5 : 12 s l o p e . Members were 2 by 4'5 and the j o i n t s were made w i t h metal p l a t e connectors o f unknown d e s i g n . The ceiling of rhe house had 6 in. of insulation assumed
to be rockwool installed so t h a t t h e lower chords of t h e trusses
were completely buried (Figure 3 ) .
It was reported that rhe c e i l i n g o f t h i s house and o t h e r
similar ones d e f l e c t e d upward 1/4 t o 1 / 2
in.
in w i n t e r . This became evident as cracks appeared at the junction of t h e ceilingand partition w a l l s , cracks which could not be e x p l a i n e d by settlements.
Calculation Assumntions
Tn o r d e r t o study the possibility of t e m p e r a t u r e and m o i s t u r e being responsible for t h e deflections it was necessary
to make t h e following assumptions:
( I ) Locarion
-
Montreal[ 2 3 January and July were taken as t h e extreme conditions and from R e f . 13) the folloiving data was obtained:
Mean January Temperature - 14 O F
Mean January RH
-
75%Mean July Temperature - 7 0 ' ~
Mean July ME - 67%
( 3 ) A t e i c space ventilated b u t mean winter temperature unknown. Values 0, 5 , 10 and 2 0 ' ~ above outdoor temperature a s s u m e d .
( 4 ) A t t i c assumed to a t t a i n peak summer temperature o f 105°F
b u t mean temperature taken as average of 1 0 5 " ~ and a 70°F
that the mean summer attic space temperature was 100°F was a l s o examined.
(5) S l o p e s o f 4:12 and 3:12 were examined as well as the actual
5:12 s l o p e .
( 6 ) Calculations were made assurnfng only 4
in.
of insulationw a s used.
(79 The plywood r o o f deck was assumed n o t to p a r t i c i p a t e in the truss action because of j o i n t s , h i g h e r shrinkage and minimum
nai ling.
CaIculation Method
Dcf1ect;ions of trusses due t o l i n e a r changes in length
caused by temperature and moisture movements were calculated by the v i r t u a l work method ( 9 ) and as exemplified by Hansen f o r wood
trusses (10). It was c o n s i d e r e d t h a t joint s l i p , i f any, under dead load would occur when t h e trusses were installed and f o r zero
and small live l o a d conditions j o i n t s l i p would n o t
e n t e r
the calculation of subsequent potential movements.RESULTS
F i g u r e 4 shows t h e p r e d i c t e d upward d e f l e c t i o n s under
t h e assumptions d e s c r i b e d . Curve A is t h e b a s i c case for a span o f 28ft 6 in., 5 : 1 2 slope, 6 in. i n s u l a t i o n , and a
summer
a t t i ctemperature of 8 7 . s ° F . Curves C and D illustrate t h e suppression
o f deflections l i k e l y because of an increase of the downward dead load d e f l e c t i o n caused by creep and due
t o
a light 10 p s f snow load. Curve 5 illustrates the e f f e c t o f assuming a 100°F mean summer a t t i c temperature.A l l of t h e values obtained are about t h e same magnitude
as t h e deflections reported.
Figure 5 shows the probable r e l a t i v e e f f e c t s , and in general:
(a] A decrease af slope results in greater upward d e f l e c t i o n .
(b) A reduction o f t h e i n s u l a t i o n from 6 to 4
in.
on t h e bottomchord decreases the deflection because it allows the chord
to have a lower winter temperature and thus a h i g h e r
( c ) The calculated d e f l e c t i o n s f o r a 2 0 - f t span, 5:12 sLope,
and 6 in. of insulation were lower than f a r a span o f
28 ft 6 in.
DISCUSSION OF RESULTS
None of the factors studied suppressed the p o t e n t i a l up-
ward movement t o any g r e a t degree, although it is e v i d e n t t h a t a f u l l d e s i g n snow l a a d of 50 p s f would substantially prevent the
upward t r u s s movements.
Sincc t h e r e are many
houses
where upward d e f l e c t i o n oft h e c e i l i n g is not e v i d e n t , t h e r e must be o t h e r f a c t o r s not e x p l a i n e d by t h i s s t u d y . Some may b e :
(a) T r u s s e s and p a r t i t i o n s installed in Spring
or
Fall wouldprobably e x h i b i t movements on t h e average o f about one-half t h o s e calculated;
(b) The deflections would probably be unnoticed in a hause with
no partitions and t h e i n c i d e n c e o f cracking would probably depend, t o same degree, on t h e partition layout;
(c) T i g h t wedging of p a r t i t i o n s a g a i n s t t h e trusses would, i n
some i n s t a n c e s , prestress the trusses and prevent d i f f e r -
e n t i a l movements; and
(dl
Improper assumptions. Obviously, actual cases and rhermal- moisture regimes would have t o be s t u d i e d to e s t a b l i s h a l lt h e f a c t s . CONCLUSION
This Technical Note was written with t h e hope that it
would h e l p to e x p l a i n t h e upward d e f l e c t i o n o f wood trusses
observed in some r o o f s . It is also hoped t h a t it will encourage
t h e r e p o r t i n g of o t h e r cases of this problem so that i t s prevalence can be evaluated.
References
9, Johnson,
L.B.,
Bryan, C.W., and Turneaure,C-E.
Modern frameds t r u c t u r e s , Part 11, 9th Ed. John Wiley
E
Sons,N.Y.,
1 9 1 7 .2. tlodgc, R.E. The moisture content of roof timbers. Forest Products Research Laboratory (Reprinted from Timber Technology,
V o l . 68, London 1960, p. 416-419).
3 , Millett,
R.S.
Variation i n m o i s t u r e content i n w o o d e x p o s c d to indoor conditions. Forest Products Laboratories Division,F o r e s t r y Branch, Dept. o f Resources and Development of Canada, (Reprinted from Timber of Canada, March 19533.
4 . Canadiannormals, Vol. 1, Temperature, 1973 Climaticnormals,
Vol
.
4, EIumidity, 1968, Meteorological Branch, Canada Department of Transport, Toronto.5. Canadian woods, t h e i r properties and uses, Forestry Branch,
Forest Products Laboratories
Division,
Department of Resourcesand Development, Ottawa, May 1951.
6 . f l e d l i n ,
C.P.
Relative h u m i d i t i e s for Douglas f i r wood between10 and 70°F, National Research Council of Canada, Division of
B u i l d i n g Research, Research Paper No. 410, 1969,
(NRCC
10955).
7. IIutcheon, N.B., and Jenkins, J.H.Some
implications of t h ep r o p e r t i e s of wood. National Research Council o f Canada,
Division of Building Research, Canadian B u i l d i n g Digest 86, Ottawa, 1967.
8 , Wood handbook. Forest Products Laboratory, U-S. Department
of Agriculture, Washington, 1940.
9 . Suthe~land, P I . , and Bowman, H . L . Structural t h e o r y , 3rd
e d i t i o n . John Wiley
G
Sons, N . Y . , 1947.10. IIanscn, A.T. D e f l e c t i o n s o f wooden roof trusses based on
simple joint t e s t s . National Research Council o f Canada,
Division o f Building
Research,
Research Paper No. 334,196 7,N A I L TO
I
1 X 3 C O N T . T R U S S S P A C E R S I D E W A L L N A I L E D TO E A C H C E N T E R BLOCK X 3 S l D E RA l L I B E R B O A R D NOTE: INTERIOR P A R T I T I O N S ARE S C R E W E D TO R A F T E R 5 OR TO L A D D E R S SPACED 2 4 " O . C . B E T W E E N R A F T E R S FIGURE 1 MOBILE H O M E ROOFL O C A T I O N - L E T H B R I D G E , A L T A . M E A N J A N . TEMP. 1 4 . 5 " F M E A W J A N . RJH 71% M E A N J U L Y T E M P . 6 5 - F M E A N J U L Y R/H 5 0 % W I N T E R A T T I C T E M P E R A T U R E , 'F F I G U R E 2 C A L C U L A T E D D E F L E C T I O N O F T I M B E R A R C H
-
T R U S S ROOF O F M O B I L E HOME M f ~ r a - 2CONNECTIONS MADE WITH
(METAL TRUSS PLATES
P L Y TOP C H O R D (6) FIGURE 3 SKETCH OF H O W € TRUSS \ C E I L I N G A S S U M E E F F E C T lVE V A P O U R BARRIER BOTTOM C H O R D
u. M L A N J A N . T E M P . 1 4 - f d M E A N J A N . A , i F 1 0 . 9
-
M E A N J U L Y T E M P . . - . 7 0 " ~ M C A N J U L Y R r H 4 7 < , > 0 . 8 A - R E F E R E N C E C A S E - S P A N 2 8 ' - 6 " S L O P E 5 : 1 2 0 . 7 I I N S U L 4 T I C N 6 " L 5 R " - A " , m r .,.
, , , ...
. - - - 1 I-7 -m t 4 N -J U L Y A T T I C T E M P . . - . . .-
u . o r L r ) 87.5"F I 0 - A S ' A ' B U T M E A N J U L Y A T T I C u T E M P . A S S U M E D F O O m F C - C A S E ' A ' A D J U S T E D FOR DOVJN- W A R D C R E E P DUE TO D E A D L O A D 0 - C A S E ' C ' W I T H F U R T H E R A D J U S T M E N T FOR 1 0 P S F 0.3 Z N O W L O A P n 7s
W I N T E R ( J A N U A R Y ) A T T I C T E M P E R A T U R I . O F F I G U R E 4 C A L C U L A T E D U P W A R D D E F L E C T I O N OF T I M B E R ( H O W E ) H O U S E ROOF T R U S S E S J U L Y T O J A N U A R Y , L O C A T I O N - M O N T R E A L n n f " r 3 . 4BASE C A S E
