|NDT.net - March 2001, Vol. 6 No. 03|
Forest Products Journal
Editor Erin Bosch,
Forest Products Society
Lumber strength grading using x-ray scanningGary S. Schajer
Forest Products Society Member.
Published in Forest Products Journal J.51 (1) pp. 43-50.
Bending stiffness measurement (6) is the most common mechanical lumber grading method. This method is based on the observation that stronger lumber pieces tend to have higher bending stiffness. In practical operation, lumber strength is estimated by measuring the bending stiffness along the length of each board, and then applying a statistical relationship to determine lumber strength. However, the relationship between lumber strength and bending stiffness is not a well-defined one. Correlation coefficients between estimated and measured strengths are quite modest, with typical r2 values in the range 0.50 to 0.60 (8). The associated uncertainty in the indicated lumber strength seriously impairs the ability to segregate lumber into distinct strength classes. Consequently, greatly varying strengths are present within a given lumber grade, combined with large overlaps in the strengths of nominally distinct grades of lumber. For safety, design strength has to be based on the weakest expected boards within a grade. Thus, the majority of stronger boards are undervalued (14).
There are two main reasons for the modest strength-indicating capability of the bending-stiffness method. The first is the low spatial resolution of the measurements. Bending stiffness is measured over a 36- to 48-inch span, with a main contribution from the central 12 to 20 inches (3). In comparison, the main strength-controlling features, the knots, are typically only 0.5 to 2 inches in diameter. The second reason is the entirely statistical nature of the lumber strength identification. There is no mechanistic consideration of how the structure of the lumber controls its strength. Thus, variations in raw material source and quality cause unknown deviations from the previously established statistical strength vs. stiffness correlations.
This paper describes an alternative method for estimating lumber strength based on x-ray measurements of lumber density (11,15). This method seeks to overcome the shortcomings of the bending-stiffness method by using a spatial measurement resolution of 1 inch, which is about the same scale as the main strength-controlling features, the knots. The method also uses the measured density data to characterize the lumber material properties and structure so that the strength identification procedure can include these features. Tests of the density measurement system have indicated an improved lumber strength identification capability. Typical r2 values are in the range 0.65 to 0.75. These results directly translate into improved yields of high-value products and less undervaluation of stronger material. A lumber strength grading machine incorporating an x-ray scanner of the type described here has now been commercialized (4). The design has proven to be robust in a sawmill environment, with industrial versions now operating in several North American sawmills.
In addition to its superior strengthestimation capabilities, x-ray scanning also has some operational advantages over bending-based lumber grading. There is no contact between the sensor and the wood. The lumber and the conveyor system are the only moving parts. Thus, maintenance costs are low and service reliability is high. The scanner is also very compact and can conveniently be installed behind a planer. This arrangement saves floor space and minimizes the need for special material infeed systems.
|Fig 1: Schematic diagram of a single-detector lumber density scanner.|
During the initial tests done in this study, the radiation was provided by an Americium 241 source instead of an x-ray source. The radiations from these two source types are very similar and can be used interchangeably. For industrial use, an x-ray source is preferable because it avoids the use of nuclear materials and can be switched off easily. Also, the higher beam intensity allows measurements to be made at practical industrial speeds. Using the basic arrangement shown in Figure 1, a specific gravity resolution better than 0.01 was achieved in measurements along the length of 2 by 4 lumber pieces. The associated spatial resolution was 1 inch inlength and the full 3.5 inches in width. After initial tests to demonstrate the measurement concept and the wood strength grading potential, the 3-detector arrangement shown in Figure 2 was built. In this variation, the radiation passes through the thickness of the lumber instead of its width, and is subsequently measured by three separate detectors. This arrangement increases the spatial resolution of the density measurement to about 1 inch in both length and width.
Figure 3 shows a typical density profile measured along the length of a board, as measured by one of the radiation detectors in Figure 2 or the singledetector in Figure 1. The flat areas of the profile correspond to clear wood and the sharp peaks correspond to knots. The sharp measured density increases occur because the density of knot material is about twice that of clear wood. The local density represented by the solid line in Figure 2 is designated r.
The additional dashed line in Figure 3 shows the computed clear wood density, excluding the effects of knots. For clarity, this line has been displaced slightly downwards. It represents the estimated density profile of the board if no knots were present. The computed clear wood density, also called the reference density, equals the measured wood density in areas of clear wood. In areas containing knots, it is determined by interpolating between the adjacent clear wood areas. The reference density, designated 0, is useful when identifying clear wood properties and when measuring the sizes of the knot peaks.
|Fig 2: Schematic diagram of a multiple-detector lumber density scanner.||Fig 3: Typical measured density profile along the length of a board.|
The wood strength-estimation method interprets the measured density profile to identify the two main board strength-controlling factors:
These two factors form the basis of the wood strength estimate, which is of the following conceptual form (1):
The sizes of the localized density increases control the wood structural factor. This is the strength-reduction factor caused by the presence of knots. Larger localized density increases correspond to larger knots, which in turn correspond to a larger Wood Structural (strength-reducing) Factor. For a single-detector system, this factor is assumed dependent on the relative height of the localized density increases as follows:
|Wood Structural Factor =|
|Wood Structural Factor =|
These equations are combined to calculate an estimated board strength profile from the measured density profile(s). It is assumed that failure occurs within a single cross section. The estimated board strength is determined from the cross section with the minimum calculated strength. When comparing with actual strength tests, the strength calculation was limited to the particular area of each board that was significantly loaded. This was done to avoid confusing the strength calculation with data from parts of the boards that were not loaded during the subsequent destructive strength tests.
Table 1 summarizes the six groups of tension, compression, and bending strength estimation tests that were done using six groups of mill-run southern yellow pine 2 by 4s, 12 to 16 feet long, supplied from sawmills in Arkansas and Mississippi. All of the boards except group 4 were evaluated by the bending-stiffness method at their mill of origin using standard industrial testing machines (7). The boards were then density-scanned over their entire lengths, barring 2 inches on either end. The board transport system that was used did not allow scanning in these end regions. (The industrial x-ray scanner developed from the laboratory prototype scans full-length, including the end regions.) The boards in groups 1 to 3 were single profile-scanned as shown in Figure 1. The boards in groups 4 to 6 were three-profile-scanned corresponding to Figure 2. The laboratory system that was used for these tests had only one detector. Three-profile scanning was simulated by repeated single-scanning along three different paths.
The destructive tests to determine actual board strengths were done using American Society for Testing and Materials standard procedures (2). For the tension tests, the boards were tested full length. The 2-foot sections at either end of the boards were used for gripping, and were not subject to the full tensile load. Wherever possible, the board positions were slightly adjusted so that significant defects were not contained within the areas of stress concentration close to the boundaries of the grips.
For the bending tests (third-point loading), the load span was 73-1/2 inches, typically chosen to contain the most serious defect in the board. This choice was made visually and emphasized the major defects that were on or close to the tensile edge of each board. Such defects have a great influence on bending strength, and should represent the minimum bending strength of each board. To accommodate other testing needs, part of group 3 and all of group 4 were loaded at pre-determined locations, not related to the presence of defects. Since the region of significant bending load is a very small fraction of the total board length, this choice of load position can have a large influence on the measured strength value.
For the compression tests, the specimen length was 9 inches, chosen to contain the largest available visual defect in the undamaged material from group 5 remaining after completion of the bending tests. Because of this procedure, the specimens typically did not contain the largest defect originally in the board. However, the remaining visual defects were usually comparable in size to the original largest defect. In the same way as the bending test, choice of specimen position can have a large influence on the measured strength value.
|Board group no.||Test type||No. of boards||Origin||No. of density profiles||Remarks|
|2||Tension||248||Arkansas||1||Groups 2 and 3 taken from same shipment|
|6||Compression||131||Arkansas||3||Same boards as no. 5|
|Table 1: Board strength tests.|
|Board group no.||Test type||No. of tests||r2||SEE||Optimal coefficients|
|Table 2: Single-density profile board strength estimates.|
Table 3 lists the corresponding strength estimates from the bending-stiffness measurements. The industrial bending-stiffness testing machines that were used reported both the average and the minimum value of Young's modulus measured along the length of each board. These two quantities are designated Eave and Emin. To allow maximum strength-estimation capability, both of these values were used in a multiple-regression calculation. Table 2 lists the corresponding regression coefficients. The boards in group 4 were not stiffness-tested at their originating sawmill. The bending stiffness of these boards was measured in joist configuration using a laboratory testing machine. These data were used in the single regression reported in Table 2.
|Board group no.||Test type||No. of tests||r2||SEE||Optimal coefficients|
|Table 3: Board strength estimates from bending stiffness.|
In Tables 2 and 3, the coefficient of determination, r2 , indicates if the estimated board strengths have a straight-line relationship with the actual measured board strengths. The Standard Error of the Estimate (SEE) indicates the size of the typical error between the estimated and measured board strengths. In all cases, the board strength estimates from the density measurements are significantly more accurate than those from the bending-stiffness measurements. The r2 values are 0.1 to 0.2 higher and SEE is 200 to 600 psi lower. The main reason for this superior strength-estimation accuracy is believed to be the finer spatial resolution of the density measurements compared with the bending-stiffness measurements.
The tension and compression tests have the most accurate strength estimates in Table 2. This is because the applied stresses are uniform for these loading types. Knot location within a cross section is therefore not a major factor. As a result, single-profile density measurements are sufficient in these cases.
Table 2 shows that single-profile density measurements are less effective for estimating bending strength, although still superior to bending-stiffness measurements. This occurs because bending loading creates highly non-uniform stresses within a cross section much greater at the edges than in the middle. Single-profile density measurements do not take into account this stress variation. The strength-estimation accuracy for board group 4 is anomalously low for both density- and bending-stiffnessbased results. This occurred because the experimental procedure for this board group was non-standard. To accommodate other testing needs, the bending load was applied at a fixed location on each board, independent of observed defect locations. Consequently, the measured bending strength often differed quite substantially from the bending strength at the weakest location on the board.
The calculated wood strength values (Sc ) in Table 2 are all similar. They are also similar to the small, clear specimen strengths quoted in Table 4-2 of the Wood Handbook(12) for loblolly pine:
Bending strength = 12,800 psi
Compression strength = 7,130 psi
The calculated knot sensitivity factor (B) is greatest for tensile loading because knots at any point within a cross section can cause strength reductions. Knots are prime crack initiation sites for tensile failures. The factor B is smaller for bending loading because, for such loadings, only those knots close to the tensile edge cause significant strength reductions. The knot sensitivity factor is smallest for compressive loading because these failures occur by crushing of the wood material rather than by the crack propagation typical of tensile and bending failures. Crack initiation aroundknots is not an important factor affecting wood crushing strength.
The r2 and SEE are statistical measures that describe the optimal fit (regression) between two independent quantities, here the measured and estimated strengths of groups of boards. However, for the non-optimal case of interest here, no regression has been done, so r2and SEE are not appropriate. The RMSE between the measured and estimated strengths of the boards in each group is a more meaningful measure. This quantity indicates typical board strength-estimation accuracy. In general, RMSE is larger than SEE. It equals SEE only when the calibration coefficients equal the optimal values for the boards being evaluated, and the regression line passes through the origin.
Tables 4 and 5 show the effects of applying the optimal regression coefficients from one board sample group to a different board group. The negligible increases in RMSE caused by the change of coefficients in Table 4 indicates high reliability in the density-based strength predictions. The larger increases in strength-prediction errors listed in Table 5 indicate much less reliable results when using bending stiffness as the strength predictor.
|1||Tension||10,250||6.14||1,320||Coeffs. from no. 2|
|2||Tension||9,680||5.42||1,190||Coeffs. from no. 1|
|3||Bending||11,750||4.06||1,800||Coeffs. from no. 5|
|5||Bending||11,710||3.68||2,210||Coeffs. from no. 4|
|Table 4: Root mean square errors (RMSE) for density-based strength predictions.|
|1||Tension||-2.62||.0135||.0412||2,690||Coeffs. from no. 2|
|2||Tension||-3.07||.0602||-.0088||2,340||Coeffs. from no. 1|
|3||Bending||-4.48||.0469||.0409||2,310||Coeffs. from no. 5|
|5||Bending||-2.10||.0358||.0315||2,640||Coeffs. from no. 4|
|Table 5: Root mean square errors for bending-stiffness-based strength predictions.|
Board groups 4, 5, and 6 were 3-profile-scanned corresponding to Figure 2. In the single-profile results reported in Table 2, the three density profiles had been averaged to simulate the single-profile arrangement in Figure 1. Here, the data from the three measured density profiles are used individually. Table 6 summarizes the strength estimates from the 3-profile density measurements with board groups 4, 5, and 6, and also the corresponding bending-stiffness results.
Table 6 expands on the data in Tables 2 and 3 to include the effects of the weights (wi). For bending loadings, weight w1 represents the compressive edge, w2 the center, and w3 the tensile edge of the board. Three calculationsare done for each of the board groups. The "1-profile" calculation uses equal weights to simulate the effect of singleprofile density scanning. This reproduces the results in Table 2. The "3-symmetric" calculation uses all three weights to represent 3-profile density scanning. In this calculation, weights w 1 and w3 are constrained to be the same, to correspond to the symmetrical case where the board can be loaded eitherway up. The final "3-unsymmetric" case is a general 3-profile calculation where the weights are allowed to be unsymmetrical. These results refer to loading the board a specific way up.
The sequence of calculations in Table 6 represents an increasing degree of detailed knowledge of the position of the knots in the board samples. For the bending strength calculations, this detailed knowledge allows increasingly more accurate predictions of board strength. The r2 values are increased by over 0.10 and SEE values are decreased by 300 to 400 psi. The large values of weights w1 and w3 in 3-profile calculations confirm the sensitivity of bending strength to knots close to the board edges, particularly the tensile edge. The negative values of w2 are unexpected. They occur because of the large strength sensitivity to edge knots.
The symmetric 3-profile case (3-symmetric) is probably the most suitable for practical bending strength estimations because it applies to loadings either way up. In general, service load direction is not known in advance. If the direction of service load can be specified, strength-prediction accuracy can be enhanced by using the unsymmetric 3-profile calculation instead.
Figure 4 shows comparisons of the measured and estimated strengths of the boards in group 5 determined using the bending-stiffness, 1-profile, and symmetric 3-profile density methods. The reduced scatter in Figures 4b and 4c clearly demonstrates the improved strength-estimation capabilities of the density method compared to the bend ing-stiffness method. The graphs also illustrate the further improvement that can be achieved by using multiple-profile scanning when estimating bending strength.
|Test type||Method||r2||SEE||Optimal coefficients|
|Table 6: Comparison of bending-stiffness and various density-based strength estimates.|
For compression-strength calculations, detailed knowledge of knot position within a cross section provides no significant advantage because compression strength is relatively insensitive to knot position. For board sample group 6 in Table 6, all density-based calculations give similar r2 and SEE values. Tensile strength is also relatively insensitive to knot position within the board cross section. Multiple-profile measurements made during another study on a sample of Douglas-fir tested in tension showed similar insensitivity to knot position. Thus, for tension or compression strength predictions, 1-profile scanning or equal-weight multiple-profile scanning is sufficient.
A related question is how well density scanning can be expected to indicate board strength when it evaluates only two strength-controlling factors: knots and clear wood density. It does not indicate other important strength-controlling factors such as grain direction. However, in practice, even when board failure occurs because of other factors such as grain direction, the density-based method still gives reasonable strength estimates. This behavior probably occurs because board strength is a "weak link" process. That is, the weakest area of a board controls the strength of the entire board. When board failure occurs because another factor has caused the most serious area of weakness, it is likely that there are also other areas where knots have caused almost equal weaknesses. Of course, improvement in strength estimation can be expected if the ihother factorslo are explicitly included in the calculation.
When comparing measured and estimated wood strength data, the assumption is often implicitly made that the measured data are ideal and that all discrepancies are contained in the estimated data. In Figure 4, this corresponds to all the uncertainty being contained in the abscissa, and none in the ordinate. However, it is clear that the measured strength data do actually contain significant uncertainty. This uncertainty occurs because the standard tests used for determining bending and compression strengths only apply significant load to a very small fraction of each test board. To make the test represent all the board material, the test technician has to choose the loading zone according to a personal judgment of the weakest region in the board. This choice is a subjective one, and can vary substantially among different test personnel. The destructive nature of the strength testing often means that other potentially weak regions of a board cannot subsequently be tested to validate the original load position choice.
|Fig 4:Measured and estimated bending strengths of board group 5 determined by different methods:a) bending stiffness; b) 1-profile density; and c) 3-profile density (symmetric).|
The bending and compression strength test uncertainty becomes a significant issue when seeking to make strength predictions without knowing in advance where the boards are going to be loaded. This circumstance is likely to be the case in practical quality control procedures in sawmill operations. Such quality control procedures combine the uncertainties due to the test and the prediction method, and unfairly attribute them both to the prediction method. Misattribution of the uncertainty in board strength becomes increasingly significant when assessing the performance of higher accuracy strength-prediction procedures.
When load position is not known, the strength prediction is based on the calculated weakest location in a board. This calculation includes large areas of the board that are not subsequently loaded. Inclusion of data from such untested areas can detrimentally affect the strength prediction, especially if the load position choice is poor. Table 7 compares the strength predictions possible both with and without knowing the test load positions. The ihknown load positionln results come from calculations using density data only from within the region of applied load. The "unknown load position". calculations use density data from the entire length of the boards. Table 7 includes all six board groups, using 1-profile calculations for groups 1, 2, and 3, and unsymmetric 3-profile calculations for groups 4, 5, and 6.
For the bending test groups 3, 4, and 5, uncertainty of the load position impairs the strength-prediction accuracy by 0.06 to 0.18 for r2 and by 150 to 450 psi for SEE. This reduction in accuracy has two main causes: incorrect choice of weakest board location and strength-prediction uncertainty. The first type ofuncertainty occurs when the chosen load position does not contain the actual weakest location in the board. The second type occurs when the predicted weakest location differs from the actual weakest location. It is hard to separate these two uncertainties.
Board group 4 was tested in a non-standard way. The bending load was applied at a fixed location on each board, independent of observed defect locations. Because of this, the measured bending strength often differed quite substantially from the bending strength at the weakest location on the board. This effect caused the abnormally large difference in the results in Table 7 for known and unknown load positions.
The data for compression test group 6 also show a large difference between known and unknown load positions. The test uncertainties are magnified here because of the very small size of the tested region and also the limitation of having to take the specimens from the unbroken material remaining after bending testing. Care was taken not to include any material damaged by the previous bending testing.
The tension tests 1 and 2 are complementary to the bending and compression tests. Here, the entire length of the board is loaded during the test, and so there is no uncertainty associated with choice of load position. The known load position result in Table 7 refers to the strength prediction made using density data from around the actual break positions. The smallness of the difference between the known and unknown load positions suggests that the density method is successful in assessing the weakest board location.
Comparative calculations for the effect of knowing the loading position on bending-stiffness-based measurements could not be made here. The testing machines used in this study only reported the average and minimum E-values. Unfortunately, they did not provide the along-length measurements of E-profile needed for a load position analysis. Some recent models of industrial bending-stiffness testers do provide the ability to indicate E-profile. Based on the results shown in Table 7, some improvement in strength-estimation capability could be expected from such machines. However, the size of that improvement cannot be conjectured here.
|Board group no.||Test type||Known load position||Unknown load position|
|Table 7: Strength predictions with and without knowledge of load position.|
X-ray lumber density scanning gives board strength estimates that are significantly superior to those from bending-stiffness measurements. For several groups of southern yellow pine boards totaling over 800 pieces, correlations of estimated vs. destructively measured strength gave r2 values in the range 0.68 to 0.78, and SEE values in the range 900 to 1,800 psi. The corresponding results from bending-stiffness grading are r2 = 0.50 to 0.60 and SEE = 1,200 to 2,500 psi. This increase in lumber strength grading accuracy directly translates into increased yields of higher value stressrated products. The results presented in this study are for southern yellow pine lumber. Other tests with western species such as fir and hemlock also show strength-prediction capabilities superior to those from bending-stiffness grading, although with r2 and SEE values slightly inferior to those for the southern yellow pine considered here. This difference is probably due to the larger knot size typically found in southern yellow pine.
The x-ray method is equally successful for tension, compression, and bending strength estimations. All three of these strength values can be simultaneously estimated from the measured board density data. Multiple-profile density measurements significantly improve the accuracy of bending strength estimations. For tension and compression strength estimations, single-profile measurements are sufficient because in these cases the applied stresses are uniform within the lumber cross section.
The data presented here indicate a significant uncertainty in the measured bending and compression strengths. This uncertainty occurs because both tests use very localized loadings. The test technician must attempt to make the loaded part of each board represent the entire board by visual choice of the "weakest" board location. Although made conscientiously, this choice often appears not to be the best one. The test position uncertainty becomes a significant issue when endeavoring to make higher accuracy strength predictions. In measured vs. predicted strength comparisons, the measurement uncertainty is unfairly classified as increased prediction uncertainty.
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