Shear characteristics of wood dowel shear joint and practical application example

FUKUYAMA Hiroshi Researcher, Dr.

Timber Engineering Laboratory, The University of TokyoTokyo, Japan

(KAIRI Matti, HIRSI Hannu; Helsinki University of Technology, INAYAMA Masahiro, ANDO Naoto; The University of Tokyo)

1. Intoroduction

2. Theoretical calculation2.1 Bearing characteristics

・ Bearing stress distributes in radial direction, not in one loading direction. And dowel in timber has little flexibility of distension as shown in Fig. 2.1. Therefore, under bearing stress, stresses in dowel become close to 2-axis compression. This effect could be assumed nominal hardening of dowel, comparing with normal characteristics of compression perpendicular to grain.

・ The nominal hardening effect was verified with complex bearing tests of timbers and wood dowels, comparing with normal partial-compression perpendicular-to-grain tests of several cases. Bearing characteristics of joints for theoretical calculations are decided directly from those results or predicted from those.

{ }min. ,

e k cvfcp

e k cvf

e cp e F cvf

k kk

k k

F F F

αα

α

⋅=

+

= ............................................................................ [1]

Where,3

3

3

N/mm

N/mm

N/mm

: complex bearing stiffness

: bearing stiffness in timber

: embedding stiffness in fastener

: embedment stiffnening coefficient (1.6~3.5; d18 bearing test)

cp

e

cvf

k

k

k

kα

2

2

2

N/mm

N/mm

N/mm

: complex bearing yield stress

: bearing yield stress in timber

: embedment yield stress in fastener

: amplification coefficient on embedment yield stress (1.9; d18 b

ecp

e

cvf

F

F

F

Fα

eraing test)

Wooden dowel joint could have merit of less energy consumption and fear of condensation than steel dowels. This paper mainly focuses on basic information of shear characteristics. As dowel materials, pine, birch, oak, cypress and compressed bamboo were used. From the specimens of over 200 of 30 cases, simple assortment and calculation method for shear characteristics of wooden dowel joint were obtained. And points for joint design were also clarified.

transverse strain

increment of bearing stress

(2a) (2b)(1a) (1b) (3a) (3b1) (3b2) (3b1,2)

member 1

(7-shear)

(4a) (4b1) (4b2) (4b1,2)

(6a) (6b1) (6b2) (6b1,2)

(5a) (5b1) (5b2) (5b1,2)

member 1

member 2

member 1

member 2

member 1

member 2

member 2

member 1member 1

member 2

member 2

member 1

member 1

member 2

member 1

member 2

member 2

member 1

member 2

member 1

member 2

member 1

member 1

member 2

member 1

member 2

member 1

member 2

member 1

member 2

member 1

member 2

member 1

member 2

member 2member 2

member 1

member 2

member 1

member 2

member 1

Fig. 2.1 Bearing stress state

Fig. 2.3 Yield modes of single shear2.2 Strength calculations

・ Johansen's yield theory was applied. Bending capacity of dowel was determined by elastic modulus of section. Both possibilities of bearing yield of timber and of dowel are considered. And shear-crack-in-grain capacity was also taken into account.

・ Bearing yield of dowel, preceding to that of timber, is accompanied with shear cut of grains. These phenomena can be seen also on normal partial compression perpendicular to the grain.Shear-cut-of-grain capacity of dowel was demarcated from shear-crack-in-grain capacity and was assumed as embedding yield of dowel in the formula.

[ ]( )[ ]( )

( ) ( )[ ]( )

( )( )

( )[ ]( )

( )( )

( )

2 3 2 2

2 2

1 1

2 2

2 2

1 1

1 1

1 1

1 1

1 1

1 1

2 2 2 1

1

4 2 1

22 2

4 2 1

2 12 1 2 1

mode 1

mode 2

mode 3

mode 4min .

mo

y

ecp

y

ecp

ecp

ecp

ecp

ecp

ecp

y EYT

M

d L F

M

d L F

d L Fd L F

d L F

d L F

d L F

P

α β α α β β β α

β

β β β β

ββ β

β α β β αβ

ββ β

αβ

+ + + + − +

+

⋅ ++ −

+⋅ ⋅ + +

⋅ ++ −

+⋅ ⋅ + +

⋅ ⋅

⋅ ⋅ ×

⋅ ⋅ ×

⋅ ⋅ ×

⋅ ⋅ ×

=

[ ]( )

[ ]( )

[ ]( )

1

de 5

mode 6

mode 7-shear

4

1ecp y

SQy

d F M

F AP

k

β

β

⋅ ⋅ ⋅

+

⋅=

′

[2]

Where,

[ ][ ]

1

2

21

22

22

1 1

mm

mm

N/mm

N/mm

: embedding length in member 1 : embedding length in member 2

: complex bearing yield stress in member 1

: complex bearing yield stress in member 1

,

ecp

ecp

ecp

ecp

LL

F

FFL

L F

M

α β

= =

( )3

2

2

N/mm

N/mm

32: bending strength of dowel

: shear strength of dowel

y b

b

s

d F

F

F

π= ⋅

) ( )1 2case 1 1.6L Ld µ+ >

( ) ( )( ) ( )

1 1 2 2

1 17 3 7 34 4

1 2

12

1 2 1 23 3

1 1 2 2 1 1 2 2

min . min .0.333 0.333

3 4.81 1min.

cp cp

cp cp

cp cp cp cp

dk L dk L

Ed k Ed k

L L d L Ld

k L k L k L k L

Kγ γ

µ

1 2

−

⋅ ⋅

× ×

+ − ++ +

+

×

=

............... [3]

) ( )1 2case 2 1.6L Ld µ+ ≤

1

1 1 2 2

1 1

cp cp

K dk L k L

−

= +

.............................................................................. [4]

Where,

( )

31

32

N/mm

N/mm

shear stress at neutral plane average shear stress in section

: complex bearing stiffness in member 1

: complex bearing stiffness in member 2

' : shear correction factor

: Shear

cp

cp

k

kkG

[ ]

2

2

N/mm

N/mm

mm

modulus of rigidity, dowel

: modulus of elasticity, dowel

: diameter of dowel

Ed

0.5 0.50.5 0.5

1 21 0.188 1 0.188,cp cpEk d Ek dG Gγ γ

− −

1 2+ × + × = =

[ ][ ]

1

2

21

22

22

1 1

mm

mm

N/mm

N/mm

: embedding length in member 1 : embedding length in member 2

: complex bearing yield stress in member 1

: complex bearing yield stress in member 1

,

ecp

ecp

ecp

ecp

LL

F

FFL

L F

M

α β

= =

( )3

2

2

N/mm

N/mm

32: bending strength of dowel

: shear strength of dowel

y b

b

s

d F

F

F

π= ⋅

2.3 Stiffness calculations

・ a Beam on Elastic Foundation (aBEF) theory was applied for stiffness calculation. To apply for wood-based material dowel, shear deformation of dowel was taken into basic differential equation.

・ About short single shear connection, deformation of joint generates withdrawal of dowel from the first phase of deformation. Therefore, friction between dowel surface and timber hole has important role for stiffness. Rigid beam Rotation with Friction between dowel and timber (RRF) theory was established and applied for the calculation of this fat type. Assuming dowel as rigid beam without bending/shear deformation and considering frictional effort into force balances, 2nd term of [3] and [4] were obtained.

3. Experiment

All patterns of 6 specimens are parted in each 2 specimens as shown below,

Load in R direction RT 45° direction T direction

4. Results and discussion

Fig. 3.2 Loading directions

Fig. 3.1 Single shear test setup

4.1 Test results and characteristics

Test results and theoretical results are shown in Fig. 4.1 and Table 4.1. Values of characteristics of load - displacement curves were determined by the way shown in Fig. 4.2.・ Dowels of slender types break at around displacement of 1d (0.8 ~ 1.5d). And generally dowels

of larger diameter had larger ultimate displacements. ・ Load-displacement curve of slender type dowels showed 3-steps of process. Firstly it was in the

elastic phase, Secondly in moderate load increasing phase till displacement of around 0.5d, and then load becomes constant till break.

・ Dowels of fat types showed non-linear characteristics from the very first phase of deformation. ・ Dowels of fat types of less embedding length than 2.5d in each members (d=18mm) showed

good ductility because of timber yield. Those dowels didn't break even after displacement of 2d.・ Dowels without prevention of separation of shear plane break just after elastic phase.

4.2 Comparison of theoretical results and test results

・ Shear-crack-in-grain capacity of PQy had good coincidences with Py of tests in the case load -displacement curve had 3 deformation steps.

・ In almost all cases except the HB case, PyEYT had good coincidences with Pmax of tests.・ Stiffness calculation results of Kcal had also good coincidences with K of test. For fat dowels,

numerical results seemed to coincide with secant modulus for yield load of non-linear curve.

Single shear tests were conducted in the way shown in Fig. 3.1. Universal test machines of Zwick MTS and Instron 4204 were used for loading. Loading speed was controlled to 1/5 ~ 1/10d/min. Parameters of tests were; 1. Dowel species 2. Timber species 3. Diameter 4. Slenderness, including case of unsymmetrical lengths in eachEach pattern of tests was basically with 6 specimens. And loading directions for dowel grain were 3 directions as shown in Fig. 5.2. Each 2 of 6 specimens were assigned in those. About geometry, distance between dowels and that between dowels and loading planes of top and bottom were more than 7d. And extra lengths of timbers were more than 4d. Tightness (d/D) of dowel diameter by hole diameter were 0.98 ~ 1.00. It required light hammering in almost all the specimens. In the figure, there's cut around shear plane, but it's special specimen for visible versions. Normally, there were no cut around shear plane and the numerical results of cut version were not included in data in next section. It's because of the big difference in both strength and stiffness caused by lessening of nominal hardening effect of dowel.

0

3

6

9

12

15

18

0 5 10 15 20 25 30 35 40Displacment [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25 30 35 40Displacment [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25 30 35 40Displacment [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25 30 35 40Displacment [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25 30 35 40Displacment [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25 30 35 40Displacment [mm]

Load [kN]

PH28-50 BR22sq-50

PR28-50

PX28-50PR28-5015

BR28-50

0

3

6

9

12

15

18

0 5 10 15 20 25 30 35 40Displacment [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25 30 35 40Displacment [mm]

Load [kN]

0

6

12

18

24

30

36

0 5 10 15 20 25 30 35 40Displacment [mm]

Load [kN]

0

8

16

24

32

40

48

0 5 10 15 20 25 30 35 40Displacment [mm]

Load [kN]

PR45-25 BR45-25

PR15-50 BR15-50

KS18-50 KB18-50

KS24-50 KS12-50

HS18-50 HB18-50

TS18-50 TB18-50

0

3

6

9

12

15

18

0 5 10 15 20 25Displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25Displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25Displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25Displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25Displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25Displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25Displacement[mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25Dispalcement [mm]

Load [kN]

Kcal

PQy

PyEYT

0

3

6

9

12

15

18

0 5 10 15 20 25 displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25 displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25displacement [mm]

Load [kN]

0

3

6

9

12

15

18

0 5 10 15 20 25displacement [mm]

Load [kN]

KS18-10 KB18-15

KS18-20 KS18-25

KS18-30 KS18-40

KS18-50 KS18-80

PR28-50slenderness ratio x 10(2 digits: symmetrical, 4 digits: slenderness in each)

dowel species

timber typesdiameter(sq:square)

Fig. 4.1 Experimental and theoretical results. And name of specimens

0 Displacement

Load

Py (tentative)

0.8 Py (tentative)

0.2 Py (tentative)

:K

d×0.05

Py

line shiftt for Py determination

K : obtained by method of least squares applied oninterval between 0.2 - 0.8 Py(tentative)

Fig. 4.2 Determinations of characteristics value

dowel diameter timber K cal [kN/mm]

KS18-50 18 2.7 ± 0.7 5.0 ± 0.5 9.1 ± 1.2 2.9 4.6 7-shear 8.0 6a

KS24-50 24 4.8 ± 0.6 8.8 ± 0.3 14.4 ± 1.4 4.0 8.2 7-shear 14.2 6a

KS12-50 12 1.2 ± 0.3 3.5 ± 0.8 4.4 ± 0.5 1.7 2.1 7-shear 3.5 6a

KB18-50 Douglas-Fir (Fir) 4.5 ± 0.3 5.8 ± 0.7 8.8 ± 1.0 4.0 4.6 7-shear 9.9 6a

HS18-50 Cedar 2.4 ± 0.5 3.2 ± 0.1 6.0 ± 0.8 2.0 2.9 7-shear 5.3 6b1,2

HB18-50 Fir 4.1 ± 0.9 3.5 ± 0.3 3.9 ± 0.4 2.6 2.9 7-shear 5.4 6b1,2

TS18-50 Cedar 2.8 ± 0.8 5.8 ± 0.3 10.8 ± 1.6 2.4 2.5 7-shear 9.7 6a

TB18-50 Fir 3.7 ± 0.7 7.1 ± 0.4 12.7 ± 0.8 3.2 2.5 7-shear 12.0 6a

KS18-10 1.5 ± 0.5 2.6 ± 0.1 4.0 ± 0.7 1.6 2.9 3a 2.9 3a

KS18-15 2.7 ± 0.9 3.9 ± 0.5 5.9 ± 0.4 2.0 4.3 3a 4.3 3a

KS18-20 2.9 ± 0.5 4.3 ± 0.2 7.2 ± 1.0 2.6 4.6 7-shear 5.8 3a

KS18-25 2.5 ± 0.3 4.5 ± 0.6 8.7 ± 1.2 2.9 4.6 7-shear 7.2 3a

KS18-30 3.5 ± 0.6 5.0 ± 0.3 9.6 ± 0.7 2.9 4.6 7-shear 8.0 6a

KS18-40 3.0 ± 0.4 4.8 ± 0.5 9.7 ± 2.0 2.9 4.6 7-shear 8.0 6a

KS18-80 5.0 ± 2.4 4.7 ± 0.7 12.8 ± 1.6 2.9 4.6 7-shear 8.0 6a

PR28-50 Finnish Pine (pine) 2.4 ± 0.6 8.0 ± 1.0 11.4 ± 1.6 2.9 5.7 7-shear 13.0 6b1,2

PH28-50 Pine, 3mm layer gap 2.3 ± 0.5 7.9 ± 1.8 12.2 ± 1.8 2.9 5.7 7-shear 13.0 6b1,2

PR28-5015 2.4 ± 0.7 8.0 ± 1.8 9.7 ± 1.0 2.8 5.7 7-shear 10.1 5b1,2

PR15-50 15 1.0 ± 0.3 2.9 ± 0.5 4.0 ± 0.3 1.5 2.3 7-shear 3.9 6b1,2

PR45-25 45 5.2 ± 0.3 17.8 ± 2.2 24.9 ± 3.3 5.3 12.2 7-shear 27.9 3b1,2

PX28-50 28 Pine, perpendicula grain 1.6 ± 0.3 7.9 ± 1.7 11.5 ± 1.6 1.8 5.7 7-shear 10.8 6a

BR28-50 28 3.1 ± 0.3 11.2 ± 1.1 12.3 ± 1.0 3.6 8.3 7-shear 14.7 6b1,2

BR15-50 15 1.5 ± 0.2 3.7 ± 0.7 4.6 ± 0.2 1.8 2.4 7-shear 3.6 6b1,2

BR45-25 45 7.6 ± 1.0 28.5 ± 3.0 36.1 ± 2.9 5.6 17.8 7-shear 34.0 3b1,2

BR22sq-50 22sq 2.1 ± 0.6 8.9 ± 1.0 11.0 ± 1.3 2.5 6.4 7-shear 8.2 6b1,2

Pine

Name and Conditions of Specimens

18

Japansese cedar(cedar)

Cedar

Pine

Finnish Pine

Finnish Birch

18

28

White Oak

JapaneseCypress

Compressedbamboo

White Oak

P u cal [kN]

Experimaental ResultsK [kN/mm] P y0.05d [kN] P max [kN] P y cal [kN]

Analytical Results

0 Displacement

Load

shear crackpararell to grains

breaking of dowel

shear crack

+

bearing yield

of timbers

bearing yield

of timbers

(by bending tensile and shear tensile stress)

breaking of dowel[effect of gap-increment/initial-gap]

withdrawal of dowel

4.3 Summary of joint yield process

From visible test result and comparison between experimental and theoretical results, patterns of load-displacement characteristics can be classified as Fig. 4.3.

Table. 4.1 Experimaental and theoretical results

Fig. 4.3 Pattern classification of yield process

4.4 Points for joint design

・ Dowels of halfway length, just shorter than length of bending break in ultimate state, have stable stiffness, strength and ductility.

・ Nominal hardening effect has important role for joint calculation.・ Yield theory and aBEF theory can be applicable with appropriate modification of calculation

formula.・ Shear crack means first yield of joint when it occurs. But it doesn't mean ultimate yield of joint

if shear planes are still in contact.

0 3d1d 2d

03d 1d2d5d 4d

4.3 Assumption of stress distribution after shear crack in grain

It's easy to understand phenomenon of ductile reaction when dowels are relatively short and ultimate states are on bearing yield of timbers. It requires detailed discussion about numerical coincidence between calculated results of PyEYT, including bending break of dowel, and Pmax of tests. After shear crack in grain, dowel around shear plane becomes piled beams fixed at crack end as shown in Fig. 4.4.It could be assumed; under concentrated stress around shear plane, those piled beams have slight allowance for shear declination of layers and can carry shear stress each other through friction. And piled beams react almost close to combined normal beam. So even after shear crack in grain, joint load can increase till the state assumed by yield theory, including bending break of dowel.With this assumption, the coincidence of PyEYT and Pmax can be explained. Bending crack positions of dowels had also good coincidence with calculated results. Dowel after test is shown in Fig 4.4 and its calculated bending crack position is 1.1d from shear plane. In the case of larger bending capacity of compressed bamboo, both calculated result and test result of crack length are larger. And those had good coincidence with each other.

Fig. 4.5 Deformation process of Finnish Pine dowel d28 with Finnish pine as timber

initial state shear crack in grain beginning

grain cut beginning (load constant) just before break-up load released

Fig. 4.4 Assumption of stress distribution (Left) and breaking crack position of KS18 (Right)

290 36

3636

600

0

2

4

6

8

10

12

14

16

0.00 0.05 0.10 0.15 0.20 0.25

deformation angle [rad]

moment [kN･m]

4 double shear wood-dowels

8 single shear wood-dowels

+1 double shear screw

10 double shear screws

assumed moment capacityof timber members

6. Coclusion

Fig. 5.2 Moment test results of beam- beam connection

Fig. 5.1 Frame concept and connection geometry

Basic yield process of wood dowel shear joint were almost clarified. And proposed theoretical calculation methods showed good applicability for prediction of yield process of joint. And from the knowledge obtained, better solution for joint design was also indicated.

References

1) Johansen, KW. : Theory of timber connections, pp.249-262, 19492) Kuenzi E.W. : ”Theoretical Design of a nailed or bolted joint under lateral load”, no. D1951,

Forest Product Laboratory, Madison, U.S. Department of Agriculture, Forest Service, 19553) Patton-Mallory, M., Pellicane, P. J., Smith, F. W.: “Modeling bolted connections in wood:

Review” Journal of Structural Engineering, pp1054-1063, 19974) Soltis, L.A., Rammer, D.R.,: “Shear strength of unchecked glued-laminated beams”, Forest

Product Journal, 44(1), pp.51-57, 19945) Sandberg, L. B., Bulleit, W. M., Reid, E. H. : “Strength and Stiffness of oak pegs in traditional

timber-frame joints”, Journal of Structural Engineering, pp.717-723, 20006) Wilkinson, T.L.: “Bolted Connection Strength and Bolt Hole Size”, FPL-RP-524, Forest

Products Laboratory, Madison, U.S. Department of Agriculture, Forest Service, 19937) M. Tei, A. Kitamori, A. J. Leijten, K. Komatsu, : Mokuzai-Gakkaishi, 52(6), pp. 358-367, 2006

It's a case of beam-beam connection. The total structure consists of single directional rahmen frames by lapped glue joins. And at small moment areas, several mechanical joints were applied in order to make yiled hinges in the frame. In the conditions, beam-to-beam connections requires enough ductility and stiffness.Each layer member thickness is 36mm. And with 3 layers, 108mm in total beam thickness. Beam depth was 290mm and length of connecting area were 600mm. Fig 5.1 shows concept of the structure and connection pattern diagram.Screws (f6, l=100mm) and White Oak (f15, l=72mm and l=108mm) dowels were applied for the connection tests. Stiffnesses and yield strengths were designed on the same level in every case and all showed enough stiffness and strength for requirement. Single shear wood-dowel of halfway length, as mentioned 4.4, showed enough ductility while double shear wood-dowel broke on too early phase by contrast. Ultimate deformation angle of single shear case was almost same level as screws.

5. Practical application example based on 4.4