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Effect of wood sample position on Calculation of flexural elastic modulus

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https://www.eduzhai.net International Journal of M aterials Engineering 2013, 3(3): 41-46 DOI: 10.5923/j.ijme.20130303.03 Influence of the Wood Specimen Position on Calculus of the Bending Modulus of Elasticity Felipe Hideyoshi Icimoto1, Fabiane Salles Ferro1, Diego Henrique de Almeida2, André Luis Christoforo3,*, Francisco Antonio Rocco Lahr2 1Department of Science and M aterial Engineering, Engineering School of São Carlos (EESC/USP), São Carlos, 13566-590, Brazil 2Department of Structural Engineering, Engineering School of São Carlos (EESC/USP), São Carlos, 13566-590, Brazil 3Department of M echanical Engineering, Federal University of São João del-Rei, São João del-Rei, 36307-352, Brazil Abstract For the anisotropy presented by wood, the established positions of the specimens in the bending test can significantly alter the properties of strength and stiffness. This study aimed to evaluate, with the aid of the Brazilian standard ABNT NBR 7190:1997, the influence of the wood specimens position to determine the bending modulus of elasticity. The wood species used in the trials (three point static bending) were Corymbia citriodora and Pinus elliottii, and used six specimens per species. Each piece gave rise to four experiments, performed with a non-destructive form, differentiated only by the position of the specimen in the bending test(sides: A - lowest; B; C; D - higher value), providing four va lues of elastic modulus per specimens. The experiments were considered non-destructive for the largest displacement value in trials does not exceed the measure L/200 (L-usable length of the specimen), ensuring physical and geometriclinearity fo r the woods tested, as established by the Brazilian standard. The results of analyses of variance showed statistical equivalency between the modulus of elasticity of both wood species, resulting in independence of the specimen position to determine the bending stiffness. Ho wever, by the orthotropic behaviour of wood, the results obtainedcannot be extrapolated to other woods of the same or different species, thereby justifying the change of the specimenposition in the bending test, allowing evaluate the equivalence or not between the modulus of elasticity. Keywords Bending, Stiffness, Wood Anisotropy 1. Introduction The wood is one of the oldest building materials, being used main ly because of its availability in nature, ease of handling, manufacturing and excellent weight/strength relatio n s h ip [1 -3 ]. The timber presented as a cellular material, produced by a continuous mechanism growth of p lants. There are several species of trees throughout the world, but with all co mmon features such as a cellu lar structure with an arrangement in the form of concentric rings, which ensures orthotropic mechanical properties of wood, directly related to its orientation relat ive to the main axis[4]. Chemical and mechanical propert ies can d iffer for the same species of wood acco rding to the locat ion o f their ext ract ion . Ot her paramet ers such as climate and so il cond it ions can affect th e g ro wth o f th e t ree, d irect ly influencing their properties. Moreover, factors such as the presence of node, opening cracks during drying and fiber * Corresponding author: alchristoforo@yahoo.com.br (André Luis Christoforo) Published online at https://www.eduzhai.net Copyright © 2013 Scientific & Academic Publishing. All Rights Reserved inclinations promote great variations in physical and mechanica l properties[5-7]. According to[1], the mechanical properties of wood are dependent on the density, percentage of juvenile wood, the width of the rings, the angle of the micro fibrils, the amount of extractives, moisture content, the intensity of insect attack, the type and location and number of nodes, among other factors, making it difficult to obtain all their elastic parameters to be used in structural projects[8, 9]. In order to enable the rational use of wood in structures, mechanical tests are performed to obtain the equivalent properties, obtained from experiments and calculation procedures of standardized normat ive docu ments, such as the ABNT NBR 7190[10]standard, widely used by engineers, architects and designers for material characterizat ion due to mechanical stresses and also for proper and safe design of structural ele ments. Among the mechanical p roperties of materials used in the design of a structure, highlights the modulus of elasticity (MOE), enabling the setting to provide displaced and deformations in structural components subjected to the action of the imposed loads (limit state). Be of g reat interest for the knowledge of the bending modulus of elasticity, allowing the design of wooden 42 Felipe Hideyoshi Icimoto et al.: Influence of the Wood Specimen Position on Calculus of the Bending M odulus of Elasticity structural elements subject to bending stresses, several studies have been conducted[11-18], in order to verify experimentally and numerically the influence of co mposition anatomical tissue timber (anisotropy) in physical, chemical and mechanical properties, as well as to characterize wood species not yet known. However, in bending tests, the positioning of the specimens can influence the results of elastic moduli, justified by the anisotropy of wood[19]. This study aimed to investigate the influence of using four different positions of wood specimens in bending tests to obtain the bending modulus of elasticity, enabling determine possible diffe rences between the stiffness values obtained. 2. Material and Methods The wood species used in this study were Corymbia citriodora (Strength Class C 40) and Pinus elliottii (Strength Class C30), being manufactured six specimens per type of timber for hold ing bending test[10], ext racted fro m different parts of a batch considered homogeneous, with mo isture content near 12%, as established by the Brazilian standard [10]. The specimens were manufactured with square cross section of 5.0cm and 115cm of length[10], and are free of defects. The dimensions of the sides of the specimens were performed with a calliper accurate to 0.1 mm. The three points static bending test (Figure 1)was the structural model used to determine the modulus of elasticity, conducted non-destructivelyby the high values of displacements in the trials are limited to L/200 measured[10], L being the distance between supports in the bending test. This ratio ensures physical and geometric linearityof the wood specimenstested. section respectively. MOE = 4 F ⋅δ ⋅ L3 ⋅b⋅ h3 (1) To check the statistical equivalence between the modulus of elasticity for the two species of wood, the analysis of variance (ANOVA)was used, performedby the software Minitab® version 14. 3. Results Tables 1 and 2 present the descriptive statistics concerning the bendingmodulus of elasticity (MOE-A; EOM B; EOM C;-D MOE) of Corymbia citriodora and Pinus elliottii wood species respectively, obtained fro m four different positions of the specimens in trials, Xm being the arithmet ic mean, SD standard deviation and CVthe coefficient of variation of the s amp les . Table 1. Modulus of elasticity of the Corymbia citriodora wood species S pecimen 1 2 3 4 5 6 Xm SD VC (%) S pecimen 1 2 3 4 5 6 Xm SD VC (%) MO E-A (MPa) 15504 13623 14283 16689 18704 16681 15914 1847 12 MO E-C (MPa) 15058 13165 12931 17053 18554 16772 15589 2261 15 MO E-B (MPa) 15593 12255 15634 16825 18504 16226 15840 2058 13 MO E-D (MPa) 15370 12293 12075 16962 18905 16817 15404 2737 18 Figure 1. Corymbia citriodora timber specimen in the bending test Each specimen was tested four t imes in bending, giv ing four values of modulus of elasticity (MOE) per specimen and per type of wood species used, only differentiated by the positions of the elements in the experiments(sides: A lowest; B; C; D - higher value). The modulus of elasticity of the wood pieces were obtained with the use of Equation 1, F being the value of the load responsible for the displace ment δ = L/200, L the effective length of the specimen and b and hmeasures concerning the width and height of the cross Table 2. Modulus of elast icity of Pinus elliottii wood species Specimen MO E-A (MPa) MO E-B (MPa) 1 13938 13672 2 12077 12283 3 14439 15805 4 13028 14394 5 13824 13870 6 13251 14508 Xm 13426 14089 SD 831 1157 VC (%) 6 8 Specimen MO E-C (MPa) MO E-D (MPa) 1 13850 13547 2 11940 12186 3 14530 15669 4 13073 14349 5 13687 13824 6 13565 14598 Xm 13440,8 14028,8 SD 873,8 1165,1 VC (%) 6,5 8,3 International Journal of M aterials Engineering 2013, 3(3): 41-46 43 Figures 2 and 3 illustrate respectively the normality plots of modulus of elasticity for the Corymbia citriodora and Pinus elliottiiwood species. Percent 99 95 90 80 70 60 50 40 30 20 10 5 1 12000130001400015000160001700018000190002000021000 MOE-A (MPa) Mean 15914 StDev 1847 N 6 AD 0,210 P-Value 0,747 (a) Percent 99 95 90 80 70 60 50 40 30 20 10 5 1 10000 12000 14000 16000 18000 20000 22000 MOE-B (MPa) Mean 15840 StDev 2058 N 6 AD 0,356 P-Value 0,320 (b) Percent 99 95 90 80 70 60 50 40 30 20 10 5 1 10000 12000 14000 16000 18000 20000 22000 MOE-C (MPa) Mean 15589 StDev 2261 N 6 AD 0,272 P-Value 0,527 (c) Percent 99 95 90 80 70 60 50 40 30 20 10 5 1 10000 12000 14000 16000 18000 20000 22000 MOE-D (MPa) Mean StDev N AD P-Value 15404 2737 6 0,324 0,395 (d) Figure 2. Normality plot for the bending modulus of elasticity of Corymbia citriodora wood species Percent 99 95 90 80 70 60 50 40 30 20 10 5 1 11000 12000 13000 14000 15000 MOE-A (MPa) (a) Mean 13426 StDev 831,3 N 6 AD 0,206 P-Value 0,761 Percent 99 95 90 80 70 60 5400 30 20 10 5 1 11000 12000 13000 14000 15000 16000 17000 MOE-B (MPa) Mean 14089 StDev 1157 N 6 AD 0,237 P-Value 0,640 (b) Percent 99 Mean 13441 95 StDev 873,8 90 N 6 80 AD 0,292 70 60 P-Value 0,482 50 40 30 20 10 5 1 11000 12000 13000 14000 15000 16000 MOE-C (MPa) (c) Percent 99 Mean 14029 95 StDev 1165 90 N 6 80 AD 0,185 70 60 P-Value 0,836 50 40 30 20 10 5 1 11000 12000 13000 14000 15000 16000 17000 MOE-D (MPa) (d) Figure 3. Normality plot for the bending modulus of elasticity of Pinus elliottii wood species The P-values of Anderson-Darling´s normality tests (Figure 2) of the modulus of elasticity for the Corymbiacitri odora and Pinus elliottii woods were both greater than 0.05, proving to be normal distribution of data[20]. 44 Felipe Hideyoshi Icimoto et al.: Influence of the Wood Specimen Position on Calculus of the Bending M odulus of Elasticity Table 3 shows the results of the ANOVA of the position factor for the specimento determine the modulus of elasticity (MOE-A; EOM B; EOM C; M OE-D). Table 3. P-values from the ANOVAfor the MOE P-value R2(Adj.) Corymbia citriodora 0,978 0,00% Pinus elliottii 0,531 0,00% Figure 4 shows the main effect p lots for the MOE. Mean Main Effects Plot for MOE (MPa) 15900 15800 15700 15600 15500 15400 A B C D Position (a) Mean Main Effects Plot for MOE (MPa) 14100 14000 13900 13800 13700 13600 13500 13400 A B C D Position (b) Figure 4. Main effects plot for the MOE ofCorymbia citriodora (a) and Pinus elliottii (b) wood species P-values obtained fro m ANOVA for the MOE of the two wood species being greater than 0.05[20], notes the equivalence between the values, indicating that the specimen position is not significant to determine the properties of stiffness evaluated. Percent 99 95 90 80 70 60 50 40 30 20 10 5 1 -2000 -1000 0 1000 2000 MOE (Pinus elliottii) Mean 0 StDev 950,0 N 24 AD 0,491 P-Value 0,199 Figure 6. Residuals plot of ANOVA on MOE of Pinus elliottii wood species Residual Versus Order (response is MOE (MPa)) 4000 3000 2000 1000 0 -1000 -2000 -3000 -4000 2 4 6 8 10 12 14 16 18 20 22 24 Observation Order (a) Residual 4000 3000 2000 1000 0 -1000 -2000 -3000 -4000 15400 Versus Fits (response is MOE (MPa)) 15500 15600 15700 15800 15900 Fitted Value (b) Figure 7. Independence (a) andhomogeneity (b) residuals of ANOVA on the MOE of Corymbia citriodora wood species Percent 99 Mean 0 95 StDev 2098 90 N 24 80 AD 0,379 70 60 P-Value 0,378 50 40 30 20 10 5 1 -5000 -2500 0 2500 5000 MOE (Corymbia citriodora) Figure 5. Residuals plot of ANOVA on MOE of Corymbia citriodora wood species Residual Versus Order (response is MOE (MPa)) 2000 1000 0 -1000 -2000 2 4 6 8 10 12 14 16 18 20 22 24 Observation Order (a) International Journal of M aterials Engineering 2013, 3(3): 41-46 45 Residual Versus Fits (response is MOE (MPa)) 2000 1000 0 -1000 -2000 13400 13500 13600 13700 13800 13900 14000 14100 Fitted Value (b) Figure 8. Independence (a) andhomogeneity (b) residuals of ANOVA on the MOE of Pinus elliottii wood species To validate the results of the ANOVA, it is necessary to ensure normality, independence and homogeneity of the residualsfor the MOE. Figures 5 and 6 shows the results of the normality tests of the residuals fro m ANOVA, and the independence and homogeneity present in Figures 7 and 8. The results obtained from the graphs of Figures 2-8 validate the ANOVA model, proving to be the equivalent the bendingmodulus of elasticity of the wood species in v es tig ated . 4. Conclusions The results of the analysis of variance revealedstatistical equivalencebetween the modulus of elasticity of the wood species, showing, for the specimens tested, not be significant the position of the specimen to determine the bending modulus of elasticity. As the wood an anisotropic material, the results obtained in this study cannot be extrapolated to the same or d ifferent wood species, imply ing the use of four diffe rent positions of the specimen in bending tests, enabling judge the equivalence or otherwise of elastic moduli obtained. REFERENCES madeira com laminados de carbono pré-esforçados. 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Holz als Roh - und 46 Felipe Hideyoshi Icimoto et al.: Influence of the Wood Specimen Position on Calculus of the Bending M odulus of Elasticity Werkstoff, v. 60, n. 5, p. 325-327, 2002. [18] Tonosaki, M .; Saito, S.; Hiramatsu, Y. Evaluation of non-homogeneity in wood by longitudinal and flexural vibration tests II. Distribution of vibrational properties and FEM simulation of sugi boxed heart square sawn timber. Journal of the Japan Wood Research Society, v. 47, n. 2, p. 92-96, 2001. [19] Icimoto, F. H.; Ferro, F. S.; Almeida, D. H.; Rocco Lahr, F. A. Influência das condições de ensaio nos valores do módulo de elasticidade da madeira na flexão estática. In: XX Congresso Brasileiro de Engenharia e Ciência dos M ateriais, 2012, Joinville, SC. Anais do XX CBECIM AT, 2012. v. único. p. 5362-5369. [20] M ontgomery, D. C. Design and analysis of experiments. John Wiley & Sons Inc., 6a edition, Arizona, 2005.

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