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Measurement of dynamic modulus of elasticity and damping ratio of wood-based composites using the cantilever beam vibration technique
Construction and Building Materials 28 (2012) 831–834
Contents lists available at SciVerse ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Technical Note
Measurement of dynamic modulus of elasticity and damping ratio of wood-based composites using the cantilever beam vibration technique Zheng Wang a,⇑, Ling Li a,b, Meng Gong b a b
College of Wood Science and Technology, Nanjing Forestry University, Nanjing, Jiangsu 210037, China Faculty of Forestry and Environmental Management, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
a r t i c l e
i n f o
Article history: Received 12 November 2010 Received in revised form 20 August 2011 Accepted 1 September 2011 Available online 21 November 2011 Keywords: M. Material property databases N. Non-destructive testing C. Composites
a b s t r a c t The non-destructive testing technique has been widely used to determine the dynamic mechanical properties of wood and wood-based composites, such as dynamic modulus of elasticity (Ed) and damping ratio (f). The cantilever beam vibration method is a cost-efficient and time-saving technique that was employed in this study to measure Ed and f values of three commercial wood-based composites, i.e. plywood (PLW), high density fiberboard (HDF), and oriented strand board (OSB). The Ed and f values were determined in light of the spectral analysis on the first natural frequency and the first and fifth amplitudes of vibration in the vertical direction, which was triggered by tapping one end of a specimen free of the support. To verify the values, the static bending tests were conducted. It was found that the Ed values of three kinds of wood composites tested were slightly higher than the static modulus of elasticity (Es). There existed a good linear agreement between Ed and Es. The f value of PLW was the largest among three composites, and the OSB showed the lowest f. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The vibration methods have been successfully used to estimate the physical and mechanical properties of wood and wood-based composites for several decades in scientific research and forest products industry [1–3]. In comparison to the conventional bending tests, the vibration methods are non-destructive, rapid, convenience of use and money-saving. Therefore, they have being used for grading structural lumbers and evaluating the quality of laminated materials for several decades [4–7]. Besides, another application of these vibration methods is to conduct an in situ assessment of wood/wood-based members in buildings [2,8,9]. To accurately estimate the mechanical and physical properties of individual wood-based composites using non-destructive vibration methods is therefore of great importance. Typical wood-based composites, such as plywood (PLW) and oriented strand board (OSB), are very commonly used in light wood frame construction, such as sheathing materials of shear walls. The dynamic properties of individual wood-based composites, such as dynamic modulus of elasticity (Ed) and damping ratio (f), need to be well understood. The cantilever beam vibration (CBV) technique is one of nondestructive methods, which can figure out Ed and f by measuring the first natural frequency and amplitudes at different cycles of a ⇑ Corresponding author. Tel./fax: +86 025 85427653 (O). E-mail addresses: [email protected] (Z. Wang), [email protected] (L. Li), [email protected] (M. Gong). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.09.001
material [10]. Ed is defined as the ratio of stress to strain for a material under dynamic loading conditions, which is used to judge if a material is stiff enough for structural uses. Besides, Ed has been used for control quality purpose in production of wood-based composites. f of a material is used to evaluate the capability of absorbing vibration energy, which can be used to reflect resistance to dynamic loading. The higher f value a material has, the smaller vibration amplitude a material has, and the less appreciable energy loss is. Pellerin [11] and Perstorper [12] studied the correlation between Ed and Es with an aim at verifying the accuracy of vibration methods. Turk et al. [10] discovered that the CBV technique was a preferred approach to obtain the vibration characteristics of small size specimens. Machek et al. [13] showed that the evaluation of Ed via the CBV technique could partially fulfill the demand for a fast and reliable examination on scots pine (Pinus sylvestris) attacked by fungi at the early stage. Naghipour et al. [14] measured the f values of five kinds of three-layer glued laminated lumber beams reinforced using three lay-ups of glass-reinforced-polymer (GRP) sheets. These GRP sheets were arranged in beams with different thickness, orientation, and location. The species used was the group of spruce–pine–fir lumber. The logarithmic decrement analysis technique was used to determine the f value via the frequency response function. Their results showed that the average f values of the reinforced beams were close to or about 12% higher than that of those beams without GRP reinforcement. The largest average f value of the GRP reinforced beams was about 0.07.
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Z. Wang et al. / Construction and Building Materials 28 (2012) 831–834
This study was aimed at employing the cantilever beam vibration technique to measure Ed and f values of three commercial wood-based composites, i.e. PLW, high density fiberboard (HDF), and OSB. The relationship between Ed and Es of the composites tested was established as well.
2. Materials and methods Fig. 2. Schematic of the first natural frequency spectrum of an OSB specimen. 2.1. Materials Three types of test materials of No. 1 grade (i.e. the highest grade) were purchased from the market, PLW, HDF, and OSB. The density values of PLW, HDF and OSB were about 860, 740 and 550 kg/m3, respectively. Six specimens were cut from PLW along the parallel-to-grain direction (surface layer), the dimensions of which were 310 mm in length (l) 52 mm in width (b) 28 mm in height (h). As for HDF and OSB, six replicates were randomly cut from each composite panel. The thicknesses of HDF and OSB were 17 mm and 14 mm, respectively. The length and width of each HDF or OSB specimen were the same as PLW. All the specimens were conditioned at least 2 weeks prior to testing in a chamber of a temperature of 20 ± 2 °C and relative humidity of 65 ± 2%.
2.2. Testing An experimental device was developed to hold one end of a specimen and free the other end. A cantilever beam specimen was used to perform dynamic tests, Fig. 1. The frequency spectrum of each specimen was triggered using a rubber hammer to tap the free end and received by a laser displacement transducer placed under the free end of the bottom side, Fig. 2. A commercial data acquisition system was employed to capture and analyze the spectrum. To verify the accuracy and reliability of Ed values, static cantilever bending tests were also performed using the same setup as the dynamic tests, Fig. 1. A series of dead weights were applied onto the free end of a cantilever beam specimen, at the bottom of which the corresponding deflections were measured via a dial gauge of an accuracy of 0.001 mm. The load–deflection curve of each specimen tested was thereafter plotted, the slope of which was used to calculate Es.
2.3. Calculation of dynamic modulus of elasticity (Ed), damping ratio (f), and static modulus of elasticity (Es) The Ed is calculated using Eq. (1) [15], 3
Ed ¼ 16p2 ½M þ ð33=140Þml f12 =bh
3
ð1Þ
where M is the acceleration mass (g) having a value of 29 g in this study; m is the mass (g) of a specimen; and f1 (Hz) is the first natural frequency measured from the spectrum (Fig. 2) by locating the first peak value in a vibration test; l, b and h are the length, width and height of a specimen, respectively. The f is determined in Eq. (2), in which the logarithmic decrement analysis technique is used [15]. The effects of shear force and rotary motion of a specimen are ignored in this study.
f ¼ lnðA1 =A5 Þ=10p
ð2Þ
where A1 and A5 (mm/s2) are the first and fifth acceleration amplitude values, Fig. 3. The Es is calculated using Eq. (3) [15], 3
3
Es ¼ ðDP=DdÞ ð4l =bh Þ
ð3Þ
where DP/Dd is the slope of a load versus deflection curve within the linear elastic region, which is calculated using the linear regression method.
Fig. 3. Acceleration amplitude response of a free vibration test on an OSB specimen.
3. Results and discussion 3.1. Dynamic modulus of elasticity (Ed) and damping ratio (f) The mean values and standard deviation (SD) of the first natural frequency and the first and fifth amplitudes of PLW, HDF, and OSB specimens are given in Table 1. The mean values and SD of Ed and f of three types of specimens are also given in Table 1. The average Ed of OSB shows the highest Ed value, which is higher by 230% and 237% than that of PLW and HDF, respectively. This could be mainly due to its uniquely oriented arrangement of wood strands. The f values of three wood-based composites are different, which is dependent on the structure and dimensions of each composite. The results show that the f value of OSB is 0.013, the smallest value among three kinds of composites tested. This suggests that OSB could not be, in comparison to PLW and HDF, a good damping material absorbing impact or vibration energy. It seems that a higher density material has a higher f value. 3.2. Relationship between dynamic (Ed) and static modulus of elasticity (Es) The Es is calculated using Eq. (3); Fig. 4 illustrates the mean values and 3 SD of Ed and Es of three kinds of wood-based
Fig. 1. Schematic of an experimental setup for cantilever beam vibration testing.
833
Z. Wang et al. / Construction and Building Materials 28 (2012) 831–834 Table 1 Mean values and SD of parameters measured. Material
f1 (Hz)
A1 (mm/s2)
A5 (mm/s2)
Ed (MPa)
f
PLW
Mean SD
61.72 (0.31)
39.10 (0.72)
18.88 (1.4)
1942.37 (18.93)
0.023 (1.8E3)
HDF
Mean SD
37.11 (0.07)
29.66 (0.59)
15.26 (1.30)
1890.83 (7.23)
0.021 (2.7E3)
OSB
Mean SD
48.44 (0.12)
103.66 (2.69)
70.00 (5.05)
4482.54 (22.89)
0.013 (1.9E3)
Note: The sampling size for each material was six (6).
Fig. 4. Mean ± 3 SD of Ed and Es of wood-based composites.
Fig. 6. Coefficient of variation of Ed and Es of wood-based composites tested.
composites. It can be found that the Ed values are slightly larger than the Es values, which is independent of the type of a composite. The percentage difference between Ed and Es is 3.83%, 6.21%, and 9.86% for PLW, HDF, and OSB, respectively. This difference might be attributed to the structure and density of a composite panel. It seems that such a difference increases with a decrease in density and thickness of a composite panel. Fig. 5 illustrates a good linear correlation (R2 = 0.97) between Ed and Es among three kinds of wood-based composites studied. The coefficient of variation (COV) values of Ed and Es of PLW, HDF, and OSB are plotted in Fig. 6. It can be discovered that the COV values of Ed are larger than those of Es among three kinds of
wood-based composites. Especially, the PLW produces the largest COV of Ed, reaching 2.24%. The reason is not clear. However, such a COV value is very small in comparison with solid wood that could be as high as about 20%. This further demonstrates that the woodbased composites exhibit a more uniform structure than solid wood. 4. Conclusions Based on the above results and discussion, it verified the cantilever-beam vibration technique is a reliable approach providing a quick non-destructive measurement of dynamic modulus of elasticity and damping ratio of wood-based composites. It could be concluded as well: (1) the Ed values of plywood (PLW), high density fiberboard (HDF), and oriented strand board (OSB) were slightly higher than the Es values; (2) there was a good linear correlation between Ed and Es among three wood-based composites tested; (3) the variation of Ed was larger than that of Es; and (4) OSB showed the lowest f value and PLW had the highest value. Acknowledgment This study was funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). References
Fig. 5. Ed versus Es of wood-based composites tested.
[1] Moslemi AA. Dynamic viscoelasticity in hardboard. Forest Prod J 1967;17(1):25–33. [2] Ross RJ, Pellerin RF. Nondestructive testing for assessing wood members in structures: a review. USDA Forest service Forest Products Laboratory, General tech. rep. FPL-GTR-70; 1994. [3] Ilic J. Dynamic MOE of 55 species using small wood beams. Holz Roh Werkst 2003;61(3):167–72.
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Z. Wang et al. / Construction and Building Materials 28 (2012) 831–834
[4] Bell ER, Peck EC, Krueger NT. Young’s modulus of wood determined by a dynamic method. Report 1775. Madison, (WI): US Department of Agriculture, Forest Service, Forest Products Laboratory; 1950. [5] Senft JF, Suddarth SK, Angleton HD. A new approach to stress grading of lumber. Forest Prod J 1962;12(4):183–6. [6] Ross RJ, Bradshaw BK, Pellerin RF. Nondestructive evaluation of wood. Forest Prod J 1998;48(1):14–9. [7] Green DW, Gorman TM, Evans JW, Murphy JF. Improved grading system for structural logs for log homes. Forest Prod J 2004;54(9):52–62. [8] Soltis LA, Wang X, Ross RJ, Hunt MO. Vibration testing of timber floor systems. Forest Prod J 2002;52(10):75–81. [9] Wang X, Ross RJ, Hunt MO, Erickson JR. Low frequency vibration approach for assessing performance of wood floor systems. Wood Fiber Sci 2005;37(3): 371–8. [10] Turk C, Hunt JF, Marr DJ. Cantilever-beam dynamic modulus for wood composite products: part 1 apparatus. Research note FPL-RN-0308. Madison,
[11] [12]
[13]
[14]
[15]
WI: US Department of Agriculture, Forest Service, Forest Products Laboratory; 2008. Pellerin RF. A vibrational approach to nondestructive testing of structural lumber. Forest Prod J 1965;15(3):93–101. Perstorper M. Dynamic modal tests of timber evaluation according to Euler and Timoshenko theory. In: Quality of structural timber: end–user requirements and performance control; 1994. p. IIb-1–21. Machek L, Militz H, Gard W. Use of modulus of rupture and modulus of elasticity in natural durability testing. International Research Group on Wood Preservation; 2004 [document IRG/WP/97-20117]. Naghipour M, Taheri F, Zou GP. Evaluation of vibration damping of glassreinforced–polymer-reinforced glulam composite beams. J Struct Eng 2005;131:1044–51. Zhao JJ. Theory of mechanics (part II). Beijing: Higher Education Press, Harbin Industry University; 1982.
Contents lists available at SciVerse ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Technical Note
Measurement of dynamic modulus of elasticity and damping ratio of wood-based composites using the cantilever beam vibration technique Zheng Wang a,⇑, Ling Li a,b, Meng Gong b a b
College of Wood Science and Technology, Nanjing Forestry University, Nanjing, Jiangsu 210037, China Faculty of Forestry and Environmental Management, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
a r t i c l e
i n f o
Article history: Received 12 November 2010 Received in revised form 20 August 2011 Accepted 1 September 2011 Available online 21 November 2011 Keywords: M. Material property databases N. Non-destructive testing C. Composites
a b s t r a c t The non-destructive testing technique has been widely used to determine the dynamic mechanical properties of wood and wood-based composites, such as dynamic modulus of elasticity (Ed) and damping ratio (f). The cantilever beam vibration method is a cost-efficient and time-saving technique that was employed in this study to measure Ed and f values of three commercial wood-based composites, i.e. plywood (PLW), high density fiberboard (HDF), and oriented strand board (OSB). The Ed and f values were determined in light of the spectral analysis on the first natural frequency and the first and fifth amplitudes of vibration in the vertical direction, which was triggered by tapping one end of a specimen free of the support. To verify the values, the static bending tests were conducted. It was found that the Ed values of three kinds of wood composites tested were slightly higher than the static modulus of elasticity (Es). There existed a good linear agreement between Ed and Es. The f value of PLW was the largest among three composites, and the OSB showed the lowest f. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The vibration methods have been successfully used to estimate the physical and mechanical properties of wood and wood-based composites for several decades in scientific research and forest products industry [1–3]. In comparison to the conventional bending tests, the vibration methods are non-destructive, rapid, convenience of use and money-saving. Therefore, they have being used for grading structural lumbers and evaluating the quality of laminated materials for several decades [4–7]. Besides, another application of these vibration methods is to conduct an in situ assessment of wood/wood-based members in buildings [2,8,9]. To accurately estimate the mechanical and physical properties of individual wood-based composites using non-destructive vibration methods is therefore of great importance. Typical wood-based composites, such as plywood (PLW) and oriented strand board (OSB), are very commonly used in light wood frame construction, such as sheathing materials of shear walls. The dynamic properties of individual wood-based composites, such as dynamic modulus of elasticity (Ed) and damping ratio (f), need to be well understood. The cantilever beam vibration (CBV) technique is one of nondestructive methods, which can figure out Ed and f by measuring the first natural frequency and amplitudes at different cycles of a ⇑ Corresponding author. Tel./fax: +86 025 85427653 (O). E-mail addresses: [email protected] (Z. Wang), [email protected] (L. Li), [email protected] (M. Gong). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.09.001
material [10]. Ed is defined as the ratio of stress to strain for a material under dynamic loading conditions, which is used to judge if a material is stiff enough for structural uses. Besides, Ed has been used for control quality purpose in production of wood-based composites. f of a material is used to evaluate the capability of absorbing vibration energy, which can be used to reflect resistance to dynamic loading. The higher f value a material has, the smaller vibration amplitude a material has, and the less appreciable energy loss is. Pellerin [11] and Perstorper [12] studied the correlation between Ed and Es with an aim at verifying the accuracy of vibration methods. Turk et al. [10] discovered that the CBV technique was a preferred approach to obtain the vibration characteristics of small size specimens. Machek et al. [13] showed that the evaluation of Ed via the CBV technique could partially fulfill the demand for a fast and reliable examination on scots pine (Pinus sylvestris) attacked by fungi at the early stage. Naghipour et al. [14] measured the f values of five kinds of three-layer glued laminated lumber beams reinforced using three lay-ups of glass-reinforced-polymer (GRP) sheets. These GRP sheets were arranged in beams with different thickness, orientation, and location. The species used was the group of spruce–pine–fir lumber. The logarithmic decrement analysis technique was used to determine the f value via the frequency response function. Their results showed that the average f values of the reinforced beams were close to or about 12% higher than that of those beams without GRP reinforcement. The largest average f value of the GRP reinforced beams was about 0.07.
832
Z. Wang et al. / Construction and Building Materials 28 (2012) 831–834
This study was aimed at employing the cantilever beam vibration technique to measure Ed and f values of three commercial wood-based composites, i.e. PLW, high density fiberboard (HDF), and OSB. The relationship between Ed and Es of the composites tested was established as well.
2. Materials and methods Fig. 2. Schematic of the first natural frequency spectrum of an OSB specimen. 2.1. Materials Three types of test materials of No. 1 grade (i.e. the highest grade) were purchased from the market, PLW, HDF, and OSB. The density values of PLW, HDF and OSB were about 860, 740 and 550 kg/m3, respectively. Six specimens were cut from PLW along the parallel-to-grain direction (surface layer), the dimensions of which were 310 mm in length (l) 52 mm in width (b) 28 mm in height (h). As for HDF and OSB, six replicates were randomly cut from each composite panel. The thicknesses of HDF and OSB were 17 mm and 14 mm, respectively. The length and width of each HDF or OSB specimen were the same as PLW. All the specimens were conditioned at least 2 weeks prior to testing in a chamber of a temperature of 20 ± 2 °C and relative humidity of 65 ± 2%.
2.2. Testing An experimental device was developed to hold one end of a specimen and free the other end. A cantilever beam specimen was used to perform dynamic tests, Fig. 1. The frequency spectrum of each specimen was triggered using a rubber hammer to tap the free end and received by a laser displacement transducer placed under the free end of the bottom side, Fig. 2. A commercial data acquisition system was employed to capture and analyze the spectrum. To verify the accuracy and reliability of Ed values, static cantilever bending tests were also performed using the same setup as the dynamic tests, Fig. 1. A series of dead weights were applied onto the free end of a cantilever beam specimen, at the bottom of which the corresponding deflections were measured via a dial gauge of an accuracy of 0.001 mm. The load–deflection curve of each specimen tested was thereafter plotted, the slope of which was used to calculate Es.
2.3. Calculation of dynamic modulus of elasticity (Ed), damping ratio (f), and static modulus of elasticity (Es) The Ed is calculated using Eq. (1) [15], 3
Ed ¼ 16p2 ½M þ ð33=140Þml f12 =bh
3
ð1Þ
where M is the acceleration mass (g) having a value of 29 g in this study; m is the mass (g) of a specimen; and f1 (Hz) is the first natural frequency measured from the spectrum (Fig. 2) by locating the first peak value in a vibration test; l, b and h are the length, width and height of a specimen, respectively. The f is determined in Eq. (2), in which the logarithmic decrement analysis technique is used [15]. The effects of shear force and rotary motion of a specimen are ignored in this study.
f ¼ lnðA1 =A5 Þ=10p
ð2Þ
where A1 and A5 (mm/s2) are the first and fifth acceleration amplitude values, Fig. 3. The Es is calculated using Eq. (3) [15], 3
3
Es ¼ ðDP=DdÞ ð4l =bh Þ
ð3Þ
where DP/Dd is the slope of a load versus deflection curve within the linear elastic region, which is calculated using the linear regression method.
Fig. 3. Acceleration amplitude response of a free vibration test on an OSB specimen.
3. Results and discussion 3.1. Dynamic modulus of elasticity (Ed) and damping ratio (f) The mean values and standard deviation (SD) of the first natural frequency and the first and fifth amplitudes of PLW, HDF, and OSB specimens are given in Table 1. The mean values and SD of Ed and f of three types of specimens are also given in Table 1. The average Ed of OSB shows the highest Ed value, which is higher by 230% and 237% than that of PLW and HDF, respectively. This could be mainly due to its uniquely oriented arrangement of wood strands. The f values of three wood-based composites are different, which is dependent on the structure and dimensions of each composite. The results show that the f value of OSB is 0.013, the smallest value among three kinds of composites tested. This suggests that OSB could not be, in comparison to PLW and HDF, a good damping material absorbing impact or vibration energy. It seems that a higher density material has a higher f value. 3.2. Relationship between dynamic (Ed) and static modulus of elasticity (Es) The Es is calculated using Eq. (3); Fig. 4 illustrates the mean values and 3 SD of Ed and Es of three kinds of wood-based
Fig. 1. Schematic of an experimental setup for cantilever beam vibration testing.
833
Z. Wang et al. / Construction and Building Materials 28 (2012) 831–834 Table 1 Mean values and SD of parameters measured. Material
f1 (Hz)
A1 (mm/s2)
A5 (mm/s2)
Ed (MPa)
f
PLW
Mean SD
61.72 (0.31)
39.10 (0.72)
18.88 (1.4)
1942.37 (18.93)
0.023 (1.8E3)
HDF
Mean SD
37.11 (0.07)
29.66 (0.59)
15.26 (1.30)
1890.83 (7.23)
0.021 (2.7E3)
OSB
Mean SD
48.44 (0.12)
103.66 (2.69)
70.00 (5.05)
4482.54 (22.89)
0.013 (1.9E3)
Note: The sampling size for each material was six (6).
Fig. 4. Mean ± 3 SD of Ed and Es of wood-based composites.
Fig. 6. Coefficient of variation of Ed and Es of wood-based composites tested.
composites. It can be found that the Ed values are slightly larger than the Es values, which is independent of the type of a composite. The percentage difference between Ed and Es is 3.83%, 6.21%, and 9.86% for PLW, HDF, and OSB, respectively. This difference might be attributed to the structure and density of a composite panel. It seems that such a difference increases with a decrease in density and thickness of a composite panel. Fig. 5 illustrates a good linear correlation (R2 = 0.97) between Ed and Es among three kinds of wood-based composites studied. The coefficient of variation (COV) values of Ed and Es of PLW, HDF, and OSB are plotted in Fig. 6. It can be discovered that the COV values of Ed are larger than those of Es among three kinds of
wood-based composites. Especially, the PLW produces the largest COV of Ed, reaching 2.24%. The reason is not clear. However, such a COV value is very small in comparison with solid wood that could be as high as about 20%. This further demonstrates that the woodbased composites exhibit a more uniform structure than solid wood. 4. Conclusions Based on the above results and discussion, it verified the cantilever-beam vibration technique is a reliable approach providing a quick non-destructive measurement of dynamic modulus of elasticity and damping ratio of wood-based composites. It could be concluded as well: (1) the Ed values of plywood (PLW), high density fiberboard (HDF), and oriented strand board (OSB) were slightly higher than the Es values; (2) there was a good linear correlation between Ed and Es among three wood-based composites tested; (3) the variation of Ed was larger than that of Es; and (4) OSB showed the lowest f value and PLW had the highest value. Acknowledgment This study was funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). References
Fig. 5. Ed versus Es of wood-based composites tested.
[1] Moslemi AA. Dynamic viscoelasticity in hardboard. Forest Prod J 1967;17(1):25–33. [2] Ross RJ, Pellerin RF. Nondestructive testing for assessing wood members in structures: a review. USDA Forest service Forest Products Laboratory, General tech. rep. FPL-GTR-70; 1994. [3] Ilic J. Dynamic MOE of 55 species using small wood beams. Holz Roh Werkst 2003;61(3):167–72.
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Z. Wang et al. / Construction and Building Materials 28 (2012) 831–834
[4] Bell ER, Peck EC, Krueger NT. Young’s modulus of wood determined by a dynamic method. Report 1775. Madison, (WI): US Department of Agriculture, Forest Service, Forest Products Laboratory; 1950. [5] Senft JF, Suddarth SK, Angleton HD. A new approach to stress grading of lumber. Forest Prod J 1962;12(4):183–6. [6] Ross RJ, Bradshaw BK, Pellerin RF. Nondestructive evaluation of wood. Forest Prod J 1998;48(1):14–9. [7] Green DW, Gorman TM, Evans JW, Murphy JF. Improved grading system for structural logs for log homes. Forest Prod J 2004;54(9):52–62. [8] Soltis LA, Wang X, Ross RJ, Hunt MO. Vibration testing of timber floor systems. Forest Prod J 2002;52(10):75–81. [9] Wang X, Ross RJ, Hunt MO, Erickson JR. Low frequency vibration approach for assessing performance of wood floor systems. Wood Fiber Sci 2005;37(3): 371–8. [10] Turk C, Hunt JF, Marr DJ. Cantilever-beam dynamic modulus for wood composite products: part 1 apparatus. Research note FPL-RN-0308. Madison,
[11] [12]
[13]
[14]
[15]
WI: US Department of Agriculture, Forest Service, Forest Products Laboratory; 2008. Pellerin RF. A vibrational approach to nondestructive testing of structural lumber. Forest Prod J 1965;15(3):93–101. Perstorper M. Dynamic modal tests of timber evaluation according to Euler and Timoshenko theory. In: Quality of structural timber: end–user requirements and performance control; 1994. p. IIb-1–21. Machek L, Militz H, Gard W. Use of modulus of rupture and modulus of elasticity in natural durability testing. International Research Group on Wood Preservation; 2004 [document IRG/WP/97-20117]. Naghipour M, Taheri F, Zou GP. Evaluation of vibration damping of glassreinforced–polymer-reinforced glulam composite beams. J Struct Eng 2005;131:1044–51. Zhao JJ. Theory of mechanics (part II). Beijing: Higher Education Press, Harbin Industry University; 1982.