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Content uploaded by Laurent Daudeville
Author content
All content in this area was uploaded by Laurent Daudeville
Content may be subject to copyright.
Prediction of the load carrying capacity of bolted
timber joints
L. Daudeville, L. Davenne, M. Yasumura
Abstract Failure of bolted timber joints is analyzed experimentally and
numerically. In this study, the prediction of the load-carrying capacity of dowel-
type joints with one dowel under static loading is based on the analysis of fracture
in wood contrarily to most engineering methods that are based on the yield
theory. Mechanical joints consist of glued laminated spruce members and steel
dowels. In the different analyzed tests, the bolt loads the wood parallel or
perpendicular to the grain. The wood member thickness is chosen suf®ciently
thin to avoid the fastener from presenting plastic hinges. The in¯uences of
different structural parameters such as the dowel diameter, the edge- and end-
distances are investigated. The fracture propagation analysis is carried out with
the Finite Element (FE) method in the framework of Linear Elastic Fracture
Mechanics (LEFM). The only identi®ed parameter is the critical energy release
rate in mode I (G
Ic
). The comparison between experimental and numerical results
shows that the fracture must be considered for a correct prediction of the ultimate
load and that LEFM can help to improve design codes.
Introduction
Most engineering methods for the design of bolted or nailed joints in timber are
based on the Johansen's yielding theory (1949) (EC5, 1993) (Aune et al., 1986)
which assumes plasticity in both the wood and the fastener. For the purpose of a
reliable design of joints, fracture of wood should be considered in a large class of
mechanical joints because it may lead to brittle failure especially in the case of a
loading perpendicular to the grain. Some recommendations exist in design codes
about spacing, end- and edge-distances (a
3,t
and a
4,t
, Fig. 1) in order to avoid
Wood Science and Technology 33 (1999) 15±29 ÓSpringer-Verlag 1999
Received 11 August 1997
L. Daudeville, L. Davenne
Laboratoire de Me
Âcanique et Technologie,
ENS Cachan/CNRS/Universite
ÂParis 6,
61 avenue du Pre
Âsident Wilson, 94235 Cachan, France
email: Laurent.Daudeville@lmt.ens-cachan.fr
M. Yasumura
Department of Forest Resources Science,
Faculty of Agriculture,
Shizuoka University,
836 Ohya, Shizuoka 422, Japan
Correspondence to: L. Daudeville
15
brittle failure in connections, but they are essentially based on empirical rules.
The design recommendations for multiple fasteners joints are generally based on
the response of the single bolt joint.
Application of fracture mechanics to structural elements concerned essentially
beams with end splits, side cracks, knots and notches (Valentin et al., 1991).
Fracture mechanics methods have been scarcely applied to the analysis of me-
chanical joints. Wilkinson et al. (1981), Rahman et al. (1991) and Bouchain et al.
(1996) made FE analyzes of joints loaded parallel to grain. These studies are very
interesting investigating the in¯uences of bolt-spacing, of end- and edge-dis-
tances of a multiple fastener joint, but the ultimate loads were not predicted.
The aim of this paper is to show that LEFM provides an ef®cient tool for the
prediction of the load-carrying capacity of timber mechanical joints. Coupled
with an FE analysis, it allows completing engineering methods proposed in codes
for the design of timber mechanical joints by taking into account the in¯uence of
a possible crack and of structural parameters.
Three test programs were carried out corresponding to three kinds of loading:
tension perpendicular to the grain (Fig. 1a), tension parallel to the grain (Fig. 1b),
and bending (Fig. 1c). In order to prevent the dowel from bending, the wood
members are relatively thin compared to the dowel diameter (d). The in¯uences
of d, of the end- and edge-distances (a
3,t
and a
4,t
) are investigated.
The failure mode is a propagation of a crack parallel to the grain. Some em-
bedding of the bolt into the wood was sometimes observed prior to failure.
A simpli®ed approach is proposed for the prediction of the ultimate load of
these tests. The crack propagation is analyzed by the use of LEFM and with the FE
Fig. 1a±c. Specimens: atension perpendicular to the grain, btension parallel to the grain, c
bending; a
3,t
end-distance, a
4,t
edge-distance
16
code CASTEM 2000 of CEA (Commissariat a
Ál'Energie Atomique) on the as-
sumption of elastic bodies. According to experimental observations, this as-
sumption seems valid for a load perpendicular to the grain (Fig. 1a and 1c) but it
is certainly coarse in the latter case (Fig. 1b). A two dimensional analysis is
carried out in a plane perpendicular to the fastener because the bolt does not
bend. The in¯uence of friction was investigated (Talland, 1996). Essentially, it has
an in¯uence on the location of crack initiation. It seems possible to neglect
friction at the steel and wood contacts in the study of propagation. The presented
results are based on this assumption.
In the case of bending or tension parallel to the grain, the stress state is a
combination of shear and tensile stress perpendicular to the grain. Thus, a pos-
sible mixed mode of fracture (mode I and II) is investigated, the two energy
release rates G
I
and G
II
are computed by the local crack closure technique.
A Wu's criterion (1967) based on G
Ic
is used for the propagation analysis. The
critical energy release rate value is chosen in order to obtain the best comparison
between the results of tests performed on joints and numerical results.
The ultimate load of each test is computed according to the present analytical
theory used in (EC5, 1993). On one hand, it is based on the Johansen yield theory
and on the other on a shear stress criterion. In order to compare experimental,
numerical and analytical results, mean material parameters are used. The mean
embedding strength of spruce is derived from experimental results (Chaplain,
1996). The design loads (EC5, 1993) are calculated with characteristic material
parameters and compared with experimental results.
Experiment
All the tests were conducted on glued laminated spruce with no knots and no glue
interface near the loaded hole. There was no allowance between the dowels and
the wood. Two steel plates connected with steel dowels load the wood member.
No plasticity in steel elements was observed.
Tension perpendicular to the grain
Tests were performed at LMT Cachan, France (Fig. 1a). The test results were
already presented in Daudeville et al. (1996). The mean density and moisture
content of the wood were 460 kg/m
3
and 10% respectively. Table 1 gives the
structural parameters and the experimental maximum loads. The edge- and end-
distances are greater than the EC5 minimum recommended distances.
Table 1. Specimen con®gurations and ultimate loads in tension perpendicular to the grain
Reference d
(mm)
t
2
/d a
3,t
/d a
4,t
/d P
exp
(kN/m)
nb
(COV %)
P
EC5
(kN/m)
A1 4 140 5 (3) 112
A2 12 3 7 8 148 4 (10) 224
A3 12 143 3 (5) 247
B1 16 3 7 4 204 3 (12) 149
B2 20 3 7 4 230 4 (9) 187
C1 4 173 2 (1) 112
C2 12 3 25 8 223 2 (12) 224
C3 12 264 2 (10) 247
17
A stable crack propagation could be observed, especially with a
3,t
25d. In
general the crack propagation was not symmetrical. A crack could propagate on
one side, stop its propagation, and then a crack could propagate on the other side
of the loaded hole. The non-linearity of the load-slip curve was not very im-
portant.
Tension parallel to the grain
Tests were performed at BRI Tsukuba, Japan (Fig. 1b). The test results were
already presented in Davenne et al. (1996). The mean density and moisture
content of the wood were 406 kg/m
3
and 10% respectively. Table 2 gives the
structural parameters and the experimental maximum loads. Some end-distance
(a
3,t
) values were chosen to be less than the minimum value recommended in
EC5. For large end-distance values, an important non linearity of the load-slip
curve due to the embedding of the two bolts into the wood could be observed
(Fig. 2). For short end-distance values, the behaviour could be very brittle. 80% of
the specimens developed a central crack.
Bending
Tests were performed at BRI (Fig. 1c). The test results were presented in (Ya-
sumura et al., 1987). Table 3 gives the structural parameters and the experimental
maximum loads. Other information are unknown.
Present theory of Eurocode 5
The present theory of EC5 is based on the Johansen's yield theory (1949). A shear
criterion also has to be veri®ed in order to avoid brittle failure with a load
perpendicular to the grain. According to the classical yield theory classi®cation
(EC5-6.2.2.h), (Aune et al., 1986), the failure mode is a mode 1 double shear
(different from the ®rst mode of fracture).
Table 2. Specimen con®gurations and ultimate loads in tension parallel to the grain
Reference d
(mm)
t
2
/d a
4,t
/d a
3,t
/d P
exp
(kN/m)
nb
(COV %)
P
EC5
(kN/m)
D1 2.5 266 4 (4)
D2 8 2 3 4 324 5 (10) 233
D3 7 312 5 (15)
D4 10 336 5 (13)
E1 2.5 332 4 (41)
E2 12 2 3 4 382 4 (30) 334
E3 7 421 5 (19)
E4 10 422 5 (12)
F1 2.5 300 3 (30)
F2 16 2 2.5 4 531 3 (11) 425
F3 7 576 3 (1)
G1 2.5 313 3 (20)
G2 16 4 2.5 4 568 3 (11) 425
G3 7 621 3 (1)
G4 10 715 3 (8)
H1 2.5 459 5 (14)
H2 20 2 3 4 541 5 (23) 506
H3 7 681 3 (28)
H4 10 751 5 (9)
18
EC5 recommendations are based on characteristic values (®ve percentile val-
ues, subscript k). The design load on the dowel per unit wood member thickness
for the three problems is examined here (Fig. 1):
PEC5 min kmod=cMfh;a;kd (1)
2=3fv;ka4;t(2)
f
h,a,k
is the characteristic embedding strength for a load at an angle awith the
grain, d is the bolt diameter. k
mod
takes into account the variation of the loading
with time (EC5-3.1.7), it is chosen: k
mod
1 and cM1. For glulam, the
characteristic density (qk) and shear strength (f
v,k
) can be obtained with the mean
density (q) from the norm prEN1194.
Note that criterion (2) does not take into account the real degradation mode
that is a cracking parallel to the grain.
The characteristic embedding strength (f
h,a,k
) (N/mm
2
) is (EC5-6.5.1.4):
Fig. 2. Load-slip curves for a
tension parallel to the grain
Table 3. Specimen con®gurations and ultimate loads on the dowel in bending
Reference d
(mm)
t
2
/d a
3,t
/d a
4,t
/d P
exp
(kN/m)
nb
(COV %)
P
EC5
(kN/m)
I1 16 4 4 4 184 3 (15) 119
I2 7 260 3 (4) 209
J1 16 8 4 4 187 3 (10) 119
J2 7 253 3 (7) 209
K1 4 244 3 (17) 119
K2 16 4 7 7 287 3 (7) 209
K3 10 465 3 (16) 267
L1 4 193 3 (35) 119
L2 16 8 7 7 356 3 (6) 209
L3 10 423 3 (5) 267
19
fh;0;k0:0821ÿ0:01dqk
fh;90;kfh;0;k=k90 fh;0;k=1:35 0:015d
3
disinmm,qkis in (kg/m
3
). (3) is derived from experimental determinations of
the embedding strength according to an ASTM test (Larsen, 1973) (Fig. 3).
EC5 recommends an end-distance greater than 7d and an edge distance greater
than 4d (load perpendicular to the grain) and 2d (load parallel to the grain). Note
that the yield theory (1) does not take into account the in¯uence of these dis-
tances. The edge-distance is taken into account in (2).
The comparison between design loads (P
EC5
) and experimental ones (P
exp
)is
important, from a safety point of view. But it in order to estimate the validity of a
model by comparisons with mean experimental results, it is necessary to use
mean material values in (1)±(3) (no subscript k).
An experimental program for the determination of the mean embedding
strength (f
h,a
) of spruce was carried out (Chaplain, 1996). The ASTM tests used in
(Larsen, 1973) were performed on 179 specimens with a unique dowel diameter
(14 mm). The mean density and moisture content were 400 kg/m
3
and 8.7%
respectively. Fig. 3 shows the specimens and the observed degradation modes.
Note that a central crack is generally observed for a load parallel to the grain as
observed in joint tests.
It is assumed that the dependence of f h;awith d proposed by Larsen in (3) is
valid. Then the mean embedding strength of spruce parallel to the grain (f
h,0
) for
every density and bolt diameter can be obtained with the experimental strength
for the considered diameter and mean density (36.2 MPa) (Chaplain, 1996):
fh;00:1061ÿ0:01dq
fh;90 fh;0=k90 fh;0=1:35 0:015d
4
The calculation of f
h,90
with k
90
given in (3) and (4) gives an excellent concor-
dance with the experimental value obtained in tests (24.3 MPa).
Fig. 3. ASTM specimens and degradation modes (Chaplain, 1996)
20
According to the present theory, the mean ultimate load per unit thickness is
used in EC5:
Pmin fh;ad
2=3fva4;t
5
Table 4 gives the characteristic and mean parameter values used in (1)±(5) rel-
ative to the three con®gurations (a), (b) and (c) (Fig. 1) with d 16 mm.
The EC5 design loads are given in Tables 1, 2 and 3. The mean ultimate loads
according to (1)±(5) are given in Fig. 8±12.
Modeling
The modeling assumptions are:
H1: Plane stress state ± H2: Wood is linear-elastic to failure ± H3: The bolt is a
rigid body ± H4: The transverse T and radial R directions are not distinguished ±
H5: Friction, on the wood and bolt contact is neglected.
The assumption H5 is valid for propagation analyzes (Talland, 1996) but
friction is important for the determination of the crack initiation location.
In a plane stress problem, the radial R and transverse T directions cannot be
distinguished, so a mean behavior is considered . The elastic moduli were chosen
by extrapolation of the results (Guitard, 1987) with respect to the mean density. x
direction corresponds to the L direction.
ExEL15000 MPa;EyETER
2600 MPa
Gxy GTLGRL
2700 MPa;vxy 0:5
(6
Crack propagation analysis
LEFM assumes that all non linear phenomena are concentrated at the crack tip.
Non linear fracture mechanics or damage mechanics consider a process zone
where non linear damage phenomena occur. For the studied problem, the size of
the process zone can be neglected compared with the dimensions of the crack and
of the structure. In such a case, the LEFM approach can be applied.
The energy release rate is:
G(P,a) GIGII ÿ1
t2
oW
oa7
Table 4. Density and strength: mean and characteristic values
Tests (Fig. 1) (a) (b) and (c)
q(kg/m
3
) 460 406
q
k
= 0.95 q(kg/m
3
) (prEN1194) 437 386
f
v
(N/mm
2
) (CTBA, 1995) 8 8
f
v,k
(N/mm
2
) (prEN1194) 3.5 2.8
f
h,0
(N/mm
2
) (4) 41 36.1
f
h,0,k
(N/mm
2
) (3) 30.1 26.6
f
h,90
(N/mm
2
) (4) 25.8 22.7
f
h,90,k
(N/mm
2
) (3) 18.9 16.7
21
P is the load applied to the structure, W is the potential energy, a is the crack
length, t
2
is the wood member thickness.
The computation of the global energy release rate can be carried out by means
of two FE calculations 1 and 2. The crack propagation is modeled by separating
two connected lines (Fig. 4±5):
GP2
2a2ÿa1
1
k2
ÿ1
k1
t28
With Daa2ÿa1a; k stiffness; P(N/m).
Eq. (8) is obtained on the assumption that the applied load P does not vary
during the elementary crack increment. A similar relation can be obtained with
prescribed displacement. Both methods lead to very similar results (La¯otte,
1997).
Eq. (8) can be used only in the case of a pure mode of fracture in association
with a Grif®th's criterion (1920). Because of the orthotropic feature of wood, a
partition of modes is necessary in order to use the following criterion issued from
the Wu's one (1967) that was originally based on stress intensity factors:
GI
GIc
sGII
GIIc
19
The previous criterion is the Grif®th's one in the case of a pure mode I or II. G
I
and G
II
are obtained separately by a local method, the crack closure technique
that is based on the necessary work to close the crack during a propagation Da:
Fig. 4. Finite element mesh for a tension parallel to the grain and a central crack
Fig. 5. Crack closure technique
22
GI1
2t2
FyDv
Da;GII 1
2t2
FxDu
Da10
where Fxand Fyare the nodal forces in the grain (x) and perpendicular to the
grain (y) directions (obtained in the ®rst FE computation). Du and Dv are the
relative displacements of the released node in the x and y directions (second FE
computation) (Fig. 5).
In both the local and the global method, the mesh re®nement at the crack tip is
constant during the crack propagation.
According to Valentin et al. (1991), Mans®eld-Williams (1995) and Petersson
(1995) a good approximation is:
GIIc 3:5GIc 11
The load P that leads to a crack propagation of a joint is computed for different
crack lengths with (8)±(11) and for a given G
Ic
. The maximum load gives the
calculated load carrying capacity P
calc
of the joint and the critical crack length.
Fig. 6 shows the computed load with respect to the crack length of a joint loaded
perpendicular to the grain.
Fracture initiation
Experimentally, the initiation of a crack was always observed at h0°(Fig. 7)
for a perpendicular tension. Under bending, the experimental observations show
that the initiation angle is h0°but the way of propagation (from the dowel to
the edge or from the dowel to the central load) is a priori unknown. In the case of
a tension parallel to the grain, hwas in general close to zero but sometimes an
initiation at an angle hbetween 0°and 45°was observed.
Results
Identi®cation
The fracture process is a priori unknown (initiation location, one non-symmet-
rical crack or two symmetrical cracks). Thus different fracture processes were
Fig. 6. Load versus crack length in
tension perpendicular to the grain
23
analyzed for each test. The best concordance between the calculated and exper-
imental maximum loads gives the fracture process.
The only unknown material parameter G
Ic
is identi®ed in order to obtain the
best comparison between experimental and numerical results. Note that the
knowledge of the fracture process is very important. For instance for a tension
perpendicular to the grain, the propagation of two symmetrical cracks needs
Fig. 7. Initiation of cracking
Fig. 8a, b. Tension perpen-
dicular to the grain
24
about twice the energy necessary to propagate one single crack. Fig. 8±12 give the
calculated load-carrying capacities of joints with:
GIc 100 Nm/m212
This value is about half of the fracture energy G
f
obtained with classical fracture
tests (Daudeville et al., 1996) and can be considered as low. Note that G
f
and G
Ic
are equal for a perfectly brittle material only and that the ultimate load depends
on the square root of G
Ic
. Thus, an error of 50% on the estimation of G
Ic
leads to
an error of 22.4% only on the estimation of the ultimate load.
Discussions
Tension perpendicular to the grain (Fig. 1a, Fig. 8±9).
According to the simulations, the more probable fracture process from the ini-
tiation to the maximum load is the propagation of only one crack on one side of
the loaded hole. A second crack can be obtained after this maximum load.
Fig. 8a gives the in¯uence of the dowel diameter, Fig. 8b gives the in¯uence of
the edge-distance for two end-distances. LEFM allows correct predictions and
gives the good trends. The present theory's EC5 predictions are much greater than
experimental results. It is alarming to notice that the design load is on the unsafe
side for joints A2, A3 and C2.
Fig. 9a, b. Tension parallel
to the grain ± In¯uence of
bolt diameter ± Short end-
distances
25
In that case, the present theory of EC5 cannot predict correctly the load-
carrying capacity of the joint because the main degradation that leads to failure is
cracking.
Also note that the yield theory does not take into account the in¯uences of the
end- and edge-distances that are correctly described by the FE analysis.
Tension parallel to the grain (Fig. 1b, Fig. 9±11)
The experimental results of Fig. 9±11 with d 16 mm are an average of tests F
and G. According to the simulations, the more probable fracture process is a
cracking in the mid-plane (Fig. 4). This is con®rmed by the experimental ob-
servations.
Fig. 9±10 give the in¯uence of the bolt diameter for different end-distances.
The FE analysis gives correct results and trends.
Fig. 11 gives the in¯uence of the end-distance for two bolt diameters. The yield
approach gives good results for an end-distance greater than 7d that is the
minimum requirement according to EC5. This is normal because the embedding
strength was identi®ed for an end-distance close to that value. Also note that the
yield theory does not take into account the in¯uence of the end-distance. LEFM
could give information on this in¯uence if it was decided to reduce the present
minimum requirement.
In that case, the present design recommendations of EC5 are correct because
yielding occurs (Table 2).
Fig. 10a, b. Tension paral-
lel to the grain ± In¯uence
of bolt diameter ± Con-
forming to the EC5 end-
distances
26
Bending (Fig. 1c, Fig. 12)
The experimental results of Fig. 12 are an average of, on one hand, tests I and J
and, on the other hand of tests K and L.
The solicitation on the bolt depends a lot on the edge-distance (a
4,t
). The
higher a
4,t
, the more sheared is the wood around the bolt. In this case, a mixed
mode of fracture occurs (tearing + shear).
Fig. 12. Bending. In¯uence
of the end- and edge-
distances
Fig. 11a, b. Tension parallel
to the grain ± In¯uence of
the end-distance
27
The way of propagation depends on a
4,t
. According to the simulations, the
more probable fracture process from the initiation to the maximum load, is
always a crack propagation from the bolt to the edge except for a
4,t
10d. In the
latter case the crack propagates from the bolt to the central load.
Once again, LEFM gives excellent results and is able to predict the in¯uence of
the structural parameters. The present theory of EC5 does not give the correct
trends and predictions of the load-carrying capacity.
Conclusion
LEFM is a simpli®ed approach consisting in the comparison of the energy release
rate with a critical value. This method has been applied for the determination of
the load carrying-capacity of mechanical joints with a single bolt. Correct pre-
dictions con®rm that failure of joints is fracture controlled. This approach can be
considered as a possible tool to complement the present codes.
Present theory of Eurocode 5 is based on the yield theory and on a shear
criterion. The in¯uences of structural parameters that are not taken into account
in the present theory may be considered with LEFM.
The yield theory is valid when the load is parallel to the grain. This approach is
very simple, it is analytical. It is particularly convenient when the main degra-
dation phenomenon is plasticity rather than splitting. In complex joints, per-
pendicular to the grain stresses generally exist.
The shear criterion does not take into account the actual degradation process
for a load perpendicular to the grain and does not allow correct predictions of the
load carrying capacity of single bolt joints.
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