00694 Pouyan Zarnani - Timber Design Society

PREDICTVE ANALYTICAL MODEL FOR WOOD CAPACITY OF 

RIVET CONNECTIONS IN GLULAM AND LVL 

Pouyan Zarnani 1 and Pierre Quenneville 2 

ABSTRACT: Timber rivets are hardened nails with a rectangular cross section for making connections with high load 

transfer capacity, high stiffness and more ductility. Rivets are a cost effective alternative to large fasteners such as bolts 

which cause large localized stresses and force brittle ruptures in the timber. Rivets are part of the Canadian and U.S. 

structural wood design standards. However, in the current standards there is no closed form solution for the wood 

strength prediction. Also, the standards restrict the use of rivets to specific configurations and for glulam and sawn 

timber of some limited species. A simple close-form analytical method to determine the resistance of wood in rivet 

connection in timber products is proposed. For the wood strength, the stiffness and strength of the planes subjected to 

shear and tension stresses are taken into account. An algorithm is presented which allows the designer to predict the 

different possible brittle, ductile and mixed failure modes. Results of tests on New Zealand Radiata Pine LVL and 

glulam and data available from literature confirm the validity of this new method and show that the proposed analytical 

method can be used as design provision for timber riveted connections. 

KEYWORDS: Timber rivet, connection, wood capacity, failure mode, LVL, glulam 

1 INTRODUCTION 

1.1 GENERAL 123 

The timber rivet connections have been used in Canada 

and U.S. in different types of structures over the last 3 

decades such as in connections of a glulam arch 

spanning 100 meters. Rivets are a cost effective 

alternative to large fasteners such as bolts which cause 

large localized stresses and force brittle ruptures in the 

timber. Also, rivets have lower variability in strength 

and deflection properties than most other conventional 

connectors and have more ductile behaviour under 

dynamic loads. 

For riveted connections, there are two major mechanisms 

of failure; the brittle tear-out of a plug of wood defined 

by the rivet’s perimeter and the ductile yielding of rivets 

with localized wood crushing [1]. The brittle failure 

mode should be avoided since it induces the brittle 

downfall of the whole structure and the ability to predict 

it is important. In addition, a mixed failure mode is also 

possible and is investigated in this study. An algorithm is 

presented for the prediction of connection strength in this 

failure mode. 

The objective of this study is to develop a set of design 

equations to predict the strength and failure mode of the 

riveted connections of different configurations in diverse 

species loaded parallel-to-grain. 

1 Pouyan Zarnani, University of Auckland, Department of Civil 

and Environmental Engineering, 20 Symonds St., Auckland, 

New Zealand. Email: pzar004@aucklanduni.ac.nz 

2 Pierre Quenneville, University of Auckland, Department of 

Civil and Environmental Eng., 20 Symonds St., Auckland, 

New Zealand. Email: p.quenneville@auckland.ac.nz 

1.2 BACKGROUND 

The most significant work on timber rivets is that of 

Foschi and Longworth [2] which became the basis for 

the timber rivet design procedures in the Canadian O86- 

09 [3] and the U.S. NDS [4] codes. The authors 

proposed a prediction model (Eq. 1) based on finite 

element analysis for wood strength, P w , loaded parallelto-grain 

in brittle failure which involves the tensile, P t , 

and shear, P v , capacities of the failure areas of wood. 

The authors provided tables of values for the numerically 

derived factors K, β, α and γ which are related to the 

connection geometry parameters. 

ft, 

k At 

Pt 

 

Kttt 

h 

P w = min (1) 

fv, 

k Av 

Pv 

 

K 

s 

s 

h 

In Eurocode 5 [5], Annex A, the wood resistance of 

dowel-type timber connections in plug shear failure is 

determined using Equation 2. The European equation is 

based on the maximum of the tensile resistance of the 

end face or the sum of the shear resistances of the side 

and bottom faces correspondent to the effective wood 

depth, t ef , which depends on the governing failure mode. 

1.5A 

t, 

ef ft, 

k 

P w = max (2) 

0.7 f 

A v, 

ef v, 

k 

Stahl et al. [6] presented a simplified analysis for wood 

strength. They assumed that the tensile and the shear 

capacities are additive. Their proposed equation (Eq. 3) 

is based on three possible wood failure modes shown in 

Figure 1. Their proposed model for wood strength in

ittle failure mode had better predictions in comparison 

to the ones from the Canadian code. 

P w = min (P a , P b , P c ), P i = 0.2 f t,k + 0.2 f v,k (3) 

(a) (b) (c) 

Figure 1: Proposed wood failure modes by Stahl (2004) 

1.3 MOTIVATION 

In the models which have been proposed for the wood 

strength so far, the minimum, maximum or the 

summation of the tensile and shear capacities of the 

failed wood block resisting planes is considered as the 

wood strength of the connection. These methods might 

not be appropriate since the stiffness in tensile and shear 

planes differs and this results in uneven load distribution 

amongst the resisting planes [1,7]. For instance, in a plug 

shear failure (Fig. 1a), the contribution of the bottom or 

lateral shear planes to the wood resistance cannot simply 

be considered as a function of their respective area as the 

connection load is not shared uniformly among the 

resisting planes due to the unequal stiffness of the 

adjacent wood. In the proposed analysis, the 

shortcomings of the existing predictive models are taken 

into account. 

2 NEW ANALYSIS FOR WOOD 

STRENGTH 

The proposed analysis for wood strength is based on a 

linear elastic spring system in which the applied load 

transfers from the main loaded wood block to the contact 

planes in conformity with the relative stiffness ratio of 

each resisting plane (Fig. 2). By predicting these 

stiffnesses, the contribution of each plane to lateral 

resistance and finally the ultimate load that cause brittle 

failure on these planes can be derived. 

Head 

tensile plane - h 

Bottom 

shear plane - b 

Lateral 

shear planes - l 

Figure 2: Proposed elastic spring model 

The difference in the stiffness of the tensile and shear 

planes is a function of the differences between the 

modulus of elasticity and modulus of rigidity, the wood 

surrounding the loaded block (bottom, end and edge 

distances-d z , d a and d e ) and also the connection 

geometry. 

2.1 HEAD TENSILE PLANE STIFFNESS 

In the rivet connection, the load is transferred from the 

plate to the wood block through the rivets. The load 

which applied to the wood increases as it reaches the 

head of the joint (Fig. 3). The load distribution in the 

row of rivets is assumed to be linear. Johnsson and Stehn 

P w 

K h 

K b 

P w 

Main loaded 

block 

K l 

P h P b P l 

Δ 

[7], using a load distribution model based on a spring 

system, showed that the maximum variation from the 

linear assumption, on the distributed loads among 

fasteners in a nail connection with 10 nails in a row 

before yielding was approximately 12%. The head 

tensile plane stiffness can then be derived by considering 

the tensile deformation of the loaded block, Δ, which is 

given by 

L 

 

EA ( N 

(4) 

where E is the modulus of elasticity, L is the length 

subjected to the tensile stress and A th the area subjected 

to the tensile stress at the head of the block. Thus, the 

average tensile stiffness for the head plane would be 

K 

h 

th 

2EA 

 

L 

th 

C 

(5) 

These equations use the connection geometry variables 

shown in Figure 4 and all dimensions are in mm. 

Figure 3: Simplified analytical model 

2.2 BOTTOM SHEAR PLANE STIFFNESS 

By developing an FE model, Foschi and Longworth [2] 

studied the effect of the bottom distance d z on the bottom 

plane shear stress. They observed that the shear stresses 

vary when d z is less than 2 times the rivet penetration, L p . 

They considered L p as the thickness of the failed block, 

t ef . This observation is applied when considering the 

effective depth of the wood bottom block in contact with 

the main loaded block in order to simplify the model 

(Fig. 3) to estimate the distortion of the bottom block 

which is considered fixed at the bottom edge and is 

subjected to shear stress on the top surface. Dividing the 

sum of the bottom shear forces P b by the total area over 

which they act A sb defines the average shear stress τ sb : 

 

Fixed 

edge 

sb 

Pb 

 

A 

sb 

in which G is the modulus of rigidity, γ sb the shear strain 

and X b the maximum effective depth of the bottom block 

defined as X b =2t ef . Thus, the average pure shear stiffness 

would be K GA X . 

sb 

1) 

Nc 

1 

Ph 

i 

 

i1 

NC 

 

 

sbG 

G 

X 

sb 

b 

b 

Ph 

L 

 

2EA 

da 

P l 

P 

Main loaded 

L 

t 

P h block 

ef 

P b 

P b 

X b=2t ef 

d z ≥ X b 

In contact 

bottom block 

Tensile force 

distribution 

L 

da 

However, as it is shown in Figure 3, the bottom block 

has a fixed edge at its head on its entire cross section 

which increases the stiffness and prevents deformation 

under the applied shear force. 

th 

X b 

Bottom block 

Fixed edge 

Shear force 

distribution 

(6)

the lateral blocks and is Atl 

2tef 

Xl 

. Consequently, the 

average lateral shear planes stiffness can be defined by 

Kl 

( 1 

F)( 

Ksl 

Ktl) 

(11) 

in which F is the reduction factor for lateral shear planes 

stiffness [1]. The reduction factor for the lateral shear 

plane, F, is determined using: 

F=0 , If d e ≥ 1.25X l 

F=0.16 (2.5- d e / (X l /2)) 2 , If d e < 1.25X l 

(12) 

Figure 4: Definition of connection geometry variables 

If Δ is the whole deformation of the bottom block at the 

top, then it decreases rapidly in a nonlinear form as it 

reaches the bottom. Adjacent to the bottom fixed edge, 

the deflection curve would be tangential as the stress 

diminishes and approaches zero. It is assumed that the 

deformed shape is a polynomial curve with order nine 

(n=9). Therefore, the average deflection for the whole 

cross section can be theoretically considered as Δ/(n+1) 

equal to Δ/10 in case of tensile deformation. Thus, the 

additional average tensile stiffness for the whole cross 

section, K tb , can be estimated as 

K 

tb 

(7) 

where A tb is the effective tensile area of the bottom block 

given as A tb =S q X b (N R -1). Therefore, the average bottom 

shear plane stiffness can be defined by 

K 

b 

(8) 

Foschi and Longworth [2] observed that when the 

bottom distance d z becomes less than X b ,the bottom shear 

stress decreases and the load thus released is transferred 

almost in its entirety to the tensile plane. To take this 

effect into account, a factor H is proposed [1]. This 

factor can be considered as the reduction rate of the 

bottom shear plane stiffness, H (Eq. 9), as a result of 

decreasing the bottom distance d z less than X b . 

H=0 , If d z ≥ X b 

H=0.25 (2- d z / t ef ) 2 , If d z < X b 

Thus, 

EAtb 

 

10L 

K 

sb 

K 

2.3 LATERAL SHEAR PLANES STIFFNESS 

(10) 

Assuming that the mechanical properties of the wood for 

lateral and bottom shear planes are the same, the 

correspondent equations for the two side lateral shear 

planes can be developed similarly. The average pure 

shear stiffness for the lateral planes would become 

Ksl 

AslG 

X 

l 

where A sl is the summation of the areas 

subjected to the lateral shear stress and X l the maximum 

effective edge distance (equal to 2 times the half of the 

distance between the first and the last rows, which is 

comparable to X b =2t ef for the bottom shear plane). The 

additional average tensile stiffness can be given as 

K EA L in which A tl is the effective tensile area of 

tl tl 

10 

tb 

Kb 

( 1 

H)( 

Ksb 

Ktb) 

(9) 

2.4 CLOSED-FORM APPROACH 

By predicting the stiffness of the wood surrounding each 

of the failure planes (K h , K b and K l ), one can predict the 

proportion of the total connection load applied to each 

plane, R K K 

 

i i 

. 

By further establishing the resistance of each of the 

failure planes as a function of a strength criterion, one 

can verify which of the failure planes governs the 

resistance of the entire connection. Thus, the wood load 

carrying capacity of the connection (Eq. 13) is the load 

which results in the earlier failure of one of the resisting 

planes due to being overloaded and equals to the 

minimum of P wh , P wb and P wl . In other words, the wood 

strength of the connection is the total capacity of the one 

plane which fails first plus a portion of strength capacity 

of the other planes. Moreover, while one plane fails then 

the load transfers to the rest of the planes in accordance 

with their relative stiffness ratios. It could be possible 

that the occurrence of the first failure of one plane does 

not correspond with the maximum load of the 

connection. 

Kb 

Kl 

Pwh 

ft, 

m Ath 

(1 ) 

K h K h 

Kh 

Kl 

P w = N p .min Pwb 

fv, 

mCab 

Asb 

(1 ) (13) 

Kb 

Kb 

Cal 

Asl 

Kb 

Pwl 

Pwb 

C A K 

ab 

sb 

Here f t,m is the wood mean strength in tension parallel to 

the grain (MPa) and f v,m is the wood mean strength in 

shear along the grain (MPa). Also, C ab and C al are the 

ratios of the average to maximum stresses on the bottom 

and lateral shear planes respectively given by Equations 

14 and 15. These coefficients are derived based on the 

increasing load distribution on the shear planes (Fig. 3). 

The factor of k e is applied to C al to account for the 

reduction of the resisting area due to the cracks 

formation on the lateral planes, estimated at 20% of the 

failed block thickness while d e is less than 1.25X l . 

C 

ab 

S 

p( 

N 

 

C k C 

al 

e 

ab 

C 

( N 

C 

C 

1)/ 

2 1) 

d 

N ( L d ) 

k e 

k e 

1 

0.8 

a 

(14) 

(15) 

For a connection having only one plate, N p =1, the 

member thickness value, b, to be used to determine 

d z = b/2-t ef is twice the thickness of the wood. 

l 

a 

, If d e 1.25X l 

, If d e

2.5 EFFECTIVE WOOD THICKNESS 

2.5.1 BRITTLE FAILURE 

In current tests on LVL and glulam, the average 

thickness of the failed block, t block , in the majority of the 

brittle failures was observed around 0.85L p . This 

thickness corresponds to the elastic deformation of the 

rivets since there were no observed plastic deflections. 

For brittle failure modes, the effective wood thickness 

(Eq. 16) is determined from the elastic deformation of 

the rivet modelled as a beam on an elasto-plastic 

foundation (Fig. 5). The rivet is supported by springs 

with bilinear response that simulate the local nonlinear 

embedding behaviour of the timber surrounding it. For 

more details regarding the model refer to Zarnani and 

Quenneville [8]. 

Rivet 

flexural axis 

k h 

Embedding 

stiffness 

Figure 5: Spring model of elastic deformation of rivet as 

a beam on an elasto-plastic foundation 

0.95L p , for L p equals to 28.5 mm 

t ef,e ~ 0.85L p , for L p equals to 53.5 mm (16) 

0.75L p , for L p equals to 78.5 mm 

2.5.2 MIXED FAILURE 

Wood effective thickness 

w(x) 

For some connection groups, considerable decrease of 

t block combined to a distortion of rivets was visible. This 

failure mode is defined as the mixed mode since the 

wood fails with some deflection of the rivets before they 

reach complete yielding. In these groups, t block 

corresponded to the effective wood thickness, t ef , 

depending on the governing failure mode of the rivets 

(Fig. 6). 

Mode I m Mode III m Mode IV 

Figure 6: Effective thickness based on the rivet 

embedded length in different failure modes 

x 

w 

Rotationally fixed 

Rivet head 

t ef can be derived using Equation 17 based on the 

Johansen’s yield theory [9] which is the foundation for 

the EYM prediction formulas in Eurocode 5 [5]. The 

proposed prediction for the wood strength showed good 

agreement with observed values of t block for these groups. 

t ef,y = 

f h 

L p 

t ef 

2 

L p 

f 

P r 

M 

f 

2 

y, l Lp 

d 

h,0 

l 

h,0 

y, 

l 

d 

l 

2 

f h 

M 

L p 

t ef 

P r 

M y 

o 

P 

f h 

M y 

Mode I m 

Mode III m 

Mode IV 

L p 

t ef 

P r 

(17) 

M y 

d l is the rivet cross-section dimension bearing on the 

wood parallel-to-grain, (equal to 3.2 mm); ƒ h,0 is the 

embedment strength of the wood which can be 

determined as a function of d l and the density of the 

wood [10]; and M y,l is the parallel-to-grain moment 

capacity of the rivet, equal to 30000 Nmm [6]. 

2.6 PROPOSED PROCEDURE 

Based on the observation that the effective wood 

thickness differs in brittle and mixed failure modes 

which affect the wood strength, the following procedure 

(Fig. 7) is suggested to determine the load carrying 

capacity of the riveted connection for the possible brittle, 

ductile and mixed failure modes. In this paper, the rivet 

strength and its yielding mode is based on experimental 

results which also can be predicted by a consistent yield 

model proposed by Zarnani and Quenneville [10]. 

Assume t block = t ef,e corresponding to rivet elastic 

deformation to predict wood strength P w 

from Eq. 13 and compare with rivet yielding strength P r 

If P w 

No 

If P w ≥ P r 

No 

P u = P w 

(Mixed failure) 

Figure 7: Proposed algorithm for different possible brittle, 

ductile and mixed failure modes 

3 EXPERIMENTAL PROGRAM 

3.1 SPECIMENS 

Yes 

Assume t block =t ef,y corresponding to 

rivet yielding mode to predict P w 

Yes 

Load carrying capacity of 

connection P u = P w 

(Brittle failure) 

P u = P r 

(Ductile failure) 

The laboratory tests were set up to evaluate the effect of 

bottom, edge and end distances on connection strength 

and to force and observe the possible connection wood 

modes of failure. Specimens were manufactured from 

New Zealand Radiata Pine LVL grade 10 and glulam 

with grade of 8. The tests series were divided into 26 

groups for LVL (Table 1) and 6 groups for glulam 

(Table 2). 3 replicates were tested for each group of 

specimens for LVL and 4 replicates for glulam. The 

parameters for connection geometries (Fig. 4) used 

varied from 4 to 8 for N R and N C ; from 15 to 25 mm for 

S q and 25 to 50 mm for S p ; L p from 28.5 to 78.5 mm 

(with rivet lengths L r of 40, 65 and 90 mm); d z from 

0.1X b to 1.1X b ; d e from 0.2X l to 1.9X l and d a from 50 to 

125 mm. The specimens had riveted plates on both faces 

of timber, making a symmetric connection that better 

simulates real applications. The steel side plates were 8.4

Grain 

1200 mm 

Load F [kN]nt 

mm thick of 300 grade with predrilled 6.8 mm holes to 

ensure adequate fixity of the rivet head. 

In the majority of the groups, the characteristics were 

specified in order to prompt wood failure and maximize 

the amount of observations on the brittle mechanism. 

This is why many specimens have identical row spacing 

of 15 mm. After observing the test results, the groups 

were matched and named based on the modes of failure. 

In Table 1 and 2, BRG, MIG and DUG stand for tests 

series with brittle, mixed and ductile modes of failure 

respectively, also, L for LVL and G for glulam. All 

specimens were conditioned to 20°C and 65% relative 

humidity to attain a target 12% equilibrium moisture 

condition (EMC). At the time of the test the wood had an 

average density of 590 and 480 kg/m 3 with a coefficient 

of variation of 4% and 9% at an average moisture 

content of 11.5% and 11% for LVL and glulam 

respectively. 

3.2 TEST SETUP 

Testing procedures outlined in ISO 6891 [11] were 

followed. The load was applied to the specimens using 

an MTS loading system. The deformation of the 

connection was measured continously with a pair of 

symmetrically placed LVDTs. Data was recorded with a 

frequency of 2 Hz. The specimens were loaded in 

tension parallel-to-grain and were fabricated with riveted 

connection in one end and bolts on the other end. The 

bolted connection was sufficiently strong to allow failure 

of the tested riveted connections to be observed in all 

cases. Additional plates were added between the grip 

and the rivet plate with the total thikness of 25 mm to 

limit the plate deformation and also provide resistance 

for the out-of-plane moment of the rivet plate resulting 

from eccentricities at time of failure. The loading rate 

was adjusted to 1 mm/min and kept constant until the 

occurence of failure in both or either side of the riveted 

connections. A typical specimen in the testing frame in 

shown in Figure 8. 

4 RESULTS AND DISCUSSION 

4.1 GENERAL 

The load-slip curve of each group was plotted (Fig. 9) 

and the ultimate load and the type of failure were 

recorded. The peak loads ranged from 159 kN to 468 kN. 

The effect of failure modes on the load-displacement 

plots is shown in Figure 9. The displacements observed 

in ductile failures with complete yielding of the rivets 

are far beyond the usual range of serviceability, but they 

indicate that the connections would be suitable for use in 

seismic design if rivet yielding failure mode controls 

[12]. In case of brittle failures, the maximum connection 

deformation was 2 to 3 mm and the wood rupture 

occurred suddenly. For mixed mode failures in which 

wood failed before final yielding of the rivets, more 

deflection can be seen compared to brittle failures due to 

slight deflection on rivets. The highest deformation for 

the mixed failures belongs to specimen MIG23-L in 

which the rivet and wood strengths are very close. 

Results for the LVL and glulam groups tested are listed 

in Table 3 and 4 respectively. The thickness of the failed 

blocks and predominant modes of failure observed are 

also listed in the tables. Along with the results, 

connection capacities have been calculated using the 

proposed analysis. 

The wood tensile and shear strengths (f t,m , f v,m ) used in 

the analysis were determined from the conducted 

material property tests (Fig.10). The average tensile 

and shear strengths in these tests were 34.3 MPa 

(COV=12%) and 6.8 MPa (COV=10%) for RP-LVL and 

24.1 MPa (COV=24%) and 4.2 MPa (COV=15%) for 

RP-glulam (samples from inner laminations) 

respectively. For the stiffness properties, based on the 

codes an average ratio of modulus of rigidity to modulus 

of elasticity (G/E) is considered equal to 0.045 and 0.069 

for LVL and glulam respectively in order to make the 

planes’ stiffness equations independent of G and E 

values. 

500 

450 

Rivets, 

along 

grain 

400 

350 

300 

250 

200 

LVDTs 

8/M20 

bolts 

Grip 

plates 

150 

100 

Brittle failure Mode 

50 

Ductile failure Mode 

Mixed failure Mode 

0 

0 1 2 3 4 5 6 

Displacement U [mm]nt 

Figure 9: Load-slip plots for joint tensile tests loaded 

parallel to grain in brittle, mixed and ductile failure modes 

Figure 8: Typical specimen in testing apparatus

LVL 

groups 

No. of 

rows by 

columns 

Row 

spacing 

Table 1: Configuration for the tested connections on LVL 

Column 

spacing 

Rivet 

penetration 

Member 

thickness 

Member 

width 

End 

distance 

Bottom 

distance 

Edge 

distance 

(N R*N C) 

S p S q L p b W d a d z d e 

(mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) 

BRG1-L 25 15 28.5 90 220 75 17 58 

BRG2-L 25 15 28.5 126 220 75 35 58 

BRG3-L 25 15 28.5 180 220 75 62 58 

BRG4-L 25 15 28.5 126 300 75 35 98 

BRG5-L 25 15 28.5 126 370 75 35 133 

BRG6-L 8*8 25 15 28.5 126 220 100 35 58 

BRG7-L 25 15 28.5 126 220 125 35 58 

BRG8-L 25 15 53.5 126 220 50 10 58 

BRG9-L 25 15 53.5 126 220 50 10 58 

BRG10-L 25 15 53.5 180 220 50 37 58 

BRG11-L 25 15 53.5 216 220 50 55 58 

BRG12-L * 25 15 53.5 216 220 50 55 58 

BRG13-L 25 15 53.5 180 300 50 37 98 

BRG14-L 8*6 25 15 53.5 180 370 50 37 133 

BRG15-L 25 15 53.5 180 220 75 37 58 

BRG16-L 25 15 53.5 180 220 100 37 58 

BRG17-L 

50 15 53.5 126 220 75 10 88 

4*8 

BRG18-L 25 15 28.5 126 220 75 35 73 

BRG19-L 25 15 53.5 180 260 50 37 93 

MIG20-L 6*6 25 15 78.5 216 220 50 30 73 

MIG21-L 25 15 78.5 216 220 75 30 88 

MIG22-L 25 15 53.5 180 300 75 37 128 

MIG23-L 4*6 25 15 28.5 180 220 75 62 88 

DUG24-L 

DUG25-L 

8*6 

6*6 

25 25 28.5 126 260 125 35 43 

25 25 53.5 180 260 125 37 68 

DUG26-L 

25 25 78.5 216 260 125 30 93 

4*4 

* 

In all groups except BRG12, rivets were installed on the faces of the specimen. In BRG12, rivets were driven into the other 

sides of the specimen with the same configuration as BRG11. 

Glulam 

groups 

No. of 

rows by 

columns 

Row 

spacing 

Table 2: Configuration for the tested connections on glulam 

Column 

spacing 

Rivet 

penetration 

Member 

thickness 

Member 

width 

End 

distance 

Bottom 

distance 

Edge 

distance 

(N R*N C) 

S p S q L p b W d a d z d e 

(mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) 

BRG1-G 8*8 25 15 53.5 135 225 75 14 60 

BRG2-G 8*6 25 15 53.5 180 225 75 37 60 

BRG3-G 6*8 25 15 28.5 135 225 75 39 75 

BRG4-G 4*8 50 15 53.5 135 225 75 14 90 

MIG5-G 4*6 25 15 78.5 230 225 75 37 90 

DUG6-G 6*6 25 25 53.5 180 270 125 37 73 

Note: In all groups, rivets were installed on the faces of the specimen. 

(a) 

(b) 

Fig. 10: Material property tests; (a) Tensile strength - European testing standards 

EN 408:2003 [13], (b) Shear strength - AS/NZS 4063.1 [14] by Lindsay [15]

Test groups with tightly spaced rivet pattern exhibited a 

failure with a brittle manner (Fig. 11). A sudden plug 

shear failure happened while a block of wood bounded 

by the rivets perimeter was pulled away from either one 

side or both sides of the specimens. As shown in Table 3 

and 4, in BRG test series the failed block thickness t block 

were observed at approximately 0.85L p which 

corresponds to the elastic deformation of the rivets since 

no plastic deflection was observed as in Figure 11a. 

However, in MIG test series, there was a considerable 

decrease on t block with visible distortion of the rivets (Fig. 

11b). This failure mode is defined as mixed mode since 

the wood fails before final yielding of the rivets. In this 

case the load-carrying capacity of the wood is based on 

the stiffness and strength of the tensile and shear planes 

corresponding to the effective depth of the wood, t ef,y . 

5 VALIDATION OF NEW ANALYSIS 

AND COMPARISON WITH OTHER 

MODELS 

Strength predictions of the current tests and tests from 

the literature were made using the new analytical method 

to compare it with codes equations and other analytical 

models. The CSA O86-09 [3], Eurocode 5 [5] and the 

prediction model proposed by Stahl et al. [6] were used 

in the comparison. Using the U.S. (NDS) code [4], 

results in similar predictions as the O86 code ones after 

correcting for limit state definition since the rivets are 

adopted from CSA [6]. 

5.1 CURRENT TEST DATA 

Based on the proposed analysis, in the BRG test groups 

(Table 3 and 4), the wood strength for t block =t ef,e was 

lower than the rivets yielding strength P r and 

consequently the failure mode was brittle. However, in 

the MIG test groups, the wood strength for t block = t ef,e 

was more than the rivets strength. The strength of the 

connection was thus checked for the possible mixed or 

ductile modes of failure. Since in these test series the 

wood strength for t block =t ef,y was weaker than the rivets 

strength, therefore a mixed mode failure occurred for the 

connection with a load carrying capacity less than the 

rivets resistance. As shown in Table 3 and 4, there is 

very good agreement between the predictions and 

observations for the thickness of the failed block, the 

governing failure mode, and the strength of the 

connection. 

Fig. 12 shows the strength predictions of the 

experimental groups using the new analysis and the 

predictions from O86-09, EC5 and Stahl’s method. The 

proposed analysis results in more precise predictions 

with a correlation coefficient (r 2 ) of 0.91 and a mean 

absolute error (MAE) of -2.6% and standard deviation 

(STDEV) of 9.8%. 

(a) 

(b) 

t block ~t ef,y (Mode IV) 

Brittle plug shear 

t block ~t ef,y (Mode III m) 

t block ~t ef,y (Mode IV) 

Brittle plug shear 

Figure 11: Thickness of the failed block in LVL and glulam; (a) Brittle failure mode, (b) Mixed failure mode

LVL 

groups 

Rivet 

penetration 

Table 3: Strength and failure mode predictions using the proposed method 

compared to experimental results on LVL 

Proposed 

wood strength 

P w 

(kN) 

Rivet 

strength 

P r * 

(kN) 

t block 

(mm) 

Proposed/Observed 

Proposed 

wood 

strength P w 

(kN) 

Connection strength 

(prediction/test result) 

Mean 

ultimate 

load † Failure mode 

L p 

(mm) 

t block =t ef,e t block =t ef,y P u 

(kN) 

BRG1-L 28.5 314 "461" 27.1(t ef,e ) / 23 - 314/358 Brittle/Brittle 
















BRG17-L 53.5 441 "345" 40.1(t ef,y ) / 50 362 345/290 Ductile/Brittle 



MIG20-L 78.5 436 "417" 26.7(t ef,y ) / 29 233 233/245 Mixed IV/Mixed IV 

MIG21-L 78.5 338 "278" 26.7(t ef,y ) / 27 176 176/207 Mixed IV/Mixed IV 

MIG22-L 53.5 255 "259" 45.5(t ef,e ) / 35 - 255/214 Brittle/Mixed III m 

MIG23-L 28.5 178 "172" 24.2(t ef,y ) / 19 166 166/159 Mixed III m/Mixed III m 

DUG24-L 28.5 505 "345" 24.2(t ef,y ) / - 498 - /345 Ductile III m/Ductile III m 

DUG25-L 53.5 515 "388" 40.1(t ef,y ) / - 479 - /388 Ductile III m/Ductile III m 

DUG26-L 78.5 419 "185" 26.7(t ef,y ) / - 213 - /185 Ductile IV/Ductile IV 

* The rivet strength in BRG and MIG groups are based on the rivet capacity derived from DUG tests. 

† Coefficient of variation (COV%) for brittle/mixed failure modes 4-9 % and for ductile failure modes 2-4%. 

Table 4: Strength and failure mode predictions using the proposed method 

compared to experimental results on glulam 

Proposed 

t block 

Connection strength 

Proposed 

wood 

Rivet 

Rivet 

(mm) 

(prediction/test result) 

wood 

strength 

Glulam penetration 

strength 

strength P w 

Mean 

P 

groups 

w 

P r 

(kN) ultimate 

(kN) (kN) Proposed/Observed 

load † 

Failure mode 

L p t block =t ef,e 

P 

t 

(mm) 

block =t u 

ef,y 

(kN) 

BRG1-G 53.5 340 "531" 45.5(t ef,e ) / 46 - 340/335 Brittle/Brittle 


BRG3-G 28.5 188 272 * 27.1(t ef,e ) / 25 - 188/224 Brittle/Brittle 


MIG5-G 78.5 222 "217 * " 29.7(t ef,y ) / 28 127 127/160 Mixed IV/Mixed IV 

DUG6-G 53.5 397 "298" 40.6(t ef,y ) / - 379 - /298 Ductile III m /Ductile III m 

† Coefficient of variation (COV%) for brittle/mixed failure modes 11-17 % and for ductile failure modes 8%. 

* 

Values are based on the tests conducted by Buchanan and Lai [16] on Radiata Pine glulam with the same density. 

One can note that the predictions using the other models 

are mostly constant for the tests with approximate 

capacities of 350 kN to 450 kN (Fig. 12b). These are the 

tests series conducted to observe the effects of bottom, 

edge and end distances. For instance, as the bottom 

distance d z gets larger due to increase in timber 

thickness, the capacity of the connection gets higher as 

asserted by Stahl et al. [6] as well. 

The predictions based on the proposed analysis are 

shown in Table 5 for test groups BRG1-L to BRG3-L 

which are identical in every parameter except the bottom 

distance. Thicker specimen with larger d z induces more 

stiffness for the resisting bottom shear plane. Therefore, 

the stiffness ratio of the resisting bottom plane increases 

and for the other resisting planes reduces. Subsequently, 

a higher proportion of the applied load transfers to the

Predicted Average Strength [kN] 


bottom resisting plane and the maximum stress lowers 

on the lateral shear and head tensile planes in 

comparison to the stresses for a thinner specimen. 

Regarding the fact that in these test series the earlier 

failure belongs to the head tensile plane which gets first 

overloaded, so the connection capacity gets higher. The 

same behavior happens in respect of increasing the edge 

distance d e . However, the predictions by the O86 code 

show an opposite behavior with a decreasing trend in 

thicker specimens. The reason is the fact that the 

Canadian code includes a volume effect on the shear 

strength which affects the connection capacity. The 

results from current tests and Stahl et al. [6] disprove the 

size effect based on Weibull weakest link theory of 

brittle failure adopted by Canadian and also U.S. codes. 

In fact, the size of the wood surrounding the main loaded 

block affects mostly the stiffness of the resisting shear 

planes rather than the shear strength of the wood. For 

instance, the strength of a connection with minimal edge 

and bottom distances can be simply predicted as the 

(a) 

(b) 

550 

450 

350 

250 

600 

500 

400 

300 

200 

New Analytical M. 

r² = 0.91 

MAE=-2.6% 

STDEV=9.8% 

150 

Radiata Pine-LVL 

Radiata Pine-Glulam 

Narrow connection 

50 

50 150 250 350 450 550 

Observed Average Test Strength [kN] 

700 

Unsafe 

Conservative 

100 

Stahl Method 

O86-09 Code 

0 

EC5 

0 100 200 300 400 500 600 700 


Figure 12: Comparison of analyses and the current test 

data in brittle/mixed failure modes; (a) New analysis, (b) 

Stahl’s method, O86 code and EC5 

tensile capacity of the head plane since shear planes have 

no significant stiffness to carry any load. Also, the 

predictions for narrow connections are overestimated by 

EC5 and Stahl’s models; on the other hand, 

underestimated by O86 code (Fig. 12b). Moreover, for 

mixed failures, the predictions using Stahl’s method are 

non-conservative. These overestimated values are due to 

the fact that Stahl’s equation considers the full length of 

the rivet penetration as the effective wood thickness and 

to the fact that the possibility of mixed mode failure is 

not included. Thus, the necessity for predicting the 

connection strength under a mixed mode of failure is 

required. 

5.2 DATA AVAILABLE IN THE LITERATURE 

A similar comparison was made using data available in 

the literature and current test data (Fig. 13). Five sets of 

data were considered from the literature: tests performed 

by Foschi and Longworth [2] on Douglas Fir-Larch 

glulam, Buchanan and Lai [16] on Radiata Pine glulam, 

Karacabeyli et al. [17] on Hem-Fir solid timber, Stahl et 

al. [6] on Southern Pine glulam, and Marjerrison [18] on 

Douglas Fir-Larch and Spruce Pine glulam. It should be 

mentioned that the practice codes report the connection 

strengths at the 5 th percentile level. Therefore, a 

conversion was made to compare mean ultimate test 

strengths with 5 th percentile values from the code 

estimated at 75% confidence level. Coefficients of 

variation (COV) of 20% and 15% were considered for 

brittle/mixed failures on glulam and LVL 

correspondingly. In addition, a load duration factor was 

applied to the wood strength values taken from the codes 

to consider the short term loading effect for experiments. 

Based on the codes, a load duration factor of 1.25 was 

used for O86 values and 1.10 for EC5. 

By comparing the prediction models (Fig. 13), it can be 

deduced that there is more conformity between the 

predictions using the proposed analysis and the available 

test data. The predictive new analysis results in a higher 

correlation coefficient of 0.87 and less MAE of +0.9%. 

The method proposed by Stahl and the O86 code 

predictions are better than the ones using the EC5 model. 

The values obtained using Stahl’s method are scattered 

(Fig. 13b) which leads to higher STDEV compared to 

the one using O86 (Fig. 13c). There is considerable over 

prediction for the strength of a connection with large end 

distance by Stahl’s method and EC5. This sample 

supports the fact that by adding to the end distance, the 

load carrying capacity of the connection doesn’t increase 

correspondingly to the additional shear resistance surface 

due to larger end distance. On the other hand, O86 

code’s values are underestimated and too conservative. 

Table 5: The effect of increasing the bottom distance on the stiffness ratio of resisting planes and the wood capacity 

Specimens 

Bottom 

distance 

d z 

Stiffness ratios of 

resisting planes 

Maximum load causing 

failure on each plane (kN) 

Capacity 

prediction 

(min P wi *2) 

Test 

result 

(mm) 

R h R b R l P wh P wb P wl 

(kN) (kN) 

BRG1-L 17 (0.3X b ) 58% 30% 12% 157 281 298 314 358 

BRG2-L 35 (0.6X b ) 51% 39% 10% 181 214 344 362 370 

BRG3-L 62 (1.1X b ) 49% 42% 9% 190 205 355 380 375




(a) 

(b) 

(c) 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

1600 

1400 

1200 

1000 

800 


r² = 0.87 

MAE=+0.9% 

STDEV=20.3% 

200 


0 

0 200 400 600 800 1000 1200 1400 1600 1800 


Stahl's Method 

r² = 0.78 

MAE=+2.1% 

STDEV=29.4% 

0 

0 200 400 600 800 1000 1200 1400 1600 


EC5 

r² = 0.67 

MAE=+2.8% 

STDEV=28.7% 

Stahl's Method 

600 

O86-09 Code 

r² = 0.78 

400 

MAE=-23.2% 

STDEV=18.5% 

200 

O86-09 Code 

0 

EC5 

0 200 400 600 800 1000 1200 1400 1600 


Figure 13: Comparison of analyses and test data 

(current and literature data) in brittle/mixed failure modes; 

(a) new analytical method, (b) Stahl’s method, (c) O86 

code and EC5 

6 CONCLUSONS 

A close form stiffness-based analytical model to 

determine the wood resistance of riveted connections in 

timber products is proposed. It takes into account the 

stiffness and strength of the failure planes subjected to 

non-uniform shear and tension stresses in wood. Results 

of current tests and data available from literature confirm 

that this closed form analytical method can be used as 

design provision with more precise predictions for 

timber riveted connections. Based on the proposed 

design model, an efficient connection design can be 

made by decreasing the difference between the capacity 

of the wood and the rivets. The proposed method can be 

extended to other small dowel type fastener; e.g. nails 

and screws for connection design improvement and 

failure modes prediction. 

ACKNOWLEDGEMENTS 

The authors wish to thank the Structural Timber 

Innovation Company (STIC) for funding this research 

work. 

REFERENCES 

[1] Zarnani P., Quenneville P.: New analytical method and 

experimental verification of timber rivet connections 

loaded parallel-to-grain. In proceedings of the CSCE 

Annual Conference, Struct Div, Ottawa, Canada, 2011. 

[2] Foschi R. O., Longworth J.: Analysis and design of 

griplam nailed connections. J Struct Div ASCE, 

101(12):2537-2555, 1975. 

[3] Canadian Standards Association (CSA). CAN/CSA- 

O86.09: Engineering design in wood (limit states 

design). Mississauga, Ontario, 2009. 

[4] American Forest and Paper Association (AF&PA). 

NDS-2001: National design specification (NDS) for 

wood construction. Washington, DC, 2001. 

[5] European Committee for Standardization (CEN). EN 

1995-1-1:2004: Eurocode 5-Design of timber 

structures. Brussels, Belgium, 2004. 

[6] Stahl D. C. , Wolfe R. W. , and Begel M.: Improved 

analysis of timber rivet connections. J Struct Eng 

ASCE, 130(8):1272-1279, 2004. 

[7] Johnsson H., Stehn L.: Plug shear failure in nailed 

timber connections: load distribution and failure 

initiation. Holz-als Roh und Werkstoff, 62:455-464, 

2004. 

[8] Zarnani P., Quenneville P.: Wood effective thickness in 

brittle and mixed failure modes of timber rivet 

connections. In proceedings of 12 th World Conference 

on Timber Engineering, New Zealand, 2012. 

[9] Johansen K. W.: Theory of timber connections. 

Publications of International Association for Bridge 

and Structural Engineering, 9:249-262, 1949. 

[10] Zarnani P., Quenneville P.: Consistent yield model for 

strength prediction of timber rivet connection under 

ductile failure. In proceedings of 12 th World 

Conference on Timber Engineering, New Zealand, 

2012. 

[11] International Organization for Standardization (ISO). 

ISO 6891:1983. 

[12] Begel M., Wolfe R. W., and Stahl D. C.: Timber rivet 

connections in US domestic species. Res Pap FPL-RP- 

619. Madison, WI: US Department of Agriculture, 

Forest Service, Forest Products Laboratory, 2004. 

[13] European Committee for Standardization (CEN). N 

408:2003: Structural timber and glued laminated 

timber-Determination of some physical and mechanical 

properties. Brussels, Belgium, 2003. 

[14] Standards Australia/ Standards New Zealand 

(AS/NZS). AS/NZS 4063.1, 2009. 

[15] Lindsay B.: Determination of characteristic shear 

strength values for Radiata Pine and LVL. Final Year 

Research Project Report, DCEE, University of 

Auckland, New Zealand, 2010. 

[16] Buchanan A. H., Lai J. C.: Glulam rivets in Radiata 

Pine. Can J Civ Eng, 21(2):340-350, 1994. 

[17] Karacabeyli E., Fraser H., and Deacon W.: Lateral and 

withdrawal load resistance of glulam rivet connections 

made with sawn timber. CJCE, 25(1):128-138, 1998. 

[18] Marjerrison M. R.: Analysis of timber rivet 

connections loaded parallel to grain. MSc dissertation, 

Department of Civil Eng, The Royal Military College 

of Canada, Kingston, Ontario, Canada, 2007.

00694 Pouyan Zarnani - Timber Design Society

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