2.1. General
A large variety of joint typologies and technologies exist for modern timber structures; in the case of high performance requirements, the majority of joints are effected by dowels, including GiR or STS.
Joints with laterally loaded metal dowels are, for example, used in combination with slotted-in or outer steel plates in trusses [
4], medium- to high-rise buildings [
5], and in bridges [
21]. In the design, the rotational stiffness of closely spaced small groups of dowels is often neglected even if they are subjected to moment action due to eccentricities [
20]. Larger groups of dowels and groups with larger spacing between the dowels can be employed as moment-resisting joints, e.g., in frame corners, where the dowels are positioned at a distance around the center of rotation [
22].
GiR rely on the bond between the timber and (steel) rod by means of adhesive, which provides a degree of slipness but brittle joints through the bondline. Therefore, GiR are well suited for applications requiring high stiffness. GiR can be used to couple a steel member with a timber member or to join two timber elements. Joints with GiR are often used to realize moment-resisting joints, such as beam-to-column or beam-to-beam joints, with or without steel profiles [
22] or column foundation [
23]. Ductile behaviour can be archived under monotonic and cyclic loading if the relevant failure is the yielding of the steel and not the failure modes associated with the timber. GiR are also used for the reinforcement and repair of timber members [
24].
Axially loaded STS provide high resistance and stiffness; therefore, shear joints with inclined STS are used for high-performance joints, e.g., in moment-resisting joints in domes [
4] and grid-shells [
25], or in large structures, such as arches as interior joints to restore the continuity of the arch [
26], and in beam-column joints [
4]. Ductile behaviour of STS joints can be obtained if the screws are mostly laterally loaded or if the screws are placed in a combined arrangement, i.e., inclined and perpendicular to the shear plane [
27].
STS represent the state-of-art joining technique in CLT-based structures [
27]. In fact, STS are used in CLT-based structures, i.e., to realize butt joints, half-lap joints or spine joints. STS can also be used, if inclined, to connect two orthogonally positioned CLT walls [
28], or, if coupled with steel plates, as angle brackets and hold-downs in wall-to-floor and wall-to-wall joints [
16]. Fully threaded STS are also frequently applied as reinforcement against stresses in the weak directions of timber members, e.g., as reinforcement in laterally loaded dowel-type joints [
29].
Laterally loaded dowels and bolts are very frequently used in joints, due to their good performance [
30]; they possess moderate load-carrying capacity and, when well-designed, considerable ductility. In addition, they are cheap and easy to install. GiR in joints are most often subjected to pure axial tension or predominant axial tension and minor lateral forces, while STS in joints are often subjected to a combination of lateral and axial forces, especially when STS are inclined with respect to the shear plane. For this reason, in the following subsections, the parameters of influence on the load-displacement behaviour of joints with laterally loaded metal dowels loaded laterally, GiR loaded axially, and STS loaded in combined shear and axial loading are analyzed.
The shape of the load-displacement curves changes according to the typology of the joints, i.e., depending on the type, the configuration (e.g., spacing, edge distances, number of rows) of the fasteners, and the failure mode of the joint. However, the load-displacement of all joints broadly shows three distinct regions (see
Figure 1) [
31]:
- –
A region of low or “zero stiffness”, at very low load levels, usually due to delayed contact between parts [
31,
32].
- –
An elastic region, characterized by a quasi-proportional relationship between the displacement and the load [
31].
- –
A plastic region [
31] that can further develop with a softening branch, with a plateau, or with a hardening branch. A hardening branch may occur due to the so-called rope effect in laterally loaded fasteners, which is caused, among other things, by normal forces in the fasteners and friction in the shear plane [
33].
The failure point can be located in the elastic or the plastic region. In the event it is in the elastic region, the failure is brittle due to the fracture of the wood or the steel rupture (e.g., if the fastener is also axially loaded) before major ductile mechanisms can take place [
34]. When the failure point is situated in the plastic region, the failure can be described as moderately ductile or ductile. In the event that the plastic region has limited extension, the failure is typically due to the fracture of the wood after some yielding of fasteners has occurred or because of an early rupture of the fasteners (moderately ductile failure). The more the plastic region is extended, the more ductile the behaviour of the entire joint (ductile failure). Final failure is reached when the displacement capacities of either the fastener or the timber are exceeded. In experiments and for classification, failure is often defined as the state when the load falls below a certain level in the softening branch or when a deformation criterion is reached.
Ductility is a desirable characteristic in timber joints since it benefits the robustness, reliability, and seismic performance of the structures [
2,
12,
35]. For example, in statically indeterminate structures, the joints can behave as a source of ductility and energy dissipation, so the rotational ductility is a very important characteristic to be determined [
35]. A review of the relative and the absolute definitions of ductility is given in [
35,
36,
37]. The majority of definitions are displacement-based and they are written as a function of the displacement at the yielding point
and of the ultimate displacement (maximum load
)
or of displacement at failure
(after the maximum load
has occurred) (
Figure 1). These two points are illustrated in
Figure 1. The most common relative definitions are the following [
35,
36,
37]:
And the corresponding absolute definitions are:
To complicate the definition of ductility, multiple methods to determine the yielding point exist. In [
38], it was found that the value of the yielding point based on the modified method of EN 12512 [
39] is the most appropriate since it gives the most suitable yielding point compared to the other methods. According to EN 12512 [
39], the yielding point is found as the intersection between the initial stiffness
and the tangential stiffness to the graph with an inclination equal to
. However, this gives a point that is not situated on the graph and, therefore, a modified version, where this point is projected onto the curve, was proposed. Regarding
, in [
40], it is suggested to take the displacement at 98% of the maximum load or as the displacement at failure, while in EN 12512 [
39], it is suggested to take
as the displacement at failure, as the displacement at 80% of the maximum force
, or as 30 mm, whichever occurs first. The present paper will refer to these two last definitions of
and ultimate displacement
to evaluate the ductility of timber joints.
In [
40], an approach to classify fasteners in timber structures based on ductility ratios is provided (see
Table 1). The limits are based on the indications contained in Eurocode 8 [
11]. The classification creates the possibility of grouping certain joints based on their load-displacement behaviour:
The absolute values and the shape of the load-displacement curve of the joints can show considerable differences and depend not only on the type of fastener and joint configuration but also on several other parameters. These parameters can be grouped as follows:
- –
geometricalparameters: the fastener diameter, the type of fastener, the thickness of the timber members, the tolerances and the edge and end distances, the embedment or anchorage length and the spacing, the hole clearance, and the off-centring of the fasteners.
- –
materialparameters: the density of the timber, the steel grade, the moisture content, the timber product wood species, the failure model, and the glue type.
- –
loadingandenvironmentalparameters: the load-to-grain angle, the load-to-surface angle, the load-to-fastener angle, monotonic or cyclic loading, the loading speed and load duration, the temperature, the moisture content, and the change in moisture content
The diverse shapes of the load-displacement curve are discussed in the following sub-sections, linking them, when possible, to the parameters of influence or the underlying physical phenomena.
2.2. Dowels and Bolts
In the case of joints with dowels and bolts, typical load-displacement curves may show all three previously identified regions (
Figure 1). Some examples of typical shapes of the load-displacement curves of such joints are shown in
Figure 2. These curves are representative of joints with dowels in double shear. In the case of bolted joints or steel-to-timber joints with dowels, the curve usually includes a more pronounced region of “zero stiffness” (curve D1 or D2 in
Figure 2) compared to other types of fasteners, such as STS [
32]. In fact, hole clearance and tolerances are responsible for the presence of a zero-stiffness region in the load-displacement curve [
32] due to the delayed contact between the wood and the fasteners. This effect is diminished with the increasing number of fasteners in the joint due to the compensation of the stochastic arrangement [
32], but is not fully eliminated. The joint may, under some circumstances, fail before entering the plastic region, showing only an elastic response up to failure (curve D1 in
Figure 2). This happens when the joint is unable to exploit its full “potential” if its load-carrying capacity and ductility are limited by brittle timber failure (splitting, plug shear failure, block shear, etc). Brittle failure happens due to limited edge distances or, in the case of multi-fastener joints, to limited spacing. If the spacing or edge distances are reduced, the general shape of the curve stays the same and the failure point will be located at different positions along the curve. However, in this case the stiffness in the elastic branch remains unaffected [
31,
41,
42]. For example, when the spacing is increased from 3d to 7d, the load-displacement curve can go from curve D1 to curve D2 in
Figure 2. In general, in a multi-fastener joint, the load-carrying capacity and the ductility might also be limited by the failure mode of each fastener. In fact, the ductility decreases with decreasing values of the slenderness ratio, defined as the ratio between the embedment length and the diameter of the fastener. With increasing slenderness of the fasteners, whether it is due to a change in diameter or in the embedment length, the embedment capacity of the timber in the contact area to the fastener increases in relation to the yield capacity of the fastener. As a result, the displacement capacity and the plastic region of the load-displacement curve increase with increasing slenderness as long as timber failure is avoided [
31].
In the plastic region, the curve can show a plastic plateau with clear identification of the maximum load-carrying capacity (curve D2 in
Figure 2), it can show a hardening branch with an increase in load (curve D3 in
Figure 2), or it can terminate with a softening branch (curve D4 in
Figure 2).
Figure 2.
Curves of joints with dowels or bolts as fasteners. Details of the joint are reported in
Table 2.
Figure 2.
Curves of joints with dowels or bolts as fasteners. Details of the joint are reported in
Table 2.
Load-displacement curves with a hardening branch are typical for joints with fasteners whose ends are fixed, i.e., for bolts, due to the increased load from the rope effect with increased fastener displacement [
44], which is similar to curve D3 in
Figure 2. Similar shapes, i.e., characterized by hardening, can be found in joints loaded perpendicular to the grain. In fact, the load-displacement curve of the embedment of dowels loaded perpendicularly to the grain shows a lower stiffness, but the hardening occurs at higher displacements compared to dowels loaded parallel to the grain where higher initial stiffness and a more flat plastic plateau is reached. This is also reflected in the load-displacement curve of the entire joint. The hardening behaviour is possibly due to the densification of the wood in the contact area below the dowel and a rope effect in the wood fibers that are loaded in tension parallel to the grain [
45].
The reinforcement of joints against tension perpendicular to the grain prevents splitting, which enables the joint to reach larger displacements along the plastic region of the load-displacement curve [
46], and, thus, leads to more ductile behavior of the joint [
31]. In the case of an interaction between the reinforcement and the fasteners, the embedment of the fastener can be enhanced, which leads to an increase in the load-carrying capacity and possible hardening of the curve [
43]. Adding reinforcement in a joint can transform the load-displacement curve, like D3 in
Figure 2 in the load-displacement curve, similar to D5 in
Figure 2. In the latter case, the load-displacement curve looks like D5 in
Figure 2 that shows extended plastic displacement with hardening, making it difficult to clearly identify the maximum load-carrying capacity.
2.3. Glued-in Rods
Joints with axially loaded GiRs can show very high performance with respect to the load-carrying capacity and stiffness per unit of the connected cross-sectional area and can outperform similar joints with laterally loaded dowel-type fasteners. However, GiR joints can exhibit a variety of complex and brittle failure modes, which is why they are in reality often much less ductile than joints with laterally loaded dowel-type fasteners. The possible failure modes of axially loaded GiR are defined in the 2022 draft of EC5 [
47] as one of the following four modes: (1) failure of the adhesive in the bondline and its bond with the rod and timber, (2) shear failure of the timber adjacent to the bondline, (3) splitting of the timber departing from the GiR, or (4) timber failure of the member in the surrounding of the GiR, and (5) yielding of the rod. Only with the last listed failure mode can ductile behaviour be achieved.
The behaviour of laterally loaded GiRs is considered to be quite similar to dowelled or bolted joints [
48], with the failure modes according to the EYM. The adhesive bond of the rod in the timber is typically neglected in this case.
The resulting load-displacement curves describing the behaviour of joints with GiRs can be quite different depending on the failure mode, as shown in the examples in
Figure 3. The examples provided in
Figure 3 are related to joints realized with solid timber and glulam and they do not apply to GiRs in CLT. The load-displacement curve of axially loaded GiRs can be characterized by an initial linear elastic component with very high stiffness, which originates from the stiff bond created by the adhesive. Depending on the design of the GiR and the resulting failure mode, the curve can be limited by a brittle failure with no plastic displacement (curve G1 in
Figure 3, typical for a bondline or timber failure of rods inserted parallel to the grain) or by a peak followed by a softening branch (curve G2, typical for a bondline and timber failure of rods inserted perpendicular to the grain). Where the GiRs are designed for the ductile tensile capacity of the steel rods, the linear elastic part of the curve is followed by a ductile branch (curve G3 in
Figure 3). The choice of the geometric and material properties of the rod, adhesive, and timber determines the failure mode, and, consequently, the ductility of joints with GiRs. For example, reducing the diameter of the rod (i.e., increasing its slenderness) and, hence, reducing the yield capacity of the rod, can lead to a more ductile failure mode [
49]. In contrast, increasing the rod diameter with a constant anchorage length results in a higher relative increase in the rod capacity and can stimulate brittle failure modes [
50,
51]. Rods made of low- and medium-steel-grade rods typically have a higher displacement capacity and a greater ratio between the ultimate strength and the yield strength compared to rods made of a high steel grade and, hence, are recommended for achieving ductility [
52,
53].
Figure 3.
Examples of shapes of load-displacement curves of joints with GiRs. Characteristics of joints are reported in
Table 3.
Figure 3.
Examples of shapes of load-displacement curves of joints with GiRs. Characteristics of joints are reported in
Table 3.
This ductility can be utilized to balance and equalize the possible non-uniform force distribution in joints with multiple GiRs and to utilize the full capacity of each GiR [
54,
55,
56]. In order to achieve a desired displacement, a sufficient free unbounded length of the steel rod should be provided [
57,
58].
Laterally loaded GiRs do not benefit from high stiffness of the adhesion in the bondline and can show very soft and ductile behaviour (curve G4).
Table 3.
Characteristics of GiR joint represented in
Figure 3.
Table 3.
Characteristics of GiR joint represented in
Figure 3.
Name | GiR | Loading and Application Angle | Timber | Diameter [mm] | Length [mm] |
---|
G1 [59] | 1 | Axial, parallel to grain | LVL | 12 | 150 |
G2 [59] | 1 | Axial, perpendicular to grain | ST | 12 | 150 |
G3 [52] | 4 | Axial, parallel to grain | ST | 20 | 300 |
G4 [60] | 1 | Lateral, parallel to grain | ST | 16 | 320 |
2.5. Summary of Connection Behaviour
As discussed in the previous sections, the load-displacement behaviour of timber joints with dowels, bolts, GiRs, and STS is very diverse and can be highly nonlinear, which should be reflected in the assumptions made in design. However, in the current design codes, such as EC5, a rather simplistic, uniform and mostly linear elastic load-displacement behaviour is considered for joints. The existing nonlinearity means that a considerable difference between the initial elastic stiffness and the stiffness at ULS at maximum load and/or maximum displacement exists.
The evolution of secant stiffness
in relation to the secant stiffness (
) to
and
(as suggested in [
63]) is shown in
Figure 5 for the load-displacement curves from
Figure 2,
Figure 3 and
Figure 4 in relation of the load level in the joints. The load level is defined as the ratio of the load value at which the secant stiffness is calculated, divided by the ultimate load
. The latter is defined as the maximum force or the force at a displacement of 15 mm, whichever occurred first. In the elastic range of the represented joints, the ratio
is approximately 1 for all the joints. The value of the ratio
that is assumed by EC5 for the ratio at the ultimate limit state is, in most cases, reached in the range of 60–100% of
, except for load-displacement curves characterized by a brittle failure mode, when the ratio stays around 1 up to
(see curves G1 and G2). Assuming that the joint will attract less load than in reality at the ultimate limit state can be an unsafe assumption in the case of a statically indeterminate structure, leading to an increased probability of failure [
12].
The relative
and absolute
ratios of all the previously shown load-displacement curves are reported in
Figure 6. The yielding point is identified based on a modified version of EN 12512 [
39] and the used definition of ductility corresponds to Equations (
1) and (
3).
was taken as the point that corresponds to the the failure, a load drop of
, or a maximum displacement of 30 mm, whichever occurred first (as indicated in [
39]).
In general, fasteners in timber structures show low to high ductile behavior (see
Figure 6). Even joints with GiRs, where the bondline behaviour is stiff and brittle, can show some ductility, if properly designed for yielding of the steel rods. However, it can be seen that it is necessary to differentiate between the relative value
and the absolute value
for some curves, for example, D2 of
Figure 2. In that case, according to the absolute ductility definition, it is classified as a high ductile joint, while for relative ductility, it is classified as a low ductility joint.
Figure 5 and
Figure 6 show that the mechanical behaviour of the joints is highly nonlinear. This shows that the formulas for the load-carrying capacity and the stiffness of joints given in EC5 are not sufficient to represent the behaviour of modern timber joints in the structural analysis of timber structures.
Therefore, more precise and realistic descriptions of the load-displacement curves of timber joints, including the ductility also, are needed. In the following section, different analytical models are presented, and their suitability to model the diverse and complex joint behavior is evaluated.
The curves selected for further analysis are the ones that show more ductile behavior and more diverse shapes: curve D5 as a curve with a plastic plateau and a complex shape, D3 as a curve with a hardening branch, S1 as a curve with a strong hardening effect after the yield point, and S3 as a curve with a highly nonlinear softening branch. The curves D2 and D4 were selected to study the sensitivity of the regression models to the approximation of the initial slip and the displacement range, respectively. The curves that show brittle and, in general, less nonlinear behavior have been excluded since the analyzed models are expected to represent the brittle curves easily and in a comparable way. The selected load-displacement curves are represented in
Figure 7: