*4.3. Results of Test with Drilling Resistance Method*

The purpose of testing the beams by measuring the drilling resistance was first to determine FF and RM values. The results are presented in Tables 8 and 9 and in Figures 9–11.

Based on the FF and RM values determined, statistical analyses were carried out to find the relationship between these values and the MOR, MOE, and density of elements on the technical scale.

The aim of the first statistical analysis was to check whether the differences in the median values of RM obtained in the measurement for individual beams were statistically significant. Based on the Shapiro–Wilk test, it was determined that not all distributions were normal for beams A01, A02, A03 (*p* = .250, *p* = .110, *p* = .017). There was heterogeneity of variance for all beams, as assessed by Levene's test for equality of variance (*p* < .001). Due to the fact that not all distributions were normal, and variances were heterogeneous, we decided to perform Kruskal–Wallis test with the Games–Howell post-hoc test. The conducted analysis showed a statistically significant difference in the mean RM values measured for individual beams (*p* < .001). The post-hoc test showed a statistically significant difference in the median values between groups A01-A02, A02-A03.

**Table 8.** Mean drilling resistance test results.


**Table 9.** Mean feed force test results.


**Figure 9.** Box plots: (**a**) Resistance Measure–RM, (**b**) Feed Force–FF.

**Figure 10.** Empirical cumulative distribution function: (**a**) Resistance Measure–RM, (**b**) FF–Feed Force.

**Figure 11.** *Cont.*

**Figure 11.** Correlation plots of Resistance Measure and Feed Force results (**a**) correlation between RM and FF, (**b**) correlation between RM and FF for beams separately, (**c**) correlation between RM and density, (**d**) correlation between FF and density, (**e**) correlation between RM and MOR obtained from structural size beam bending test, (**f**) correlation between FF and MOR obtained from structural size beam bending test, (**g**) correlation between RM and MOE obtained from structural size beam bending test, (**h**) correlation between FF and MOE obtained from structural size beam bending test.

In the second statistical analysis it was checked whether the differences in the median values of FF obtained in the basic measurement for individual beams were statistically significant. Based on the Shapiro–Wilk test, it was determined that not all distributions were normal for the beams (*p* = .22, *p* = .20, *p* = .23). There was heterogeneity of variance for all beams, as assessed by Levene's test for equality of variance (*p* < .001). Due to the fact that not all distributions were normal, and variances were heterogeneous, we decided to perform Kruskal- Wallis test with the Games–Howell post-hoc test. The conducted analysis showed a statistically significant difference in the mean FF values measured for individual beams (*p* < .001). The post-hoc test showed a statistically significant difference in the median values between all beams.

Pearson correlation coefficients between FF and RM for the three different beams were equal 0.78, 0.68, and 0.76 for beams A01, A02, and A03, respectively. Figure 11b shows parallel trends for beams A02 and A03, indicating the same effects of RM on FF for those two beams. A higher trend effect was observed for beam A01. Linear regression models were fitted first for FF response and RM as the predictor separately for all three beams. The estimates from these models are presented in Table 10. The regression coefficients are significantly different from 0 for all three beams, indicating a significant correlation between FF and RM. For beam A01, with 1 unit increase of RM, FF increases by 0.96 units. For beam A02 with one unit increase of RM, FF increases by 0.55 and for beam A03 by 0.58. To investigate the differences in these trend effects between the beams, one regression model was fitted with FF as the response, RM and beam as the predictors, as well as the RM\*beam interaction term. The results for this model are presented in Table 11. As can be observed, there is a significant value of beam A03 versus A01 as well as significant

interaction terms confirming differences between the trend effect of RM on FF between beam A01 and the other two beams. The equality of effects for beams A02 and A03 were not tested in this model since beam A01 was the reference beam. However, in the model with changed reference beam group, the equality of these two effects were confirmed (results omitted).


**Table 10.** Estimates for regression models of FF vs. RM for different beams.

**Table 11.** Estimates for regression models of FF with RM beam as the predictor and RM\*Beam interaction term.


Therefore, it can be concluded that the effect of RM on FF is the same for beams A02 and A03 and higher for beam A01.

To investigate the effect of density on FF and RM, the regression model was fitted with only density as the continuous predictor and FF or RM as the response. The results are presented in Table 12. Pearson correlation coefficient between density and RM was equal 0.74, between density and FF 0.76. The fitted linear trends are presented in Figure 11c,d. As can be seen, the effect of density is significant both for FF and RM. With 1 unit increase in density, both FF and RM increase by around 0.36 and 0.28 units, respectively. Similar models were fitted for FF and RM and MOR or MOE as predictors (Tables 13 and 14). Pearson correlation coefficient between MOR and RM was equal 0.70, between MOR and FF 0.77. The fitted linear trends are presented in Figure 11e,f. Pearson correlation coefficient between MOE and RM was equal 0.76, between MOE and FF 0.79. The fitted linear trends are presented in Figure 11g,h. With 1 unit increase in MOR, both FF and RM increase by around 0.33 and 0.24 for FF and RM %, respectively (Table 13). On the other hand, with 1 unit increase in MOE, both FF and RM increase by around 5.7 and 4.4 for FF and RM %, respectively (Table 14).

**Table 12.** Estimates for regression models of FF and RM with density as the predictor.



**Table 13.** Estimates for regression models of FF and RM with MOR as the predictor.

**Table 14.** Estimates for regression models of FF and RM with MOE as the predictor.


#### *4.4. Results of Tests of Small Clear Specimens and Their Adjustment to Structural Size Beams*

The purpose of the small specimen test was to determine MOR and MOE values. The following Table 15 and Figures 12–14 show the results of the conducted tests. The estimation of the 5% exclusion limit values can be done by several approaches, for example, according to ISO 12491:1997 [63] using classical statistics (EN 14358:2016 [64]) or Bayesian approach (PN-EN 1990 [65]). The 5% exclusion limit values indicated in Table 15 were determined according to PN-EN 1990 [65].

#### **Table 15.** Results of small clear specimen bending tests.


**Figure 12.** Box plots: (**a**) MOR, (**b**) MOE.

**Figure 13.** Empirical cumulative distribution function: (**a**) MOR, (**b**) MOE.

**Figure 14.** Correlation between MOE and MOR: (**a**) Group 1, (**b**) Group 2, (**c**) both Groups.

Statistical analyses were performed to determine whether there were significant differences between Group 1 and Group 2.

The aim of the first statistical analysis was to check whether the differences in the mean values of MOR between Group 1 and Group 2 were statistically significant. Based on the Shapiro–Wilk test, it was determined that both distributions were normal (*p* = .738, *p* = .134). There was heterogeneity of variance, as assessed by Levene's test for equality of variance (*p* = .010). Due to the fact that both distributions were normal, and variances were heterogeneous, we decided to perform Welch's *t*-test. The analysis showed no significant differences between the mean MOR values (*p* = .137).

In the second statistical analysis, we checked whether the differences in the mean values of MOE were statistically significant. Based on the Shapiro–Wilk test, it was determined that both distributions were normal (*p* = .166, *p* = .565). There was heterogeneity of

variance, as assessed by Levene's test for equality of variance (*p* < .001). Due to the fact that both distributions were normal, and variances were heterogeneous, we decided to perform a Welch's *t*-test. The analysis showed statistically significant differences between the mean MOE values (*p* < .001).

Pearson correlation coefficients between MOE and MOR in both groups were equal 0.78 and 0.83 for Group 1 and Group 2, respectively. Linear regression models were fitted for MOR response and MOR as the predictor separately for both groups and the fitted linear trends are presented in Figure 14.

The estimates from these models are presented in Table 16. As can be seen, the regression coefficients are significantly different from zero for both groups, indicating a significant correlation between MOE and MOR. For Group 1 with 1 unit increase of MOE, MOR increases by 6.52 units and for Group 2 with one unit increase of MOE, MOR increases by 6.86. To investigate the differences in these trend effects between the groups, a regression model was fitted with MOR as the response, MOE and Group as the predictors, as well as the MOE \* Group interaction term. The results for this model are presented in Table 17. As can be observed, there is no significance of Group, neither the significant interaction term. Therefore, there are no significant differences between the trend effect of MOE on MOR between Group 1 and Group 2.

**Table 16.** Estimates for regression models of MOR vs. MOE for Groups 1 and 2.


**Table 17.** Estimates for regression models of MOR with MOE, Group as the predictor and MOE \* Group interaction term.


This is depicted in Figure 14. The fitted trend lines are almost parallel.

The wood defects that occurred on individual beams and potentially determined their load-carrying capacity according to ASTM D245 [44] are presented in Figure 15.

The results of the MOR and MOE values adjustment determined on small clear specimens of technical scale beams using the factors indicated in ASTM D245 [44] are presented in Table 18.

Standard ASTM D245 [44] aims to define an allowable property based on formulas (6) and (7). In laboratory testing of single elements, it seems appropriate to compare the MOR and MOE of technical scale beams with the "Characteristic" and "Mean" values of the MOR and "Mean" value of MOE estimated from small clear specimens (Table 18). The MOR "Characteristic" values of the beams were very similar in both groups. The MOE values estimated in Group 1 for beams A01, A02, A03 were 11.7 GPa, 10.5 GPa, 11.7 GPa respectively, and differed from the values obtained in the destructive test of technical scale beams by 0.7%, 3.2%, 0.7%. The MOE values estimated in Group 2 for beams A01, A02, A03 were 13.8 GPa, 12.4 GPa, 13.8 GPa respectively, and differed significantly from the values obtained in the destructive test of technical - the differences were 18.8%, 14.3%, 18.8% respectively. The MOE values do not consider the shear deformation. The procedure for assigning strength classes in PN-EN 384 [28] includes formulas to take into account the effect of shear deformation. The E0 modules determined in accordance with

the standard [28], based on MOE, taking into account the influence of shear deformation, were for Group 1: E0 A01 = 12.52 GPa, E0 A02 = 11.00 GPa, E0 A03 = 12.52 GPa, for Group 2: E0 A01 = 15.25 GPa, E0 A02 = 13.46 GPa, E0 A03 = 15.25 GPa. Based on the determined values of MOR ("CHARACTERISTIC") and E0, it can be concluded that the beams A01, A02, A03 for Group 1 met the criteria of the classes C30, C24, C30 respectively, and for Group 2: C30, C27, C35 [46].

(**c**)

**Figure 15.** Defects indicated according to ASTM D245 [44] and potentially determining the loadbearing capacity of the beams: (**a**) beam A01-damage initiation caused by crushing of compressed fibers in the corner knot area (compression near knot [52]), (**b**) beam A02-damage initiation caused by rupture of tensioned fibers near the corner knot and slope of grain (cross grain tension/diagonal tension [33,52]) (**c**) beam A03-damage initiation caused by crushing of compressed fibers in corner knot area (cross grain tension/diagonal tension caused by compression near knot [33,52]).

**Table 18.** Estimation of MOR and MOE of technical scale beams from small clear specimens according to the standard ASTM [44].


<sup>1</sup> kp—special factor for 4-point bending was determined based on the formula proposed in [61]. <sup>2</sup> kd—strength ratio dependent on wood defects [44].

### **5. Discussion**

The main objective of this paper was to attempt to indicate the practical aspect of testing timber elements in existing structures, especially historic ones, and to interpret the results. A strict analysis of three elements with similar MOE but significantly different MOR values is presented. The focus was on the interpretation of the results oriented towards single elements, which also refers to the study of historic structures, where sometimes even a single element subjected to multiple tests may be of interest. The authors were mainly interested in practical conclusions, while statistical analyses were carried out to complete the research overview. The authors were concerned to indicate that NDT and SDT methods should not be used selectively (alone) in timber assessment.

Those testing methods were chosen which were considered to be the most applicable, fast, useful in-situ, and uncomplicated in terms of conducting the tests and processing the results. The acoustic method and resistance drilling are well known in the literature. Especially the reliability and effectiveness of the former has been proven [24,25]. Most often, the literature looks for correlations between the results obtained and the mechanical properties, while the practical aspect of interpreting the results is neglected. In addition, the standards for testing existing structures are not unambiguous and the interpretation of the research results is largely unsystematic.

Studies reported in the literature indicate strong correlations between MOEdyn values obtained from the acoustic method and actual MOEstat values from DT testing. Based on the study, MOEstat values differing from the actual values within 5% were obtained for beams A01 and A02, but for beam A03 the difference was more than 11%. Such a difference in MOEstat values can result in incorrect timber assignment, even by several classes.

The resistance drilling method study indicated the presence of statistically significant correlations between FF and RM values and density, MOE and MOR, but they are so weak that it seems inappropriate to infer strength properties on their basis. Nevertheless, the drilling resistance method has excellent applications in qualitative wood assessment—e.g., determining the degree of biological degradation and finding hidden defects within the element.

In addition, small samples without defects were tested and the results were interpreted in accordance with ASTM D245. The use of ASTM D245 in combination with EN and ISO standards, especially for testing historic elements, seems unique but possible. By using simple statistical methods and the methodology of reducing the strength properties of clear wood without defects based on ASTM D245, good results and an accurate classification in the reference group (Group 1) were obtained. However, it should be noted that it is not always possible to extract enough material from an existing structure for testing and accurate visual assessment is not always possible.

### **6. Conclusions**

The primary goal of this paper was to consider possible methods useful in determining MOR and MOE in existing structures where testing capabilities are limited. Attention is drawn to the problem of obtaining a sufficient amount of material for testing and comprehensive assessment of wood. On the basis of the conducted non-destructive, semidestructive and destructive tests, it was possible to determine the following conclusions:


It should be noted that the research was conducted on elements made of pine (*Pinus sylvestris*), which, due to its good availability, low price, and good strength properties, is the most popular structural wood in Poland [66]. The results of wood testing should be considered in the context of a specific species.

Numerous ISO, EN and ASTM standards were used in the analyses. Special care should be taken when combining the standards. The material properties to be compared should be determined from the analogous, well-known formulas and the relationships from materials mechanics.

The laboratory tests and analyses presented in this paper are part of an ongoing research project. Due to limited data, the conclusions and observations presented should be considered possible but not certain.

**Author Contributions:** Conceptualization, T.N., A.K. and F.P.; methodology, T.N. and F.P.; software, F.P.; validation, T.N., A.K. and F.P.; formal analysis, T.N., A.K. and F.P.; investigation, T.N., A.K. and F.P.; resources, T.N., A.K. and F.P.; data curation, T.N., A.K. and F.P.; writing—original draft preparation, T.N., A.K. and F.P.; writing—review and editing T.N., A.K. and F.P.; visualization, F.P.; supervision, T.N.; project administration, T.N., A.K. and F.P.; funding acquisition, T.N., A.K. and F.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Science Centre, grant number 2015/19/N/ST8/00787.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Acknowledgments:** We thank Krzysztof Wujczyk for his help in preparing the specimens.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

