Influence of moisture content on the dynamic modulus of elasticity

Pinus forests are the second most planted in Brazil and the wood obtained from them is mainly used as structural elements in the civil construction sector. The Brazilian standard that deals with calculations of wooden structures projects recommends the use of wood in the range of 10% to 20% of moisture content. Thus, this study aimed to present an investigation about the influence of moisture content on the static modulus of elasticity (MOE st ) of wooden beams by transverse vibration tests. The MOE st was evaluated by static bending tests and transverse vibration tests for various moisture content. The transverse vibration test was performed in a free condition using an accelerometer and an impulse hammer, and the dynamic modulus of elasticity (MOE d ) was determined from the frequency of the first bending vibration mode. A total of 20 wooden beams were obtained from freshly cut Pinus spp. logs with initial high moisture content were used, with nominal dimensions of 5 cm × 10 cm × 200 cm (thickness × width × length). It was observed that the MOE d is also affected by moisture content according to the non-linear regression model. There were significant changes in the dynamic modulus of elasticity (MOE d ) for the moisture contents (M) below 25% (near the fiber saturation point - FSP).


Introduction
Wood elements are widely used in civil construction for being a renewable material from natural forest or reforestation.
Their use in rural and urban construction is a global trend to move towards cleaner production with an environmentally friendly raw material (Souza et al., 2018). Therefore, it is essential to know its mechanical properties to recommend its correct use and any procedure aimed at reducing the number of mechanical tests (need of several samples and destructive tests) is greatly desirable (Almeida et al., 2020).
The bending static modulus of elasticity (MOEst) can be evaluated by static tests (destructive technique -DT) or transverse vibration dynamic tests (non destructive techniques -NDT), among others. Some of the advantages of transverse vibration tests are shorter execution times, repeatability and possibility to obtain the MOEst considering the shear stress-induced deformation.
The transverse vibration test technique has shown good results to estimate the MOEd of wood elements (Carreira et al., , 2017Medeiros Neto et al., 2016;Segundinho et al., 2012Segundinho et al., , 2013. The transverse vibration NDT techniques can be used successfully as part of an automated structural lumber grading system (França et al., 2018).
The differential equation 1 describes the transverse displacement (v) of a wooden beam in free transverse vibration over time (t), neglecting the shear effects (Clough & Penzien, 2003;Timoshenko, 2007). Equation 1 is valid for wooden beams whose length is much greater than the height of the cross section, in which case the shear stress effects can be neglected (Cho, 2007).
There are several references in the literature regarding the effect of moisture content on measuring the bending MOEst with transverse vibration testing (França et al., 2018;Teixeira, 2016). In an experimental investigation of the moisture content effect on measurements of MOEd of wooden beams, were added extra weights (dead weights) distributed along the beam length to simulate the addition of free water (moisture content > fiber saturation point -FSP ≈ 30%) (Barrett & Hong, 2010). The authors found that the dynamic modulus of elasticity remains constant by adding load to simulate moisture contents above 30%.
Corrections for the MOEd,12 of spruce species were proposed to evaluate the moisture content influence on MOEd of wooden beams for moisture content below (equation 3) and above (equation 4) FSP, respectively (Unterwieser & Schickhofer, 2011).
Information on the advantages of the rational use of wooden elements in the construction of structural design and their physical-mechanical properties are essential to develop research mainly aimed at the consumer market (Almeida et al., 2020).
Thus, the objective of this article is to present an experimental investigation about the influence of the moisture content on the dynamic modulus of elasticity (MOEd) of wooden beams by transverse vibration tests.

Material and Methods
A total of 20 sawn wooden beams of Pinus spp. with nominal dimensions of 5.0 cm × 10.0 cm × 200.0 cm (thickness × width × length) extracted from freshly cut logs were used. The beams were kept in an acclimatized room (temperature of 21.4 °C -24.6 °C and relative humidity -RH of 55% -65%). The moisture content was estimated by the weight of each wooden beam calculated daily, and the initial moisture content (M) was estimated from specimens taken from each beam. The static bending and transverse vibration tests were performed at approximately every 5% moisture content decrease until reaching equilibrium moisture content (M) equal to 12%. The oven-dry weight of the beams was obtained, from which the actual moisture contents during the tests were obtained.
The static bending test was done with a concentrated load at the half length of a simply supported wooden beam attending  (Chui, 1991). The cords were tied to low rigidity springs so that the rigid body mode frequency was less than 10% of the natural Research, Society and Development, v. 11, n. 11, e232111133687, 2022 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v11i11.33687 4 frequency of the first bending mode vibration, thereby ensuring the free suspension behavior (McConnell & Varoto, 2008). In which: MOEd -dynamic modulus of elasticity (Pa); MOEd,12 -dynamic modulus of elasticity (Pa) for moisture content equal to 12%; Mrel -relative moisture content; M -moisture content (%); C -dimensionless coefficient.

Influence of moisture content
A graph of the dimensionless coefficient (C) values versus the relative moisture content (Mrel) was developed based on equations 6 and 7 (Figure 2). It is observed that there was an agglomeration of the C values to relative moisture content (Mrel) < 2%, and a decrease of the same. A constant dispersion of C values is observed from (Mrel) ≥ 2, with mean values around 0.9.
Thus, the dynamic modulus of elasticity (MOEd) remains virtually constant for moisture content above 25% (Mrel greater than 2) (Figure 2). In Larix gmelinii wood, the MOEd decreased with the increase in moisture content (Cheng et al., 2020).
However, the trends began to slow down when the moisture content was higher than the FSP.

Source: Authors.
A preliminary statistical analysis of the relation between C and Mrel considering moisture content below 25% showed the presence of five outliers, all identified from only one beam. Discarding the data for this beam, the regression curve between C and Mrel was obtained for Mrel less than or equal to 2.08 (M ≤ 25%) ( Figure 3) with a good coefficient of determination (R 2 equal to 0.72).   Source: Authors.
Next, the theoretical frequency of vibration was calculated from equation 2 to verify this assumption for moisture contents above 25%. The calculation admitted that the MOEd and the cross-section dimensions remain constant and equal to the values measured for moisture content equal to 25%. The wooden beam probably absorbs moisture near the FSP or capillary condensation caused by lowering the water vapor pressure, and the stress wave reflects and refracts between the wood fiber and the resulting water molecule. These phenomena affect the stress wave propagation velocity (Cheng et al., 2020).  Research, Society andDevelopment, v. 11, n. 11, e232111133687, 2022 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v11i11.33687 7 If the cross-section dimensions do not change significantly for moisture content above 25%, it can be concluded that the MOEst did not change significantly for moisture contents above the FSP, assumed as constants for moisture contents above than 25%. Theoretical and experimental results for Larix gmelinii wood showed that when the moisture content did not reach the FSP, the wood properties sharply decreased with increased moisture (Cheng et al., 2020). However, the trends began to slow down when the M was higher than the FSP.
We can obtain equation 9 by replacing moisture equal to 25% in equation 8, which corrects the MOEd value obtained for M greater than 25%, for the MOEst,12 value for moisture content equal to 12% (MOEst,12).

Determining the modulus of elasticity for moisture at 12%
Correction methods shown in the literature (Clough & Penzien, 2003;Timoshenko, 2007), and the non-linear regression model by least-squares fit were evaluated ( Figure 3) in order to compare the correction methods, the percentage (residual) error between the measured and estimated MORst with each method, both with M equal to 12%. Figure 6 and Figure 7 show the graphs obtained for M ≤ 25% and for M > 25%, respectively.
It is observed that the adjusted model for moisture contents below 25% results in lesser intensity residues, with the average of residues at around zero. Differently from that indicated in the literature (Associação On the other hand, the residues for moisture contents greater than 25% obtained by the corrections equations proposed in the same literature are equivalent.

Conclusion
Considering the correlations obtained and the residual analysis, it can be concluded that the non-linear regression adjusted model resulted in more accurate estimates for the wood samples studied and that the MOEd is also affected by moisture content according to the non-linear regression model.
It was concluded that the equations proposed to calculate the MOEd,12 in the moisture content equal to 12% results in values more than those obtained using the equation recommended by the Brazilian Standard. That is, the MOEst for moisture content (M) equal to 12% can be estimated for moisture content below 25%.
It can be assumed that the MOEd remains constant for moisture contents above 25%. Thus, the results of dynamic tests performed with moisture contents above 25% will not be affected by moisture content variation for the Pinus sp. wood species studied for structural classification purposes.
It is suggested that this type of research is also expanded to native species, as to other exotic species, because in this way it will be possible to know their behavior in determining the dynamic modulus of elasticity due to humidity variation.