Deflections of wooden roof trusses based on simple joint tests

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Deflections of wooden roof trusses based on simple joint tests

Hansen, A. T.

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NATIONAL RESEARCH COUNCIL O F CANADA

CONSEIL NATIONAL DE RECHERCHES DU CANADA

DEFLECTIONS O F WOODEN ROOF TRUSSES

BASED ON SIMPLE JOINT TESTS

by

A. T. Hansen

P r e s e n t e d a t t h e International Symposium on J o i n t s

in T i m b e r S t r u c t u r e s organized by T i m b e r R e s e a r c h

and Development Association and CIB C o m m i s s i o n

W - 1 8

held in London, England,

30

-

31

M a r c h

1965

R e s e a r c h P a p e r No.

3 3 4

of the

Division.- of Building R e s e a r c h

OTTAWA

November

1967

DEFLECTIONS OF WOODEN ROOF TRUSSES

BASED ON SIMPLE JOINT TESTS

by

A. T. Hansen*

It i s common practice among residential wood roof t r u s s

~

fabricators in Canada to determine t r u s s deflections by load testing

each new t r u s s design. This can be expensive, particularly

i f

a s e r i e s

of t e s t s i s undertaken t o develop a family of t r u s s designs. T h e r e i s

some advantage in being able t o predict deflection without resorting to

full-size t e s t s , not only in developing new designs, but a l s o in checking

the r e s u l t s of a t r u s s t e s t t o ensure that the test was truly indicative

of an average t r u s s and not an atypical one. This paper p r e s e n t s a

method of computing the deflections of simple

"W" t r u s s e s and Howe

t r u s s e s , the two most common configurations used in house construction.

A comparison between the deflections obtained from actual t e s t s on a

number of these t r u s s e s with those obtained by calculation i s a l s o

included to compare the accuracy of the proposed method over a range

of roof slopes, spans, and joint connections.

CAUSE OF DEFLECTION

When a roof t r u s s i s loaded, the resulting deflection at any

panel point where m e m b e r s intersect to form a joint i s due both to the

Housing Section, Division of Building Research, National R e s e a r c h

Council. Ottawa, Canada.

axial lengthening or shortening of the m e m b e r s and to the slippage a t the joints. Where glued joints a r e used, t h i s slippage i s negligible and can be ignored (1). In s ' W 8 1 tr u s s e s the deflection a t the c e n t r e of the t r u s s i s somewhat g r e a t e r than a t the adjacent panel points due to bending In the lower chord and m u s t a l s o be considered.

DEFLECTION DUE TO AXIAL STRAIN

The deflection a t any panel point due to axial s t r a i n in the m e m b e r s m a y be calculated using the f o r m u l a

w h e r e

h e

=

panel point deflection due t o a x i a l s t r a i n S = the f o r c e on e a c h m e m b e r due t o the roof and

ceiling loads

U

=

the f o r c e on each m e m b e r caused by applying a unit load a t the panel point for which the deflection i s t o be calculated and in the direction the deflection i s to be m e a s u r e d k = length of each m e m b e r

A

=

c r o s s -sectional a r e a of each m e m b e r

E

=

modulus of e l a s t i c i t y in the a x i a l direction.

T h e value S U ~ / A E must be calculated s e p a r a t e l y for each panel m e m b e r and h e found by adding t h e s e together. The values for S , and

k

_have

been calculated by the author for simple Howe and s'W" t r u s s e s and a r e l i s t e d in T a b l e s I and 11. F o r Howe t r u s s e s the U s t r e s s e s a r e f o r a unit load applied a t m i d - s p a n of t h e lower c h o r d ; for "W8s t r u s s e s , the U values a r e for a unit load applied a t the t h i r d point of the lower chord.

T h e values shown i r i T a b l e s I and I1 a s s u m e s i m p l e pin- connected joints. T h i s m a y be questioned because t r u s s joints v a r y in rigidity f r o m glued joints t o split-ring joints; r i g i d i t y of nailed and toothed connector plate joints i s somewhere between these e x t r e m e s . In calculating deflections due t o axial s t r a i n in the

m e m b e r s , however, the r i g i d i t y of the joints is r e l a t i v e l y unimportant, and f o r p r a c t i c a l p u r p o s e s t h e assumption of pin-connected joints i s c o n s i d e r e d sufficiently a c c u r a t e

(2).

T a b l e s I and I1 show that for a given t r u s s g e o m e t r y and w h e r e the load and slope a r e constant, the values of

R

_{and S e a c h v a r y}

d i r e c t l y in proportion t o the span of the t r u s s . F o r the Howe t r u s s (Table 11) the axial load S v a r i e s d i r e c t l y a s the s u m of t h e ceiling and roof load for m o s t of the m e m b e r s . F o r "W8' t r u s s e s (Table I),

although the axial load S _{is not exactly proportional t o the sum of}

the ceiling and roof load, it i s a l m o s t so, and with t h e usual r a n g e s of ceiling and roof load one c a n a l s o consider the value of S _{a s being i n}

d i r e c t proportion t o the s u m of the total load without being i n significant e r r o r .

When a s i m i l a r s p e c i e s of lumber i s used for a l l t r u s s m e m b e r s , which i s usually the c a s e , the panel point deflection due to a x i a l s t r a i n of t r u s s e s with s i m i l a r geometry, slope, and m e m b e r c r o s s - s e c t i o n s can t h e r e f o r e be e x p r e s s e d a s

C ~ W L ~

AE

=

E

If t h i s e x p r e s s i o n i s to be applied to t r u s s e s that have different c r o s s

-

sections than those for which C i s determined, a second constant

l

must be introduced to take t h i s into account. The deflection m a y then be e x p r e s s e d a s

where

*

AE = panel point deflection due to a x i a l s t r a i n , in.

C1 = constant for a given slope and g e o m e t r y

C _{= constant for given m e m b e r s i z e and g e o m e t r y} 2

W = total load (roof plus ceiling) p e r lineal ft of t r u s s , l b

5 _{= span of t r u s s , ft}

E = modulus of elasticity, lb p e r s q in.

The values of C have been determined by the anthor for 1

both "W" t r u s s e s and s i m p l e Howe t r u s s e s ( T a b l e s I and 11) by plotting

* T h i s p a p e r gives B r i t i s h Units throughout. Loads a r e in pounds, spans a r e i n feet and deflections a r e i n inches. The values

of coefficients C and C a r e dependent on the m e a s u r i n g s y s t e m

1 2

used. When the m e t r i c s y s t e m i s used t h e r e f o r e , the constants will be different f r o m those i n Table 111.

T i m b e r s i z e s a r e given a s nominal inch dimensions, The a c t u a l s i z e s a r e l i s t e d below:

Nominal Size, Canadian .Lumber Stan

-

M e t r i c Equiva- in. d a r d D r e s s e d Size, in. lent, c m

Conversion f a c t o r s t o t h e m e t r i c s y s t e m a r e a s follows:

roof load

-

lb/sq f t x 4,88

=

~ ~ / s q m

s t r e s s , o r modulus

the values of

_L

_-

_a

_-

for 2/12, 3/12, 4/12, and 5/12 slope t r u s s e s . a s s u m i n g n o m i n a l 2

-

by 4-in, m e m b e r s throughout. T h e v a l u e s of

Y- S U L

LAE

w e r e a l s o c a l c u l a t e d a s s u m i n g 2 - by 6-in. top and 2 - by 4-in. bottom c h o r d s , 2 - by 4-in. top and 2

-

by 6-in. bottom c h o r d s and

2 - _{by $-in. top and bottom c h o r d s . As the values of C w e r e d e t e r -}

1

mined a s s u m i n g 2 - by 4-in. m e m b e r s throughout, the value of C _{i s} 2 unity f o r t h i s condition. The values of C f o r other m e m b e r s i z e s

2

w e r e c a l c u i a t e d by dividing the deflections f o r t r u s s e s with other

m e m b e r s i z e s by that of t r u s s e s with 2 - by 4-in. m e m b e r s throughout. T h e values of C and C t h u s c a l c u l a t e d a r e shown in T a b l e 111.

1 2

D E F L E C T I O N DUE T O J O I N T S L I P

Movement of the wooden m e m b e r s r e l a t i v e t o the g u s s e t p l a t e s c a u s e s deflection a t a p a n e l point in much the s a m e m a n n e r a s a x i a l s t r a i n in the m e m b e r s ,

T h e contribution of e a c h m e m b e r toward the t o t a i deflection will be t h e p r o d u c t of the f o r c e U for that m e m b e r due t o the unit load, multiplied by the n e t change in effective length c a u s e d by t h e joint slippage a t both e n d s of that m e m b e r due t o the t o t a l load W. If t h e d i s p l a c e m e n t of a connector i s known f o r a given load the contribution t o deflection a t a p a n e l point c a u s e d by joint s l i p f o r e a c h m e m b e r c a n be calculated.

T h e deflection due t o joint slippage, t h e r e f o r e , m a y be e x p r e s s e d a s

A P

=

C U A R

. . .

(4)

w h e r e

A R = the change in m e m b e r length due t o joint slip.

In an idealized t r u s s design, the load p e r unit of connector will be the s a m e a t e v e r y joint. In an idealized connector the d i s p l a c e - ment, d, of the connector r e l a t i v e t o the t r u s s m e m b e r s will be

approximately the s a m e a t a given load r e g a r d l e s s of the orientation of the connector t o the direction of loading.

At any given t r u s s loading W, the change in m e m b e r length, AR, will be p r o p o r t i o n a l t o d. T h e r e f o r e , for given slope and

g e o m e t r y of t r u s s , the deflection due to connector slippage c a n be e x p r e s s e d a s

w h e r e

C 3 i s a constant for a p a r t i c u l a r slope and t r u s s g e o m e t r y

d i s displace.ment of a connector a t a load of P , lb p e r unit of connector, corresponding to a total load, W, lb p e r l i n e a l ft of t r u s s .

C t h e r e f o r e m a y be e x p r e s s e d a s being equal to

1

.

The following a s s u m p t i o n s w e r e made in calculating

C

3"

In a typical "W" t r u s s ( F i g u r e l a ) with m e t a l or plywood p l a t e s a t a l l joints, the change in length of L L and L U will be equal to d.

0 1 0 1

Member L L however, will have a change in length equal to 2d 1 2'

since the s l i p will be equal to d on both ends of the splice plate of the lower chord. The long diagonal L U will have a change i n length

1 2

equal to 4d since the slip o c c u r s between the top chord and gusset plate and between the g u s s e t p l a t e and diagonal m e m b e r a t the top end, and between the gusset plate and diagonal m e m b e r and gusset plate and lower c h o r d a t the bottom end. The slippage in U U will be z e r o i f

1 2

t h e m e m b e r s a r e in good b e a r i n g conta.ct a t t h e peak. M e m b e r s

U

L

L U and L U can be ignored because t h e i r U s t r e s s i s zero. 1 1 ' 2 2 2 3

S i m i l a r l y , in a typical Howe t r u s s (Table 11), the change in length of L L L L L L

0 1' 1 2' 2 3' L3L4' LOUl and L 4 3 U will be equal t o d in each c a s e . The movement in U U and U 3 will be z e r o for

1 2 2 3

m e m b e r s in good b e a r i n g contact. In the v e r t i c a l m e m b e r , U L 2 2' movement o c c u r s between the g u s s e t plate and the upper c h o r d s and between the gusset plate and the upright a t the top end, and between the g u s s e t plate and upright and between the gusset plate and lower c h o r d s a t the bottom end. T h e l a t t e r movement, however, should be considerably l e s s than d since the connector will be r e l a t i v e l y lightly loaded In the

v e r t i c a l direction. The over - a l l change in length of L U t h e r e f o r e , 2 2'

was a s s u m e d to be 3d. The remaining m e m b e r s , L I U l , L2U1, L3U3. and L

U

can be neglected a s their

U

s t r e s s will be equal t o

2

3 zero.

Values of C have been calculated by the author for these 3

idealized t r u s s and connector conditions for both

"WD'

and Howe t r u s s e s for various slopes (Table 111).

The value d can be determined on the b a s i s of a loading t e s t on a simple joint t o determine the slip c h a r a c t e r i s t i c s , The assumptions used in developing the values of C in Table I11 w e r e

3

that the connectors w e r e designed s o that t h e r e would be the s a m e displacement between m e m b e r and plate a t , e a c h joint. Although t h i s condition i s approached for nailed connectors, i t m a y not be the c a s e where c e r t a i n plate connectors a r e used which would involve consideration of the orientation of the teeth t o the direction of loading. Some judgment m a y have t o be exercised, therefore, in using the values of d determined f r o m a load t e s t on a simple joint. If the

displacement of the wood o r m e t a l plate d at a given load p e r connector unit (nail or tooth) i s known, it then becomes possible t o predict the

deflection at any panel point in the full-size t r u s s .

DETERMINATION O F JOINT SLIP, d

Simple loading t e s t s w e r e c a r r i e d out on t h r e e types of

connectors: nailed plywood; light -gauge, short-tooth p l a t e s ( F i g u r e 2); and heavy-gauge, long-tooth p l a t e s ( F i g u r e 3). The joints for the

f r a m i n g lumber w e r e t e s t e d in t h r e e conditions: a s s e m b l e d d r y and t e s t e d d r y ; a s s e m b l e d g r e e n and t e s t e d g r e e n ; and a s s e m b l e d g r e e n and t e s t e d dry. T h r e e t e s t s w e r e conducted on each plate and for each condition t o obtain average r e s u l t s . T e s t r e s u l t s of the joints a r e shown in F i g u r e s 4, 5, and 6 . _{T e s t s on joints w e r e conducted} generally in the manner recommended by the U. S. T r u s s P l a t e Institute ( 3 ) . The joints w e r e t e s t e d in a testing machine which loaded the joints in tension in i n c r e m e n t s , with each i n c r e m e n t

applied for 5 minutes before displacements w e r e r e c o r d e d . D i s p l a c e - ments w e r e m e a s u r e d f r o m wood m e m b e r to wood m e m b e r ; the values plotted in F i g u r e s 4, 5, and

6

a r e half t h e s e displacements t o r e p r e s e n t the movement between plate and m e m b e r only, or d.

The connectors w e r e t e s t e d i n only one direction, although it would have been p r e f e r a b l e in the c a s e of toothed p l a t e s t o have

included t e s t s where the load was applied a t various tooth o r i e ~ t a t i o n s t o the direction of load t o obtain a better a s s e s s m e n t of t h e factor d for u s e in calculating o v e r - a l l t r u s s deflections. It i s hoped that this will be investigated in future testing. In joint t e s t s on t h e light

-

gauge p l a t e s , one s p i r a l n a i l p e r eight teeth was used, s i m i l a r t o t h e plate m a n u f a c t u r e r a s directions for the u s e of t h e s e p l a t e s in t r u s s e s . T h i s was found t o be approximately the proportions used in t h e t r u s s e s that w e r e t e s t e d which had been fabricated by the t r u s s p l a t e m a n u - factur e r

.

TOTAL DEFLECTION

T h e t o t a l deflection a t the c e n t r e l i n e of a Howe o r the t h i r d point of a "WP1 t r u s s m a y b e c a l c u l a t e d by adding f o r m u l a e (3) and ( 5 ) : w h e r e A = t o t a l deflection, .in. W = t h e t o t a l load on a t r u s s (ceiling p l u s r o o f ) , l b p e r l i n e a l f t of t r u s s L

=

s p a n of t r u s s , ft

E = modulus of e l a s t i c i t y under a x i a l loading, p s i d

=

d i s p l a c e m e n t of p l a t e r e l a t i v e t o the m e m b e r

a t the loading being c o n s i d e r e d ( F i g u r e s 4, 5,

and 6 ) , in. ( V a l u e s for C

1 ' C 2 , and C a r e given in T a b l e 111. ) 3 Although t h i s f o r m u l a g i v e s the t h i r d point deflections of t h e bottom c h o r d in a P I W " t r u s s , t h e c e n t r e l i n e deflection of P'W't t r u s s e s i s u s u a l l y what i s d e s i r e d . It i s difficult t o d e t e r m i n e t h i s

deflection in p u r e l y t h e o r e t i c a l t e r m s b e c a u s e i t o c c u r s between p a n e l points. T h e t h i r d point deflections w e r e plotted a g a i n s t c e n t r e line

deflections f r o m t h e r e s u l t s of a n u m b e r of t e s t s on "W" t r u s s e s ( F i g u r e 7 ) . T h e r e l a t i o n s h i p between the t h i r d point and c e n t r e l i n e

deflection a p p e a r s t o be p r a c t i c a l l y a straight line that v a r i e s little with roof slope or span and c o r r e s p o n d s approximately to the

relationship:

c e n t r e line deflection

=

1. 30 t i m e s the panel point deflection.

The c e n t r e line deflection of a D'W8' tr u s s can, t h e r e f o r e , be d e t e r - mined using the formula:

COMPARISON O F MEASURED AND CALCULATED RESULTS A number of t e s t s on s'Ws' t r u s s e s with nailed plywood

gusset plates had been previously completed by the Division of Building R e s e a r c h ( 5 ) ( F i g u r e 1) s o that the m e a s u r e d deflections for t h e s e c r u s s e s of different slopes, s p a n s , and m e m b e r s i z e s could be checked against calculated values using f o r m u l a (7). The t r u s s e s in F i g u r e l a r e p r e s e n t the type f o r which the constant C in Table

I11

for 'lWt'

3

t r u s s e s would apply because of the typical a r r a n g e m e n t of gusset plates. A f a i r l y l a r g e number of t e s t s had a l s o been completed on a

slightly different type of 'lW" t r u s s ( F i g u r e l b ) incorporating 1

-

by 8 -in. -long diagonals r a t h e r than 2

-

by 4-in. m e m b e r s . The difference between these two types of t r u s s e s is not g r e a t , however, and the s a m e constants w e r e applied t o the t h e o r e t i c a l calculation of deflections f o r both types of t r u s s e s in o r d e r t o check a wider s p e c t r u m of spans and

Additional t e s t s w e r e conducted on 4/12 slope t r u s s e s of

2 8 - i t span m a d e with t h e two types of m e t a l connector p l a t e s d e s c r i b e d in F i g u r e s 2 and 3. T r u s s e s made with the plate d e s c r i b e d in F i g u r e 2 w e r e "W" type ( 3 t e s t s ) and Howe t r u s s (1 t e s t ) . T r u s s e s m a d e with p l a t e s shown in F i g u r e 3 w e r e "W" type ( 3 t e s t s ) . T h e t r u s s e s w e r e t e s t e d in p a i r s in a c c o r d a n c e with the method d e s c r i b e d (5) u s i n g h y d r a u l i c t e n s i o n j a c k s t o supply t h e roof load t o t h e top c h o r d s , and l e a d weights t o supply t h e ceiling load t o t h e lower c h o r d ( F i g u r e 8).

T h e a x i a l modulus of e l a s t i c i t y of white s p r u c e h a s been found t o a v e r a g e 1 , 2 7 0 , 0 0 0 p s i f o r t h e g r e e n condition and 1, 550,000 p s i for the a i r d r y condition (4). In t h e s e calculations t h e value of

1 , 500,000 p s i w a s a s s u m e d t o be r e p r e s e n t a t i v e of t h e l u m b e r ( n e a r l y d r y ) a t the t i m e of the t e s t .

The values of d u s e d in calculations for t h e nailed t r u s s e s w e r e t h o s e f o r t r u s s e s m a n u f a c t u r e d d r y and t e s t e d d r y ; t h o s e f o r t h e m e t a l - p l a t e - c o n n e c t e d t r u s s e s w e r e for t r u s s e s m a d e g r e e n and t e s t e d dry. T h e s e conditions w e r e c o n s i d e r e d r e p r e s e n t a t i v e for t h e s e t r u s s e s . In s e l e c t i n g t h e value of d t o be u s e d in t h e s e c a l c u l a t i o n s f r o m F i g u r e s 4, 5, and

6

the dead weight of t h e t r u s s and loading equipment ( a p p r o x i m a t e l y 5 l b / s q f t ) w a s taken into account. T h e load t e s t i n g p r o c e d u r e w a s s u c h t h a t t h e z e r o deflection w a s r e c o r d e d with t h e dead weight of t h e t r u s s and t e s t equipment in p l a c e , s o that subsequent m e a s u r e d deflections r e c o r d e d only t h a t deflection c a u s e d by the applied roof and ceiling load.

The values of d s e l e c t e d f r o m F i g u r e s 4, 5, and

6,

t h e r e f o r e , w e r e determined by calculating the load p e r unit of connector c a u s e d by the applied load plus the dead load and subtracting the s l i p caused by the dead load only. In calculating the deflection caused by a x i a l s t r a i n t h i s p r o c e d u r e w a s not n e c e s s a r y s i n c e t h i s deflection h a s a s t r a i g h t line relationship with t h e applied load w h e r e a s the connector s l i p h a s not. The calculated deflections in Table IV a r e t h o s e c a u s e d by the

addition of the ceiling and roof loads, a f t e r the dead load of 5 p s f was applied.

In calculating t h e deflections for t h e nailed plywood t r u s s e s , the constants ( C in T a b l e 111) w e r e divided by an additional factor of

2

1. 10 which is approximately the r a t i o of the c r o s s - s e c t i o n a l a r e a of lumber cut t o the older s i z e ( E a s t e r n Canadian) which was u s e d in t h e s e t r u s s e s , t o that of the c u r r e n t Canadian Lumber Standard s i z e s f o r which the values of C _{in Table IV w e r e calculated. Since C I S - s i z e}

2

lumber was used in the metal-plate-connected t r u s s e s , t h e constant C

2

used in calculating t h e i r deflections was the s a m e a s shown in T a b l e 111. DISCUSSION

The m e a s u r e d deflections in Table

IV

a r e based on t h r e e t e s t s except where o t h e r w i s e noted. T a b l e IV shows that in m o s t

c a s e s the calculated r e s u l t s a g r e e r e l a t i v e l y c l o s e l y with the calculated deflections, when one t a k e s into consideration the n a t u r a l v a r i a b i l i t y of the p r o p e r t i e s of wood.

The e r r o r s obtained for the metal-plate -connected t r u s s e s in Table IV a r e a l s o r e l a t i v e l y s m a l l except for the #'W" t r u s s m a d e with light-gauge p l a t e s a t a total load of 65 psf (50 p s f snow load plus ceiling load and dead load). T h i s m a x i m u m e r r o r w a s 0. 1 7 .in. The calculated deflection e r r o r for the s a m e t r u s s a t a t o t a l load of

35 p s f , however, w a s only 0 . 0 6 in.

It w a s noted that in the t e s t s on t h e s e t r u s s e s , under higher loads the h e e l p l a t e s buckled in c o m p r e s s i o n which f o r c e d a number of t e e t h out of the wood thus considerably reducing the joint stiffness ( F i g u r e

9).

T h i s probably led t o substantially g r e a t e r m o v e m e n t s a t t h e s e joints than was determined by calculation. T h e Howe t r u s s e s , which did not exhibit t h i s plate buckling tendency to the s a m e d e g r e e even though the s a m e type of p l a t e s w a s used, showed c l o s e a g r e e m e n t between m e a s u r e d and calculated deflections. It was noted that t h e h e e l p l a t e s of the 9'Ws' t r u s s e s with the light-gauge p l a t e s w e r e placed

s o that they extended below the bottom chord of the t r u s s and t h e r e f o r e b o r e the weight of the t r u s s a t the end supports. T h i s probably

contributed to the p r e m a t u r e plate buckling that l e d to the g r e a t e r -than- expected deflections for t h e s e t r u s s e s . P l a t e buckling a t the h e e l joint m a y a l s o b e c a u s e d by the t r u s s e s being made of v e r y g r e e n l u m b e r which, on drying, s h r i n k s and c a u s e s the plate t o buckle. In addition, t h i s shrinkage would c a u s e the t r u s s m e m b e r s a t the h e e l joint t o

h a s to be t r a n s f e r r e d t o the bottom c h o r d through the thin w a l l s of the plate which a r e not able to withstand high loads without buckling,

In determining the joint slip c h a r a c t e r i s t i c s of connectors by s i m p l e joint t e s t s , one should be s u r e that the joint h a s the s a m e h i s t o r y of fabrication a s the t r u s s for which deflections a r e to be

calculated. That i s , i f the t r u s s e s a r e t o be manufactured f r o m g r e e n l u m b e r , the joint t e s t s p e c i m e n s should a l s o be manufactured f r o m g r e e n l u m b e r and a l l joint t e s t s should p r e f e r a b l y be conducted a f t e r the wood h a s d r i e d t o about 10 to 12 p e r cent which i s c l o s e t o t h e final m o i s t u r e content of the wood i n s e r v i c e .

F i g u r e s

4, 5,

and

6

show t h e substantial d i f f e r e n c e s in connector displacement depending upon the condition of the wood a t the t i m e of a s s e m b l y and at the t i m e of t e s t , When joints a r e

a s s e m b l e d with d r y wood and a r e t e s t e d dry, the c o n n e c t o r s display t h e i r g r e a t e s t stiffness. J o i n t s a s s e m b l e d g r e e n display g r e a t e r displacement under a given load.

It should be emphasized that t h e s e calculated r e s u l t s a r e valid only for s h o r t - t e r m t e s t s

( 5

m i n u t e s e duration). F o r longer

-

t e r m loading the calculated r e s u l t s should be i n c r e a s e d a p p r o x i m a t e l y

5 p e r cent for 1 - h r loading, 2 5 p e r cent for 24-hr loading,

55

p e r c e n t for a one-week loading, and 100 p e r cent for a one-month loading. T h e s e i n c r e a s e s a r e based on o b s e r v a t i o n s of nailed 8'W90 t r u s s e s (5)

suggested that these values be applied to tooth-plate-connected t r u s s e s a s well.

There a r e , of course, roof t r u s s e s used in residential construction of other geometries than those tested. These other types, however, have not been load tested by DBR/NRC and a

comparison of theoretical deflections with measured deflections h a s not been made for t r u s s e s other than a s described in this paper.

CONCLUSION

It would appear that this method of computing centre line deflections i s reliable for the kinds of t r u s s e s tested and could be used for the design of t r u s s e s for deflections where t e s t r e s u l t s f o r full-size t r u s s e s a r e not available. Because the displacement of the toothed-plate connectors was determined on the basis of t e s t s in one loading direction the agreement between the calculated and measured deflections i s v e r y good. In determining the joint slip c h a r a c t e r i s t i c s of connectors by simple joint t e s t s , it i s essential that the joint h a s the same h i s t o r y of fabrication a s the t r u s s for which the deflection i s to be calculated.

REFERENCES

(1) Luxfor d,

R.

F, Lightweight Roof T r u s s e s , T r a n s a c t i o n s , American Society of Civil E n g i n e e r s , Vol. 126, P a r t 2, P a p e r No. 3090, 1962.

(2) P a r c e l , John I r a and R. B. B. Moorman. An E l e m e n t a r y T r e a t i s e on S t a t i s t i c a l l y Indeterminate S t r e s s e s , Wiley, New York, 1955.

( 3 ) Design Specifications for Light Metal P l a t e Connected Wood T r u s s e s , T r u s s . P l a t e Institute, TPI-62, Miami, Florida.

(4) Strength and Related P r o p e r t i e s of Wood Grown in Canada, Department of F o r e s t r y , F o r e s t P r o d u c t s R e s e a r c h Branch, Technical Note No. 3 , Ottawa, 1956.

(5) Hansen, A. T. T r u s s e d R a f t e r s for Houses, National R e s e a r c h Council, Division of Building R e s e a r c h , NRC 7532, Ottawa, September 1963.

T A B L E I

VALUES O F S , U, AND

Q

F O R W TRUSSES

W h c r e S _{= a x i a l f o r c e on m e m b e r} M e m b e r S U I L

Lo

L1

+

1/3

-

h L/ 3 L

+

1/6 L / 3

I

L 2 3

L

I

L2L3

+

2 h ( 8

-

-

1

+ -

i w 2 )

+

1/6

-

h L!/ 3 L L ~ " l 3 h

- -

3 h

I

'2'3

P w

+ - w

u 3 L 3

-

-(

2 h 8 1 3 2)

-

-

U = f o r c e c a u s e d b y unit load applied v e r t i c a l l y a t t h i r d point of l o w e r c h o r d L l U 2 u l L l u2L2 L2u3

I

= l e n g t h of m e m b e r

W1 = l o a d p e r unit l e n g t h of t r u s s along top c h o r d W7

_-

= l o a d p e r unit l e n g t h of t r u s s along b o t t o m c h o r d

- -

L = s p a n of t r u s s h = height of t r u s s a t p e a l < 6 h 0 0 0 1/6

d

m

1/12 J3

-T A B L E I1

V A L U E S O F S , U , A N D P F O R H O W E T R U S S E S

Member

I

Where S = axial f o r c e on m e m b e r

U = f o r c e c a u s e d by unit load applied v e r t i c a l l y at the c e n t r e of the lower c h o r d

I = length of m e m b e r

W 1 = load p e r unit length of t r u s s along top chord

W = load p e r unit length of t r u s s along bottom chord 2

L = s p a n of t r u s s

T A B L E

I11

VALUES O F C1, C2, C3 FOR "W" AND HOWE TRUSSES

Coefficient C1 C2 C3 Slope 2/12 3/12 4/12 5/12 All Slopes 2/12 3/12 4/12 5/12 Chord M e m b e r S i z e All Chord S i z e s

2 x

4

top and bottom

2 x

6

top and 2 x 4 bottom 2 x

4

top and 2 x 6 b o t t o m 2 x 6 top and bottom

All Chord S i z e s T y p e of W 2 4 . 4 1 1 . 2 6 . 6 4 . 5 1 . 0 0 0. 81 0 . 8 6 0.67 25. 0 17. 5 13. 8 11.7 T r u s s Howe 25. 8 11. 8 6 . 9 4 . 7 1 . 0 0

.

84 - 8 3 0 . 6 6 2 1 . 1 15. 1 1 2 . 2 1 0 . 4

.

T A B L E IV C o m p a r i s o n o f C a l c u l a t e d a n d M e a s u r e d D e f i e c

t

_{i o n s of V a r i o u s S p r u c e T r u s s e s}

W

t y p e

-

N a i l e d 2 6 p l y w o o d g u s s e t s ( s e e F i g . l a ) 2 8 2 8 ( S i n g l e ~ e s t ) 2 8 ( S i n g l e T e s t ) 2 8 ( s i n g l e T e s t ) 2 8 h' t y p e

-

N a i l e d 2 4 1 2 2 x 4 p l y w o o d g u s s e t s 2 x 4 ( s e e F i g . l b ) 2 4 4 / 1 2 2 x 4 2 x 4 2 6 5 / 1 2 2 x 4 2 x 4 2 6 4 / 1 2 2 x 4 2 x 4 2 8 5 / 1 2 2 x 4 2 x 4 2 8 4 / 1 2 2 x 4 2 x 4 T y p e o f T r u s s W t y p e w i t h g l u e d 2 4 5 / 1 2 2 x 4 p l y w o o d g u s s e t s 2 x 4 l:J t y p e w i t h l i g h t - 2 8 16/12 2 x 4 gauge m e t a l c o n -

I

n c c t O r s S p a n , f t C h o r d Top S i z e , nominal W t y p e w i t h h e a v y - 2 8 ' 8 " 4 / 1 2 2 x 4 g a u g e m e t a l c o n - ( S i n g l e n e c t o r s ~ e s t ) S l o p e B o t t o m C h o r d S i z e , nominal D e f l e c t i o n s , i n . Howe t y p e w i t h 2 8 4 / 1 2 2 x 4 l i g h t - g a u g e m e t a l c o n n e c t o r s C a l c u l a t e d M e a s u r e d D i f f e r e n c e

FIGURE I

N A I L E D " W " T R U S S E S W I T H PLYWOOD G U S S E T S

F i g u r e 2 Light -gauge toothed p l a t e s in tension t e s t

F i g u r e 3 Heavy-gauge toothed p l a t e s in t e n s i o n t e s t

-

-

-

Nailed Green

-

-

-

-

-

-

-

-

-

-

-

-

-

Note

-

1" Lbuglas Fir Plywood Plates

_-

and 3" x 0.144" Dia Common Nails

-

I

I

0 .010

.On

.ON .040 .050 .060 .070 ,080 .OW .1M) S L I P P A G E O F P L A T E R E L A T I V E T O W O O D "d", I N .

F I G U R E 4

0 .005 .010 .015 .020 .025

.ON

.035 .040 .045 .050 .055

S L I P P A G E O F P L A T E R E L A T I V E T O W O O D "d", I N .

I

I

I

I

1

-

-

-

Note

-

20 g. Toothed Plates with 318" High

_-

x

5116" Wide Triangular Teeth.

-

One 11 g. x

lf"

Spiral Nail Per

8 Teeth

-

-

-

-

-

-

-

-

-

Pressed l nto Green Wood (259b)

-

Tested Dry (8)

-

-

--0

-

Tested Dry

/'\pressed Into Green Wood

Tested Green (23%)

-

-

-

-

-

F I G U R E 5 S L I P " d " O F L I G H T G A U G E T O O T H E D P L A T E S I N S P R U C E

I

I

I

I

I

I

Plates Pressed Plates Pressed

Tested Green (23%)

Note

-

14 g. Toothed Plates with

3/4" x 118" Prongs

.005 .010 .015 .020 .025 . O X .035 .040 .045 .050 .055 .060

S L I P O F P L A T E R E L A T I V E T O T H E W O O D "d", I N .

F I G U R E 6

Z

-

,

-

1.4 I n 2 cc t 1.2 LL 0 a cc _Deflection = 1.30 x t h e T h i r d Point Deflection

g

1.0 U oz W 3 0 26'

-

4/12 Slope

3

_{. 8} o 28'

-

3/12 Slope LL 24'

-

4/12 Slope o 24'

-

5/12 slope I- z A 28'

-

4/12 Slope

-

- 6 0 A 28'

-

5/12 Slope n x 26'

-

5/12 slope 0 oz

-

=

. 4 t t a z 0

-

t . 2 U W -1 LL W a 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 1.10 1.12 D E F L E C T I O N A T C E N T R E L I N E , I N . F I G U R E 7 R E L A T I O N S H I P B E T W E E N T H I R D P O I N T D E F L E C T I O N S A N D M I D S P A N D E F L E C T I O N S F O R N A I L E D W T R U S S E S

F i g u r e 9 P l a t e failure at heel of "W" t r u s s e s made with light -gauge plates