MATEC Web of Conferences 303, 030 0 3 (2019) https://doi.org/10.

1051/matecconf/2019303030 03
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Theoretical Evaluation of Moment Resistance for Bolted Timber

Connections

Junting Guo1,a and Zhan Shu2

1
The College of Architecture,Washington University in St.Louis, Brookings,DR, Campus Box 1083, Saint Louis, MO 63130,US
2
Department of Civil Engineering, Shanghai University, Shanghai 200444, China

Abstract. Timber construction is nowadays becoming more and more favorable due to multiple advantages. In this
paper, the connection type and material of timber building were first highlighted. Then, the bolted joints with
slotted-in steel plates were systematically tested and analyzed. A typical slotted-in bolted glulam connection was
simulated using the software Abaqus. Furthermore, a few important design variables were measured and used to
numerically estimate the embedment strength, the shear force per plane, and the ultimate moment capacity of the
connections. At last, multiple configurations of joint design were compared in the paper, and a parametric design was
made. The results were systematically explained.

1. Introduction wood structure, cross laminated wood timber structure and

timber hybrid structures. Light-frame wood construction,
Wood is a traditional construction material that has been using smaller members spaced closely together in load
widely used along with human civilization. Considering sharing arrangements, offers economy, strength, and
sustainable development, wood could become a renewable flexibility that can be applied to not only residential houses
and environmentally friendly construction material when but also large commercial buildings. Post-and-beam timber
the forest resource is properly arranged [1]. Most of the frame structures are widely used in commercial and public
current construction materials such as concrete and steel buildings as the large space between their beams and
produce massive dust and various wastes during columns provides flexible space to use.
construction. Considering such an escalated environmental In addition, modern timber frame structure could be
problem, timber-made structures become a more favorable categorized to timber frame bracing structure and timber
choice in the field of civil engineering. frame shear wall structure. The vertical load is mainly
Besides, timber structures have many other advantages supported by beam-column elements, while the horizontal
other than their environmentally friendly attributes. (1) load is mainly supported by supporting shear wall and other
Living in a timber structure makes people feel themselves lateral elements. With the aid of modern technology, taller
closer to nature, therefore brings comfort and reduces timber structures become possible. The Canadians used to
pressure. (2) Raising up a timber frame is a quick process. hold the world’s record for the tallest residential timber
A timber frame can be erected on site faster than a tower. The Commons Tallwood House (shown in Figure 1)
comparable steel or cement construction [2]. (3) As human is 164 feet tall. The structure is a student residence, topped
labor is required less in timber construction, the general out in the year of 2017 at the University of British
construction costs also decrease. According to the UK Columbia (UBC), in Vancouver. The current tallest timber
Timber Frame Association, labor requirements for timber structure stands in Norway, named Mjøstårnet. It was
type of construction can lower labor needs by 20 percent. designed by Norwegian practice Voll Arkitekter. The
Building a timber frame home will range in cost from $150 18-story mixed-use building contains apartments, hotel,
to $175 per square foot for basic designs [3]. In addition, swimming pool, office space, and a restaurant, shown in
rehabilitation and repairing techniques of timber structures Figure 2 [3]. In addition, a Tokyo skyscraper is set to
involving structural adhesives has proved to be both become the world's tallest wooden building in the future
structurally efficient and economically competitive when [3].
compared with alternative repair procedures [5]. The increasing height of timber structure cannot leave
Common wood structures include light-frame wood without materials. Glu-laminated timber (Glulam),
structure, post-and-beam timber frame structure, space cross-laminated timber (CLT), Laminated Veneer Lumber
a
Corresponding author: shuz@shu.edu.cn

© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0
(http://creativecommons.org/licenses/by/4.0/).
MATEC Web of Conferences 303, 030 0 3 (2019) https://doi.org/10.1051/matecconf/2019303030 03
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(LVL), parallel strand 1umber (PSL) are some of the

modern timber materials over the world that were
developed based on the newest technologies.

Figure 1. UBC residential timber building, Figure 2. Tallest timber structure, Mjøstårnet, Norway [4].
Vancouver, Canada, 53 METRES [6].
lasts for about 100 years [7].
(shown in Figure 4). Glulam, which is the most commonly Moreover, the connection part is crucial for timber
used material currently, has a high strength-to-weight ratio. structures. The strength of the connection is highly relevant
Its shape can be changed into long a span bending form to the overall performance of the whole timber structure.
available for the construction of indoor stadiums. Better yet Different connections could be selected for different timber
more expensive materials, such as PSL were made of structures. For tall structures, the connections are desired to
strands that were clipped-veneer elements having a be stiff enough to hold the strong winds and/or earthquakes.
minimum dimension of 0.25 inches and an average length For many traditional timber buildings in China and the
of at least 300 times this least dimension. The Douglas-fir, Middle East, mortise and tenon connection is the common
southern pine, western hemlock, and yellow-poplar are type. The tenon, formed on the end of a member generally
commonly chosen for PSL because of their superior referred to as a rail, fits into a square or rectangular hole cut
strength [7]. Studies have shown that the tensile strength of into the other, corresponding member [14]. In modern
timber is much higher than that of concrete, which proves connections, fasteners are also commonly used as they
the strength and superiority of timber material [21]. could increase the strength of the connections. When
Furthermore, along with the invention of new timber fasteners have plastic deformation, ductile performance
materials, the likelihood of the inflammability of timber is occurs. In dowel-type fasteners (e.g. nails, screws, dowels
also significantly reduced. These large modern timbers and bolts), ductility is achieved by means of the plastic
covered with unburnt varnish. Even if the fire accidentally deformation in metallic connectors [13].
appears, a few centimeters of unburnt char will form, which
protects the timber inside (shown in Figure 3). Failure of
the beam or struct will occur only when the cross-sectional
area of the unburnt core becomes too small to support the
load [8]. Modern technologies also provide solutions
against termite, moisture, and temperature changes to
timber materials. Timber-made homes could last two to Figure 3. Unburnt portion of timber.
three times as long as the standard modern home, which

(a) (b) (c) (d)

Figure 4. Different timber materials, (a)PSL [9]; (b) Glulam [10]; (c) CLT [11]; (d) LVL [12]..

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rotational strength. The obtained results include multiple

design configurations that were systematically analyzed. At
last, a parametric design was created based on the hand
calculation model.

2. Finite element analysis model with

Abaqus
(a) (b)
Figure 5. Existing timber connections (a) Mortise and Tenon
2.1. Finite element analysis
connection [15]; (b) Slotted Bolted Connection [16].
This study provides a comprehensive study of the rotational
In the current prevalent laminated timber beam-column performance of glulam bolted joints. A finite element model
system, the laminated timber beams and columns are often was made in Abaqus, and hand calculation model was
connected by slotted-in bolted joints, which is the type of performed in Matlab. A comparison between the Abaqus
connection presented in this study. The slotted-in bolted model and hand-calculation model was made. The finite
joints with steel plate connection has high resistance to element method (FEM), is a numerical method for solving
horizontal load, but earthquakes usually push the building problems of engineering and mathematical physics. Typical
in the horizontal direction, adding demand of the moment problem areas of interest include structural analysis, heat
resistance of such connections. Typical pinching transfer, fluid flow, mass transport, and electromagnetic
phenomena can be observed in the hysteresis behavior of potential. The analytical solution of these problems
nailed connections in walls, and in nailed frames, while generally requires the solution to boundary value problems
stable dissipating hysteresis loops and limited stiffness for partial differential equations. The finite element method
degradation can be found with glulam connections formulation of the problem results in a system of algebraic
proposed by Buchanan and Fairweather [17] [18]. The equations. The method approximates the unknown function
beam-column joints are the weak part of the structure due over the domain [23]. In the software Abaqus, it uses FEM
to the gap between the reserved holes and bolts of this kind as the basis of creating the model and simulating the
of joints, which is mainly manifested in the yield of metal deformation of the model relating to the force on it.
joints and the plastic deformation of wood. Nonetheless, The FEM model could also be used to provide
unlike steel or reinforced concrete joints whose moment estimations of the rotational strength for different designs of
resisting capacities could be directly hand calculated, the bolted timber joints. The contact surface between the
glulam bolted connections have not got a reliable and direct nut and the wood was slightly increased as the washers
method to obtain their mechanical properties. To do were not included in the model. Friction contact was not
mathematical analysis for timber slotted-in bolt joints defined in the model. Hard contacts were defined between
timber connection, the main components that need to be the bolts and the steel holes. All the other contacts were soft
considered include the material itself, steel plates, and the contacts, setting the surfaces of the steel elements as main
fasteners connecting the timber members [19-22] surfaces and the surfaces of the wood elements as the slave
This study focuses on the moment resistance for bolted surfaces.
timber connections. Joints with larger fastener sizes (i.e.,
diameters of 20mm or more), which are more commonly
used sizes, were selected. Associated with these conditions, 2.2. Test setup & model design
the brittle performance of wood was expected, which was
proved from multiple sets of experimental results. Finite The model is a joint of a post & beam timber structure,
element model was established to evaluate the rotational which is a prototype slotted-in steel plate bolted timber
performance of such joints. A series of estimation formulas joint. This model is an assembly of several components,
were adopted from an existing study, which could provide shown in Figure 6:
estimations for the moment capacity, coupled shear and

(a) (b) (c)

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(d) (e) (f)

Figure 6. (a) beam bolts (Length: 150mm); (b) column bolts (Length: 292mm); (c) beam (830mm×130mm×305mm); (d) nut (Radius:
15mm Thickness:10mm); (e) column (1000mm×272mm× 305mm); (f) steel plate (9.5mm×305mm×745mm).

The elastic performance of the bolted timber joints is 2.3. Specific parameters of model
usually decided by the embedment strength of glulam
material. To consider the ductile performance at the local Table 5. Specific parameters of model.
level, a common approach is to weaken the elastic modulus Variable Explanation Value
near the pre-drilled holes on the glulam elements. The Layer The Number of fasteners on the layer 2
elastic property and other properties of materials are Column The Number of fasteners on columns 2
summarized in Tables 1 to 5. ED The End Distance (Distance from fastener to the post) 120mm
VD The Vertical distance 85mm 110mm 85mm
Table 1. Isotropic steel material properties specified for steel
HD The Horizontal Distance 105mm
bolts.
Bsec The Width of the section 180mm
Elastic Plastic tsteel The Thickness of steel member 12mm
Young’s Poisson’s Ratio Yield Plastic G Specific gravity 400 kg/m3
Modulus Stress Strain d Diameter of the bolts 20mm
bh2 Flutes pitch of the bolts 2.5mm
1 200000 0.3 1 640 0
ft Tensile strength 600 N/mm2
2 640 2 fc,⊥ Compression strength perpendicular to the grain 2.5 N/mm2

Young’s Modulus Poisson’s Ratio fc,// Compression strength parallel to the grain 10 N/mm2
ρ Density of wood 399kg/m3
1 200000 0.3
k mod 0.8
γ mod 1.25
Table 2. Isotropic behavior of steel plates.
Hst Size of the pre-drilled holes on the side timber elements 22mm
Elastic isotropic behavior Plastic isotropic behavior
Hms Size of the pre-drilled holes on the middle steel elements 22mm
Young’s Modulus Poisson’s Ratio Yield Stress Plastic Strain
dBC Gap length between the beam and the column 3mm
fe,0 Embedment Strength parallel to the grain, unit in MPa Need to be calculated

1 200000 0.3 1 390 0 fe,90 Embedment Strength perpendicular to the grain, unit in MPa Need to be calculated
Mu Ultimate moment capacity of bolted joint, unit in kN`m
2 390 2
Hload How far the applied load to the rotational center is. 1337.5mm

Table 3. Wood foundation potential isotropic plastic behavior.

Isotropic plastic behavior
Yield Stress Plastic Strain
1 20.85 0
2 20.85 2

Table 4. Timber elastic engineering constants.

Elastic Engineering Constants
E1 E2 E3 Nu12 Nu13
12000 500 500 0.35 0.35
Nu23 G12 G13 G23 Figure 7. Fasteners of connection in Matlab.
0.4 600 600 600
2.4. Definition of yield from moment-rotation curve
Isotropic plastic behavior is:
Yield Stress Plastic Strain The yield point of a system (the red dot on line in Figure 7)
1 35 0 is usually defined as a point on a hysteretic or monotonic
2 35 2 backbone curve where plastic deformation begins. For the
timber structural elements, however, the nonlinearity often

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occurs at an earlier stage. Consequently, a normal yield FEM, the numerical model was created and the result was
point is commonly defined on a monotonic pushover curve. got. Assuming the ductile performance of the element, the
shear strength of a bolted connection is highly influenced
2.5. Simulation results by the embedment strength of wood. The Stress distribution
All model parts were loaded until they were fully damaged. of the deformed specimen is presented in Figure 8.
The damage condition is shown below. With the created

(a) (b)
Figure 8. (a) Stress; (b) Stress distribution of the deformed specimen.
(3) The column element and the steel plates suffer no
Shown from the above study, some assumptions were damage;
made according to some preliminary estimation of the (4) The shear force is evenly resisted by all the n
moment carrying capacities for a type of timber-timber fasteners (shown in Figure 9(b)). That is, the horizontal
joints (shown in Figure 9(a)). The shear and rotational shear Fh,d = Hd/n, and the vertical shear Fv,d = Vd/n;
analyses were presented in the figure. (5) The rotational strength is dominated by the shear
Assumption: capacity perpendicular to the moment arm of each fastener
(1) The center of rotation is the geometric centroid of the Fm,d), whose direction is perpendicular to the line between
fasteners; the fastener and the geometric centroid (shown in Figure
(2) The deformations within the timber elements are 9(c));
small such that the relative locations of the holes do not (6) The dowel load is the vector addition of three forces,
change; i.e. Fm,d, Fh,d, and Fv,d.
y
y y
Fastener, A

Fi A
A Hd / n
Fastener, i ri
Vd / n rmax Fm,d,max
x x
Md
Hd
x

Vd

(a) (b) (c)

Figure 9. Load carrying capacities of bolted timber joints (a) simplified timber-timber joint; (b) shear resistance; (c) moment resistance.
ES0  0.082  k  (1  0.01  bh1 )
(1)
3. Hand calculation  0.082  400 kg 3  (1  0.01  0.02m)
m
3.1. Embedment strength calculation
The coefficient compression of wood is then calculated
The elastic performance of the bolted timber joints is following Eq. (2).
usually decided by the embedment strength of glulam. The K90 =1.35+0.15  0.02m  1.353 (2)
strength of multiple fastener connections does not equal the To calculate the sum of the total embedment strength after,
strength of the single fastener connection multiplied by the a series of formula called Eurocode need to be used. Eq. (3)
number of fasteners. Generally, the connection fails at a – (6)
lower load because the timber splits or because the wood is
softened, which can be explained by the complicated stress Following Eurocode
distribution around the fastener position. For this case, the
initial embedment strength (ES0, in the unit of MPA) is fe,0  0.082 1-0.01d  k (3)
expressed by Eq. (1). The result is 32.79MPA.

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f e,0
f e,90 
k90 (4)
fe,0 FV FV Farthest bolt
fe, 

h1
FM,1
k90 sin 2   cos 2  2 1 FM,2

h1
(5) FV FV Center of rotation

h2

θ1
θ2
2 1
4 3 r2 r1 F

h2
ᵝ h (1- ᵝ ) h
θ4 FM,4θ3
M,3

h1
k90 =1.35+0.015d
(6) x1 x2 r4 4 3

h1
r3

1
Fc x1 x2

3.2. Estimation of shear and rotational strength (a) (b)

The ultimate moment (Mu) capacity or shear force is also an FV
Farthest bolt
F1 F1
important attribute to determine the moment resistance of FM,1 Farthest bolt F2

h1
Center of rotation

θ1
θ2
2 1

θ1
r2
timber structure. Mu is influenced by the compression

1
r1 F

ᵝ h (1-ᵝ ) h

h2
1 θ4 F 4 θ 3 3
α1 r4 4 3

strength (fc,//) parallel to the grain. fc,// is linear when the

h1
r3

1
Fc x1 x2

deformation is small, and it reaches a cap when Center of rotation

deformation becomes larger, which is shown in Figure 11. (c)

The ith bolt is angled θi from the grain and has a distance Figure 10. Internal forces of bolted timber joints (a) pure shear; (b)
of ri from the rotation center. Shown from the Figure 7, bolt pure bending moment; (c) coupled shear and bending moment.
# 1 in this case has the longest distance from the rotation
center, which is the red dot on the line. Thus, it can be The hand simulation result was made in Matlab, and the
assumed that when the joint reaches its capacity, bolt # 1 graph was presented in Figure 11.
has the largest shear force out of all the bolts, and the shear
force of the ith bolt could be assumed to have a linear
correlation with Eq. 7.
ri (7)
FM ,i  FM ,1
r1
while calculating Mu, a check needs to be done to make
sure that bolt # 1 has largest shear stress. Then, the design
ultimate moment resisting capacity of the joint with n bolts
is expressed in Eq. 8 to 11.
n
M b   ri FM ,i (8)
i 1

n
Fc   FM ,i cosi (9)
i 1

 2 Fc h1
 3

 f bh
 when Fc  c ,/ / 1
 2 (10)
Mc  
1 1  

2 2

 f c ,/ / bh12     2
 f c ,/ / bh

  2  3
 Figure 11. Key points defining the estimated moment-rotation
 when f c ,/ / bh1  F  f bh ,  = 2 Fc  1
 2
c c ,/ / 1
f c ,/ / bh1 curves for the bolted timber joint.

Mu  Mb  Mc (11) 3.3. Compare and analysis
The FEM simulated result and the hand calculated result of
The shear force may have different effect on the timber the prototype bolted joint were compared. Shown in Figure
model if the angle of the force is applied differently. The 12.
rotation center will also determine the effect of shear force. When rotation occurs from rad 0 to rad 0.9, there is no
The following study simulated some hypothesized cases moment resistance for both the Abaqus model and
when timber structure joints under different shear force. hand-calculation model. This is because the size of the
For the cases when the joints were under pure shear, the pre-drilled hole is larger than the diameter of the fastener,
shear force is equally resisted by all the bolts (as shown in which creates a small gap between the hole and the timber.
Figure 10(a)). For the cases when the joint is under a pure In this gap, the rotation of structure will not result in
bending moment, a portion of the beam might touch and moment resistance because there is no contact, which
squeeze the column surface. This type of case is shown in creates the initial horizontal line.
Figure 8(b). For most of the cases, the shear force and the When timber contact with the surface of the fastener, an
moment are coupled together, which is shown in Figure increase in moment resistance occurs in both models.
8(c)) [1]. Because the stiffness and strength of both models are

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approximately the same, the increase slope and value are

50
almost the same.
On rad 0.026 (1.49 degree), a slip occurs on the
40
hand-calculation model. This is because the
hand-calculation model considered the split of the wood,

Moment (kN-m)
30
and the joint is broken, which means ductile. This joint is
plastic. The ideal ductility means that the joint still works
20
when the split is over 3%.
There might be two reasons for the plasticity of timber:
10 2x2
1. The large size of fastener. The fasteners take over 2x3
the most part of the surface, which makes the hole large. As 3x2
a result of that, the timber is easier to split. 0
0 0.02 0.04 0.06 0.08
2. The diameter of cross-section is small, only 130mm. Rotation (rad)
130mm is not enough for a normal beam in the real Figure 13. Moment-Rotation graphs of connections with different
construction. fasteners.
While in the FEM model, because the split of timber 2. Change column width
was not defined initially, the strength did not have an Once the width changed, the moment resistance of the
obvious reduction, shown in graph 12. connection changed significantly. Its ductility bond doubled,
as the width of the column doubled, which is shown in
Figure14.

Figure 12. Hand calculation model vs. Abaqus FEM model.

On rad 0.026 to 0.033, the hand calculation model Figure 14. The change in width of column section.
estimates that the plastic deformation will occur, and
moment starts to reduce. The hand-calculating graph 3. Change fastener diameters
stopped at radian 0.033, because after 0.033, the hand The large size of fastener provides more moment
calculation model considers the joint not hold any moment resistance to the connection. However, it also makes the
resistance, which means it is broken totally. timber easier to split. According to Figure 15, the increased
Parametric Design: size of fastener brings more moment resistance, but also
Parametric design can be applied in Matlab with the makes the ductile performance occur more easily in less
hand-calculation equations, which would help to analyze rotational radians.
which type of connection is more suitable in real-world
construction.
1. Change fasteners
Besides 2×2, more fasteners could be added to the joints.
Accordingly, the diameter of the fastener was changed
smaller in order to adjust the new joint. 2×2, 2×3, 3×2,
were made in Matlab, and the graphs were given in Figure
13.

Figure 15. The change in diameter of fastener.

4. Conclusions and future work

To comprehend the moment resistance of glulam bolted

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