**Analysis of relations between the moduli of elasticity in compression, tension, and static bending of hardwoods**,"

*BioRes.*15(2), 3278-3288.

#### Abstract

Accurate estimation of average modulus of elasticity in compression parallel to the grain (Ec0) is of paramount importance for rational sizing of timber structures, given the use of this property in the estimation of stability of compressed parts (ultimate limit state, ULS) and in calculation of excessive strains (serviceability limit state, SLS). In Brazil, if values cannot be experimentally determined, ABNT NBR 7190 (1997) allows for estimation of Ec0 through relations to average modulus of elasticity both in tension parallel to the grain (Et0) (Ec0 = Et0) and in bending (EM) (Ec0 = EM/0.90). This research aimed to access the efficiency of these relations by testing 30 tropical wood species. The analysis of variance results showed that Ec0 and Et0 were statistically equal. However, Ec0 and EM/0.90 were not statistically equal, and the method of least squares resulted in a coefficient of 0.98, which was 8.89% higher than the one suggested by ABNT NBR 7190 (1997) and close to 1, thus, validating the results of ANOVA, which pointed on the equivalence between Ec0 and EM (Ec0 = EM). As an alternative to simplified equations of the standard, two-parameter regression models were used. The geometric model with R² = 91.67% proved to be the model of best fit, which demonstrated that Ec0 could be calculated as a function of EM.

Download PDF

#### Full Article

**Analysis of Relations between the Moduli of Elasticity in Compression, Tension, and Static Bending of Hardwoods**

João P. B. Almeida,^{a,}* Vinícius B. M. Aquino,^{b} Anderson R. V. Wolenski,^{c }Cristiane I. Campos,^{d} Julio C. Molina,^{d} Eduardo Chahud,^{e} Francisco A. R. Lahr,^{f} and André L. Christoforo ^{a}

Accurate estimation of average modulus of elasticity in compression parallel to the grain (*E*_{c0}) is of paramount importance for rational sizing of timber structures, given the use of this property in the estimation of stability of compressed parts (ultimate limit state, ULS) and in calculation of excessive strains (serviceability limit state, SLS). In Brazil, if values cannot be experimentally determined, ABNT NBR 7190 (1997) allows for estimation of *E*_{c0} through relations to average modulus of elasticity both in tension parallel to the grain (*E*_{t0}) (*E*_{c0} = *E*_{t0}) and in bending (*E*_{M}) (*E*_{c0} = *E*_{M}/0.90). This research aimed to access the efficiency of these relations by testing 30 tropical wood species. The analysis of variance results showed that *E*_{c0} and *E*_{t0} were statistically equal. However, *E*_{c0} and *E*_{M}/0.90 were not statistically equal, and the method of least squares resulted in a coefficient of 0.98, which was 8.89% higher than the one suggested by ABNT NBR 7190 (1997) and close to 1, thus, validating the results of ANOVA, which pointed on the equivalence between *E*_{c0} and *E*_{M} (*E*_{c0} = *E*_{M}). As an alternative to simplified equations of the standard, two-parameter regression models were used. The geometric model with R² = 91.67% proved to be the model of best fit, which demonstrated that *E*_{c0} could be calculated as a function of *E*_{M}.

*Keywords: Hardwood; Regression model; Mechanical properties; Timber structure*

*Contact information: a: Department of Civil Engineering, Federal University of São Carlos (UFSCar), São Carlos, Brazil; b: Institute of Engineering of Araguaia, Federal University of Southern and Southeastern Pará (UNIFESSPA), Santana do Araguaia, Brazil; c: Federal Institute of Santa Catarina (IFSC), São Carlos, Brazil; d: São Paulo State University (UNESP), Itapeva, Brazil; e: Federal University of Minas Gerais (UFMG), Belo Horizonte, Brazil; f: Department of Structural Engineering, University of São Carlos (EESC/USP), São Carlos, Brazil; *Corresponding author: boff.joaopaulo@gmail.com*

**INTRODUCTION**

Considered the material of the future (Kuzman and Sandberg 2017; Żmijewki and Wojtowicz-Jankowska 2017), timber is becoming increasingly popular and widely applied in civil construction (Wieruszewski and Mazela 2017). This is not only because wood is a natural, biodegradable, renewable, recyclable and, hence, environmentally friendly raw material (Wang *et al*. 2014; Araujo *et al*. 2016; Lima, Jr. *et al*. 2018; Souza *et al*. 2018), but also due to characteristics that make it an efficient building material compared to traditionally used steel and concrete (Ramage *et al*. 2017).

One such characteristic of wood is its excellent mechanical strength-to-density ratio (Pries and Mai 2013; Ramage *et al*. 2017; Huber *et al*. 2018; Lima, Jr. *et al*. 2018) that favors the use of wood in construction applications where weight of the structure itself presents a considerable load (*e.g.*, roofs, bridges, and tall buildings) as well as in buildings subjected to seismic loading, given that heavier structures are subjected to higher seismic load (Ramage *et al*. 2017).

Given the effectiveness of wood as a structural element, timber constructions have become the most common, practical, and economical housing solution for most countries in the northern hemisphere (Araujo *et al*. 2016), leading to widespread use of timber in countries such as Austria, Japan, Scotland, and New Zealand, where 40%, 45%, 83%, and 85% of houses are made of wood, respectively (Mahapatra *et al*. 2012; Hurmekoski *et al*. 2015; Araujo *et al*. 2018).

Nevertheless, in Brazil, despite having the largest biodiversity of species on the planet (Beech *et al*. 2017), with evident reforestation potential, and a growing demand for housing, the use of timber for dwelling construction is still low (Araujo *et al*. 2018). This motivates the development of research that disseminates, mainly to the consumer market, information regarding benefits of timber constructions and physical-mechanical properties of wood that are necessary for rational elaboration of structural design.

Among these properties, average value of modulus of elasticity in compression parallel to the grain (*E*_{c0}) is of paramount importance, given its use in checks of stability of compressed parts (buckling) in the ultimate limit state (ULS) and in calculation of excessive strains in compliance with the serviceability limit state (SLS).

In Brazil, Annex B of ABNT NBR 7190 (1997) “Design of wooden structures” provides experimental methods for the determination of physical-mechanical properties of wood. Given that there are 17 physical-mechanical properties that need to be estimated, a complete characterization of species requires an extensive number of tests. The execution of these tests is time-consuming, expensive, and implies expenditure with materials and labor.

Given the many catalogued tree species in the Amazonian region as a whole, and in the Brazilian Amazon specifically (12000 and 7696, respectively, according to Steege *et al*. (2016)), any procedure aimed at reducing the number of tests is greatly desirable.

To simplify the assessment of *E*_{c0}, ABNT NBR 7190 (1997) allows estimation of the *E*_{c0} value through relation with the average value of modulus of elasticity in tension parallel to the grain (*E*_{t0}) and static three-point bending (*E*_{M}), as shown in Eqs. 1 and 2, respectively:

^{ }(1)

^{ }(2)

Several previous works have sought to determine correlations between wood properties, particularly, with bulk density (*ρ*_{ap} – an easily determinable physical property), which proves the academic interest in simplifying the characterization of wood.

Igartúa *et al*. (2015) studied the Argentinian species *Acacia melanoxyon* and found a strong correlation (with coefficient of determination (R²) above 70%) between *ρ*_{ap} and parallel and normal to the grain compressive strength, as well as between *ρ*_{ap} and modulus of elasticity and conventional bending strength.

Silva *et al*. (2018) used regression models to study whether physical-mechanical properties of *Goupia glabra* Aubl. (popularly called Cupiúba in Brazil) can be estimated as a function of *ρ*_{ap}. They obtained regression models with good precision (R² ≈ 70%) for 15 studied relations. The most significant relation (R² = 87.96%) was between *ρ*_{ap} and hardness parallel to the grain.

Almeida *et al.* (2017) and Dias *et al.* (2019) studied wood shrinkage estimation as a function of *ρ*_{ap} with regression models based on experimental results from 15 and 43 tropical wood species, respectively. In both works, analysis of variance (ANOVA) results demonstrated weak correlation between investigated parameters, showing that *ρ*_{ap} is not a reliable estimator for dimensional stability of wood.

In recent years, research has assessed the accuracy of estimated properties obtained through relationships provided by ABNT NBR 7190 (1997) and determined coefficients that best fit the proposed relationships. Matos and Molina (2016) studied correlations between characteristic shear strength (*f*_{v0,k}) and compressive strength parallel to the grain (*f*_{c0,k}) of conifer (*f*_{v0,k }= 0.15∙*f*_{c0,k}) and dicot (*f*_{v0,k }= 0.12∙*f*_{c0,k}) woods. The authors evaluated *Pinus elliotti* and *Eucalyptus saligna* species and for conifer woods obtained a relation approximately 95% higher compared to that from ABNT NBR 7190 (1997).

Based on three- and four-point static bending tests, Lahr *et al*. (2017) determined a relation between longitudinal (*E*) and tangential (*G*) modulus of elasticity. From the results obtained of five different tropical wood species tested, the authors determined the relation *E* = 35∙*G*, with the coefficient being 75% higher than the one given by ABNT NBR 7190 (1997) (*E* = 20∙*G*).

Recently, Christoforo *et al*. (2019) studied relations between characteristic compression strength (*f*_{c0,k}), characteristic tensile strength parallel to the grain (*f*_{t0,k}), and characteristic shear strength (*f*_{v0,k}). The coefficients (*α*) they obtained after testing five tropical wood species were 0.96 and 0.23 for relations *f*_{c0,k} = *α*∙*f*_{t0,k} and *f*_{v0,k} = *α*∙*f*_{c0,k}, respectively, which were 25% and 92% higher than the coefficients specified by ABNT NBR 7190 (1997).

These studies demonstrate that some relations between properties of wood prescribed by ABNT NBR 7190 (1997) need to be revised to obtain reliable estimates for structural design. Thus, the aim of this work was to investigate statistical equivalence between modulus of elasticity obtained in bending, compression, and tension parallel to the grain (Eq. 1 and Eq. 2) and, in case equivalence is not confirmed, to define correlations between these properties that would give more accurate *E*_{c0} estimates.

**EXPERIMENTAL**

**Materials**

Thirty different wood species were used in this study (Table 1), and these were obtained, from local companies, in the same manner as timber used in Brazilian civil construction, in the form of boards sized approximately 6 cm × 11 cm × 200 cm. Therefore, it was not possible to identify origin and age for the trees.

The wood was properly stocked and tested in three different research labs in the country: the Laboratory of Wood and Timber Structure (LaMEM) of the University of São Paulo (USP); the laboratories of Federal University of Minas Gerais (UFMG), campus Belo Horizonte (State of Minas Gerais); and at the laboratories of São Paulo State University (UNESP), campus Itapeva (State of São Paulo).

**Methods**

To determine *E*_{c0}, *E*_{t0}, and *E*_{M}, the static three-point bending test (Fig. 1a), compression (Fig. 1b), and tensile test (Fig. 1c) parallel to the grain were performed, respectively.

**Table 1. **Brazilian Tropical Wood Species Used in the Study

For each species and mechanical property, 12 specimens were produced and tested, which gave a total of 1080 experimental results. All the tests were conducted on the universal testing machine AMSLER (250 kN loading capacity) (Shimadzu Corporation, Kyoto, Japan) following the procedure described in Annex B (Determination of wood properties for structural design) of ABNT NBR 7190 (1997).

(a) |
(b) |
(c) |

**Fig. 1.** Static bending test (a), compression test parallel to the grain (b), and tensile test parallel to the grain (c)

The wooden boards were ambient-dried. After drying, the boards presented moisture level around 12%. According to the ABNT NBR 7190 (1997), 12% is a reference moisture level for presentation of the experimental results. Values of stiffness properties (*E*_{c0}, *E*_{t0},_{ }and_{ }E_{M}) obtained with moisture levels (U%) different from 12% were adjusted for 12% moisture level using Eq. 3, as prescribed by the ABNT NBR 7190 (1997), where *E _{12%}* and

*E*are values corresponding to moisture levels of 12% and U%, respectively.

_{U%}^{ }(3)

The accuracy of relations proposed by ABNT NBR 7190 (1997) (Eqs. 1 and 2) was evaluated using ANOVA at the 5% significance level through BioEstat5.3® software (Mamirauá Institute, Belém, PA, Brazil). A null hypothesis (*H*_{0}) was that the average of the groups (*E*_{c0 }and *E*_{t0}, *E*_{c0}, and 0.90/E_{M}) was equal, and the alternative hypothesis (*H*_{1}) was non-equivalence. Hence, a p-value higher or equal than the selected significance level (p-value ≥ 0.05) implied accepting *H*_{0}* _{ }*(tested relation was accurate). Otherwise (p-value < 0.05),

*H*

_{1}should be accepted.

Upon discovering non-equivalence (p-value < 0.05), two-parameter (*a* e *b*) regression models (Eq. 4 to Eq. 7) were used to estimate *E*_{c0} (dependent variable – *y*) as a function of *E*_{t0} and *E*_{M }(independent variables – *x*):

* *(Linear)* *(4)

* *(Exponential)* *(5)

(Logarithmic)* *(6)

* *(Geometric)* *(7)

Regression models based on ANOVA at a 5% significance level were used in considering the grouping of species and respective average values of properties. For ANOVA of regression models, a null hypothesis (*H*_{0}*: β = 0*) was that the tested models were not representative and an alternative hypothesis (*H*_{1}*: β *≠* 0*) was that they were representative.

P-values higher than the selected significance level (p-value > 0.05) implied accepting *H*_{0}* _{ }*(tested regression model was not representative – variations of

*x*did not explain variations of

*y*). In the opposite case, this hypothesis would be rejected (p-value ≤ 0.05 – regression model was representative).

In addition to ANOVA, values of coefficient of determination (R²) were obtained, which allowed for evaluation of the quality of estimated fit and determination of the most accurate representative model (p-value ≤ 0.05), that is, the model that best described variations of dependent variable *y* as a function of independent variable *x*.

Along with regression models, the least squares method (Eq. 8 and Eq. 9 – used in studies by Christoforo *et al.* (2012), Icimoto *et al.* (2015), Ferro *et al.* (2015), Lahr *et al.* (2017), Almeida *et al.* (2018), and Christoforo *et al.* (2019)) using Newton’s method with quadratic approximation was applied for determination of the optimal coefficient (*λ*) for relations *E*_{c0} = *λ*·*E*_{t0} and *E*_{c0} = *E*_{M}/*λ*:

^{ }(8)

^{ }(9)

**RESULTS AND DISCUSSION**

Table 2 shows the experimentally obtained average values (*X*_{m}) and coefficients of variation (*C*_{v}) of stiffness properties (*E*_{c0}, *E*_{t0}, and *E*_{M}) for each tested species.

**Table 2. **Stiffness Properties of 30 Studied Wood Species

Both coefficients of variation and average stiffness values were consistent with experimental results from Gonçalez and Gonçalves (2001), Grobério and Lahr (2002), Dias and Lahr (2004), Araújo (2007), Faria *et al.* (2012), Ferro *et al.* (2015), Jesus *et al.* (2015), Moreira *et al.* (2017), Lahr *et al.* (2017), Aquino *et al*. (2018), and Almeida *et al*. (2018) that determined some of the stiffness properties of the species studied here.

The values of *E*_{c0} determined in this study and found in the literature were in agreement with values presented in Appendix E (Common average strength and stiffness values of some native and afforestation woods) of ABNT NBR 7190 (1997), which includes among its 50 hardwood species 18 wood species tested in this work (*Vataireopsis araroba* (Aguiar) Ducke, *Hymenolobium *cf.* heterocarpum* Ducke, *Hymenolobium petraeum* Ducke, *Dinizia excelsa* Ducke, *Sebastiania commersoniana* (Baill.) L.B. Sm. & Downs, *Andira anthelmia* (Vell.) Benth, *Cassia ferruginea* (Schrad.) Schrad. ex DC., *Pouteria* cf. *pachyphylla* T.D.Penn., *Cedrela odotara* L., *Cedrela* cf. *fissilis* Vell., *Dypterix odotora* (Aubl.) Willd., *Goupia paraensis* Huber, *Luetzelburgia *cf.* guaissara *Toledo, *Peltophorum dubium* (Spreng.) Taub., *Hymenaea courbaril* L., *Ocotea neesiana* (Mig.) Kosterm., and *Manilkara* cf. *inundata* (Ducke) Ducke). These comparisons supported the results shown in Table 2.

The ANOVA showed that group means of *E*_{c0} and *E*_{t0 }were statistically equal because the p-value was higher than the significance level (p-value ≥ 0.05). Hence, the relation *E*_{c0} = *E*_{t0} was accurate and gave a good estimate of *E*_{c0}. For the relation between *E*_{c0} and *E*_{M}, the p-value was less than the significance level (p-value < 0.05), which indicated that group means of *E*_{c0} and *E*_{M}/0.90 were not statistically equivalent. Hence, the equation *E*_{c0} = *E*_{M}/0.90 did not estimate *E*_{c0} value accurately.

The regression models (Eq. 4 to Eq. 7) and least squares method (Eq. 9) were used as an alternative to the equation *E*_{c0} = *E*_{M}/0.90, for formulation of equations that could accurately estimate *E*_{c0} values as a function of *E*_{M}. All models (linear, exponential, logarithmic, and geometric) were significant (p-value < 0.05), and the geometric model described by Eq. 10 showed the best fit (R² = 91.67%):

^{ }(10)

The least squares method gave the optimal coefficient for the relation *E*_{c0} = *E*_{M}/*λ* for the entire group of species equal to 0.98 (Eq. 11) that was 8.89% higher than the coefficient (0.90) provided by ABNT NBR 7190 (1997):

^{ }(11)

It should be mentioned that *E*_{c0} = *E*_{M}/0.90 ratio was established by the Brazilian standard ABNT NBR 7190 (1997) without an adequate statistical analysis that would prove the reliability in the comparison of the groups of values (*E*_{c0} and *E*_{M}). In the present work, ANOVA was applied in order to investigate the relationship between *E*_{c0} and *E*_{M} (*E*_{c0} = *E*_{M}), which showed equivalence between the two groups. This result shows that the *E*_{c0} = *E*_{M} ratio is more precise than the *E*_{c0} = *E*_{M}/0.90 equation, proposed by the Brazilian standard. This highlighting the need for revision of this item in future versions.

**CONCLUSIONS**

- The ANOVA at 5% significance level demonstrated an equivalence between group means of
*E*_{c0}and*E*_{t0}, which indicated the accuracy of*E*_{c0}estimation for hardwood species through the equation*E*_{c0}=*E*_{t0}proposed by ABNT NBR 7190 (1997). - The ANOVA at 5% significance level demonstrated that group means of
*E*_{c0}and*E*_{M}/0.90 were not equal, which indicated that the coefficient of 0.90 did not give an accurate estimation of*E*_{c0}through the equation*E*_{c0}=*E*_{M}/0.90. - All regression models used for estimation of
*E*_{c0}as a function of*E*_{M}were significant and with a good fit. The best fit was achieved by the geometric model, which showed that*E*_{c0}could be estimated by Eq. 10. - The optimal coefficient obtained by the least squares method (Eq. 11) for the relation between
*E*_{c0}and*E*_{M}was higher than the one established by ABNT NBR 7190 (1997). The value of this coefficient was around 1, thus, validating the results of ANOVA that indicated equivalence between*E*_{c0}and*E*_{M}(*E*_{c0}=*E*_{M}). - Given the significant number of species tested in this study,
*E*_{c0}=*E*_{M}ratio appeared to be widely applicable model for estimation of*E*_{c0}.

**ACKNOWLEDGEMENTS**

The authors are grateful for Laboratory of Wood and Timber Structure (LaMEM) of the University of São Paulo (USP); the laboratories of Federal University of Minas Gerais (UFMG), campus Belo Horizonte (State of Minas Gerais); and the laboratories of São Paulo State University (UNESP), campus Itapeva (State of São Paulo), for providing facilities and inputs required for this study.

**REFERENCES CITED**

ABNT NBR 7190 (1997). “Projeto de estruturas de madeira [Design of wooden structures],” Brazilian Association of Technical Standards, Rio de Janeiro, Brazil.

Almeida, A. S., Lanini, T. L. S., Caetano, J. A., Christoforo, A. L., and Lahr, F. A. R. (2018). “Evaluation of stiffness in compression perpendicular to grain of Brazilian tropical wood species,” *Curr. J. Appl. Sci. Technol.* 28(5), 1-7. DOI: 10.9734/CJAST/2018/42945

Almeida, T. H., Almeida, D. H., Araujo, V. A, Silva, S. A. M., Christoforo, A. L., and Lahr, F. A. R. (2017). “Density as estimator of dimensional stability quantities of Brazilian tropical woods,” *BioResources* 12(3), 6579-6590. DOI: 10.15376/biores.12.3.6579-6590

Aquino, V. B. M., Almeida, J. P. B., Almeida, D. H., Almeida, T. H., Panzera, T. H., Christoforo, A. L., and Lahr, F. A. R. (2018). “Physical and mechanical characterization of *Copaifera *sp*. *wood species,” *Int. J. Mater. Eng.* 8(3), 55-58. DOI: 10.5923/j.ijme.20180803.03

Araújo, H. J. B. (2007). “Relações funcionais entre propriedades físicas e mecânicas de madeiras tropicais brasileiras [Functional relations between physical and mechanical properties of Brazilian tropical woods],” *Floresta* 37(3), 399-416. DOI: 10.5380/rf.v37i3.9937

Araujo, V. A., Cortez-Barbosa, J., Gava, M., Garcia, J. N., Souza, A. J. D., Savi, A. F., Morales, E. A. M., Molina, J. C., Vasconcelos, J. S., Christoforo, A. L., *et al.* (2016). “Classification of wooden housing building systems,” *BioResources* 11(3), 7889-7901. DOI: 10.15376/biores.11.3.DeAraujo

Araujo, V. A., Vasconcelos, J. S., Morales, E. A. M., Savi, A. F., Hindman, D. P., O’Brien, M. J., Negrão, J. H. J. O., Christoforo, A. L., Lahr, F. A. R., Cortez-Barbosa, J., *et al.* (2018). “Difficulties of wooden housing production sector in Brazil,” *Wood Mater. Sci. Eng.* 11(3), 1-10. DOI: 10.1080/17480272.2018.1484513

Beech, E., Rivers, M., Oldfield, S., and Smith, P. P. (2017). “GlobalTreeSearch: The first complete global database of tree species and country distributions,” *J. Sustain. For.* 36(5), 454-489. DOI: 10.1080/10549811.2017.1310049

Christoforo, A. L., Almeida, A. S., Lanini, T. L. S., Nogueira, R. S., and Lahr, F. A. R. (2019). “Estimation of the characteristic value of wood strength,” *J. Braz. Assoc. Agric. Eng.* 39(1), 127-132. DOI: 10.1590/1809-4430-Eng.Agric.v39n1p127-132/2019

Christoforo, A. L., Lahr, F. A. R., Morales, E. A. M., Panzera, T. H., and Borges, P. H. R. (2012). “Numerical evaluation of longitudinal modulus of elasticity of *Eucalyptus grandis *timber beams,” *Int. J. Agric. For.* 2(4), 166-170. DOI: 10.5923/j.ijaf.20120204.06

Dias, F. M., Almeida, T. H., Araújo, V. A., Panzera, T. H., Christoforo, A. L., and Lahr, F. A. R. (2019). “Influence of the apparent density on the shrinkage of 43 tropical wood species,” *Acta Sci. Technol.* 41(1), 2-7. DOI: 10.4025/actascitechnol.v41i2.30947

Dias, F. M., and Lahr, F. A. R. (2004). “Estimativa de propriedades de resistência e rigidez da madeira através da densidade aparente [Strength and stiffness properties of wood esteemed through the specific gravity],” *Sci. For.* 65, 102-113.

Faria, O. B., Silva, D. A. L., Lahr, F. A. R., Chahud, E., and Varanda, L. D. (2012). “Influence of wood moisture content on modulus of elasticity on tension parallel to the grain of Brazilian species,” *Eur. Int. J. Sci. Technol.* 1(2), 11-22.

Ferro, F. S., Icimoto, F. H., Almeida, D. H., Christoforo, A. L., and Lahr, F. A. R. (2015). “Influência da posição dos instrumentos de medida na determinação do módulo de elasticidade da madeira na compressão paralela às fibras (E_{c0}) [Influence of the position of the measuring instruments in the determination of the elasticity modulus of wood in compression parallel to grain (E_{c0})],” *Rev. Árvore* 39(4), 743-749. DOI: 10.1590/0100-67622015000400017

Gonçalez, J. C., and Gonçalves, D. M. (2001). “Valorização de duas espécies de madeira *Cedrelinga catenaeformis* e *Enterolobium shomburgkii* para a indústria madeireira [Valorization of two Brazilian timbers *Cedrelinga catenaeformis* and *Enterolobium shomburgkii*],” *Bras. Florestal* 71, 69-74.

Grobério, M. P., and Lahr, F. A. R. (2002). “Indicações para o emprego da madeira de espécies tropicais do Brasil [Indications for the use of wood tropical species from Brazil],” *Revista Madeira: Arquitetura e Engenharia* 3(8).

Huber, J. A. J., Ekevad, M., Girhammar, U. A., and Berg, S. (2018). “Structural robustness and timber buildings – A review,” *Wood Mater. Sci. Eng.* 14(2), 107-128. DOI: 10.1080/17480272.2018.1446052

Hurmekoski, E., Jonsson, R., and Nord, T. (2015). “Context, drivers, and future potential for wood-frame multi-story construction in Europe,” *Technol. Forecast. Soc. Change* 99, 181-196. DOI: 10.1016/j.techfore.2015.07.002

Icimoto, F. H., Ferro, F. S., Almeida, D. H., Christoforo, A. L., and Lahr, F. A. R. (2015). “Influence of specimen orientation on determination of elasticity in static bending,” *Maderas- Cienc. Tecnol.* 17(2), 229-238. DOI: 10.4067/S0718-221X2015005000022

Igartúa, D. V., Moreno, K., Piter, J. C., and Monteoliva, S. (2015). “Density and mechanical properties of Argentinean *Acacia melanoxylon*,” *Maderas- Cienc. Tecnol.* 17(4), 809-820. DOI: 10.4067/S0718-221X2015005000070

Jardim Botânico do Rio de Janeiro (2019). “Brazilian Flora 2020 under construction,” (http://floradobrasil.jbrj.gov.br/), Accessed 23 Nov 2019.

Jesus, J. M. H., Logsdon, N. B., and Finger, Z. (2015). “Classes de resistência de algumas madeiras de Mato Grosso [Strength classes of resistance of some timbers from Mato Grosso],” *Eng. Sci.* 1(3), 35-42.

Kuzman, M. K., and Sandberg, D. (2017). “Comparison of timber-house technologies and initiatives supporting use timber in Slovenia and in Sweden – The state of the art,” *iForest – Biogeosci. For.* 10(6), 930-938. DOI: 10.3832/ifor2397-010

Lahr, F. A. R., Christoforo, A. L., Varanda, L. D., Chahud, E., Araujo, V. A., and Branco, L. A. M. N. (2017). “Shear and longitudinal modulus of elasticity in wood: Relations based on static bending tests,” *Acta Sci. Technol.* 39(4), 433-437. DOI: 10.4025/actascitechnol.v39i4.30512

Lima, Jr., M. P., Biazzon, J. C., Araujo, V. A., Munis, R. A., Martins, J. C., Cortez-Barbosa, J., Gava, M., Valarelli, I. D., and Morales, E. A. M. (2018). “Mechanical properties evaluation of *Eucalyptus grandis *wood at three different heights by impulse excitation technique (IET),” *BioResources* 13(2), 3377-3385. DOI: 10.15376/biores.13.2.3377-3385

Mahapatra, K., Gustavsson, L., and Hemström, K. (2012). “Multi-storey wood-frame buildings in Germany, Sweden and the UK,” *Constr. Innovation* 12(1), 62-85. DOI: 10.1108/14714171211197508

Matos, G., and Molina, J. C. (2016). “Resistência da madeira ao cisalhamento paralelo às fibras segundo as normas ABNT NBR 7190:1997 e ISO 13910:2005 [Shear strength of wood in direction parallel to the grain according to the standards ABNT NBR 7190:1997 and ISO 13910:2005],” *Revista Matéria* 21(4), 1069-1079. DOI: 10.1590/S1517-707620160004.0098

Moreira, A. P., Silveira, E., Almeida, D. H., Almeida, T. H., Panzera, T. H., Christoforo, A. L., and Rocco, F. A. (2017). “Toughness and impact strength in dynamic bending of wood as a function of the modulus of elasticity and the strength in compression to the grain,” *Int. J. Mater. Eng.* 7(4), 61-67. DOI: 10.5923/j.ijme.20170704.01

Pries, M., and Mai, C. (2013). “Fire resistance of wood treated with a cationic silica sol,” *Eur. J. Wood Wood Prod.* 71(2), 237-244. DOI: 10.1007/s00107-013-0674-7

Ramage, M. H., Burridge, H., Busse-Wicher, M., Fereday, G., Reynolds, T., Shah, D. U., Wu, G., Yu, L., Fleming, P., Densley-Tingley, D., *et al.* (2017). “The wood from the tress: The use of timber in construction,” *Renew. Sust. Energy Rev.* 68, 333-359. DOI: 10.1016/j.rser.2016.09.107

Silva, C. E. G., Almeida, D. H., Almeida, T. H., Chahud, E., Branco, L. A. M. N., Campos, C. I., Lahr, F. A. R., and Christoforo, A. L. (2018). “Influence of the procurement site on physical and mechanical properties of Cupiúba wood species,” *BioResources* 13(2), 4118-4131. DOI: 10.15376/biores.13.2.4118-4131

Souza, A. M., Nascimento, M. F., Almeida, D. H., Lopes Silva, D. A., Almeida, T. H., Christoforo, A. L., and Lahr, F. A. R. (2018). “Wood-based composite made of wood waste and epoxy based ink-waste as adhesive: A cleaner production alternative,” *J. Clean. Prod.* 193, 549-562. DOI: 10.1016/j.jclepro.2018.05.087

Steege, H., Vaessen, R. W, Cárdenas-López, D., Sabatier, D., Antonelli, A., Oliveira, S. M., Pitman, N. C. A., Jørgensen, P. M., and Salomão, R. P. (2016). “The discovery of the Amazonian tree flora with an updated checklist of all known tree taxa,” *Sci. Rep.* 6(29549), 1-15. DOI: 10.1038/srep29549

Wang, L., Toppinen, A., and Juslin, H. (2014). “Use of wood in green building: A study of expert perspectives from the UK,” *J. Clean. Prod.* 65, 350-361. DOI: 10.1016/j.jclepro.2013.08.023

Wieruszewski, M., and Mazela, B. (2017). “Cross laminated timber (CLT) as an alternative form of construction wood,” *Drvna Ind.* 68(4), 359-367. DOI: 10.5552/drind.2017.1728

Żmijewki, T., and Wojtowicz-Jankowska, D. (2017). “Timber – Material of the future – Examples of small wooden architectural structures,” *IOP Conf. Ser.: Mater. Sci. Eng.* 245, 1-9. DOI: 10.1088/1757-899X/245/8/082019

Article submitted: December 18, 2019; Peer review completed: February 22, 2020; Revised version received and accepted: March 17, 2020; Published: March 23, 2020.

DOI: 10.15376/biores.15.2.3278-3288