1 Introduction

Sawn timber needs to be strength graded prior to its use for structural applications. In Europe, grading is based on the allocation of timber to groups called strength classes. These classes are defined by sets of statistical “characteristic values” of key properties, that allow safe design with timber by specifying minimum requirements for those values, allowing them to be used for structural calculations. For this, it is first necessary to derive relationships to predict the properties, so that the grading can correctly take place. Normally the three key wood properties investigated are bending stiffness (Em), bending strength (fm) and density (ρ). The characteristic values for stiffness (Em,0,mean) are based on the mean, whereas for strength (fm,k) and density (ρk) it is based on the lower 5th percentiles. Thus, it is the collective properties within a grade that matter, and not the properties of individual pieces of timber.

Even though grading established on the basis of bending tests is the most common method, in Europe strength grading can also be determined based on tension testing (Ridley-Ellis et al. 2016). Depending on the types of loads to which the timber will be subjected in service, one basis of grading will be more efficient than the other. While bending strength is the most common basis for grading in timber construction, tension properties are still important for elements like trusses and I-joists. Interest in mass timber construction in recent years has also raised the profile of tension-based strength classes of lamellas for glulam manufacturing. In fact, the most recent version of EN338 (CEN 2016a) includes strength classes for tension grading of softwoods (T classes) in addition to the more familiar bending classes (C classes), although tension classes had been in use for more than a decade previously. Irrespective of the testing basis being bending or tension, the strength classes are based on the characteristic values of stiffness, strength and density. While grading could conceivably be based on both tension and bending testing, the cost of this would be prohibitive. For economic and practical reasons, it is also common to use timber graded on the basis of bending in situations where tension is the dominating load. Moreover, it is often the case that bending elements need to be designed for tensile load, and vice versa. This is why the other strength property can be conservatively estimated by empirical relationships (EN 384) even though this can result in less efficient use of wood depending on the situation.

The grading process, whether done by machine or visually, uses non-destructive assessment of the wood that is indicative of the three grade determining properties. One kind of long-standing indicating property (IP) used to predict wood properties is knot indices, which is familiar for visual grading, but also, in a different form, part of grading by machines using principles such as X-rays, and optical mapping of the wood surface. In recent years, the use of non-destructive techniques based on the measurement of dynamic modulus of elasticity (Edyn) has also become broadly applied (Gil-Moreno et al. 2019b; Krajnc et al. 2019b; Ridley-Ellis et al. 2018) since it is relatively easy to apply and usually gives strong relationship with mechanical properties, even in logs and standing trees (Gil-Moreno and Ridley-Ellis 2015; Llana et al. 2020; Wang 2013). Knot index and Edyn are used in the current study as representative examples of IP, but there are also others in common use.

The empirical relationships in the standards can change when standards are revised, especially when there is new test data to inform safe, effective grading. This changes the design values for strength classes, and may need previously calculated designs to be changed in the case of reductions. The standard EN338:2009 provided Eq. (1) to determine characteristic tension strength parallel to the grain (ft,0,k) based on characteristic bending strength (fm,k), but the 2016 revision (EN384:2016, EN338:2016) changed this to a new equation, Eq. (2), which (together with the rounding used in EN338) had the effect of reducing tension strength values below C22 and increasing them for higher grades. This revision also included the listing of softwood tension strength classes, and a corresponding equation, Eq. (3), for calculating the characteristic bending strength from the characteristic tension strength. Note that the equations are conservative estimates of one property based on test results of the other (derived using the lower 75%-prediction line around the regression), and so Eq. (2) and Eq. (3) can only be applied in the direction as written.

$$f_{t,0,k} = 0.6f_{m,k}$$
(1)
$$f_{t,0,k} = - 3.07 + 0.73f_{m,k}$$
(2)
$$f_{m,k} = {3}.{66} + {1}.{213}f_{t,0,k}$$
(3)

The basis for the new equations was extensive test data on spruce and pine from the Gradewood project (Ranta-Maunus et al. 2011), summarised for the standards committee CEN TC124 WG2 in document N832, which used Edyn and the TKAR knot index (total knot area ratio) as representative IPs in the analysis. For balance, only Gradewood data from countries where both bending and tension tests were carried out were used. This comprised 429 bending tests and 423 tension tests for Scots pine (Pinus sylvestris L.), originating from Poland and Sweden, and 2615 bending tests and 1392 tension tests for Norway spruce (Picea abies L.) originating from Poland, Romania, Sweden, Slovenia, Slovakia and Ukraine.

Wood properties vary from species to species, and by country (Lavers 2002). In the N832 report, the fm,k values for each country ranged between 20 and 26 N/mm2 (average 21.9 N/mm2) for spruce, and 17–23 N/mm2 (average 19.8 N/mm2) for pine. It is common for spruce and pine from Scandinavia and Central Europe to achieve strength classes above C22 (Fischer et al. 2016, 2015; Hanhijärvi and Ranta-Maunus 2008; Høibø et al. 2013; Stöd et al. 2016). In Ireland and the UK, the main species grown for construction is Sitka spruce (Picea sitchensis (Bong) Carr.). The species is typically graded for structural timber to C16 (Em,0,mean = 8 kN/mm2, fm,k = 16 N/mm2, ρk = 310 kg/m3), but actually has superior strength and density than this requires. Grading is limited by the stiffness (Moore et al. 2013), a common feature in other species in the growing region (Gil-Moreno et al. 2016a). The lower performance compared to species growing in continental Europe is largely influenced by the shorter rotation lengths used. Typically these are 35–45 years (Moore 2011) but can be shorter (Ni Dhubháin et al. 2006). This limits the growth of the outerwood, which has higher mechanical properties (Kliger et al. 1998; Moore et al. 2012). Sitka spruce has similar properties to Norway spruce, and these are graded together as a species combination known as British spruce, recognised in the standards EN13556 and EN14081-1 (species code WPCS). Timber from Ireland and the UK is often graded using the same rules (Gil-Moreno et al. 2019b) due to the similar growing conditions that result in comparable timber characteristics. Scots pine is a native minor species, and although it can perform better than spruce, and achieve high yields of C20 (Moore et al. 2008; Fátharta et al. 2020), there is currently little information on the wood properties of the species grown in these countries. The current study covers mostly material from Ireland but conclusions are expected to also apply to UK-grown material.

To the authors’ knowledge, only two studies have addressed and published the properties of Irish timber in tension (Ó Fátharta et al. 2020; Raftery and Harte 2014), and none in the UK. There are no approved grading settings in tension for these countries, and therefore the use of timber in tension relies on the relationships given in the European standards. However, previous experience in bending on British grown conifer species showed that extrapolating models derived from other sources may not fit the characteristics of Irish and UK timber (Gil-Moreno et al. 2016b). In tension, Gil-Moreno et al. (2019a) showed that extrapolating equations derived from the Gradewood project to Irish timber reduced the grading yields.

Likewise, previous studies have found different ratios for the relationship between tension and bending strength. During the drafting of Eurocode 5, Green and Kretschmann (1989) obtained an average ft,0,k/fm,k ratio of 0.59 for different softwood species in the US and Canada, with slight changes above 55 N/mm2 tensile strength. For radiata pine timber, Tsehaye et al. (1997) compiled data from New Zealand and Australia for visual and machine grades that showed a variation of ratios between 0.3 and 0.55. Based on the brittle fracture theory, and mostly spruce from Central Europe, Burger and Glos (1997) determined a ratio ft,0,k/fm,k of 0.69 that increased for higher strengths. In parallel, using this data together with values from the literature, Burger and Glos concluded that tensile strength in EN338:1995 was overrated in the lower strength classes and the contrary for higher strength classes. On Danish-grown Sitka spruce, for a range of fm,k values between 21.7 and 33.6 N/mm2, and ft,0,k between 17.1 and 24.4 N/mm2, Bräuner et al. (2000) found ratios ft,0,k/fm,k of 0.66, 0.77 and 0.81 for visual grades T1, T2 and T2 + (from lower to higher quality). More recently, using structural mechanical tests on Norway spruce from Central Europe, Steiger and Arnold (2009) determined that the ft,0,k/fm,k ratio depends on timber quality, and based on a linear regression where 27 < fm,k < 47 N/mm2 concluded a ratio smaller than 0.6 for fm,k below 22 N/mm2.

Taking into account the variation in the relationships between wood properties with the sampling sources (Denzler 2012; Stapel and Denzler 2010), and the ratios between tension and bending properties depending on the timber quality, the current study hypothesises that the equation in EN384:2016 underestimates excessively the performance in tension of the lower bending grades in EN338. In fact, N832 states that the old conversion Eq. (1) is generally agreed to be correct for lower grades. The aim of this study is to investigate the relationships between bending and tension characteristic strength of lower-grade timber. The study uses British spruce and Scots pine grown in Ireland and the UK tested in bending and tension. The analysis uses IPs thresholds to create bending and tension subsets of equivalent quality on which to obtain pairs of characteristic values to determine the relationship. Secondly, alternative equations to those given in EN384 are examined combining the current data with those from Scandinavia and Central Europe. This knowledge is particularly important in timber engineering for the optimisation and characterisation of timber used for trusses, I-joist and glulam manufacturing.

2 Materials and methods

2.1 Materials

Three conifer species were tested in bending and/or tension, namely, Sitka spruce, Norway spruce and Scots pine. The Sitka spruce was grown in Ireland. The bending material (858 pieces) was obtained from a 23-year-old stand as described in Simic et al. (2019). The Sitka spruce specimens for tension testing (153 pieces) were provided by a sawmill in Ireland as part of the normal production. Due to the large proportion of corewood observed in the material, and aiming to increase the range of values, the tension set was supplemented with 44 additional pieces from a different source (Krajnc et al. 2019a). These additional pieces had a mean length of 1.8 m, shorter than the requirements of the standard EN384 (CEN 2018), but are valid for the purposes of this study.

The Norway spruce came from two plantations 44 years old and one 76 years old in Great Britain (Gil-Moreno et al. 2016a). It was tested in bending (143 pieces) and combined with the bending Sitka spruce dataset so that a wider range of values could be examined.

The Scots pine came from a mixed forest plantation in Ireland of Norway spruce and beech (Fagus sylvatica L.) with Scots pine being a minor component. At the time of felling, it was 77 years of age. A first subset selected 50 pairs of pieces based on similar Edyn and density, as described in Ó Fátharta et al. (2020). The remaining pieces were randomly assigned to give a total of 81 pieces tested in tension and 158 in bending.

The pieces had a nominal cross-section of 100 × 45 mm2, except for 384 pieces of Sitka spruce tested in bending which had a nominal cross-section of 75 × 35 mm2. The pieces that either slipped in the tension clamps without reaching a failure point or broke as a result of the clamping pressure were removed from the analysis. Another test was stopped due to safety concerns after reaching a load of 225 kN on a machine with a maximum capacity of 250 kN. The inclusion of these pieces in the analysis would have reduced the variation of the strength and therefore overestimate the parametric calculations of the percentiles, and it would also affect the relationship of the strength properties with the Edyn and knot index used as IPs.

2.2 Measurements

All the material was non-destructively assessed using a Timber Grader MTG 960 (Brookhuis Applied Technologies, Enschede, The Netherlands). This grading machine measures the natural frequency of the vibration produced by the impact of a hammer in the longitudinal direction, and in combination with the density measured from mass and average dimensions, allows calculation of the Edyn using Eq. (4)

$$MOE_{dyn} = {\text{D}}V^{2} = {\text{D}}(2FL)^{2} \quad {\text{N}}/{\text{m}}^{{2}}$$
(4)

where D is the density of the full timber piece (kg/m3), V is the acoustic velocity (m/s), F the longitudinal natural frequency of the first mode resonance (Hz) and L the piece length (m).

The Scots pine pieces were measured using a Goldeneye 702 Multi-Sensor Quality Scanner (Microtec, Brixen, Italy). This grading machine detects wood defects inside the pieces using the attenuation of X-ray radiation. The critical section to be tested for wood properties measurement was determined from the X-ray images captured and/or visual inspection. The test sections of the Sitka spruce pieces were determined exclusively from visual inspection of wood defects. Following, the TKAR index was measured in the test section. The TKAR is the total projected cross-section areas of all knots within 150 mm length, divided by the cross-section area of the piece. For the Sitka spruce pieces tested in bending the visual grading standard IS 127 (NSAI 2015) was followed. For the remaining pieces, the online software Web Knot Calculator v2.2 (Microtec, Brixen, Italy) was used. Pieces with TKAR above 0.7 were removed from the analysis as they would certainly be rejected by visual override in production grading.

This study is primarily concerned with the determination of strength values, but for a better characterisation of the material studied, the three key determining properties for grading: E, f and ρ, both in tension and bending, were determined following EN408 (CEN 2012). The test section was located at the centre of the span. When tested in tension, a transducer was placed on each face of the piece, and the average displacement was used for the calculations of Et. When tested in bending, the global modulus of elasticity was measured in the top face in Sitka spruce and the bottom face in the rest of the species and adjusted as given in EN384. A sample free of defects obtained from near the failure point was used for the calculation of the clear density (ρ), and moisture content (mc) according to EN13183-1 (CEN 2002). The E and ρ values were corrected to a reference 12% mc, and f was adjusted to a 150 mm reference depth following the EN384 (CEN 2018).

2.3 Data analysis

The statistical analysis was carried out with the open-source statistical environment R (R Core Team 2019).

First, a descriptive summary of the wood properties was investigated, and the linear relationships between them examined. The relationship between the strength properties and Edyn, and TKAR were examined further by conducting an analysis of variance (ANOVA) with Eq. (5) that also tested the influence of the two species groups (British spruce and Scots pine) in the relationships, both in tension and bending.

$$f = \alpha_{0} + \alpha_{1} IP + \alpha_{2} Species + \alpha_{3} IP:Species + \varepsilon$$
(5)

where α0 is the intercept term, α1 is the slope, α2 represents the additive effect of the species studied on the intercept term, α3 is the interaction term between the IP used (Edyn or TKAR) and species and ε is the residual error not explained by the model. The ANOVA conducted was type III to account for the unbalanced number of pieces in each group.

In addition, Edyn and TKAR were used in a multiple linear regression to model the strength properties in bending and tension. The models were applied by species to every piece, which allowed two additional IPs, IPm and IPt to be obtained. Thus, each piece had four IPs: Edyn, TKAR, IPm and IPt. The goodness-of-fit (R2) of the linear models was measured as the coefficient of determination, and for non-linear models as the correlation between observed and predicted values. The model performance was also assessed using the mean absolute percentage error (MAPE) and for comparison of models the Akaike’s information criterion (AIC). Next, the datasets in bending and tension were subset using different IP thresholds to create bending and tension groups of equivalent quality on which to calculate the characteristic values of fm,k and ft,0,k. Nine groups per IP were created using thresholds based on boxplots to cover the range of strength values in the datasets. The characteristic strength values were calculated according to the standard EN14358 (CEN 2016b), using the nonparametric calculation without confidence interval when n ≥ 40 pieces, and the lognormal distribution when n < 40 using 75% confidence level (to take into account the smaller number of pieces). Subsets with less than 20 pieces were removed from further analysis, leaving 35 groups for spruce and 29 for Scots pine. The relationship between the pairs of values from each subset was investigated, and the lower 75%-prediction line around the regression was established. This approach was used for deriving an empirical conversion from characteristic bending strength to characteristic tension strength and vice versa. Finally, the process was repeated combining the data obtained in the current study with the N832 data. The linear regression assumptions were examined and addressed when violated. This approach is a simplified version of real grading and is similar to the approach used in N832.

3 Results and discussion

3.1 Descriptive statistics and model fitting

A descriptive summary of the quality of the material studied is given in Table 1. Note that the comparison between species only applies to the particular data in the current study, and should not be interpreted as a broad comparison between species as the datasets are not representative for that purpose. The grading of British spruce was limited by stiffness. In bending, the whole population achieved a grade of C14, and 74% yield a grade of C16. The Sitka spruce dataset on its own did not achieve C14. This is lower than the near 100% yield of C16 normally achieved, as a consequence of the particular resource sampled. In tension, the whole population achieved a T11 strength class, and more than 90% a T12.

Table 1 Summary of the wood properties (in brackets the coefficient of variation in %)
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Scots pine was limited by strength. The whole population of Scots pine achieved C16 in bending (almost 90% a grade of C22), and T8 in tension (almost 90% T11). Table 1 shows a large variation in the strength values of Scots pine, which was reflected in lower values of fm,k and ft,0,k than expected considering that E achieves C22 and T10 requirements. The Scots pine came from one single batch, and the density values in the tension and bending datasets are comparable, but the difference observed in the Edyn at the time of testing advises against assuming an equivalence of the C16 and T8 strength classes. The tension and bending datasets of spruce came from different batches. They were comparable in terms of density, but an equivalence between properties is not expected. Spruce graded lower than Scots pine in bending (C14), but higher in tension (T11). Thus, the different behaviour of the two species, and its likely effect on the relationships between wood properties, is a first indication that the relationship between bending strength and tension strength may vary by species.

In bending, the results of spruce are slightly lower than the average reported in the literature for Irish-grown timber likely due to the large proportion of young material compared to normal saw logs. In tension (for which the spruce specimens were more typical of the normal resource), the mechanical properties are slightly higher than those reported in Ireland by Raftery (2010), who on 25 × 96 mm2 pieces obtained mean values of Et = 7.89 kN/mm2, ρ = 403 kg/m3 and ft = 20.9 kN/mm2 adjusted to the reference conditions. Higher values were found for Danish-grown Sitka spruce (Bräuner et al. 2000) and Scandinavian spruce (Briggert et al. 2020), but this difference was expected. The results for pine are comparable to those found in Scotland for pure plantations of approximately 80 years of age reported by Moore et al. (2008) and for density and E measured on clears by Auty et al. (2016). Again, higher mechanical properties are achieved for Scandinavian and Central European Scots pine, with comparable density (Hautamäki et al. 2014; Ranta-Maunus 2007; Stapel and Denzler 2010), but this is an expected result.

The strengths of the linear associations between the properties studied are shown in Table 2. The relationships were, in general, stronger in pine than in spruce. The coefficients of determination between the mechanical properties of British spruce in tension are slightly lower than those found by Bräuner et al. (2000) on Danish-grown Sitka spruce (R2 = 0.41) and by Briggert et al. (2020) on Scandinavian spruce (R2 = 0.48). For the mechanical properties in bending, Bräuner et al. (2000) reported R2 = 0.30 and R2 = 0.56 for two different populations. In the current study the linear relationship between density and the mechanical properties of spruce in tension is not significant, but in Briggert et al. (2020) density explained 23% and 53% of the variation of ft and Et, respectively. The difference may be associated with the large amount of corewood observed in the current dataset. Density in spruce decreases from near the pith during the first 10–12 years and increases thereafter (Gardiner et al. 2011; Saranpää 2003), whereas the mechanical properties increase from the pith outwards. Thus, Raftery and Harte (2014) also found a very low correlation between density and the mechanical properties of Irish spruce in tension, but a moderate correlation (R2 = 0.59) between the mechanical properties. McLean et al. (2016) did not find a significant relationship between density and Em for clears sampled from the corewood, but neither did Alteyrac et al. (2007) for 80-year-old black spruce.

Table 2 Coefficients of determination R2 and significance (p-value) of linear models where the null hypothesis is that the explanatory variable has no effect on the response variable
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Stronger relationships were found in the current study between Edyn and E in bending and tension, similar to those by Steiger and Arnold (2009) for Swiss-grown Norway spruce (R2 = 0.60 and R2 = 0.80, respectively) and slightly lower than between Edyn and f (R2 = 0.39 in bending and R2 = 0.34 in tension). In Scandinavia, Briggert et al. (2020) observed a similar relationship between Edyn and Et (R2 = 0.81), but stronger than in the current study between Edyn and ft (R2 = 0.46). This variability is not unusual within a species, and is experienced in real production. For beech, Ehrhart et al. (2016, 2018) reported poor relationships between Edyn and ft,0 (R2 = 0.22 and 0.16) whereas Westermayr et al. (2018) reported R2 = 0.51.

Using TKAR as predictor variable explained a higher percentage of the variation in f than Edyn in Scots pine, but explained very little of the variance of spruce in bending (R2 = 0.05 in Sitka and 0.24 in Norway spruce). Evidence from other studies suggests that cross-section sizes have a large influence in visual grading (Stapel and Van De Kuilen 2014), and this may partially explain the poor relationship between TKAR and fm (that included two cross-sections), but it would not explain the poor relationship observed in tension. On 83 pieces of Irish spruce, Raftery and Harte (2014) found stronger relationships, and TKAR explained 39% of the variation of ft,0.

The relationships were examined further by conducting an ANOVA type III with Eq. (5) between Edyn and the strength properties to determine whether the same prediction model could be used for both species. In bending, the slope of the relationship changed with species (F1 1154 = 16.2, p < 0.001). In tension, the slope was statistically the same for the two species (F1 205 = 2.3, p = 0.13), but there was an additive effect of species (F1 206 = 26.8, p < 0.001) that meant Sitka spruce had a higher intercept term than Scots pine. Figure 1 shows the relationship of Edyn with strength. The same test determined that the influence of knots on the strength also differed by species, affecting both the intercept and slope in bending (F1 1153 = 121, p < 0.001 and F1 1152 = 91.3, p < 0.001) and in tension (F1 198 = 48.9, p < 0.001 and F1 197 = 28.3, p < 0.001).

Fig. 1
figure 1

Relationship between Edyn and strength in tension and bending

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In a multiple linear regression, both Edyn and TKAR were significant (p < 0.001) as predictor variables of strength, with stronger relationships in Scots pine than in spruce as shown in Table 3 (with a 90% confidence interval calculated by bootstrapping for each dataset). The regressions did not improve appreciably by including density. In line with the ANOVA with Eq. (5), the large error found for the overall tension dataset (MAPE = 45%) compared to the species models (around 20%) advises against using the same equation for the prediction of strength in the two species.

Table 3 Fit statistics for the strength equations for spruce (BS) and pine (SP) in bending (m) and tension (t) for the model-fitting datasets, and validation dataset (underlined)
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The parameters of the regressions in Table 3 were quite different between the species for the same strength property, particularly for the intercept and TKAR index. These large differences were not observed in the Gradewood datasets (Ranta-Maunus et al. 2011), that showed relationships with the predictor variables more comparable between the species. If the tension equations in the Gradewood project were extrapolated to the current dataset, one piece of Scots pine and another of Sitka spruce would give negative tensile strength. Although these equations may not have been used for the document N832 (only data from countries where both bending and tension tests were carried out were used), they show the differences that can be found for different populations, and the impact when applied to different datasets. Table 3 also shows the predicted mean values of the models applied to the individual pieces, which allows a comparison of the performance of the datasets studied under bending and tension. Thus, for the predicted values the study found ratios ft / fm of 0.79 and 0.73 for spruce, 0.61 and 0.60 for pine. Likewise, Bräuner et al. (2000) found ratios ft / fm of 0.74 and 0.78 for visual grades T1 and T2 + that are comparable to C18 and C24. The relationships between bending and tension strength predicted on individual pieces from models IPt,BS, IPm,BS, IPt,SP and IPm,SP are shown in Fig. 2 together with the strength measured, in bending or tension, for each board.

Fig. 2
figure 2

Measured values of the strength properties and relationships on boards between bending and tension strength predicted from models using Edyn and TKAR as independent variables

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3.2 Conversion from characteristic bending strength to characteristic tension strength

Based on the previous analysis, the relationship between the characteristic strength values in tension and bending was determined by species in the first instance. Using nine thresholds for each IP (Edyn, TKAR, IPm and IPt), the bending and tension datasets were divided into subsets aimed at creating groups of equivalent quality on which to calculate the characteristic values of strength in bending and tension. Subsets with less than 20 pieces were discarded. Following the standard EN14358 (CEN 2016b), the nonparametric method for strength was used when n ≥ 40 pieces, and the lognormal distribution was used when n < 40 using a 75% confidence level. The analysis is inevitably sensitive to the method of calculation of percentiles. For comparison with the analysis in N832, the use of the empirical lognormal distribution was investigated irrespective of the number of pieces, resulting in higher characteristic strength values in 76% of the subsets created.

A regression analysis between the characteristic values of strength in bending and tension determined a moderate relationship for spruce (Fig. 3, R2 = 0.50 and RMSE = 0.95 N/mm2) that met the linear regression assumptions. For Scots pine, a linear regression was very strong (R2 = 0.83, RMSE = 1.06 N/mm2) and had the same slope as spruce (0.49 fm,k), but did not meet the linear regression assumptions. A logarithmical transformation of the response variable improved the relationship while keeping the linear model (R2 = 0.87, RMSE = 0.04). After fitting the regression models, the value of a new observation of the dependent variable ft,k was calculated for a 50%-prediction interval. As a result, there is a 75% probability that the predicted value will be above the lower bound. This allowed a conservative conversion to be obtained. The average strength ratio ft,k / fm,k of the subsets in spruce was 0.85, with a range between 0.68 and 0.97. The average strength ratio ft,k / fm,k in pine was 0.55, with a range between 0.47 and 0.66. Table 4 gives the conversion equations.

Fig. 3
figure 3

Regression line (solid) with 50%-confidence intervals for the prediction of characteristic tension strength for British spruce. The lower dashed bound shows the 50%-prediction for the single observations

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Table 4 Conversion equations by species and in combination with N832 data
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Establishing a linear regression for the two species together gave a weak coefficient of determination (R2 = 0.33). Figure 4 shows the large difference in the intercept term of the two species separately. The relationship however gives the same slope as the old EN384 conversion. Figure 4 also shows the lower variation of bending strength values of spruce compared to pine.

Fig. 4
figure 4

Regression lines with 95% confidence interval for different IPs and species (solid line), and for the two species together (dash line)

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A new model was further developed by combining the data from the document N832 with the current dataset. Figure 5 shows the relationship between the characteristic strength values in bending and tension for the combined dataset. The range of characteristic strength values was higher in N832 than in the current study. From the regression model of Eq. (8), a R2 = 0.79 was found, which is slightly lower than that in N832 (R2 = 0.88, Eq. (2)). Combining the data from document N832 with only the spruce dataset, a linear regression gave a coefficient of determination of R2 = 0.77, whereas combining N832 with only the pine dataset was R2 = 0.90.

Fig. 5
figure 5

Regression line (dash line) and 95% confidence interval combining the current study and data from document N832

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By using Eq. (6) the characteristic tension strength of Irish-grown spruce calculated from bending increased compared to Eq. (2). The difference is particularly large for C16, with a ratio ft,0,k / fm,k of 0.85 that decreases to 0.65 for C35. Based on the low correlation between the strength properties and the TKAR, an alternative equation was explored without the subsets created using the TKAR, but the results were similar to those given by Eq. (6). On the contrary, the resulting Eq. (7) for Scots pine offered lower characteristic tension strength values than Eq. (2), with a ratio ft,0,k / fm,k of 0.50 that increased from C22 up to 0.62 for C35. When including the N832 data the differences are lower (9% for C16 and 1% for C24), with a ratio ft,0,k / fm,k of 0.59 that increased to 0.62 for C35. A comparison can be observed in Table 5 for some of the most common strength classes.

Table 5 Characteristic strength values (N/mm2) obtained using equations in the European standards (Eq. 1, Eq. 2 and Eq. 3) and those derived in the current study (Eq. 6, Eq. 7, Eq. 8, Eq. 9, Eq. 10 and Eq. 11)
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3.3 Conversion from characteristic tension strength to characteristic bending strength

The approach used above was then used to estimate the characteristic tension strength from the bending strength. A regression analysis found a moderate relationship for spruce (R2 = 0.50; RMSE = 1.36 N/mm2), and the lower 75%-prediction equation, Eq. (9), gave lower characteristic bending strength values than the standard conversion Eq. (3). For Scots pine, a regression model (R2 = 0.83; RMSE = 1.9 N/mm2) found a slope 1.68ft,0,k, but the relationship was described better with a non-linear model. A logarithmical transformation improved the relationship, but the linear assumptions were not met. Various exponential functions were screened and analysed. An exponential model has the advantage of overcoming the uncertainties of a linear model when extrapolating beyond the data collected. Equation (10) gave the lowest Akaike’s information criterion (AIC) and the best fit (Fig. 6), explaining 90% of the variation in fm,k, and gave higher values than the standard conversion Eq. (3).

Fig. 6
figure 6

Relationship with 50%-confidence intervals for the prediction of characteristic bending strength for Scots pine. The lower dashed bound shows the 50%-prediction for the single observations

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A new model was further developed by combining the data from the document N832 with the current dataset. The regression model between the characteristic strength values in tension and bending, Eq. (11), gave a relationship of R2 = 0.78, slightly lower than that reported in N832 (R2 = 0.88; Eq. (3)). The lower 75%-prediction of the regression line produced values around 12% lower than the standard conversion, Eq. (3). The model needs to be carefully considered for values above ft,0,k > 30 N/mm2 due to the smaller number of pairs analysed and the larger confidence interval. A comparison for some of the most common strength classes is given in Table 5.

4 Conclusion

This study analysed the relationship between bending and tension strength properties of two conifer species in Ireland and the UK, with a particular focus on British spruce as the main commercial timber species in both countries. The study demonstrates the importance of timber quality and origin in the determination of the relationships between the bending and tension properties. Differences in the mechanical behaviour between species can also play an important role and may not conform with the assumed linear relationship given in the European standards. The study focused on the strength properties in bending and tension as key parameters in the conversion between bending and tension strength classes. The study examined timber with characteristic values of C14, C16, T8 and T11. For spruce, a linear regression modelled the relationship between the bending and tension characteristic strength values, whereas for Scots pine a non-linear relationship fits better.

The study finds that the conversion equation given in the European grading standards, derived using higher strength classes and extrapolated to lower grades, significantly underestimates the characteristic tension strength values of Irish-grown spruce that in Ireland typically achieves C16 bending strength classes. The contrary occurs on the reverse conversion. Smaller differences were found on Scots pine, but in this case the standard overestimates the conversion from characteristic bending strength to characteristic tension strength.

Additionally, the study combined data from continental Europe with the current dataset to establish a new conversion equation that improves the predicted tension strength of Irish spruce obtained from bending strength classes while ensuring safe values for design and economic viability. Further analysis including more pieces tested in tension and from older plantations of Sitka spruce is advised before a possible revision of the European standards could be considered.