Revista EIA, ISSN 1794-1237 Número 8, p. 37-47.

Diciembre 2007
Escuela de Ingeniería de Antioquia, Medellín (Colombia)

BOLTED TIMBER JOINTS WITH SELF-TAPPING

SCREWS

César Echavarría*

ABSTRACT

The use of self-tapping screws with continuous threads in the joint area as a reinforcement to avoid
splitting of timber members is studied. A theoretical model is developed to calculate the stress distribution
around a pin-loaded hole in a timber joint, to predict brittle failure modes in bolted connections and to cal-
culate the load in the reinforcing screws. Laboratory experiments on reinforced and non-reinforced timber
joints with 15,9-mm bolts have shown good agreement with the model predictions.
KEYWORDS: timber joints; brittle failure mode; reinforcement perpendicular-to-grain; analytical
model.

RESUMEN

En este artículo se estudia el uso de tornillos autoperforantes como refuerzo para evitar rupturas
frágiles en uniones de madera. Se presenta un modelo teórico para calcular la distribución de esfuerzos
alrededor de un perno en una unión de madera, predecir las rupturas frágiles y evaluar el esfuerzo en los
tornillos autoperforantes. Los experimentos
�������������������������������������������������������������������������
de laboratorio con uniones de madera, con pernos de 15,9 mm
de diámetro, reforzadas y no reforzadas mostraron la efectividad del modelo teórico propuesto.
PALABRAS CLAVE: uniones de madera; ruptura frágil; refuerzo perpendicular a las fibras; modelo
analítico.

* Ingeniero Civil, Universidad Nacional de Colombia; Master in Timber Structures and Docteur en Sciences, École
Polytechnique Fédérale de Lausanne, Switzerland. Ph.D. Researcher, Département des sciences du bois et de la
forêt, Université Laval, Québec. cesar.echavarria@sbf.ulaval.ca Associate Professor, Faculty of Architecture, School
of Construction, Universidad Nacional de Colombia. caechavarrial@unal.edu.co

Artículo recibido 31-VIII-2007. Aprobado 11-XI-2007

Discusión abierta hasta junio de 2008
 Bolted timber joints with self-tapping screws

1. INTRODUCTION and for shear stresses were compared with those

from a fracture mechanics model to predict ultimate
It is known that the problem of mechanically strength. Jorissen [18] found, however, that the tensile
fastened joints in timber is difficult to analyze because stresses perpendicular-to-grain were underestimated
of the anisotropic and heterogeneous nature of the and, to allow crack initiation to be detected by the
material. Since there are no available analytical solu- fracture theory, added an assumed peak stress perpen-
tions associated with loaded holes in wood, current dicular-to-grain at the bolthole location. The joint area
design procedures for mechanical fasteners are based including the stable crack propagation was modelled
on approximate or empirical solutions and exist only as a beam on elastic foundation. This assumption limits
for the simplest types of joints. the robustness of the model.

Due to the importance of the problem, bolted Moses [23] and Moses and Prion [24] proposed
joint has been studied by using numerical and ex- a material model that is based on orthotropic elas-
perimental [4, 7-10, 21, 22, 26, 29, 31, 32] methods ticity, anisotropic plasticity for non-linear behaviour
in the past. of wood in compression, and the Weibull’s weakest
link theory to predict brittle failure. Linear elastic
Patton-Mallory et al. [27] developed and
behaviour was assumed for tension and shear. The
evaluated a three-dimensional numerical model of
weakest link theory provides a probabilistic approach
a bolted wood connection loaded parallel to grain.
to predicting the failure based on the stressed volume
Nonlinear parallel to grain compression of wood and
of wood and can be used for cases when the ultimate
degradation of shear stress stiffness were described
strength of the single bolt connection is governed
using a trilinear stress-strain relationship. The con-
by brittle failure (such as shear and tension per-
nection model also accounted for an elastic-perfectly
pendicular-to-grain). This three-dimensional model
plastic steel pin, oversized hole, and a changing con-
was implemented using finite element analysis for a
tact surface at the pin-hole interface. The numerically
single-bolt connection specimen.
predicted load-displacement curves were stiffer than
the experimental curves. Regrettably, experiments and numerical
methods do not produce open-form solutions as a
In Kharouf et al. [19], a nonlinear numerical
result of the high amount of possible combinations of
model is developed to study the behaviour of timber
involved parameters. In contrast, it would be practi-
connections with relatively low member thickness-
cal to have equations developed using the detailed
to-fastener diameter ratios. A plasticity-based com-
analytical basis.
pressive constitutive material model is proposed to
represent wood as elastoplastic orthotropic material The objective of this paper is to present
in regions of biaxial compression. Linear elastic or- a comprehensive analytical method capable of
thotropic material response was used otherwise with predicting the ultimate strength of reinforced and
maximum stresses taken as the basis for predicting non-reinforced timber bolted joints. The method of
failure criteria. Nonlinear geometry due to increased complex functions [20, 25] for anisotropic materials
sliding contact between the bolt and the hole is mod- is used to obtain the stress distributions. The solution
elled using the Lagrange multiplier algorithm. is compared directly to results of laboratory tests.

Jorissen [18] attempted to account for brittle This study examined as well the technical feasi-
fracture in timber joints using the European Yield bility of reinforcing the wood at bolted joints with self-
Model by calculating stress distributions along poten- tapping screws. The purpose of local reinforcements
tially critical load paths within the wood member. The in a joint is to improve its load-carrying capacity and
average stresses for tension perpendicular-to-grain stiffness and to improve its ductility.

38 Revista EIA
 arbitrary loading direction. Composite Structures 1985; 3:119-143.

[32] Zhang K., Ueng C. Stresses around a pin-loaded hole in orthotropic plates with
arbitrary loading direction. Composite Structures 1985; 3:119-143.

This paper reports test results of various con-

nection configurations with reduced end distances,
with and without reinforcement.

2. STRESS DISTRIBUTION
AROUND A PIN-LOADED
HOLE IN AN ELASTICALLY
ORTHOTROPIC PLATE

In this paper, the stress distribution around a

pin-loaded hole in an elastically orthotropic plate is Fig. 1. Double-lap mechanical joint
investigated for the main member of a double-lap Fig. 1. Double-lap mechanical joint
Figure 1. Double-lap mechanical joint
mechanically fastened joint. Consider a homoge-
neous, orthotropic plate of width b with a circular
hole of diameter d as is shown in Fig. 1. Let the x-
and y-axes be the principal axes of the plate, and the
direction of the pin load F be the same as the positive
y-axis. The hole is at a distance e from the free end
of the plate. The clearance between the pin and the
hole is denoted as λ.
The pin-hole problem is essentially a two-
body-contact problem. In order to determine contact
surfaces and stresses the inverse method is used, a
value for the contact angle between the bolt and
the timber is assumed and the corresponding load
is calculated. The process is repeated for a series
of prescribed contact angles. The assumption of a
value for the contact angle has the advantage of
simplicity. Fig. 2. Geometry for the joint and boundary conditions

It is assumed that the hole is loaded without

friction on a portion of its edge by an infinitely rigid
Fig. 2. Geometry for the joint and boundary conditions
pin of diameter d. The loading pin is represented Figure 2. Geometry for the joint and boundary
by compressive edge loads distributed around the conditions
hemispherical contact area. The resulting force F
equals 2pRt, where p is the average bearing stress
The method of complex functions (Lekhnitskii
according to the classical definition, R is the radius
[20], Muskhelishvili [25]) for anisotropic materials
of the hole and t is the unit thickness of the plate.
is used to obtain the stress distributions. For plane
The analytical model with its boundary and loading
stress situations in orthotropic plates the stresses can
conditions is shown in Fig. 2.
be expressed by means of derivatives of two stress
complex functions ϕ (z 1 ) and Ψ (z 2 ) :

Escuela de Ingeniería de Antioquia

39
 Ψ (z 2 ) = B L nζ 2 + Ξ 0 (ζ 2 ) + 4b μ − μ ⎨ ζ − μ + μ z 2 ⎬
F μ1 ⎧ R 4μb μ 22 − ⎫μ 11 ⎩⎩ζ 22 μ11 + μ 22 ⎭⎭
Ψ (z 22 ) = B L nζ 22 + Ξ 00 (ζd22ϕ) + d ϕ d1ζ 1 ⎨ F − F μ 2 11 μ⎧1z 22 ⎬⎧RR d ζ 1 μ1 μ 2 ⎫(7)⎫
ϕ ' (z 1 )Ψ=(z 2 ) =d=ϕ4BbLμnζ22d2−ϕ+μΞ1d1 0+ ζ⎩(ζ1ζ 222 ) +Fμ11 + μμ222⎨− ⎭⎧⎨ 2 R− d − ζ 1 z 2 ⎬μ 2⎬ ⎫ (7)
ϕ ' (z 1 )dz= 1 d ϕ d=ζ 1ddz ϕ d ζ 4 +
b μF 4 −b μ
μμ −⎩ μ ζ
⎧
⎨ −ζ dz
R μ d ζ+1μμ−12 + μ⎭μμ22⎭ ⎫⎬⎫
ϕ ' ( z ) = ddzϕ1 = dζϕ1 ddz 1 ζ 111 + 4Fb μ1μ−222μ 2 1⎧⎩⎨⎩− ζ2R1 2 ddz
1 2 1 2 1 1ζ
1 − μ +2 μ ⎬
Bolted timber joints with self-tapping screws ϕ ' (z 1 ) = dz = d ζ dz + 4b μ − μ ⎨ − ζ 2 dz 1 − μ1 + μ 2 ⎬⎭
1
d ϕ d ϕ d ζ 11 Fdz 11 μ 22 d ζ 1⎧1 dzR11 d ζ4b11 μ 11 −μμ22 22 ⎩⎩⎫ ζ 11 dz 11 μ11 (8) +μ2⎭
ϕ ' (z 11 ) = = +d Ψ d ϕd Ψ ddϕ⎨ζ−d ζ 1 22F F −μμ 2 ⎧⎧ ⎬RR ddζζ1 μ 2 μ ⎫ ⎫2 ⎭
dz 11 Ψd' ζ(z112dz ' 11(z 1 )4=bd =
ϕ) = μ11 −=μdd22ζΨ⎩ dz
Ψ 2 ζ 1 + dz 1
d ζ+12 4bF1μ −1μμ11μ+1⎨⎨μ−−22 ζ⎧⎭ 22 dz R 2−d ζ−μ2 + μ 1 ⎬μ1⎬ ⎫
(8)
Ψ ' (z 2 )d=z 2d dz d1 =ζ 2d dz 1 d ζ1 4+ μ 1− μ μ 2 ⎩ ζ ⎧ 1− R d z21 2d ζ 12μ−1 +2 μ ⎭ ⎫
ddζz 22 − μ1μμ+211⎭μ 2 ⎫⎬⎭⎬
Ψ Ψ b F 11⎩ ⎧ 2 R ⎨
Ψ ' ( z ) = d Ψ
z = d ζΨ 2d ζ 2
dz + F
4 b 2
μ μ − μ ⎨
⎩ − ζ
Ψ' (dzζ222) = Fd z 2 =μ11d ζ
2 1
d Ψ dΨ +d ζ4b μ −μμ ⎨−⎫ ζ 2 d z − μ +(8)
2(1) 2 2 2 2 1 2
⎧ dzR
2
μ ⎬
where,Ψ ' (z 22 ) = = + d zd 2Ψ ddζΨ2⎨2 −ddz ζ 222 2 F4b22 μ −μ221− μ⎧1111 ⎩⎩⎬R ζ d22ζ 2d z 22 μ1μ 1(9) 1+⎫ μ 22 ⎭⎭
where, d z 22 d ζ 22 Ψdz' (2(2) z )= = 2+ ⎨− − (9)
2 2 4bd μ z 222 − μ d ζ11 2⎩ dzζ222 d4bz 22μ 2 −μμ11 1+⎩μ22ζ⎭2 2 d z 2 μ1 + μ 2 ⎭
⎬

where,
where, dϕ A d Γ0 (9)
where, where, (3) d =ϕ +A d Γ

d ζ 1d ϕ ζ=1 Ad+ζ 1d Γ 00
d Γ00 d ζϕ = ζA + ddΓζ
d ϕ = Awhere + ddϕζ 1 =Aζ 1 +d Γd0ζ01 (10) (10)
where ϕ (z 1 ) and Ψ (z 2 ) are arbitrary functions d ζof11 ζ 11 d ζ 11 d Ψddζζ11 Bζζ1 1d dΞζd01ζ 1
1= +1 1
(10)
the complex variables z 1 and z 2 : d= Ψ +B d Ξ 0
d ζ 2d Ψζ=2 B d+ ζ 2d Ξ 0
d Ψ B d Ξ 00 ddΨ ζΨ2 ==BζB2 ++ d Ξdd0Ξζ 02 (11) (11)
z 1 = x + µ1 y (4) = + d ζ = ζ+ d ζ (11)
The values of complex constants d ζ 22 ζ 22 A dand ζ 22 B dare dζζ22found2 ζζ2 2 from:
2 d ζd2ζ 2 2

z 2 = x + µ 2 y The values of complex (5) constants A and B are found from:

The values
The values of complex
of complex constants
constants AAThe andvalues
and BBare
B arefound
offoundcomplex
from:from: constants A and B are
The values of complex The values constantsof complex
A and Bconstants are found A from: and are found
" i from:
found from: A =A A = A"i
In general, the complex functions ϕ (z 1 ) AA==AA " i" i (12)
A B=" A (12)
and Ψ (z 2 ) can be estimated from the boundaryA = A " i A = A B” i= i "i (12)
B = B" i (13)
conditions of the problem. The pertinent solutionsB = B " i B = B ” iBB==B "Bi" i (13)
(13)
B = B⎧ " i u ⎫
for the pin-loaded hole in an elastically orthotropic ⎛ F ⎞
B " = ⎜ −⎛⎛ F⎟F ÷ ⎞ ⎞⎨÷ ⎧1 −⎧ u22 u⎬⎫2 ⎫
or isotropic plate problem have been obtained by B
⎛ F ⎞ ⎧ ⎝u 22 ⎜⎛⎜⎛⎫4 π44πF⎠Fπ⎟ ⎞⎟⎞⎩⎨ ⎧⎨
B "
" == −− ÷ 1⎧−1u−1 uu⎭⎬2 ⎫⎬⎫ (14) (14)
Echavarría [11] and Echavarría et al. [12]Band " = ⎜are − ⎟ ÷ ⎨1BB−""== ⎝⎝⎜⎬−− ⎠ ⎠⎟ ÷÷ ⎩ ⎨
⎩ 1 u−1 u⎭21 ⎭ ⎬ (14)
⎝ 4π ⎠ ⎩ u 11 ⎜⎝⎝⎭ 44ππ ⎟⎠⎠ ⎨⎩1 − uu 1 ⎬⎭
⎛ ⎛ FF⎞ ⎞ ⎩ 1 ⎭
summarized here.
A " = −
⎜ ⎛ ⎟ ⎞ F − B " (15) (15)
⎛ F ⎞

A""⎝==⎜⎝ ⎜⎛−4−π4 π⎠F⎟⎠ −⎟⎞ B−"B "
A
(15)
A "(6) = ⎜− ⎟ − B "A " = ⎛⎝⎜ − 4Fπ ⎞⎠⎟ − B "

⎝ 4π ⎠ A " = ⎜⎝ − 4 π ⎟⎠ − B "
where, where, u 1 and uu1 2and areuconstants
2 are constants determined
where
determined u 1 andby:uby: ⎝ are4 πconstants ⎠ determined by:
where,
where, u 11 and u 22where,are constants u 1 and u are
determined
2 constants by: determined
by:
2
u and u
where, u 11 and u 22 are constants are constants determined
determined by:
u jS= Sμ112μ+by:
(7) 2
+ S12 ( j = 1, 2) (16)
= (16)
u 2 12 ( j = 1, 2)
j S
u jj = S11 μ 2 2
+ S
j
( ju =j
11
=
1, S
2)
j
11 μ j
2
+ S 12 ( j = 1, 2) (16)
11 jj
Γ0 (ζ 1 ) and Ξ 0 (ζ 2 ) are the holomorphic
12
12 u = S μ 2j + Sof
u j = S11μ j + S12 ( j =1 1, 2)
j 11 parts 12 ϕ( (jz = ) 1,
and2) Ψ ( z ) :
Γ (ζ ) and Ξ 0 (ζ 2 ) are the holomorphic parts of ϕ (z 1 ) and Ψ (z 2 ) :
2

Γ00 (ζ 11 ) and Ξ000 Γ(ζ0 12(2 ζ) 1are ) and Ξ 0 (ζ 2 ) areparts

the holomorphic the holomorphic
of ϕ ( z 11 ) and parts Ψ ( z 22 of ) ( 1)
: ϕ z and Ψ (z 2 ) :
Γ (ζ ) and Ξ
Γ00 (ζ 11 ) and Ξ 00 (iζ σ22=−) 1are( ζ ) σ =− 1the holomorphic parts of ϕ (z ) and Ψ (z ) :
are ofω ϕ (2z 11) 2and ⎤Ψ σ (+zζ21)d:σ
⎧
⎪ the μ holomorphic parts 2
Γσσ0 =−(ζ111 ) =
∫ ( (
⎧ σ⎨=− 1 ⎡⎢ 2 4 L nσ − σ 2 + σ +
F
) 2
( F
σ +σ − 2 ⎥ ) +
⎧
∫ ∫ ) (( (
i 4Fπ ( μ1 ⎪− μ 2⎧) ⎪⎡ μ 2 F⎣ 24π i F
))) ( ( ) )
=−
i0 (ζ 1 ) =⎧⎪⎪
2 F4ωπ+ 2d 2 ⎦ ⎤σσ− + ζ 1ζ 1σ d σ
(
2
Γ Ln σ − σ + σ + σ + σ − σ + ζ d+σ
∫
i ⎡⎡ μ 22F i 4 L n⎨ −⎪⎧σ⎩=− σ =+⎡1 μ 2 F 4 F ω ⎤ F ω11
⎤ σ + ζ d σ 2 (17)
++ σ 2 −⎥⎦ 2σ ⎤⎤−σζ 1+ ζσ1 d σ +
σ =−
2 1 2 2 22 2 2
Γ00 (ζ 11 ) =
Γ = Γ ( ζ ⎨1 )4π = ( μ μ 42L) nσ −⎧⎨ σσ⎢⎣2=+41++π σiμ F++ 4 Lnσσ2 −++σσ 22 + −σ
− 22 2⎥⎥ 4+π σ 2+

) (( ))
−

∫∫∫ (
⎨ ⎢⎢ i ⎪ ⎪ ⎡
⎢ 2Fi 444πLnσ − σ 2 + σ 2⎦⎦ σ+−−F4ζω F ω
44π ( μ11 −
−Γμ 22()ζ⎪ ) = ⎣4⎣ π44π(iiμi − μ ) ⎪ σ + σ 2 ⎫− 2 ⎤⎥⎦⎥σσ +−ζζ111 dσσ +
)
0
11 σ
1
⎪⎨1 ⎡⎣⎢μ442π σ σ + ⎡σμ 2 F+ 4π
1 2
=11 4π ( μ11 − μ⎩22σ)=+
Γ 00 (ζ⎪⎩⎩11σσ) =+
∫
⎨⎩ π i σ4 Ln+ ζσ 1 d− π ⎤ σσ +2 ζ+1σd σ − 2 ⎦ σ(17) −ζ σ +
σ =+
=+
=+11 4π ( μ1 − μσ2 =+
=+ 1⎢⎣ [ μ F ]
) ⎪1⎪⎩σ σ=+=+1 1⎣ 42π i σ − ζ 1 σ
σ − L n σ
⎢⎣ 2π i 4π ⎥⎦ σ − ζ σ ⎬ ⎥⎦ σ − ζ 11 σ
σ ⎭

∫ ∫∫
σ + ζ d⎩σσ σ=+=−11 σμ +Fζ d σ σ + ζγ⎡ μ
∫∫ d σF⎫ σ ⎤ σ + ζ 1 d σ ⎫ (17)
1

∫
[μ 22FF ] + 11 dσσ[=+=+μ−−112[Fμ]⎢⎡⎢⎡σF 22]−FσζLL1+nnσζσ1⎥⎤⎥⎤ d−σ+ − 1⎢1 d2π2⎡i⎫⎬⎬μLn
− ζ 1⎣1 σ⎢⎡ ⎭⎭μ 2 F Ln
2F ⎥ ⎤ σ + ζ 1 ⎬
⎦ σ ⎥⎤−σζ 1+ ζσ1 ⎭d σ ⎬⎫
dσ ⎫

∫∫ ∫∫ ⎣
σ −− ζ 11 σ 2π iiσ 1+ ζ 1⎦⎦ dσσ−
2⎣ 2
⎣
γ[
γ μ 2 F ]σ σ +−ζζ11 dσσ γ − ⎡⎣μ22πFi Lnσ ⎤⎦σσ +−ζζ11 dσσ ⎫⎭⎬
σ =− 1[ μ 2 F ] σ − ζ 1 σ − γ ⎢⎢
σ =− 1
⎣ 22ππii Lnσ ⎥⎥⎦σσ −−ζζ 1 σσ ⎬⎭
σ =−
σ =−11

σ =− 1
σ −ζ σ 1 γ ⎦ 1 ⎭
σ =− 1 σ =− 1 γ
⎧
Ξ 0 (ζ 2 ) =
i ⎪
⎨
4π ( μ 2 − μ1 ) ⎪ ∫
⎡ μ1F 2
(
2 Fω 2 2 ⎤ σ + ζ 2 dσ
⎢⎣ 4π i 4 Lnσ − σ + σ + 4π σ + σ − 2 ⎥⎦ σ − ζ σ +
2
) ( )
⎩σ =+ 1 (18)
σ =+ 1 (18)

∫ ∫
σ + ζ 2 dσ ⎡ μ 1F ⎤ σ + ζ 2 dσ ⎫
[ μ 1F ] − ⎢⎣ 2π i Lnσ ⎥⎦ σ − ζ σ ⎬
σ −ζ2 σ 2 ⎭
σ =− 1 γ

40 where, Revista EIA

1− Sin α (19)
ω=
Cos α
 σ =+ 1

∫ [μ ∫
σ + ζ 2 dσ ⎡ μ 1F ⎤ σ + ζ 2 dσ ⎫
1F ] − ⎢⎣ 2π i Lnσ ⎥⎦ σ − ζ σ ⎬
σ −ζ2 σ 2 ⎭
σ =− 1 γ

where Table 1. Elastic constants (MPa) of red spruce

1− Sin α (19) (Wood Handbook [30])
ω =1 – sin a
w= (19)
C o saα
cos
Ex Ey Gxy νyx
2
π ⎧e − 2 d ⎫ π ⎧e − 2 d ⎫ 470 (20) 11100 670 0,470
α= ⎨ ⎬− ⎨ ⎬ 2d ≤ e ≤ 5d (20)
5⎩ d ⎭ 30 ⎩ d ⎭

3 π π ⎧e − 5 d ⎫ Table 2. Predicted peak stresses at a joint

(21)
α = + ⎨ ⎬ 5 d ≤ e ≤ 14 d (21) of red spruce
10 45 ⎩ d ⎭
Shear stress at Perpendicular-to-grain
In this manner, stress functions ϕ (z 1 ) and e/d θ = 60° stress at θ = 90°
ner, stress functions (z 1completely
Ψ (z 2 ) ϕare ) and Ψ (z 2 determined.
) are completely determined. Evidently, τ / p
Evidently, σx / p
xy
nalytical method, it is
with this possiblemethod,
analytical to estimate the stresses
it is possible in any point of the
to estimate
2 0,80 0,52
joint and to show the stress
the stresses distribution
in any around
point of the a pin-loaded
orthotropic joint hole
and in an elastically
plate. The effect of material properties and geometry of the joint3 can be 0,50
to show the stress distribution around a pin-loaded
0,20
analytically. Although it was developed for orthotropic composite materials, 4 the 0,34 0,04
hole in an elastically orthotropic plate. The effect of
pproach is equally effective for analyzing mechanical joints involving solid 5
wood 0,31 0,01
material properties and geometry of the joint can be
ased composites.
determined analytically. Although it was developed 7 0,28 -0,03
for orthotropic composite materials, the presented 10 0,18 -0,13
E FAILUREapproach
OF A BOLTED
is equallyTIMBER JOINT
effective for AND
analyzing IMPROVING LOAD-
mechani-
G CAPACITY cal joints involving solid wood and wood-based
composites.
ed model can be used to determine analytically the points of stress concentrations
of contact between the fastener and the timber and predict the brittle modes of
owel-type timber
3. joints.
BRITTLE FAILURE OF A
der, for instance, theBOLTED TIMBER
stress distributions JOINT
calculated for a wood element of a unit
AND IMPROVING LOAD-
and width b = 4d assuming the elastic properties of red spruce shown in Table 1.
CARRYING
mmarizes the peak stresses xy and xCAPACITY
at corresponding angles for red spruce
n this example. The calculated stresses are normalized by the average bearing
/d and are shown along the hole edge
The proposed ascan
model a function
be usedof
to angle (as defined in Fig.
determine
Figure 3. Angle θ
analytically the points of stress concentrations in the Fig. 3. Angle
zone of contact between the fastener and the timber
ompletely tension perpendicular-to-grain and shear is not ever possible. AvoidingIf not completely tension perpendicular-
and predict the brittle modes of failure in dowel-type
erly, bolts may cause undesirable brittle failure in timber due to excessive tension
to-grain and shear is not ever possible. If not placed
ar-to-grain. Atimber joints. to avoid splitting and to guarantee a plastic joint
possibility properly, bolts may cause undesirable brittle failure
s to reinforce the timber in the joint area. The tension stresses are then transferred
in timber due to excessive tension perpendicular-
Let’s consider, for instance, the stress distribu-
rcement perpendicular-to-grain. Known methods to prevent splitting of timber
tions calculated for a wood element of a unit thickness to-grain. A possibility to avoid splitting and to guar-
t and width b = 4d assuming the elastic properties of antee a plastic joint behaviour is to reinforce the
red spruce shown in Table 1. Table 2 summarizes the timber in the joint area. The tension stresses are then
peak stresses τxy and σx at corresponding angles θ for transferred by a reinforcement perpendicular-to-
red spruce calculated in this example. The calculated grain. Known methods to prevent splitting of timber
stresses are normalized by the average bearing stress members are reinforcements of the joint area with
p = F/d and are shown along the hole edge as a func- glued-on wood-based panels, pressed-on punched
tion of angle θ (as defined in Fig. 3). metal plates or glass fibre reinforcements. If wood
Fig. 4. Reinforced bolted joint

Escuela de Ingeniería de Antioquia

41
 Bolted timber joints with self-tapping screws

joint could be reinforced (Haller et al. [14], Haller

and Wehsener [15], Blass and Bejtka [5], Chen [6],
Hansen [16], Hockey et al. [17], Soltis et al. [28]),
end distance requirements could be re-evaluated,
which would allow more compact joints and an
easier installation.

The approach presented in this study is to

use self-tapping screws oriented perpendicular-to-
grain as internal reinforcement. The reinforcement
is shown in Fig. 4. Compared to the reinforcement
methods mentioned, self-tapping screws are easier
to apply and less expensive.

mbers are reinforcementsInofthis the joint

paper, area with glued-on
splitting failure wood-based
is assumedpanels,to pressed-on
nched metal platesoccur
or glassasfibre
soon reinforcements. If wood joint could be
as the perpendicular-to-grain reinforced (Haller
stress
al. [14, 15], Blass and Bejtka [5], Chen [6], Hansen [16], Hockey et al. [17], Soltis et al. Figure 4. Reinforced bolted joint
reached thecould
8]), end distance requirements strength perpendicular-to-grain
be re-evaluated, which would of the more compact
allow
wood.
nts and an easier installation.Basically, the perpendicular-to-grain strength
can be improved by reinforcement. Reinforcement
e approach presented in this
could study locally
be used is to use inself-tapping
the vicinityscrews
of a bolt.oriented
Conse-perpendicular-to-
ain as internal reinforcement. The reinforcement is shown in Fig. 4. Compared 4. to EXPERIMENTAL
the
nforcement methods quently,
mentionedthe cracks
beforemay be stopped
self-tapping screws at the
areposition
easier toofapply and less
pensive. the reinforcements and the bearing strength of the VERIFICATION
wood could be attained.
this paper, splitting failure is assumed to occur as soon as when the perpendicular-to-grain Laboratory tests on reinforced and non-rein-
ess reached the strength perpendicular-to-grain
The analytical model of the wood. Basically,
presented allows pre-the perpendicular-
grain strength can be improved by reinforcement. Reinforcement could be usedforced locally bolted
in timber joints loaded parallel to grain
dicting the load in the reinforcing screw. The force by aofsingle
vicinity of a bolt. Consequently, the cracks may be stopped at the position the bolt representing the geometry shown
nforcements and the acting strength
Fsbearing in the screw
of the is equal
wood to the
could perpendicular
be attained. in Fig. 1 were performed to verify the predictions
stress σx multiplied by the area As on which the of the proposed analytical model. The bolts were
e analytical model force
presented
acts.previously allows predicting the load in the reinforcing screw.
15,9‑mm (5/8‑in.) in diameter made of low carbon
e force Fs acting in the screw is equal to the perpendicular stress x multiplied by the area
on which the force acts. The equation that describes the area As, con- steel conforming to ASTM A307. Bolt lengths were
sidering the stresses between y=R and y=2R, has selected to ensure that threads were excluded from
e equation that describes the area As, considering the stresses between y=R and bearing y=2R, hasagainst the wood. The ratio of the wood
e following form: the following form:
member thickness to bolt diameter was small enough
As = t R As = t R (22) to induce
(22) failure in the wood, with minimum bending
deformation of the bolt. Wood plates for the joints
The force acting in the screw Theis:force acting in the screw is: were cut from 38 by 89-mm (nominal 2 by 4-in.) red
spruce kiln-dry lumber so that the joint area was free
⎧⎪⎛ ( 4 + π ) Fnω ⎞ ⎛ Fk 3 Fk ⎞ ⎛ υxy F ⎞ ⎫⎪ As
Fs = ⎨⎜⎜ ⎟⎟ − ⎜ + (23) (23) Tabla 3 and table 6 show the single-dowel
of defects.
⎟ − ⎜⎜ ⎟⎟ ⎬
⎠ ⎝ 2 b 2 Rπ ⎠ ⎝ 2 Rπ ⎠ ⎭⎪ t
2
⎩⎪⎝ 2 Rπ joint geometry.
In these circumstances local reinforcement can be very effective in ensuring a reasonable
Prior to testing, the specimens were condi-
In these circumstances local reinforcement
d-carrying capacity and stiffness and in providing the necessary ductility.
can be very effective in ensuring a reasonable load- tioned to attain 12 % equilibrium moisture content.
carrying capacity and stiffness and in providing the Specific gravity based on oven-dry mass and volume
EXPERIMENTAL VERIFICATION
necessary ductility. at 12 % moisture content of the specimens varied

Laboratory tests on reinforced and non-reinforced bolted timber joints loaded parallel to
ain by a single bolt representing the geometry shown in Fig. 1 were performed to verify the
edictions of the proposed analytical model. The bolts were 15,9-mm (5/8-in.) in diameter
42 steel conforming to ASTM A307. Bolt lengths were selected to ensure
de of low carbon Revista EIA
t threads were excluded from bearing against the wood. The ratio of the wood member
ckness to bolt diameter was small enough to induce failure in the wood, with minimum
nding deformation of the bolt. Wood plates for the joints were cut from 38 by 89-mm
ominal 2 by 4-in.) red spruce kiln-dry lumber so that the joint area was free of defects.
 Table 3. Non-reinforced single-dowel joint geometry

Bolt diameter Edge distance Thickness End distance Number of

d (mm) b/2 (mm) t (mm) e replications

2d, 3d, 4d, 5d,

15,9 44,5 38,0 53
7d and 10d

Table 4. Mechanical properties of red spruce

Strength average (MPa)

Plate thickness t (mm) σx σy τxy
Perpendicular-to-grain Embedding Shear

38,0 3,80 29,7 8,80

from 0,37 to 0,41 as determined per ASTM D2395- Fig. 4 shows the reinforcing screw used in this
02 [2]. Material shear strength parallel-to-grain and study. A screw (GRK fastener 1/4” by 3½”) with 90
tensile strength perpendicular-to-grain were deter- mm of length, 6 mm of outer diameter and 70 mm
mined using ASTM D143-94 [1]. The shearing sur- of threaded length was used. The reinforcing screw
face dimensions were identical for all shear strength is at a distance s=d from the centre of the hole.
parallel-to-grain tests. The dowel embedding strength
Tests were normally conducted on single-hole
for each bolt diameter was determined according to
specimens which had the geometry described in
ASTM D5764-97a [3]. The material properties are
Tables 5 and 7. During the course of this experimenta-
summarized in Table 4.
tion, 37 specimens were tested using reinforced joints
The joints were tested with static load applied with self-tapping screws. For comparison, 53 joints
in tension parallel-to-grain using a universal testing were tested without reinforcement perpendicular-
machine in accordance with EN 26891:1991 [13]. to-grain.

Table 5. Experimental results and analytical predictions for non-reinforced single-bolted joints

Experimental Predicted Comparison

Bolt Average
diameter e/d Number of Average Standard (F-Fexp)
Failure load bearing Prevalent
d (mm) replications failure load deviation Fexp
F (kN) stress failure mode
Fexp (kN) (%) (%)
p (MPa)
2 10 4,43 13 4,42 7,30 Splitting -0,40
3 8 12,1 7 10,6 17,6 Shear-out -12,5
4 10 17,3 4 15,6 25,9 Shear-out -9,60
15,9
5 10 18,2 9 17,2 28,4 Shear-out -5,60
7 7 20,5 7 17,9 29,7 Bearing -12,5
10 8 20,3 10 17,9 29,7 Bearing -11,4

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 Bolted timber joints with self-tapping screws

Table 6. Reinforced single-dowel joint geometry

Bolt diameter Edge distance Thickness End distance Number of

d (mm) b/2 (mm) t (mm) e replications

15,9 44,5 38,0 2d, 3d, 4d and 5d 37

Fig. 3. Angle
Table 7. Experimental results and analytical predictions for reinforced single-bolted joints

Experimental Predicted Comparison

Bolt
diameter e/d Number of Average Standard (F-Fexp)
Failure load Screw load Prevalent
d (mm) replications failure load deviation Fexp
F (kN) Fs (kN) failure mode
Fexp (kN) (%) (%)
2 10 9,76 10 6,65 1,10 Shear-out -31,9
3 9 12,7 25 10,6 1,10 Shear-out -16,5
15,9
4 9 17,4 5 15,6 0,30 Shear-out -10,3
5 9 18,4 10 17,2 0,10 Shear-out -6,5
Fig. 4. Reinforced bolted joint

The number of replications, the summary of

test results and comparison with the analytical predic-
tions for each test configuration are given in Tables 5
and 7. The load-carrying capacities were predicted
using the stresses obtained by the analytical model
and the failure criteria presented above.

The effectiveness of reinforcement methods

is studied along with the possibility of reducing the
end-distance requirements. Test results in Table 7
showed that reinforcement had positive effects on
the load-carrying capacity when the end distance
e is shortest. The predominant failure mode in
specimens loaded parallel to grain was in shear
without plug-shear-out. Little evidence of wood
crushing was observed. The screws prevent the
Fig. 5. Load ~ displacement behaviour for reinforced and non-reinforced bolted joints.
cracks from further growing. Failure modes were Figure 5. Load ~ displacement behaviour for
(d=15,9 mm, b/2=44,5 mm, t=38,0 mm, e/d=5).
reinforced and non-reinforced bolted joints.
affected by reinforcement; the propagation of crack
was reduced. Generally, the crack propagation in (d = 15,9 mm, b/2 = 44,5 mm, t = 38,0 mm, e/d = 5)
non-reinforced joints was more pronounced than
in the reinforced ones. The reinforced specimens Fig. 5 shows the load-displacement curves
with e=2d, 3d, 4d and 5d failed mainly in shear as for a non-reinforced and a reinforced joint. Table 8
predicted by the model. shows the relation between load-carrying capacity
of reinforced and non-reinforced joints. Particularly,

44 Revista EIA
the load-carrying capacity increases 120 % for the ment with the calculated load-carrying capacities
e=2d reinforced specimens with 15,9-mm bolts. It and predicted failure modes.
is clear that the increase in load-carrying capacity
is significant with the use of the reinforcing screws Nomenclature
enabling smaller joints and significant savings in
A complex constant
timber volume.
B complex constant
Table 8. Relation between load-carrying capacity of b width of plate
reinforced and non-reinforced joints
d diameter of the hole
Ratio of reinforced and e end distance
Bolt diameter
e/d non-reinforced load-carrying
d (mm) Ex perpendicular-to-grain modulus of elasticity
capacity (%)
Ey longitudinal modulus of elasticity
15,9 2 120
F resultant force
15,9 3 4,68
Fs screw load
15,9 4 0,78
Gxy shear modulus
15,9 5 1,03 p average bearing stress
R radius of the hole

5. CONCLUSIONS s screw distance

Sij elastic compliances of the plate material
The solution proposed here is entirely ana-
λ clearance
lytical and the most important results are compiled
clearly in tables.
u1 , u 2 constants
zk complex variable
This study dealt with the analytical and
experimental investigation of the effectiveness of µ1 , µ2 complex parameters of the first order
self-tapping screws as means of reinforcing bolted νyx coefficient of Poisson
timber connections loaded parallel-to-grain. Several σx perpendicular-to-grain stress
equations are presented to calculate the load-carry-
σy longitudinal stress
ing capacity of reinforced and non-reinforced timber
joints. τxy shear stress

The reinforced specimens showed a less cata- ϕ (z 1 ) , Ψ (z 2 ) complex stress functions

strophic failure mode whereas the non-reinforced

specimens failed in a brittle way. In reinforced joints it ACKNOWLEDGMENTS
is observed some increase in embedding and ultimate
strength, when compared with non-reinforced joints.
I thank CIBISA as well as the Université Laval
It is also concluded that spacing and end distances
for financial support of this project. The constructive
can be reduced.
comments of Daniela Blessent (Université Laval) and
Ultimate loads from tests on wood plates an anonymous reviewer are greatly appreciated and
loaded with a single bolt show a very good agree- have helped to improve the manuscript.

Escuela de Ingeniería de Antioquia

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 Bolted timber joints with self-tapping screws

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