MOR and MOE of Serbian Spruce (Picea omorika Pančić/Purkyně) Wood from Natural Stands

The paper presents the results of testing the bending stress of Serbian spruce wood from natural stands. In testing the samples, in addition to the modulus of rupture, the bending stress at the proportionality limit, the ratio between the stress at the proportionality limit and the modulus of rupture as well as the modulus of elasticity of wood were determined. The study included nine trees from natural stands, and a total of 261 samples were tested. Regression analysis determined the dependences of these mechanical properties on the annual ring width, the proportion of late wood and wood density, as well as the dependence of the modulus of elasticity on the modulus of rupture.


INTRODUCTION 1. UVOD
Serbian spruce (Picea omorika Pančić/Purkyně) is naturally distributed in Bosnia and Herzegovina and Serbia in the area around the middle and lower reaches of the Drina River. It is found on steep, rocky cliffs, mostly on limestone, rarely serpentine, at altitudes of 300 to 1700 m (Vidaković and Franjić, 2004).
Serbian spruce is interesting from many aspects, both to the science and profession, and to the general public. A large number of scientific and professional papers deal with various issues related to Serbian number of trees. From each locality, three trees were selected and harvested, and the average values of their characteristics by locations are given in Table 1.
Three logs, 1.2 m long, were cut from each tree. One log was taken from a height of 1.3 m, one from the part of the bole just below the first green branch, and one log was taken from the height in the middle between the two mentioned heights. From them, 30 mm thick radial planks were cut, out of which, after natural drying for three months and processing on the thickener, they were reduced to a thickness of 20 mm. From them, samples (20 mm × 20 mm × 320 mm) for bending testing were made. The test was performed at the Material Testing Laboratory at the Faculty of Mechanical Engineering, University of Banja Luka, using a Messphysik "Beta 200", a universal testing machine used to test mechanical properties of different types of materials specialized in the testing of materials ( Figure 1). The ISO 3133:1975 standard was used for bending testing.
For this test, 261 samples were selected. During selection, samples that are closest to the pith and that have natural defects were avoided. Before testing, the mass and dimensions in radial, tangential and axial directions of samples were measured. These data were used to calculate the wood density at the time of testing using Eq. 1: Where: m -sample mass at the time of testing (g) T, R, , A -sample dimensions in tangential, radial and axial direction at the time of testing (mm) The samples were scanned in cross-section in order to determine the average annual ring width and the average proportion of late wood, using CDendro 7.6 and CooRecorder 7.6. Three-point bending tests were carried out to investigate the static behavior of sam-spruce, ranging from its distribution, the configuration of the terrain as well as the habitat where it occurs (Fukarek, 1935(Fukarek, , 1950Čolić, 1953, 1957 to the latest genetic research Geburek, 2010, 2014;Mataruga et al., 2020). However, it is very difficult to find information in the literature concerning the mechanical properties of Serbian spruce wood, especially the wood originating from natural stands. Lukić-Simonović (1970) investigated in more detail the mechanical properties of Serbian spruce from its natural stands in western Serbia, while no such research has been done in Bosnia and Herzegovina.
Modulus of rupture (MOR) and modulus of elasticity (MOE) are among the most important parameters for determining the wood quality, especially for the usage of wood in construction (Bodig and Jayne, 1982). The modulus of elasticity, as a measure of stiffness, can be used to estimate strength because there is a positive correlation between stiffness and strength (Panshin and de Zeeuw, 1980). Popović (1990) states that the ratio between the bending stress at the proportionality limit and the modulus of rupture is a very important fact in the practical application of wood, where, if this ratio is known, the use of loads exceeding these values and leading to permanent deformation or fracture can be prevented.
Knowledge of the stress at the proportionality limit, maximum stress and their ratio, as well as the knowledge of the effect of certain factors on the specified bending characteristics has both scientific and practical significance. These factors are very important for designing the bending tools and for determination the stress that products can be exposed to during use (Svoboda et al., 2017).

MATERIJALI I METODE
The material for the research comes from three localities of the natural stands of Serbian spruce managed by the FE Panos -Višegrad. These are Gostilja (GO), Stolac 1 (S1) and Stolac 2 (S2). Location GO is at 1130 m above sea level, and the total area of this stand is 25.8 ha. S1 is located at 1200 m above sea level, and S2 at 960 m above sea level, while the total area of the stands is 29.5 ha.
According to Mataruga et al. (2011), Serbian spruce has been listed as an endangered plant species from 2010. Considering that, the selection of trees was taken into account when planning the research so that the relevant information was obtained with a minimum ples. Samples were placed so that they were on one radial side and the distance between the supports was 280 mm. The loading speed was set to 10 mm/min. Load-deflection graphs were obtained by testing and they were used to obtain the values of bending stress at the proportionality limit, MOR and MOE. The calculation formulas for MOR (Eq. 2) and bending stress at the proportionality limit (Eq. 3) are: Where: F max -maximum load (N) F p -load at proportionality limit (N) l -distance between supports (mm) b -width of the sample (mm) h -height of the sample (mm) The calculation formula for MOE is: The calculation formula for the ratio between the bending stress at the proportionality limit and MOR is: After the test, all samples were weighed and then dried to an oven dry state to determine moisture content at the time of testing using Eq. 6: Where: m -sample mass at the time of testing (g) m o -sample mass in oven dry state (g) In order to compare the obtained values of MOR and MOE with literature data, results of bending test were reduced to values at standard moisture content (12 %) using Eq. 7:

REZULTATI I RASPRAVA
The average values of wood density and moisture content at the time of testing the samples from all three locations are given in Table 2. The average density of investigated Serbian spruce wood is 0.517 g/ cm 3 at a moisture content of 15 %, while the average value of Serbian spruce wood density investigated by Lukić-Simonović (1955), from the territory of Serbia, at the same moisture content, was 0.482 g/cm 3 . The average annual ring width of investigated Serbian spruce wood is 1.76 mm and the average proportion of late wood is 15.24 %. Table 3 shows the average values and other statistical indicators of MOR at standard moisture content by locations. Trees from GO have the lowest average values of MOR (84.23 MPa), and trees from S1 the largest (94.86 MPa). The smallest variation in MOR was found at S2 (12.19%) and the largest at GO (16.17 %).
The average value of MOR at all locations (89.72 MPa) is slightly lower than the MOR at standard moisture content obtained in research by Lukić-Simonović (1970), namely 96.7 MPa. Studying the MOR of Serbian spruce wood from plantations in Germany, Kommert (1993) found that its average values at moisture content of 12 % are in the range of 57.6 MPa (average density of samples is 0.424 g/cm 3 ) to 86 MPa (average density of samples is 0.510 g/cm 3 ).
As the number of studies on the mechanical properties of Serbian spruce wood is limited, comparison with the mechanical properties of spruce wood was made. According to Karahasanović (1992), the MOR of spruce at a moisture content of (12 ± 3) % is 64 MPa. Gorišek et al. (2004)  In addition to the MOR, the bending stress at the proportionality limit was determined, as well as the ratio between the bending stress at the proportionality limit and MOR. The obtained values are shown in Table 4 and 5.
The average bending stress at the proportionality limit for all three locations is 44.72 MPa, while the coefficient of variation is 15.92 %. The average ratio of  Popović (1990) states that the bending stress at the proportionality limit for beech wood is on average 54.4 % and 56 % in the radial and tangential direction, respectively, from the value of the maximum bending stress. Table 6 shows the average values of modulus of elasticity (MOE) at standard moisture content as well as other statistical parameters. The lowest average value of MOE was found in trees from GO (10953.99 MPa), and the highest in trees from S2 (12161.92 MPa). The smallest variation of MOE is at S2 (9.83 %) and the largest at S1 (21.46 %).
According to Šoškić and Popović (2002), the average value of MOE for spruce is 11000 MPa, which is approximately the value of MOE for Serbian spruce obtained in this study (11566.23 MPa). Johansson and Kliger (2000) state that the average value of MOE determined from bending for spruce is 12500 MPa, according to Aanerød (2014) 12800 MPa, with a coefficient of variation of 19.5 %, while according to Pushinskis et al. (2002) it is 13660 MPa.
Analysis of the variance of MOR showed that there is statistically significant difference between the locations, while there is no difference between the locations in the ratio between bending stress at the proportionality limit and MOR. Using the Duncan test in the analysis of the variance of MOE, the locations were classified into two homogeneous groups, i.e. it was noticed that there is no statistically significant difference between the locations S1 and S2. In the analysis of the variance of the bending stress at the proportionality limit, locations were classified into two homogeneous          (Table 7).
In addition to wood density, which is considered to be the most significant factor affecting wood properties, the influence of compression and juvenile wood, the angle of the microfibrils and the width of the growth ring, which have the same, if not greater, influence on the wood properties, should not be neglected (Alteryac et al., 2006). The influence of the annual ring width on the MOR and MOE can be seen in Figure 2. According to Roemer-Orphal table for determining the strength of correlation dependence (according to Vasilj, 2000), there is a strong negative correlation between these parameters.
Proportion of late wood has a positive effect on MOR and MOE (Figure 3). Based on the correlation coefficients, it can be concluded that the correlation is moderate.
The dependence of MOR on wood density has been tested by a number of researchers. Thus, Schlyter (1927) states that this dependence is linear, while according to Baumann (1922) it is curvilinear. In any case, as the density of wood increases, the bending strength also increases, which is confirmed by this research ( Figure 4). As wood density of Serbian spruce grows, so does the modulus of elasticity, although these correlations are slightly smaller than the correlations between density and MOR. In their study, Raiskila et al. (2006) state that the same is the case with spruce wood.
In order to obtain a model for strength estimation, the regression analysis included the dependence of MOR on annual ring width and wood density. Multiple regression equation (Function 8) was obtained by stepwise multiple regression method. The parameters of the obtained equation and the regression characteristics (Table 8) show that there is a pronounced dependence of MOR on the included elements. All regression coefficients are statistically significant at the p<0.001 level, as is the regression as a whole. On the basis of the coefficient of determination, 33 % of the variation of the MOR value is explained by the variation of the observed elements. Generally, the MOE is considered the most important strength predictor parameter (Baar et al., 2015). Investigating the correlation between MOR and MOE in spruce, Johansson and Kliger (2000) found that the coefficient of determination was 0.51. The equation of relation between bending strength and modulus of elasticity reported by Johansson et al. (1992) is: The dependence of MOR on MOE examined in this paper can be seen in Figure 5. The correlation is linear and positive, and based on the correlation coefficient of 0.77, it can be concluded that the correlation is very strong.

ZAKLJUČAK
The results obtained in this paper have substantially improved the knowledge of certain mechanical properties of Serbian spruce from the territory of Bosnia and Herzegovina. It can be observed that Serbian spruce