Capacity models for timber under compression perpendicular to grain with screw reinforcement

Timber is a highly anisotropic material: the direction of the grain influences its mechanical properties (Porteous and Kermani 2013). In the direction parallel to the grain, timber is strong and stiff. On the contrary, in the direction perpendicular to the grain, the strength and stiffness are relatively lower (Porteous and Kermani 2013; Augustin et al. 2006). The fibres in timber are tubular and elongated. Therefore, the compression perpendicular to grain (CPG) failure leads to a collapse of the cellular tubes, manifesting as failure along the tubular layers (Persson 2000; Swedish Wood Stockholm, Sweden 2016), see Fig. 2.

Beams, trusses, and supports are typical design situations where CPG can occur (Hassan et al. 2014). Failure due to CPG does not generally lead to collapse. The failure in CPG is potentially a concern in the serviceability limit state (SLS). Yet, in Eurocode 5, CPG is regarded as an ultimate limit state (ULS) problem to avoid load failure of structural systems (Forening, Norske Limtreprodusenters Norway 2015). The failure mode due to the CPG occurs on the contact area of the load; see Fig. 3: as the compressive load increases, the fibres buckle. This compression will transmit to neighbouring fibres as a chain reaction. Higher loads can be achieved with higher deformation levels and dispersion lengths (Forening, Norske Limtreprodusenters Norway 2015).

The strength under CPG can be improved by using suitable reinforcements. Past and recent research (Bejtka 2005; Dietsch et al. 2015; Dietsch and Brandner 2015; Harte et al. 2015; De Santis and Fragiacomo 2021) prove that self-tapping screws are the most effective reinforcement system for timber under CPG (Kreuzinger 1999, 2001, 2002). Screws can also be used to strengthen notches, holes in beams (Aicher and Höfflin 2002, 2003; Kolb 2008; Aicher et al. 2007; Aicher and Höfflin 2009; Aicher 2011), or against tension stress perpendicular to the grain in curved or pitched cambered beams (Eurocode 2010; Tomasi et al. 2010).

Other techniques have been identified in improving the CPG of timber members. Nonetheless, reinforcement, glued-in rods or steel screws are not prescribed in Code (2005). For practical applications, screws recommended for the reinforcement of timber perpendicular to the grain are regulated by European Technical Approvals (ETA 2019), which are supplier-specific (O’Ceallaigh and Harte 2019).

Apart from screws, dowels also proved to be effective reinforcement systems of timber under CPG. Madsen et al. (2000) successfully installed steel dowels perpendicular to grain through the full height of glulam beams. Ed and Hasselqvist (2011) performed similar tests using birch dowels to enhance the compressive strength of glulam beams. Still, using self-tapping screws is the most favoured method for timber reinforcement due to several advantages. They are easy to install and may be used in various applications: to prevent splitting perpendicular to the grain, enhance dowel embedment strength, or enhance strength perpendicular-to-grain (Bejtka and Blaß 2004). Screw reinforcements can be used for in-situ and off-site manufactured frames/panels (Kildashti et al. 2021; Alinoori et al. 2020). Bejtka (2005) was among the first to study the effect of reinforcement in CPG. Pampanin (2013) used self-tapping screws to reinforce laminated veneer lumber (LVL) beams, while Dietsch et al. (2019) performed similar tests on glulam beams.

In the last decade, reinforcement under CPG is also becoming relevant for Cross Laminated Timber (CLT) elements (Mestek 2011). Serrano and Enquist (2010) tested 3-ply CLT elements and found the compressive strength dependent on the bearing area, load orientation to the surface grain, and loading positions. Bogensperger et al. (2011) compared data from glulam and CLT specimens and determined strength under CPG. Lately, Brandner (2018) published a state-of-the-art review on CLT loaded in compression perpendicular-to-plane, where a load-spreading model is proposed (van der Put 2012). Recently, Rothoblaas developed the SPIDER system to enhance the CPG strength of point-supported CLT floor systems using a steel element (Maurer and Maderebner 2021).

Steel is not the sole solution for reinforcing timber under CPG. However, there is growing mainstream research on using timber-based elements as reinforcement. In detail, some research papers propose using hardwood or densified wood dowels as reinforcement perpendicular to the grain (Conway et al. 2020, 2021; Moerman et al. 2021). This solution showed significant potential in improving the load-carrying capacity of timber perpendicular to the grain (Crocetti et al. 2012; Ed and Hasselqvist 2011), despite being outperformed by steel screw alternatives (Orlando et al. 2019).

The use of screw reinforcement for CPG is now an acknowledged solution. The draft of the next generation of Eurocodes, including a section on this topic, confirms this fact. Nonetheless, the knowledge of the actual effect of screws on the timber strength under CPG is still embryonal. The investigation of the CPG without reinforcement has a more extended chronology. Still, Leijten (2016) dashingly states that current CPG models are unreliable, and there is only one accurate model based on yield slip-line theory to be a candidate for future building design codes. He reviewed several past studies, partially itemized below, on CPG tests. They were all discarded due to misconceptions, inaccuracy or lack of adequate methodological rigour; see the studies by Kollmann et al. (2012); Graf (1921); Gehri (1997); Hübner (2013); Gaber (1940); Frey-Wyssling and Stüssi (1948); Rothmund (1944). In North America, Basta (2005) carried out CPG tests according to ASTM-D-143 (ASTM 1991), including the wood species, moisture, and annual ring orientation effects. The research by Basta (2005) was considered irrelevant since the definition of the CPG values obtained with this method was based on the proportional limit. In contrast, it is now based on a 1% deformation limit according to the standard EN 408 (EN408 2012). Hoffmeyer et al. (2000) report tests on 74 sawn timber specimens and 120 glued laminated specimens having a mean CPG strength of 2.9 N/mm\(^2\). Hoffmeyer et al. (2000) found that CPG strength does not change significantly with the specimen dimensions.

The first studies on CPG without reinforcement were carried out by Suenson (1938a). The tests highlighted that the CPG capacity depends on the loading area and the length of the unloaded part (Leijten 2016). Multiple studies confirmed these aspects in the following years (Reichegger 2004). Leijten (2016) compared different design models for CPG without reinforcement and presented nine load cases, shown in Fig. 4. The load cases distinguish different design configurations, except for load case A, defined by EN 408. In this paper, the authors will adopt the designations in Fig. 4 to identify the different load cases.

If, according to Madsen et al. (1982), CPG did not receive sufficient attention from the scientific community, CPG with reinforcement received even less (Thelandersson and Mårtensson 1997; Kevarinmäki 1992). No paper attempts to review and compare existing capacity models for CPG with reinforcement. Additionally, the deficiency of organic research in this area is further fed by exiguous experimental data. This paper attempts to fill the mentioned gap in knowledge by investigating the following aspects:The paper has the following organization. Sec.3 presents the mechanical model and some literature background. Sec.4 shows the four studies used for the database compilation, further discussed in Sec.5, where a sensitivity analysis is carried out. Finally, Sec.6 compares several mechanical models by highlighting each formulation’s possible pros and cons.

The design model in the current EN 1995-1-1 is presented as follows (EN1995 2010):where \(\sigma _{c,90,d}\) is the stress level given by the effective contact area. The factor \(k_{c,90}\) accounts for the material behaviour and the deformation perpendicular to the grain. Generally, this factor is considered equal to 1.0. Still, for specific support conditions (when higher deformation perpendicular to grain can be considered acceptable), the CPG capacity can be increased (the different support conditions are further specified in Eurocode 5 (EN1995 2010)).

In the new standard proposal (prEN1995 2021), a factor \(k_{p}\) is introduced, which also accounts for the material behaviour and the deformation perpendicular to the grain. In the new standard proposal, a coefficient \(k_{c,90}\) is introduced, but with a different physical meaning related to the effects of the load arrangement. To avoid confusion when discussing the different standard proposals, the factor \(k_{c,90}\) of the current EN 1995-1-1 version is indicated as \(k_{pr}\) (to be distinguished from \(k_{p}\), which in the new standard proposal prEN 1995 is proposed only for the un-reinforced configuration). The effective contact area, \(A_{ef}\), accounts for the contribution of adjacent fibres. A 30mm increase in the contact length on both sides of the contact area is recommended. The effective length considers the load distribution of the CPG stress, where the stress distributes to the unloaded timber parts.

The synoptic table in Table 3 shown below resumes the proposed design models for un-reinforced and reinforced timber members under CPG. A detailed definition of the notation is given at the beginning of the paper (Fig. 5). Eq. 3 shows the design model of the current Eurocode 5 proposal for non-reinforced specimens (EN1995 2010).

The new standard draft (prEN1995 2021) enclosed a design equation (Eq. 5) for reinforced timber members under CPG. The bearing capacity can be primarily increased by reinforcing the member with fully threaded self-tapping screws. The screws can vary in diameter, head, and length. Threads along the whole length reduce the risk of pushing in due to the bond between the screws and timber. The design model represents an evolution of the one in Eq. 3 for non-reinforced members. Three failure modes may occur: failure due to the withdrawal of the screw, failure due to buckling of the screw, or failure of timber, as confirmed by the investigations by Bejtka and Blaß at the University of Karlsruhe (Bejtka and Blaß 2004).

The first failure mode (Pushing-in of the screw) corresponds to the pushing-in capacity of the screws (withdrawal capacity \(F_{w,k}\)). Exceeding the bearing strength leads to penetration of the screws into the timber member. Numerous studies at the University of Karlsruhe have shown that the capacity to push in is equal to the withdrawal capacity. This failure mode occurs mainly using short screws (Bejtka 2005). The second failure mode corresponds to the buckling of the screws. This failure mode occurs mainly for long and slender screws. The third failure mode corresponds to timber failure at the screw tips. The feature of this failure mode is lateral expansion perpendicular to the grain, resulting in cracks at the screw tip.

Bejtka (2005) observed this failure mode with small loading areas and short screws. The maximum stress in the timber specimens by the screw tip depends on the effective dispersion length and width. The effective length depends on the size of the screw, the screw arrangement, and the design situation; see Fig. 7. The numerical investigations by Dietsch et al. (2019) confirmed the expression for the effective length, \(l_{ef,2}\) in the third failure mode. The study investigated the effect of self-tapping screws as single-side reinforcement in timber (Dietsch et al. 2019). The study showed that the stresses varied extensively along the screw length, with a stress concentration by the tips of the screws, as shown in Fig. 6. However, the stress concentration is compensated for by stress redistribution due to the elastic-plastic behaviour of timber.

Figure 6 depicts the distribution of stresses in a horizontal plane along \(l_{ef,2}\) with different screw groups (four, six, and ten). Figure 6 reveals that the stress increases by the screw tips. The study concludes with a recommendation for using screws with overlap to transmit the stress concentration efficiently. The first and second terms of Eq.3 correspond to the contributions by screws and timber, respectively. The withdrawal resistance, \(F_{w,k}\), the compression resistance, \(F_{c,k}\) and the number of screws, n, provide an estimate of the characteristic strength of the screws. Conversely, the effective contact length, \(l_{ef,1}\), is increased by up to 30 mm, assuming the load will disperse at a 45\(^\circ\) angle. The effective length at the screw tip is defined by \(l_{ef,2}\), as depicted in Fig. 7.

PrEN 1995 is currently under development. Therefore, the reported equations represent an intermediate step toward a definite standard proposal. The synoptic table also provides the expressions for the withdrawal resistance, \(F_{w,k}\), and compression resistance, \(F_{c,k}\), of the screws. The authors adopted the following abbreviations to indicate the different contributions to the capacity. \(A_{1}\) indicates the failure of the screw, where \(A_{11}\) and \(A_{12}\) separately express the contributions of timber and screws. \(A_{2}\) represents the capacity related to the failure of the timber at the screw tip.

The database used to validate and calibrate capacity models for reinforced specimens under CPG with steel plates is based on the following experimental tests resumed in the appendix (Electronic Supplementary Material): Bejtka (2005) wrote Volume 2 of the Karlsruhe reports on CPG with reinforcement using fully threaded screws. He investigated the failure mechanisms and the influence of the screws based on multiple laboratory tests. The table in the appendix reports the geometry of specimens, screws, experimental capacity and the relative capacity increment compared to the non-reinforced case. The test result revealed that the capacity under CPG can increase up to 329 % using six screws. Furthermore, it is possible to improve the capacity further by using more screws. FE models in Ansys and experimental tests supported the development of a design model for reinforced members. The design model, known as the Model of Karlsruhe, is described in Eq. 10 (Bejtka 2005).Where:The definition of the parameters is detailed in the initial list of symbols and notation. The model is analogous to the one in prEN 1995, except for minor discrepancies. Additionally, Bejtka (2005) validated the model using both the characteristic and mean strength perpendicular to the grain, \(f_{c,90,k}\) = 3.0 N/mm\(^{2}\) and \(f_{c,90}\) = 5.0 N/mm\(^{2}\) obtained from experimental tests. As expected, the predicted capacity is minor compared to the test results when using the characteristic value \(f_{c,90,k}\) = 3.0 N/mm\(^{2}\). A good correlation is observed with \(f_{c,90}\) = 5.0 N/mm\(^{2}\).

Nilsson (2002) wrote a master thesis on the influence of reinforcement on CPG based on experimental tests. Multiple glulam specimens with the dimensions 500 × 90 × 315 mm (length x width x height) were tested using the screws SFS WT-T 8.2 with different lengths. She considered two load cases: Torx and load case B with either one, four, six, or eight screws, where the Torx test corresponds to the test on a single screw. This research assesses the dependence between the number of screws and bearing strength. The group of screws is loaded through a steel plate with dimensions 90 × 150 × 10 mm or a timber plate with dimensions 90 x 150 x 16 mm. The failure modes depend on the load plate (Nilsson 2002), as illustrated in Fig. 8, affecting the magnitude and location of the lateral expansion. Nevertheless, the test specimen is not split to verify the failure mode of the screw. In this paper, the authors will use the sole experimental data corresponding to samples loaded by steel plates. The specimens loaded with timber plates are insufficient to develop a probabilistic capacity model.

Reichegger (2004) investigated the effect of self-tapping screws for members under CPG. The analysis is based on experimental tests and comparisons with the design model of Karlsruhe. He used spruce Glulam with strength class GL 24h according to EN 1194, with compressive strength \(f_{c,90,k}\)= 2.7  N/mm\(^2\). The test specimens had dimensions 400 × 120 × 200 mm and 600 × 120 × 400 mm (length × width × height). The tests resemble load case B, where the load is applied by steel and timber plates with dimensions 80 × 120 and 120 × 120 mm, respectively. He used two types of screws: SFS WT-T and SPAX-S, where the mutual spacing is based on the ETA (European Technical Assessment) recommendation. The compressive capacity of the non-reinforced and reinforced test specimens is obtained following EN 1193, similar to the procedure described in EN 408. Furthermore, the study compares the test result to the Karlsruhe model. With a steel plate, the capacity increases up to 33 % and 167 %. Conversely, using a timber plate leads to an increment equal to 3 % and 124 % using WT-T 6.5 × 130 mm and SPAX-S 8 × 200 mm screws, respectively.

Tomasi et al. (2023) tested the accuracy of the design model for reinforced glulam members subjected to CPG, according to the new proposal of Eurocode 5 based on the Model of Karlsruhe in Eq. 10 (Bejtka 2005). Tomasi et al. (2023) present the experimental tests of multiple timber specimens with screw reinforcement under CPG by considering different geometry, load cases, and screw arrangement. Furthermore, the predicted capacity and failure modes are compared with the test results. The experimental results show that using threaded screws as reinforcement effectively increases the capacity of timber subjected to CPG. The experimental tests do not confirm the predictions regarding failure modes and capacities for all configurations.

Before developing a probabilistic capacity model for reinforced members under CPG, a sensitivity analysis of the design model highlights the effect of variable dimensions on specimen capacity. This study and the previous experimental data will support a discussion on the limits of the current capacity model and the need for a more advanced proposal. In 2019, the CEN committee compared two models proposed in Eurocode 5 for non-reinforced members. The sensitivity study compared two approaches by Leijten and Blaß by varying the height and length of the specimen (Niebuhr and Sieder 2019). The current design model for CPG in prEN 1995 is a modified approach after Leijten. The author replicated the study in prEN 1995 for non-reinforced and reinforced members under load cases B and C, see Fig.4.

This section compares the performance of eight capacity models, resumed in the following synoptic Table 4.

To properly compare experimental data with model predictions, the mean values of the mechanical parameters replaced the characteristic ones. The first two models labelled \(F_{c,90,m}^1\) and \(F_{c,90,m}^2\), correspond to the first and the second failure mechanisms, known as \(A_1\) and \(A_2\). The authors separately compare each model prediction with the data to understand whether the proposed \(A_1\) expression performs better when used without evaluating the minimum between \(A_1\) and \(A_2\) (\(F_{c,90,m}^3\)). The fourth model, \(F_{c,90,m}^4\), is the simplistic capacity model. The timber contribution is obtained by multiplying the contact area by the strength of the timber perpendicular to the grain without any coefficient. The 5th and the 6th models, labelled \(F_{c,90,m}^5\) and \(F_{c,90,m}^6\), identify two probabilistic capacity models. The experimental data and existing capacity models prove that the higher uncertainty in the equation stands in the timber contribution. Several coefficients and arbitrary assumptions about the load diffusion affect this term, while the screw addend is generally considered as it is. Therefore, the authors calibrated a correction factor for the sole timber contribution as a function of a suite of explanatory variables. In the first probabilistic model (P.M.1), the experimental data were pre-processed with a variance stabilizing transformation. No variance stabilizing transformation is applied in the second one (P.M.2). The relevance of these models also depends on their generality. The multiplication factors, named \(\gamma _1\) and \(\gamma _2\), model an adimensional expression, the ratio between the expected and estimated timber contribution. Therefore, the authors selected adimensional geometric functions as candidate explanatory functions. A step-wise model reduction is then implemented to reduce the model, thus reaching a trade-off between complexity and accuracy. Lastly, the authors compare two deterministic models where the timber contribution is amplified by factors 2 and 1.4, respectively. The first factor is obtained from an ordinary least squares estimation, while the second is based on the formulation for CPG without reinforcement, where 1.4 is adopted.

This section might help the scholar and the practitioner understand the pros and cons of existing capacity models. This research’s principal limitation is the modest number of test data. Approximately 60 samples might not be adequate for statistics. Despite the constraints, the authors propose probabilistic capacity models, which may be subjected to further calibration if more experimental data is added to the collected database. For this reason, the authors did not implement a Bayesian calibration, which should be more appropriate when having more data samples. The model calibration has been carried out with a maximum likelihood estimation. This section will first introduce the probabilistic capacity model and then compare the eight models.

This paper reviews existing capacity models for timber elements under compression perpendicular to the grain (CPG) with screw reinforcement. Eight mechanics-based probabilistic and deterministic models have been compared against experimental values collected by the authors on test data from the past twenty years. The database consists of approximately 60 test data, which, despite being insufficient for an ideal probabilistic formulation, proved some weaknesses of existing formulations currently included in the draft of the next generation of Eurocodes. The main aspects that arise from the model’s comparison and the analysis of the experimental data are:This paper highlights the need for more experimental data for more reliable calibration of the probabilistic capacity model to extend its validity to a broader range of parameters.