Using Transverse Vibration 

Nondestructive Testing 

Techniques to Estimate 

Stiffness and Strength of 

Southern Pine Lumber

Frederico J. N. França

R. Daniel Seale

Robert J. Ross

Rubin Shmulsky

Tâmara S. F. Amorim França

United States Department of Agriculture

Forest

Service

Forest Products

Laboratory

Research Paper

FPL–RP–695

July

2018
Abstract

This research focused on evaluating the bending stiffness 

and strength of structural lumber with transverse vibration 

nondestructive testing techniques. A random sample of 

nominal 2-in.- (standard 38-mm-) thick Southern Pine 

dimension lumber was obtained from several mills in 

southeastern United States. After conditioning, the lumber 

specimens were nondestructively tested using transverse 

vibration techniques. Modulus of elasticity (MOE) was 

determined using the frequency of oscillation and density.

Static bending MOE and strength were then determined for 

each specimen. Statistical analyses were then performed to 

examine the relationships between transverse vibration 

modulus values and bending MOE and strength. Excellent 

relationships were observed between transverse vibration 

and static bending MOE values. Strong relationships were 

found between transverse vibration MOE and bending 

strength.

Keywords: transverse vibration, nondestructive, bending 

strength, modulus of elasticity

July 2018

França, Frederico José Nistal; Seale, R. Daniel; Ross, Robert J.; Shmulsky, 

Rubin; França, Tâmara Suely Filgueira Amorim. 2018. Using transverse 

vibration nondestructive testing techniques to estimate stiffness and 

strength of Southern Pine lumber. FPL–RP–695. Madison, WI: U.S. 

Department of Agriculture, Forest Service, Forest Products Laboratory. 6 p.

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Acknowledgments

The authors acknowledge the support of USDA Research, 

Education, and Economics (REE), Agriculture Research 

Service (ARS), Administrative and Financial Management 

(AFM), Financial Management and Accounting Division 

(FMAD) Grants and Agreements Management Branch 

(GAMB) under Agreement No. 5B-0202-4-001. The authors 

also acknowledge support from USDA Forest Service,

Forest Products Laboratory (FPL) in Madison, Wisconsin, 

as a major contributor of technical assistance, advice, and 

guidance to this research.

Nominal lumber size (in.) Standard lumber size (mm)

2 by 4 38 by 89

2 by 6 38 by 140

2 by 8 38 by 184

2 by 10 38 by 235

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Introduction

Transverse vibration techniques have received considerable

attention for nondestructive evaluation applications (Ross 

2015). Figure 1 illustrates a typical free transverse vibration 

test setup. Note that the specimen is simply supported at 

both ends.

A slight deflection is introduced at the specimen’s midspan 

and is then allowed to freely oscillate in the vertical 

(transverse) direction. Frequency of oscillation is 

determined and, along with the specimen weight and 

dimensions, used to compute modulus of elasticity (MOE).

This measurement of MOE is referred to as transverse MOE 

(MOEtv) and is sometimes referred to as dynamic MOE to 

differentiate it from static MOE. MOEtv is calculated from 

the following formula:

MOEtv = f 2 WS3/2.46Ig

where f is resonant frequency (Hz), W weight of the 

specimen (N), S span (m), I moment of inertia (m4

), and

g acceleration due to gravity (9.81 m/s2

).

ASTM D6874-12, “Standard Test Methods for 

Nondestructive Evaluation of Wood-Based Flexural 

Members Using Transverse Vibration,” outlines important 

aspects for using transverse vibration nondestructive testing 

(NDT) techniques to evaluate the MOE of wood materials 

(ASTM 2012). This standard outlines three elements that are 

essential when using this type of technique: the support 

apparatus, excitation system, and measurement system. A 

detailed discussion of these elements is beyond the scope of 

this report but is provided in the standard and in Ross 

(2015). It is important to note that this standard recommends 

transverse vibration testing of lumber specimens flatwise; 

this results in a low frequency vertical vibration with few 

modes. Testing edgewise complicates the test, because a 

specimen may vibrate in several modes, specifically 

vertically and horizontally, which could lead to erroneous 

results.

Pellerin (1965b) used this technique to evaluate the 

properties of several large, glued-laminated (glulam) 

timbers in an edgewise orientation. Using three Douglas-fir 

glulam timbers, he was able to obtain accurate 

Using Transverse Vibration 

Nondestructive Testing Techniques to 

Estimate Stiffness and Strength of 

Southern Pine Lumber

Frederico José Nistal França, Assistant Research Professor

R. Daniel Seale, Thompson Professor of Wood Science and Technology

Department of Sustainable Bioproducts, Mississippi State University, Starkville, Mississippi

Robert J. Ross, Supervisory Research General Engineer and Research Professor

USDA Forest Service, Forest Products Laboratory, Madison, Wisconsin

Michigan Technological University, Houghton, Michigan

Rubin Shmulsky, Professor and Department Head

Tâmara Suely Filgueira Amorim França, Postdoctoral Associate

Department of Sustainable Bioproducts, Mississippi State University, Starkville, Mississippi

Figure 1. Typical free transverse vibration test setup.
Research Paper FPL–RP–695

2

measurements of natural frequency, dynamic MOE, and the 

decay of transverse vibrations and use them to predict the 

relative strength of the timbers. It was important to test the 

timbers in an edgewise orientation, because each timber had 

a unique layup pattern, which significantly affected its 

flexural stiffness and strength. Yang and others (2015) used

this technique to evaluate southern yellow pine lumber in 

edgewise and flatwise orientations, with both yielding good 

results.

Pellerin (1965a) and O’Halloran (1969) reported on the use 

of transverse vibration techniques to evaluate the strength 

and stiffness of structural lumber. Pellerin’s research 

focused on predicting the bending MOE and strength of 

inland Douglas-fir dimension lumber. O’Halloran’s efforts 

focused on the use of the techniques to evaluate lodgepole 

pine dimension lumber. Both reported excellent empirical 

relationships between static and dynamic MOE values and 

strong relationships with strength. Wang and others (1993) 

also reported on the use of these techniques to evaluate the 

MOE of a sample of Spruce–Pine–Fir dimension lumber; 

they noted that excellent correlative relationships were 

obtained.

The objective of the research study summarized in this 

report was to investigate the relationships between 

transverse vibration characteristics, measured in flatwise 

and edgewise orientations, and the flexural MOE and 

strength of Southern Pine dimension lumber.

Materials and Methods

Table 1 summarizes a breakdown of the lumber sample 

used. More than two thousand (2039) lumber specimens, all 

visually graded as No. 2, were used. The specimens were 

randomly selected from the southeastern region of the 

United States. All specimens were conditioned (temperature 

22°C; relative humidity 61%) for approximately 90 days to 

equilibrate to an estimated 12% moisture content prior to 

testing.

The MOEtv was measured for each specimen using a 

Metriguard Model 340 Transverse Vibration E-Computer 

(Metriguard Inc., Pullman, Washington, USA). Each 

specimen was initially tested in flatwise orientation. Actual 

dimensions and weight were used in the computation of the 

transverse vibration MOE in flatwise orientation (dMOEflat).

A similar procedure was used in the measurement of the 

dynamic MOE in edgewise orientation (dMOEedge), with 

special care taken to ensure that horizontal vibration was 

minimized.

The edgewise bending test was conducted according to 

ASTM D198-15 (2015) via four-point loading, using a spanto-depth ratio of 17:1. The bending span was selected to 

match prior in-grade testing programs (Green and others

1989). The tension face of each specimen was randomly 

selected, and specimens were loaded randomly to better 

represent actual end use. Load and deflection were

continuously monitored until failure. Static bending MOE 

and strength (modulus of rupture (MOR)) were calculated 

for each specimen from their corresponding load–deflection 

diagram.

All statistical analyses of static bending (MOR and MOE) 

and dynamic MOE values obtained from transverse 

vibration tests were conducted using SAS 9.4 (SAS 2013).

Single variable linear regression analyses (α = 0.05) were 

built for each cross section and length lumber group to 

correlate the NDT outputs to bending MOE and MOR 

values. The linear regressions were conducted given the 

independent variables (x, which can be represented by 

density, dMOEedge, and dMOEflat) and the dependent 

variable (MOE, MOR). Coefficient of correlation (r), which 

measures the strength of the relationships between variables, 

was the main focus.

Results and Discussion

Table 2 presents a summary of several basic properties of 

the lumber tested. Note the following: (1) each lumber 

group had comparable density values, (2) moisture content

values for the groups were consistent, (3) the transverse 

vibration MOE values were consistent between cells, and 

(4) strength (MOR) values showed the most variability.

The mathematical regression models between the 

nondestructive test parameters (density, dMOEedge, and 

dMOEflat) and static properties (MOE and strength (MOR)) 

were assumed to be linear and of the following form:

Static property = slope × (nondestructive test parameter) 

+ intercept + error

Table 1—Summary of the sample of lumber used in 

this study

Nominal 

size

Thickness 

(mm)

Width

(mm)

Length 

(m)

Number of samples

By length Total

2 by 4 38 89 2.4 121 630

3.1 152

3.7 206

4.3 49

4.9 102

2 by 6 38 140 3.1 85 613

3.7 265

4.3 137

4.9 102

6.1 24

2 by 8 38 184 3.7 145 483

4.3 202

4.9 136

2 by 10 38 235 4.3 204 313

4.9 109
Using Transverse Vibration Nondestructive Testing Techniques to Estimate Stiffness and Strength of Southern Pine Lumber 

3 

After a statistical analysis of each combination of size and 

length, summaries of which are included in the Appendix, it

was deemed appropriate to combine 2 by 4 and 2 by 6 data 

sets for purposes of examining statistical relationships 

between transverse vibration MOE and static bending 

properties. Similarly, we combined 2 by 8 and 2 by 10 data 

sets. 

Tables 3 and 4 provide summaries obtained from these 

statistical analyses. Figure 2 shows plots of static bending 

MOE values predicted using transverse vibration MOE 

values. These plots show that strong correlative 

relationships exist. In this case, the coefficients of 

determination for MOE and dMOEflat were 0.839 and 0.794, 

respectively. For MOE and dMOEedge, they were 0.874 for 

2 by 4 and 2 by 6 and 0.887 for 2 by 8 and 2 by 10. The 

correlative relationships we developed were comparable 

with those reported in the literature (Table 5) (Pellerin 

1965a; O’Halloran 1969; Wang and others 1993; Yang and 

others 2015; Green and McDonald 1993a, 1993b).

Figure 3 shows several plots of bending strength (MOR) 

values predicted by transverse vibration MOE. Results 

obtained from the corresponding statistical analyses are 

summarized in Tables 3 and 4. Between MOR and dMOEflat, 

the coefficients of determination were 0.377 for 2 by 4 and 

2 by 6 and 0.213 for 2 by 8 and 2 by 10. For MOR and 

dMOEedge, they were 0.425 for 2 by 4 and 2 by 6 and 0.289 

for 2 by 8 and 2 by 10. 

Table 2—Summary of properties from the lumber evaluated (coefficients of variation 

(%) in parentheses)

Nominal 

size

Density 

(kg m–3) 

Moisture 

content 

(%) 

Transverse 

vibration MOE 

flatwise 

(GPa)

Transverse 

vibration MOE 

edgewise 

(GPa)

Modulus of 

elasticity 

(MPa)

Modulus of 

rupture 

(MPa)

2 by 4 548

(11.1)

11.45

(8.47)

11.51

(26.1)

11.61

(25.2)

10,855

(25.8)

55.39

(37.5)

2 by 6 548

(10.8)

11.04

(11.6)

11.31

(25.3)

11.19

(23.9)

10,414

(23.0)

45.88

(39.1)

2 by 8 542

(9.9)

11.68

(14.2)

11.06

(25.3)

10.92

(21.2)

10,519

(22.1)

38.92

(36.1)

2 by 10 560

(10.5) 

12.15

(18.7) 

10.96

(26.6) 

10.68

(22.7) 

11,059

(24.0) 

42.90

(38.3) 

Table 3—Results of linear regression analyses relating static bending modulus of elasticity (MOE) and 

strength to transverse vibration MOE for 2 by 4 and 2 by 6 Southern Pine dimension lumber

Variable MOEa MORa

Slope 

(m) 

Intercept 

(b) 

Coefficient of 

determination 

(r2) 

Standard 

error of 

estimate

Slope 

(m) 

Intercept 

(b) 

Coefficient of 

determination 

(r2) 

Standard 

error of 

estimate

Density 30.02 –5712.26 0.469 1906.58 0.192 –54.09 0.331 16.26

dMOEflat 817.41 1307.07 0.839 1048.48 4.18 3.01 0.377 15.79

dMOEedge 869.64 721.35 0.874 925.55 4.63 –2.10 0.425 15.16

a

The coefficients m and b are used in the generalized model static property = m (transverse vibration MOE) + b. 

Table 4—Results of linear regression analyses relating static bending modulus of elasticity (MOE) and 

strength to transverse vibration MOE for 2 by 8 and 2 by 10 Southern Pine dimension lumber

Variable

MOEa MORa

Slope 

(m) 

Intercept 

(b) 

Coefficient of 

determination 

(r2) 

Standard 

error of 

estimate

Slope 

(m) 

Intercept 

(b) 

Coefficient of 

determination 

(r2) 

Standard 

error of 

estimate

Density 29.24 –5,273.40 0.444 1,885.48 0.188 –52.93 0.309 16.16

dMOEflat 783.22 2,443.24 0.794 1,131.91 2.599 14.09 0.213 14.15

dMOEedge 983.65 302.82 0.887 840.10 3.60 3.35 0.289 13.45

aThe coefficients m and b are used in the generalized model static property = m (transverse vibration MOE) + b. 
Research Paper FPL–RP–695

4

Conclusions and Recommendations

This study investigated the ability of flatwise and edgewise 

transverse vibration NDT techniques to estimate the static 

bending MOE and strength (MOR) values of Southern Pine 

dimension lumber. Results revealed the following:

• Commercially available transverse vibration NDT

equipment was able to capture the vibration 

characteristics for a variety of sizes (cross sections) and 

lengths frequently used in the construction industry.

• It was possible to obtain adequate measurement of 

frequency of vibration data for dimension lumber, tested 

in both flatwise and edgewise orientations.

• Flatwise and edgewise transverse vibration MOE values 

were strongly correlated with static bending MOE values 

for Southern Pine dimension lumber.

• Useful correlative relationships were observed between 

transverse vibration MOE and corresponding strength 

values.

• Edgewise transverse vibration MOE values showed 

slightly higher correlative relative relationships with 

both static bending MOE and strength values. This was 

exhibited most strongly with larger lumber sizes (2 by 8 

and 2 by 10).

These results revealed that transverse vibration NDT

techniques can be used successfully as part of an automated 

structural lumber grading system. Lumber should be tested 

in a flatwise orientation because an edgewise orientation has 

the potential to vibrate in additional modes. which would 

complicate the design of in-line equipment.

Figure 2. Linear regression plots for each lumber size: bending modulus of elasticity (MOE) versus dynamic MOE from (a) 

edgewise transverse vibration on 2 by 4 and 2 by 6; (b) flatwise transverse vibration on 2 by 4 and 2 by 6; (c) edgewise 

transverse vibration on 2 by 8 and 2 by 10; and (d) flatwise transverse vibration on 2 by 8 and 2 by 10.

Table 5—Summary of research conducted to examine the relationship between transverse vibration modulus 

of elasticity and static bending properties (modulus of elasticity (MOE) and modulus of rupture (MOR)) of 

structural lumber

Reference Material

Comparison of transverse vibration parameters and 

properties (correlation coefficient, r)

MOE MOR

Pellerin (1965a) Inland Douglas-fir dimension lumber 0.98 0.67–0.93

O’Halloran (1969) Lodgepole pine dimension lumber 0.98 0.89

Wang and others (1993) Spruce–Pine–Fir dimension lumber 0.96–0.98 NAa

Yang and others (2015) Southern Pine dimension lumber 0.86–0.97 NA

Green and McDonald (1993a) Northern red oak lumber 0.92 0.58

Green and McDonald (1993b) Red maple lumber 0.85 0.42

a

NA, not available.
Using Transverse Vibration Nondestructive Testing Techniques to Estimate Stiffness and Strength of Southern Pine Lumber

5

Literature Cited

ASTM. 2012. D6874-12. Standard test methods for 

nondestructive evaluation of wood-based flexural members 

using transversal vibration. West Conshohocken, PA: 

ASTM International.

ASTM. 2015. D198-15. Standard test methods of static tests 

of lumber in structural sizes. West Conshohocken, PA: 

ASTM International.

Green, D.W.; McDonald, K.A. 1993a. Investigation of the 

mechanical properties of red oak 2 by 4’s. Wood and Fiber 

Science. 25(1): 35-45.

Green, D.W.; McDonald, K.A. 1993b. Mechanical 

properties of red maple structural lumber. Wood and Fiber 

Science. 25(4): 365-374.

Green, D.W.; Shelley, B.E.; Vokey, H.P. 1989. In-grade 

testing of structural lumber. Proceedings 47363. Madison, 

WI: Forest Products Society. 110 p.

O’Halloran, M.R. 1969. Nondestructive parameters for 

lodgepole pine dimension lumber. Fort Collins, CO:

Colorado State University. M.S. Thesis.

Pellerin, R.F. 1965a. A vibrational approach to 

nondestructive testing of structural lumber. Forest Products 

Journal. 15(3): 93-101.

Pellerin, R.F. 1965b. The contributions of transverse 

vibration grading to design and evaluation of 55-foot 

laminated beams. In: Proceedings, 2nd nondestructive 

testing of wood symposium; 1965 April; Spokane, WA.

Pullman, WA: Washington State University: 337-347.

Ross, R.J. 2015. Nondestructive evaluation of wood: second 

edition. Gen. Tech. Rep. FPL-GTR-238. Madison, WI: U.S. 

Department of Agriculture, Forest Service, Forest Products 

Laboratory. 169 p.

SAS. 2013. SAS version 9.4. Cary, NC: SAS Institute, Inc.

Wang, Z.; Ross, R.J.; Murphy, J.F. 1993. A comparison of 

several NDE techniques for determining the modulus of 

elasticity of lumber. World Forestry Research. 6(4): 86-88.

(In Chinese).

Yang, B.Z.; Seale, R.D.; Shmulsky, R.; Dahlen, J.; Wang, 

X. 2015. Comparison of nondestructive testing methods for 

evaluating No. 2 southern pine lumber: Part A, modulus of 

elasticity. Wood and Fiber Science. 47: (4) 375-384.

Figure 3. Linear regression plots for each lumber size: modulus of rupture (MOR) versus dynamic modulus of elasticity 

(MOE) from (a) edgewise transverse vibration on 2 by 4 and 2 by 6; (b) flatwise transverse vibration on 2 by 4 and 2 by 6; 

(c) edgewise transverse vibration on 2 by 8 and 2 by 10; and (d) flatwise transverse vibration on 2 by 8 and 2 by 10.
Research Paper FPL–RP–695

6

Appendix—Statistical Analysis

The tables in this Appendix present the complete statistical 

analysis with the MOE and MOR coefficients of 

determination for each lumber length group (f is resonant 

frequency, and d stands for dynamic).

Table A1—Coefficients of determination for 2 by 4

Length 

(m)

MOE MOR

Density fflat dMOEflat fedge dMOEedge Density fflat dMOEflat fedge dMOEedge

2.4 0.301 0.716 0.897 0.762 0.945 0.386 0.130 0.311 0.156 0.368

3.1 0.475 0.728 0.878 0.731 0.924 0.345 0.252 0.386 0.245 0.403

3.7 0.504 0.613 0.826 0.671 0.867 0.298 0.262 0.407 0.325 0.458

4.3 0.542 0.616 0.774 0.681 0.852 0.402 0.206 0.364 0.228 0.406

4.9 0.560 0.564 0.841 0.555 0.832 0.396 0.187 0.397 0.192 0.388

Overall 0.476 — 0.857 — 0.891 0.349 — 0.381 — 0.412

Table A2—Coefficients of determination for 2 by 6

Length

(m)

MOE MOR

Density fflat dMOEflat fedge dMOEedge Density fflat dMOEflat fedge dMOEedge

3.1 0.286 0.552 0.721 0.726 0.882 0.223 0.045 0.359 0.119 0.266

3.7 0.466 0.599 0.852 0.656 0.912 0.326 0.499 0.423 0.226 0.445

4.3 0.398 0.511 0.760 0.643 0.841 0.227 0.368 0.269 0.253 0.383

4.9 0.563 0.719 0.869 0.656 0.861 0.497 0.692 0.632 0.406 0.610

6.1 0.613 0.658 0.799 0.420 0.762 0.404 0.509 0.393 0.247 0.500

Overall 0.466 — 0.823 — 0.854 0.336 — 0.397 — 0.415

Table A3—Coefficients of determination for 2 by 8

Length 

(m)

MOE MOR

Density fflat dMOEflat fedge dMOEedge Density fflat dMOEflat fedge dMOEedge

3.7 0.500 0.619 0.834 0.554 0.861 0.209 0.112 0.228 0.129 0.283

4.3 0.321 0.624 0.778 0.701 0.889 0.210 0.115 0.221 0.172 0.308

4.9 0.407 0.666 0.806 0.711 0.906 0.162 0.123 0.204 0.116 0.206

Overall 0.413 — 0.797 — 0.878 0.177 — 0.201 — 0.268

Table A4—Coefficients of determination for 2 by 10

Length

(m)

MOE MOR

Density fflat dMOEflat fedge dMOEedge Density fflat dMOEflat fedge dMOEedge

4.3 0.415 0.615 0.792 0.645 0.867 0.180 0.118 0.219 0.151 0.272

4.9 0.417 0.599 0.755 0.674 0.910 0.343 0.158 0.311 0.196 0.403

Overall 0.412 — 0.767 — 0.876 0.226 — 0.235 — 0.321