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Elastic constants evaluated from plate tests compared to previous bending tests.

Abstract

Many different test methods have been used to evaluate the elastic constants and elastic constant ratios of solid sawn lumber and structural composite lumber (SCL). Previous work has noted that the elastic constant ratios of solid sawn lumber and SCL are different. The solid-sawn lumber values were measured by plate tests and bending tests, while the SCL values were measured only by bending tests. No direct comparison of solid-sawn lumber and SCL results from plate tests and bending tests has been performed. This study conducted plate bending and plate twisting tests to determine the longitudinal modulus of elasticity and in-plane shear modulus of machine stress rated (MSR) lumber and parallel strand lumber (PSL) materials. Samples were taken from the same material previously tested by Hindman et al. (2006). The E:G ratios from MSR plate testing were 40 percent less than values from ASTM D198 Bending and the five point bending test (FPBT), while the E:G ratios from PSL plate testing showed no consistent trend. Statistical comparisons of the E and G values found that the MSR E values for all three tests and the PSL G values from plate testing and ASTM D198 Bending were not significantly different. The stress distribution associated with the plate and bending tests seems to affect the shear modulus values measured. Therefore, elastic constant ratios derived from plate testing methods for MSR lumber and PSL are not directly comparable to elastic constant ratios derived from structural sized bending tests.

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Previous researchers have found differences in the elastic constants and elastic constant ratios of structural size solid-sawn lumber and structural composite lumber (SCL) materials using a variety of bending and torsion test methods. These test methods have been compared to an elastic constant ratio of 16:1 found in the Wood Handbook (USDA Forest Serv. 1999) and Bodig and Jayne (1982). This ratio is an average of many different wood species tested using plate bending and twisting tests (Bodig and Goodman 1973). Plate bending and twisting tests were performed on clear sections of wood laminated together to achieve different directional orientations (Bodig and Goodman 1973). Recent studies to evaluate the shear modulus of solid-sawn lumber and SCL materials have focused on structural sized lumber only. There has been little evidence in the research literature of the elastic constant differences from smaller-sized test methods (such as plate bending and twisting tests) and structural sized lumber testing.

Table 1 shows the modulus of elasticity (MOE) and shear modulus values determined from different studies for solid wood, solid-sawn lumber and parallel strand lumber (PSL). Bodig and Goodman (1973) performed plate bending and plate twisting tests on an extensive number of softwood and hardwood specimens. These test results are summarized by Bodig and Jayne (1982) and in the Wood Handbook. Hindman et al. (2006) compared results from ASTM D198 Bending (ASTM 2005a) and five point bending test (FPBT) to determine the elastic constants of MSR lumber and SCLs and to compare the test methods. Harrison and Hindman (2007) compared the ASTM D198 Bending, ASTM D198 Torsion (ASTM 2005a) and the FPBT for MSR lumber and LVL. Trends from both of these papers (Hindman et al. (2006) and Harrison and Hindman (2007)) demonstrated that there is no consistent pattern of equivalency between the elastic constants and elastic constant ratios measured using different test methods.

The results in Table 1 demonstrate differences between the results from plate tests and bending tests. The different species tested by Bodig and Goodman (1973) represent three of the four species that compose the southern pine species group. Examining the range of values from Bodig and Goodman (1973), the MOE values range from 11.1 to 16.0 GPa, while the shear modulus values range from 0.88 to 1.04 GPa. Examining the MSR materials, MOE values from Hindman et al. (2006) were greater than the Bodig and Goodman (1973) range, while the corresponding shear modulus values were less than the Bodig and Goodman (1973) range. The MOE values from Harrison and Hindman (2007) were greater than the Bodig and Goodman (1973) range, while the corresponding shear modulus values fall into the Bodig and Goodman (1973) range. The MOE and shear modulus from PSL (composed of southern pine species group parent material) were both within the range of the Bodig and Goodman (1973) results. The discrepancy between the elastic constant values from Hindman et al. (2006) and Harrison and Hindman (2007) in comparison to the Bodig and Goodman (1973) values calls into question the test methods used to measure the elastic constants. Therefore, the purpose of this paper is to measure the elastic and shear modulus of MSR lumber and PSL materials from a subset of material from Hindman et al. (2006) using plate bending and ASTM D3044 plate twisting test (ASTM 2005b) for comparison to previous testing results of ASTM D198 Bending and FPBT from Hindman et al. (2006).

Materials and methods

MSR and PSI. materials used for this testing were taken from an untested subset of the material used by Hindman et al. (2006). MSR lumber was southern pine (Pinus spp.) 2250f-1.9E with a MOE of 13.1 GPa (1.90 x [10.sup.6] psi). PSL was 2.0E rated southern pine (Pinus spp.) with a MOE of 13.8 GPa (2.0 x [10.sup.6] psi). Specimens were cut to 40.6 cm long by 20.3 cm wide by 8.89 mm high (16.0 in by 8.0 in by 0.35 in) for the plate bending test. Ten specimens from each material were tested. After the plate bending test was completed, the specimens were cut in half to a size of 20.3 cm long by 20.3 cm wide by 8.89 mm high (8.0 in by 8.0 in by 0.35 in) for ASTM D3044 plate twisting test (ASTM 2005b). All specimens were labeled and stored in an environmental chamber at 20 degrees C and 65 percent relative humidity. After plate twisting testing was completed, MC and SG samples were measured according to ASTM D2395 (ASTM 2005c) and ASTM D4442 (ASTM 2005d). Table 2 summarizes the rated MOE as well as the resultant moisture content (MC) and specific gravity (SG). Materials tested by Hindman et al. (2006) had a SG of 0.56 for MSR and 0.66 for PSL, demonstrating that these materials are similar to those previously tested.

Plate bending test

The determination of orthotropic elastic constants using plate bending and plate twisting methods was originally developed by Witt et al. (1953). The plate bending test uses a three-point loading on the top of the plate and a three-point support on the bottom of the plate placed in an anti-symmetric pattern. Figure 1 shows a schematic drawing of the plate bending samples indicating the position of the loading, support and deflection measurement points. This configuration allows the plate to have a constant bending moment in the center and no bending moment at the three supports. Due to the large difference in stiffness between the parallel to the grain direction and perpendicular to the grain direction, a correction factor must be applied using an alternative beam theory (Gunnerson et al. 1972).

Figure 2 shows a plate bending specimen being tested. The loading speed was set to 0.0762 cm/min (0.03 in/min). Two TransTek 351-0000 linear variable differential transformers (LVDT) (range of 5.08 mm (0.20 in) and sensitivity of 0.0091 mm (0.0025 in)) were used to measure the displacement at the point A and B under elastic range for the calculation of elastic modulus of plate.

Equation [1] shows the calculation of the MOE. The load P is the total load applied to the plate. The deflection [DELTA] is equal to the deflection at B minus one-half of the deflection at A. The length L is the span of the plate, or 29.20 cm (11.45 in).

E = (P/[DELTA])(11[L.sup.3] / 768I) [1]

where:

P/[DELTA] = load-deflection curve

L = span length of plate

I = moment of inertia = width x [height.sup.3]/12.

ASTM D3044 plate twisting

Plate twisting test procedures are detailed in ASTM D3044 (ASTM 2005b). Figure 3 shows the anticlastic plate twisting, where two diagonal comers of a square plate are supported and the other two diagonal comers are loaded. To avoid edge damage from the concentrated loads at each comer, small metal plates were clamped to the top and bottom of each comer. An MTS test machine applied a displacement rate of 0.0762 cm/min (0.03 in/min) to the specimen. Deflection was taken as the difference of the movement between the two diagonals as described in ASTM 3044 (ASTM 2005b). Deflection was measured using an LVDT (range of 5.08 mm (0.20 in) and sensitivity of 0.0091 mm (0.0025 in)) attached to a metal jig to measure the difference between the diagonal deflections. Equation [2] shows the calculation of the shear modulus.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

G = (P/[DELTA])(1.5[u.sup.2] / [h.sup.3]) [2]

where:

p/[DELTA] = load-deflection curve

u = distance from the center of plate to the point where the deflection was measured

h = thickness of plate.

Load and deflection information were collected using the TEST WORK 3.09 software for both plate bending and plate twisting test methods. All test data were exported to Microsoft[R] Excel[R] to plot the load-deflection (P/[DELTA]) curve. Three loading repetitions were applied to each specimen and the load-deflection curves were averaged. To ensure all loads were within the elastic range of the specimens, several plywood specimens of similar stiffness were tested to define the maximum loading. For the plate bending test, the maximum load and deflection of crosshead were limited to 444.8 N (100 1b) and 0.254 cm (0.1 in), respectively. For the plate twisting test, the maximum load and deflection of crosshead were limited to 44.4 N (10 lb) and 0.254 cm (0.1 in), respectively.

[FIGURE 3 OMITTED]

Once the elastic modulus and shear modulus values for MSR and PSL were obtained using plate tests, the analysis of variance (ANOVA) single factor comparison with an alpha of 0.05 was used for statistical comparison with the previous results from Hindman et al. (2006). The ANOVA null hypothesis was that all means tested were equal. Comparisons between the plate bending and FPBT results, plate testing and ASTM D198 Bending results, as well as the ASTM D3044 plate twisting and FPBT and ASTM D198 Bending were conducted.

Results and discussion

Plate bending and ASTM D3044 plate twisting results

Table 3 summarizes the MOE and shear modulus values including coefficient of variation (COV) from the plate bending and ASTM D3044 plate twisting tests. The MOE of PSL was higher than that of MSR while the shear modulus of PSL was much lower than that of MSR. The average MOE values for both materials were greater than the rated values from Table 2. The average E:G ratio for MSR was 12.9:1.0, while the average E:G ratio for PSL was 17.8:1.0.

The MOE COV values of MSR and PSL were 18.8 percent and 11.48 percent, respectively, while the shear modulus COV values for MSR and PSL were 11.34 percent and 7.58 percent, respectively. Previous results from Hindman et al. (2006) and Harrison and Hindman (2007) had MOE COV values almost uniformly lower than the shear modulus COV values, which may have resulted from the use of bending tests that contained more bending deflection than shear deflection. The use of the plate testing methods decouples the MOE and shear modulus values. The plate twisting test seemed to be an easier test to conduct, which is further demonstrated by the lower variation in the shear modulus.

Comparison of MSR lumber with previous plate testing results

Table 4 shows the comparison of selected southern pine species test results from Bodig and Goodman (1973) with the results from this study. The elastic constants of longleaf pine (P. palustris) had a MOE 0.68 percent less than the average MSR value and a shear modulus 7.96 percent less than the average MSR value. The [E.sub.1] : [G.sub.12] ratio for three southern pine groups varied from 12.3:1.0 to 18.1:1.0, with the plate testing E:G ratio falling in this range at 13.0:1.0. This comparison demonstrates that the MSR results from current testing are similar to the southern pine results from Bodig and Goodman (1973). While it is impossible to identify the exact species of the MSR lumber in the southern pine group, the fact that the plate testing E:G ratio is within the range of Bodig and Goodman (1973) values helps validate these test results.

Comparison of E:G ratios with previous results

Table 5 shows the comparison of the elastic constants and E:G ratios of MSR and PSL from plate testing with the results from Hindman et al. (2006). The plate testing results are directly comparable to Hindman et al. (2006) values since the test materials of both studies were sampled from the same population. For the MSR comparisons, the elastic constant values from plate testing had MOE values 8.69 percent and 14.5 percent less than FPBT and ASTM D198 values, respectively, while the shear modulus values were 51.1 percent to 41.3 percent greater than FPBT and ASTM D198 values, respectively. The trends between plate testing and the Hindman et al. (2006) results for MSR E:G appear consistent s for both test methods (40.2% and 40.5% greater than plate testing results). These comparisons demonstrate a consistent difference in test method between the plate testing values and the bending tests for MSR lumber.

For PSL comparisons, the trends between the plate testing and the two bending tests are not consistent. The differences in the MOE values from PSL are relatively consistent, with differences of 13.4 percent and 22.6 percent less than the plate testing values for the FPBT and ASTM D198 Bending, respectively. The shear modulus values do not show a consistent trend between FPBT and ASTM D198 Bending, with the plate twisting values 16.9 percent greater than the FPBT shear modulus values and the plate twisting values 17.5 percent less than the ASTM D198 Bending values. The differences in shear modulus values create differences in the E:G ratios of the plate testing vs. the Hindman et al. (2006) results.

Based on the comparison of the FPBT and ASTM D198 Bending tests, Hindman et al. (2006) and Harrison and Hindman (2007) reasoned that the change in E:G ratio was caused by differences in stress distribution combined and the vertical density profile for wood composites such as PSL. Gunnerson et al. (1972) demonstrated that the stress distribution of the plate bending specimen was different from a simple beam due to the high orthotropy of wood materials. These findings have led to the applied correction factor for alternative beam theory discussed above. The stress distribution applied by the plate bending method is approximated by a modified beam theory, while plate twisting uses an anticlastic plate loading. The addition of the plate bending and twisting methods with the greater orthotropic behavior associated with the PSL material may create an elastic constant ratio confounded by a multiaxial stress state and may not be comparable to the previous bending results. Some of the differences in the elastic constant values may be due to changes in density of the MSR and PSL materials for the different test methods. While the purpose of this study was to measure structurally graded material rather than study a range of density values, this factor may deserve future study.

Statistical comparison of test methods

Table 6 presents the statistical comparison of the elastic modulus and shear modulus results comparing the FPBT and ASTM D198 Bending from Hindman et al. (2006) to the plate testing results. The MSR trends for all comparisons were consistent, with the MOE comparisons accepting the null hypothesis, while the shear modulus comparisons rejected the null hypothesis. Therefore, no statistical difference was detected between the MOE values for MSR measured by each method, while the shear modulus values from each method were significantly different. Based upon these results, the MOE associated with MSR appears to be independent of the test method used for measurement, while the shear modulus term is more subjective to particular stress states and material properties.

The PSL trends for all statistical comparisons were different from the MSR results. The only PSL elastic constant comparison that did not reject the null hypothesis was the shear modulus comparison between plate twisting and ASTM D198 Bending. All other MOE and shear modulus comparisons were significantly different. These results are consistent with the high level of orthotropic behavior of PSL noted in Janowiak et al. (2001) and the differences in MSR and PSL noted by Hindman et al. (2006) for other test methods. For all shear modulus comparisons except for the PSL plate testing vs. ASTM D198 Bending, the null hypothesis was rejected. The shear modulus term appears to be test dependent for both the MSR and PSL materials.

The study of the elastic constants and elastic constant ratios from the different test methods shows significant differences, especially related to the wood composite materials and shear modulus. Differences of these elastic constants have already been noted in the application to lateral torsional buckling of materials (Hindman et al. 2005a, 2005b). Engineers and designers who use the elastic constant ratios presented from Bodig and Goodman (1973) or Bodig and Jayne (1982) should ensure adequate factors of safety and be apprised of the range of values possible from different test methods. From this study of different test methods, it does not appear to be a single uniform shear modulus term that can be applied to wood and wood composites. The best approach may be to use elastic constants determined from test methods mimicking the applied loading, as mentioned by Hindman et al. (2006) and Harrison and Hindman (2007).

Conclusion

This research studied the elastic constants measured from plate testing methods vs. ASTM D 198 Bending and FPBT for MSR lumber and PSL. The elastic constant ratios of MSR lumber from the plate testing methods demonstrated a consistent difference with both the ASTM D 198 Bending and FPBT test methods. PSL elastic constant ratios from the plate testing methods did not show a consistent relationship between the other two test methods, indicating that the MSR lumber and PSL demonstrate different elastic behaviors possibly due to the manufacture of PSL materials. Statistical comparisons of the MOE and shear modulus values indicated that the three test methods produce values that are not significantly different for the MSR MOE values and between the ASTM D3044 plate twisting and ASTM D198 Bending for the PSL shear modulus. Except for the above comparisons, the three test methods produced values that were significantly different for the MSR shear modulus and for the PSL MOE and shear modulus. Therefore, elastic constant ratios derived from plate testing methods for MSR and PSL are not directly comparable to elastic constant ratios derived from structural sized bending tests. Differences in shear modulus values appear to be related to the use of different stress states for shear modulus measurement. Elastic constant ratios should be derived from test methods mimicking the loading conditions where the values will be used.

Literature cited

American Soc. for Testing and Materials (ASTM). 2005a. Standard Test Methods of Static Tests of Lumber in Structural Sizes. Standard D 198-02. In: Annual Book of ASTM Standards, Section 4, Vol. 04.10 Wood. ASTM, West Conshohocken, Pennsylvania.

--. 2005b. Standard Test Methods for Shear Modulus of Wood-Based Structural Panels. Standard D 3044-94. In: Annual Book of ASTM Standards, Section 4, Vol. 04.10 Wood. ASTM, West Conshohocken, Pennsylvania.

--. 2005c. Standard Test Methods for Specific Gravity of Wood and Wood-Based Materials. Standard D 2395-02. In: Annual Book of ASTM Standards, Section 4, Vol. 04.10 Wood. ASTM, West Conshohocken, Pennsylvania.

--. 2005d. Standard Test Methods for Direct Moisture Content Measurement of Wood and Wood-Based Materials. Standard D 4442-92. In: Annual Book of ASTM Standards, Section 4, Vol. 04.10 Wood. ASTM, West Conshohocken, Pennsylvania.

Bodig, J. and J.R. Goodman. 1973. Prediction of elastic parameters for wood. Wood Sci. 5(4):249-264.

-- and B.A. Jayne. 1982. Mechanics of Wood and Wood Composites. Van Nostrand Reinhold Company, New York. 714 pp.

Gunnerson, R.A., J.R. Goodman, and J. Bodig. 1972. Plate tests for determination of elastic parameters of wood. Wood Sci. 5(4):241-248.

Harrison, S.K. and D.P. Hindman. 2007. Test method comparison of shear modulus evaluation of MSR and SCL products. Forest Prod. J. 57(7):32-38.

Hindman, D.P., J.J. Janowiak, and H.B. Manbeck. 2006. Comparison of ASTM D 198 and five-point bending for elastic constant ratio determination. Forest Prod. J. 56(7):85-90.

--, H.B. Manbeck, and J.J. Janowiak. 2005a. Measurement and prediction of lateral torsional buckling of composite wood materials: Rectangular sections. Forest Prod. J. 55(9):42-47.

--, --, and --. 2005b. Measurement and prediction of lateral torsional buckling of composite wood materials: I-joist sections. Forest Prod. J. 55(10):43-48.

--. 2003. Torsional rigidity and lateral stability of structural composite lumber and I-joist members. Ph.D. dissertation. The Pennsylvania State Univ., Univ. Park, Pennsylvania. 223 pp.

Janowiak, J.J., D.P. Hindman, and H.B. Manbeck. 2001. Orthotropic behavior of lumber composite materials. Wood and Fiber Sci. 33(4): 580-594.

USDA Forest Serv., Forest Products Lab. 1999. Wood Handbook: Wood as an Engineering Material. GTR-FPL-113. Forest Products Lab., Madison, Wisconsin. 463 pp.

Witt, R.K., W.H. Hoppmann, and R.S. Buxbaum. 1953. Determination of elastic constants of orthotropic materials with special reference to laminates. ASTM Bulletin No. 194:53-57.

Gi Young Jeong

Daniel P. Hindman, Forest Products Soc. Member.

The authors are, respectively, Graduate Research Assistant and Assistant Professor, Dept. of Wood Sci. and Forest Products, Virginia Polytechnic Inst. and State Univ., Brooks Forest Products Center, Blacksburg, Virginia (jeongl@vt.edu, dhindman@vt.edu). This paper was received for publication in July 2007. Article No. 10382.
Table 1.--MSR and PSL elastic and shear modulus values from previous
studies.

 Average E
 (GPa ([10.sup.6]
Researcher Material Test method psi))

Bodig and Loblolly pine Plate bending/ 11.1 (1.61)
 Goodman 1973 (P. taeda) twisting
 Longleaf pine 14.6 (2.12)
 (P. palustris)
 Slash pine 16.0 (2.317)
 (P. elliottii)
Hindman MSR lumber FPBT (1) 16.1 (2.35)
 et al. 2006 (Pinus spp.) ASTM D198 17.2 (2.51)
 Bending (2)
 PSL (Pinus spp.) FPBT (3) 13.4 (l.96)
 ASTM D198 12.4 (l.81)
 Bending (4)
Harrison and MSR lumber ASTM D198 17.4 (2.53)
 Bending
 Hindman 2007 (Pinus spp.) ASTM D198 N/A
 Torsion
 FPBT 17.5 (2.54)

 Average G
 (GPa ([10.sup.6]
Researcher Material Test method psi))

Bodig and Loblolly pine Plate bending/ 0.903 (0.131)
 Goodman 1973 (P. taeda) twisting
 Longleaf pine 1.04 (0.151)
 (P. palustris)
 Slash pine 0.883 (0.128)
 (P. elliottii)
Hindman MSR lumber FPBT (1) 0.748 (0.109)
 et al. 2006 (Pinus spp.) ASTM D198 0.800 (0.16)
 Bending (2)
 PSL (Pinus spp.) FPBT (3) 0.727 (0.106)
 ASTM D198 1.03 (0.149)
 Bending (4)
Harrison and MSR lumber ASTM D198 0.903 (0.131)
 Bending
 Hindman 2007 (Pinus spp.) ASTM D198 1.16 (0.168)
 Torsion
 FPBT 0.789 (0.114)

(1) COV values of E and G were 18.3 percent and 22.2 percent,
respectively.

(2) COV values of E and G were 22.4 percent and 43.0 percent,
respectively.

(3) COV values of E and G were 10.8 percent and 9.7 percent,
respectively.

(4) COV values of E and G were 14.9 percent and 37.1 percent,
respectively.

Table 2.--Summary of test materials.

 Rated E MC
Test material (GPa (psi)) (percent (COV))

2250f-1.9E southern 13.1 (1.9 x [10.sup.6]) 11.6 (3.10%)
 pine MSR
2.0E southern pine PSL 13.8 (2.0 x [10.sup.6]) 11.0 (3.05%)

Test material SG (COV)

2250f-1.9E southern 0.62 (8.15%)
 pine MSR
2.0E southern pine PSL 0.71 (5.12%)

Table 3.--Test results from plate bending and plate
twisting test.

 Modulus of Shear
 elasticity (1) modulus (2)
 (GPa ([10.sup.6] (GPa ([10.sup.6]
Material Psi) [COV]) Psi) [COV]) E:G ratio (3)

MSR 14.7 (2.15) [18.8] 1.13 (0.165) [11.3] 12.9:1
PSL 15.2 (2.22) [11.5] 0.85 (0.124) [7.58] 17.8:1

(1) Modulus of elasticity was measured using plate bending test
methods.

(2) Shear modulus was measured using plate twisting test methods.

(3) E:G ratio refers to the [E.sub.1]:[G.sub.12] ratio.

Table 4.--Comparison of the test results to Bodig and Goodman (1973).

 Loblolly pine
 (P. taeda)

Elastic Current Percent
property MSR value Value (1) difference (2)

[E.sub.1] 14.7 GPa 11.1 GPa -24.5
[G.sub.12] 1.13 GPa 903 MPa -20.1
[E.sub.1]:[G.sub.12] 13.0:1.0 12.3:1.0 -5.38

 Longleaf pine
 (P. palustris)

Elastic Percent
property Value (1) difference (2)

[E.sub.1] 14.6 GPa -0.68
[G.sub.12] 1.04 GPa -7.96
[E.sub.1]:[G.sub.12] 14.1:1.0 8.46

 Slash pine
 (P. elliottii)

Elastic Percent
property Value (1) difference (2)

[E.sub.1] 16.0 GPa 8.84
[G.sub.12] 883 MPa -21.9
[E.sub.1]:[G.sub.12] 18.1:1.0 39.2

(1) Values from Bodig and Goodman (1973).

(2) Percent difference = (previous result-MSR)/MSR x 100 percent.

Table 5.--Comparison of the measured [E.sub.1]:[G.sub.12]
ratios to Hindman et al. (2006).

 FPBT

 Elastic Hindman et al. Percent difference
Material property (2006) (GPa) (percent)

MSR E 16.1 -8.69
 G 0.748 51.1
 E:G 21.6:1 -40.2

PSL E 13.4 13.4
 G 0.727 16.9
 E:G 18.5:1 -3.78

 ASTM D198 Bending

 Elastic Hindman et al. Percent difference
Material property (2006) (GPa) (percent)

MSR E 17.20 -14.5
 G 0.800 41.3
 E:G 21.7:1 -40.5

PSL E 12.4 22.6
 G 1.03 -17.5
 E:G 12.1:1 47.1

(1) Percent difference = (Plate test - FPBT)/FPBT x 100 percent.

(2) Percent difference = (Plate test - ASTM D198 Bending)/ASTM
D198 Bending x 100 percent.

Table 6.--Statistical comparison of [E.sub.1] and [G.sub.12] from three
different test methods ([alpha] = 0.05).

 p-value p-value
Tests for comparison Material for E for G

Plate tests vs. FPBT (1) MSR 0.262 0.000
 PSL 0.037 0.000
Plate tests vs. ASTM D198 MSR 0.204 0.010
 Bending (2) PSL 0.000 0.182
Plate tests vs. FBPT vs. MSR 0.369 0.000
 ASTM D 198 Bending (1,12) PSL 0.001 0.004

(1) FPBT used 16 specimens (Hindman 2003).

(2) ASTM D198 Bending used 8 specimens (Hindman 2003).
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Author:Jeong, Gi Young; Hindman, Daniel P.
Publication:Forest Products Journal
Article Type:Statistical table
Geographic Code:1USA
Date:Sep 1, 2008
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