There have been many experimental and numerical studies analysing the glued-in rods in solid structural timber, glulam and LVL. However, the research related to glued-in rods in CLT is scarce. The main purpose of this section is to compare the existing design equations with the experimental data obtained on CLT. The comparison is made in Fig. 6 for the 0° specimens and in Fig. 7 for the 90° specimens. When the different design equations are compared it is necessary to consider their assumptions and the conditions of the derivation (e.g., all of the analysed equation proposals were based on specimens where the failure mode described as rod pull-out occurred). These assumptions are described in Sects. 4.1, 4.2, 4.3, 4.4, 4.5 and 4.6.
Feligioni et al. proposal
Feligioni et al. experimentally investigated the influence of different types of adhesives (brittle and ductile) on the pull-out strength of glued-in rods in structural timber (specimens from spruce wood) [3]. The tests confirmed that a ductile adhesive leads to a higher pull-out strength, since the ductility of the adhesive ensures a uniform load transfer from the rod to the timber. Hence, a design equation for the axial pull-out strength of the rod parallel to the grain was proposed that takes into account the type of adhesive:
$$F_{{{\text{ax}},0}} = \pi \cdot l_{\text{a}} \cdot \left( {f_{{{\text{v}},{\text{k}}}} \cdot d_{\text{equ}} + k \cdot \left( {d + e} \right) \cdot e} \right)\cdot a$$
(1)
$$f_{{{\text{v}},{\text{k}}}} = 1.2 \cdot 10^{ - 3} \cdot d_{\text{equ}}^{ - 0.2} \cdot \rho^{1.5}$$
(2)
where F
ax,0 is the axial pull-out strength, f
v,k is the characteristic shear strength of the adhesive-timber interface, k is an adhesive strength parameter found to be 0.086 for brittle and 1.213 and ductile adhesives, e is the thickness of the adhesive, ρ is the density of the wood and d
equ is the equivalent diameter (d
equ = min(d
h, 1.25 d)).
The following values were assumed for the CLT specimens in this study: k = 0.086, e = 2 mm and ρ = 450 kg/m3. The values l
a, d
h and d were those listed in Table 2.
The GIROD project proposal
The GIROD (Glued-In Rods) proposal for the design equation is presented in [14]. The model for the estimation was developed based on glulam specimens with thin bondlines between the rod and the timber (0.5 mm or less). The proposed equation was derived assuming a pull–compression set-up, with the aim of applying this to all situations as a simplification on the safe side. The axial pull-out strength of the rod parallel to the grain is determined by the geometry of the joint and by two empirical parameters describing the bondline and the material properties:
$$F_{{{\text{ax}},0}} = \tau_{\text{f}} \cdot \pi \cdot d \cdot l_{\text{a}} \cdot \left( {\tanh \omega /\omega } \right)$$
(3)
where τ
f is the local bondline shear strength (characteristic value) and ω is the stiffness ratio of the joint (described in [14]). The stiffness ratio is dependent on the fracture energy (G
f), the area of the rod (A
r), the modulus of elasticity (MOE) of the rod (E
r), the area of the wood (A
w), and the MOE of the wood (E
w).
In this paper the GIROD equation was used for the CLT specimens and a glue line thickness of 2 mm, which does not fit exactly with the original assumptions of the GIROD study (e.g., test data with thin bondlines and glulam specimens). Since the axial pull-out strength from CLT with different orientations of the glued layers is calculated, the stiffness of the wood was defined as a combination of the properties in the parallel and perpendicular directions (E
w·A
w = E
w,0·A
w,0 + E
w,90·A
w,90). The following values were assumed for the CLT specimens in this study: τ
f = 9.6 MPa, G
f = 1750 Nm/m2, E
r = 210 GPa, A
w,0 = 140 cm2, A
w,90 = 56 cm2, E
w,0 = 11 GPa and E
w,90 = 0.4 GPa.
Steiger, Widmann and Gehri proposal
Steiger et al. [10] conducted tests on threaded rods glued in glulam (GL24 h) parallel to the grain by means of an epoxy-type adhesive. A total of 48 tests of specimens with varying density and slenderness ratio were performed. Based on these assumptions, the following empirical pull-out strength model was proposed:
$$F_{{{\text{ax}},0,{\text{mean}}}} = f_{{{\text{v}},0,{\text{mean}}}} \cdot \pi \cdot d_{\text{h}} \cdot l_{\text{a}}$$
(4)
$$f_{{{\text{v}},0,{\text{mean}}}} = 7.8 \cdot \left( {{{\lambda_{\text{h}} } \mathord{\left/ {\vphantom {{\lambda_{\text{h}} } {10}}} \right. \kern-0pt} {10}}} \right)^{ - 1/3} \cdot \left( {{\rho \mathord{\left/ {\vphantom {\rho {480}}} \right. \kern-0pt} {480}}} \right)^{0.6}$$
(5)
where f
v,0,mean is the nominal shear strength of a single axially loaded rod parallel to the grain, dependent on the slenderness of the hole (λ
h = l
a/d
h) and the density of the wood (ρ).
A similar strength model was developed by Widmann et al. [24], who conducted 86 tests on threaded rods glued in glulam (GL24 h) perpendicular to the grain (the rod was bonded-in through several glulam layers) using an epoxy-type adhesive. The following equation was proposed:
$$F_{{{\text{ax}},90,{\text{mean}}}} = 0.045\cdot\left( {\pi \cdot d_{\text{h}} \cdot l_{\text{a}} } \right)^{0.8}$$
(6)
New Zealand design guide
The New Zealand Design Guide [25] provides an equation to predict the axial pull-out strength of a rod parallel to the grain. The equation was derived based on experimental and theoretical studies of epoxy-bonded steel connections in glued laminated timber. The proposed equation:
$$F_{{{\text{ax}},0,{\text{char}} .}} = 6.73\cdot k_{\text{b}} \cdot k_{\text{e}} \cdot k_{\text{m}} \cdot \, \left( {{{l_{\text{a}} } \mathord{\left/ {\vphantom {{l_{\text{a}} } d}} \right. \kern-0pt} d}} \right)^{0.86} \cdot \left( {{d \mathord{\left/ {\vphantom {d {20}}} \right. \kern-0pt} {20}}} \right)^{1.62} \cdot \left( {{{d_{\text{h}} } \mathord{\left/ {\vphantom {{d_{\text{h}} } d}} \right. \kern-0pt} d}} \right)^{0.5} \cdot \left( {{{e^{{\prime }} } \mathord{\left/ {\vphantom {{e^{{\prime }} } d}} \right. \kern-0pt} d}} \right)^{0.5}$$
(7)
takes into account the embedment length (l
a), bar diameter (d), edge distance (e′), hole diameter (d
h), moisture content (k
m), steel bar type (k
b) and epoxy type (k
e). In this study: k
m = k
b = k
e = 1.0 and e′ = 70 mm 0.086. The values l
a, d
h and d were taken from Table 2.
Rossignon and Espion proposal
Rossignon and Espion [6] investigated rods that were glued in manually drilled holes of glulam with a thick bondline. The failures in their tests occurred mainly due to splitting of the timber element along the anchorage length. Based on their research the F
ax,0,mean is calculated according to Eq. 4, where the mean nominal shear strength of a single axially loaded rod set parallel to the grain is given by the semi-empirical equation:
$$f_{{{\text{v}},0,{\text{mean}}}} = 5.8\cdot\left( {{{\lambda_{\text{h}} } \mathord{\left/ {\vphantom {{\lambda_{\text{h}} } {10}}} \right. \kern-0pt} {10}}} \right)^{ - 0.44}$$
(8)
Yeboah et al. proposal
Yeboah et al. [26] estimated the structural capacity of bonded-in Basalt Fibre Reinforced Polymer (BFRP) rods loaded perpendicular to the glulam lamellas. A two-component-epoxy gap-filling (thickness 2–12 mm) adhesive was used for the experiment. The axial pull-out strength of the rod perpendicular to the grain was estimated as:
$$F_{{{\text{ax}},90,{\text{mean}}}} = f_{{{\text{v}},90,{\text{mean}}}} \cdot \pi \cdot d_{\text{h}} \cdot l_{\text{a}}$$
(9)
where f
v,90,mean = 5.7 MPa.
According to [26] the design equation should only be used for l
a < 15 · d
h, since no strength improvement was observed beyond this bonded-in length.
Comparison with existing models
The design equations described above are compared to the experimental results using CLT specimens in Fig. 6. Since almost all the equations for the 0° specimens take into account the influence of the rod (hole) diameter, the results are shown separately for: (a) d
h = 20 mm (Fig. 6a) and (b) d
h = 28 mm (Fig. 6b). The experimental results are represented with a square (mean values) and a rhombus (characteristic values) indicator. The design equations are shown with blue (mean values) and red (characteristic values) curves.
From a comparison of the experiments with the design equations the following conclusions can be drawn:
- 1.
The design equations predict relatively well the ultimate tension force of the glued-in rod with small d
h and l
a (Fig. 6a). However, at higher values of d
h and l
a (Fig. 6b) the difference between the experiments and the design equations is much larger. The reason for this is that the specimens with large values of d
h and l
a exhibit different failure modes, which were not considered in the existing design Eqs.
- 2.
Most of the design equations (for both the characteristic and mean values) prove to be insufficient for a conservative estimation of the ultimate tension force of the glued-in rod (the result is overestimated in almost all cases).
- 3.
The best estimation for the ultimate tension force of the glued-in rod in CLT is the GIROD equation, as it more-or-less matches the experimental data, but in most cases it is still overestimating the ultimate tension force. This equation is not linear, it reduces the bondline strength for longer l
a, and takes into the account the grain orientation of the wood (parallel and perpendicular). This makes it the most suitable approximation for an estimation of the capacity of glued-in rods in CLT.
- 4.
On the basis of the experiments with the 0° specimens it is difficult to propose a general equation due to the large number of influencing parameters and the different failure modes obtained. Therefore, a parametric numerical study should be performed to estimate the effect of a large number of parameters that influence the failure modes and hence the load capacity of glued-in rods in CLT.
For the 90° specimens it is even more difficult to find design equations that would be directly comparable to the research performed in this paper. The design equations in [24, 26] were proposed for bonded-in rods in glulam perpendicular to the grain (the rods were bonded through several glulam layers) and therefore have a different global effective stiffness and different characteristic failure modes. This should be taken into account when evaluating the results.
Figure 7 shows only the results of the specimens with a small diameter (d
h = 20 mm) and small bonded-in lengths (l
a ≤ 240 mm). The results for the specimens with larger values of d
h and l
a are not given, since these results were strongly dependent on the CLT width (the main failure mode was splitting of the CLT). The existing design equations are therefore significantly different for larger d
h and l
a and are not comparable with the experimental data.
In contrast to Fig. 6, where most of the existing design equations overestimate the maximum tensile load, the two design equations in Fig. 7 mostly underestimate the mean experimental results. Similar to the case of the 0° specimens, there are many parameters influencing the failure mode and, consequently, the bearing capacity of the 90° specimens. Therefore, new equations should also be derived for the rods glued in CLT perpendicular to the grain.