Determination of the modulus of elasticity in bending of structural timber - comparison of two methods Holmqvist, C.1 and Boström, L.2 ABSTRACT The current method for determination of modulus of elasticity (MOE) in Europe, EN 408, does not specific enough instructions to obtain comparable results between institutes. There are different interpretations especially regarding the placements of deflection yokes and transducers and also regarding the evaluation of test results. This paper proposes a modified test method, similar to the one in the USA and Australia. The advantages would not only be consistent and reliable results but also a possibility to compare test results between Europe and North America. In order to obtain correction factors to transfer results from the current EN 408 method, called local MOE (EL), to the proposed method, called global MOE (EG), 800 beams were tested. The tests were performed at the Norwegian Institute of Technology (NTI), the Swedish National Testing and Research Institute (SP), the Swedish Institute for Wood Technology Research (Trätek) and the Technical Research Centre of Finland (VTT). An attempt to take characteristics, such as density, knot size, timber depth and sawing pattern into account was made. The results show that high or low density has no effect on the EL/EG ratio but the knot size seems to have. From where timber originates, pith or bark, does not have a clear influence. The differences are however large. Based on all material there seems not to be any effect of timber depth, but looking at each institute separately, there is. Finally, an equation for transferring test results from the current method into the proposed method was determined. This should be handled with care due to different assessment methods for EL at different institutes. INTRODUCTION The method for determining the modulus of elasticity in bending (MOE) in the European standard EN 408 does not give consistent and reliable results (Boström et al. 1996; Boström 1997; Boström 1999; Solli 1996). The determination of the MOE is based on measurement of a deflection over a relatively short span between the loading points. The deflections are small, often less than 1 mm. Hence the method is sensitive to measurement errors. Such errors can be caused by twisting of the timber during the test (Solli 1996). In addition to this, Boström et al. (1996) have shown that different MOE-values are obtained depending on where on the beam the deflection yokes are placed. It seems that measuring deflection on the top surface gives a higher MOE than at mid depth. Whether the deflection is measured on both sides of the beam or only on one also seems to have an influence (Solli 1996). It is evident that the method in EN 408 does not particularise enough where and how the measurement of deflection should be done. The method is open for different interpretations and as a result of this the MOE-values are likely to differ depending on where the tests are carried out. This is unacceptable and has lead to discussions regarding changes of the test procedures and the experimental set-up in EN 408. The objective of this project was to propose a modified test method for MOE and determine the influence it will have on the test results. It was also an aim to determine an equation or ratio to transfer the properties determined using the current EN 408 into results complying with the proposed version. The proposed test method should reduce the disadvantages of the current EN 408 to a minimum and possibly also correspond to other methods used for MOE determination. In Australia and North America the mid-span deflection in relation to the supports is measured. This is often referred to as a ”global” measurement and could possibly be an alternative to the ”local” measurement in EN 408.
1 2
MSc, SP Swedish National Testing and Research Institute, Box 857, S - 501 15 Borås, Sweden PhD, SP Swedish National Testing and Research Institute, Box 857, S - 501 15 Borås, Sweden
METHOD Experimental set-up: Testing according to the current EN 408 The EN 408 standard specifies a four-point bending test, with loads applied at the third points. The distance between supports is 18 times the beam depth, see Figure 1. The deformation is measured over a length equal to five times the beam depth centred within the test span, i.e. the deformation of point B is measured relative to points A and C. The standard does neither specify at what depth the points A, B and C should be located, nor if the deformation should be measured on both sides of the beam or not. However, at SP and NTI the deflection was measured on both sides of the specimen, while at VTT it was done on only one side. At all institutes but Trätek the points A, B and C were located at the neutral axis. At Trätek the measurement was done on the tension side as they have the experience that the repeatability is better when doing so. In all tests, the worst defect was placed centred between the loading points and randomly placed in the compression or tension zone. The resulting modulus of elasticity according to EN 408 will henceforth be called the local modulus of elasticity. P/2
P/2 E A
D FIGURE 1
B
C
F
Experimental set-up used in the present study.
Experimental set-up: Proposed test method The test set-up is the same as in the current EN 408 standard, except that the deformation is measured with one gauge at point E relative to the supports, points D and F. Only one gauge is used and it is attached centrally to the compression face of the beam. In all tests, the worst defect was placed centred between the loading points and randomly placed in the compression or tension zone. The resulting modulus of elasticity according to this method will henceforth be called the global modulus of elasticity. The advantage of the proposed method is that it is very similar to methods used elsewhere. Below the test set-ups for methods currently used in the US, Australia and New Zealand are described. Those methods, however, declare a span to depth ratio between 17 and 21. In the proposed method this ratio is fixed to 18 in order to simplify the comparison of results. Another advantage of the proposed method is that the measured deflection will become greater than in the current EN 408 since it is measured over a longer span and that not only deflection due to bending strains is present but also due to shear strains. Experimental set-up in other standards The experimental set-up for the global modulus proposed above is very similar to the North American standard ASTM D4761 which states a span-to-depth ratio of between 17 and 21. A normal practice used in the American in-grade program has been a span-to-depth ratio of 17. The critical section, i.e. the worst defect, is placed within the test span, not necessarily centred, and the tension edge is randomly chosen. The deflection measurement is made at the neutral axis over the whole length, i.e. the deformation of point B relative to points A and C as shown in Figure 2. P/2 P/2 B
A FIGURE 2
Experimental set-up according to ASTM D4761.
C
The AS/NZS 4063 standard is used in Australia and New Zealand. It deviates very little from the ASTM-standard. A fixed span-to-depth ratio of 18 is stated. The tension edge is randomly selected and the worst defect is randomly placed, i.e. not necessarily within the test span. The deformation is measured globally as the deformation of point E relative to points D and F as shown in Figure 3. P/2 P/2
D
F
E FIGURE 3
Experimental set-up in accordance with AS/NZS 4063. MATERIAL
The tests were performed on Norway spruce timber (Picea abies). A total of 800 beams of five different sizes and with different characteristics were tested. The participating institutes Norwegian Institute of Technology (NTI), SP Swedish National Testing and Research Institute (SP), Swedish Institute for Wood Technology Research (Trätek) and Technical Research Centre of Finland (VTT) tested 200 beams each divided into sub-samples according to Table 1 below. Each subsample with different characteristics consisted of 50 specimens. TABLE 1 Specimen sizes and timber characteristics of the beams in the project and geographical origin. Institute Timber sizes Timber characteristics Origin NTI: Oslo, Norway 45x120, 45x145 Close to the pith, close to the bark South-eastern Norway SP: Borås, Sweden 45x145, 70x220 High density, low density South-western Sweden Trätek: Stockholm, Sweden 45x145, 45x195 Large knots, small knots Central Sweden VTT: Esboo, Finland 34x70, 45x145 Close to the pith, close to the bark Central Finland Sampling procedure Each institute sampled its own material from the regions according to Table 1. The following guidelines with respect to knot size and density were used at the sampling: Large edge knot: Small edge knot:
22 - 26 mm < 17 mm
High density: Low density:
> 460 kg/m3 < 420 kg/m3
No special guidelines were used to separate timber taken close to the pith and timber taken close to the bark. The sampling with respect to knots was performed on 50x150 mm and 50x200 mm timber in sawn condition. A sample of 600 beams was used for each timber size. The beams with the largest knots, a total of 50 pieces for each dimension, and the beams with the smallest knots, a total of 50 pieces for each dimension, were selected from the sample. The density was determined at the saw mill in a simple way by weighing and measuring the dimensions of the specimens. 50 pieces with as high density as possible were selected for each timber dimension, and 50 pieces with as low density as possible were selected for each timber dimension. All beams were dried to 12 % moisture content and planed before testing. RESULTS AND DISCUSSION The local and global modulus of elasticity have been determined for all specimens. The mean of each sub-sample is presented in Table 2 as well as a ratio between the local and global modulus of elasticity. It is difficult to draw any conclusions from the mean ratios between local and global modulus of elasticity of each sub-sample. The general trend, however, seems to be that the local MOE is greater than the global. Equations for transferring test results from the current method into the proposed method are presented in Table 2 for the non-linear case and in Table 3 for the linear case. All test results are shown in Figure 4. Whether a linear or non-linear regression analysis is performed has no effect since the coefficients of determination are similar.
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FIGURE 4
Institute
Dimension
Relation between local and global modulus of elasticity for all specimens. TABLE 2 Selection parameter
[mm2] VTT
35x70
VTT
45x145
TRÄTEK
45x145
SP
45x145
NTI
48x123
NTI
48x148
TRÄTEK
45x195
SP
70x220
All All
45x145 -
pith bark all pith bark all small knots large knots all low density high density all pith bark all pith bark all small knots large knots all low density high density all -
Test results and non-linear regression coefficients. Mean EL Mean EG E L E G E L = A ⋅ E GB [MPa] 9400 12000 10700 12600 12300 12400 12900 11500 12200 8400 11900 10200 10000 11300 10700 10700 10800 10800 12200 10200 11200 10100 11800 11000 11400 11100
[MPa] 9600 10900 10300 11700 11200 11400 12300 11400 11800 8700 12100 10400 9300 10600 9900 9600 9700 9700 11300 9800 10600 9400 10900 10100 10800 10500
0.98 1.09 1.03 1.08 1.10 1.09 1.05 1.01 1.03 0.96 0.98 0.97 1.08 1.07 1.07 1.12 1.11 1.11 1.08 1.04 1.06 1.07 1.09 1.08 1.05 1.06
A 0.311 0.100 0.058 0.841 0.958 0.969 0.200 0.533 0.227 0.254 0.303 0.354 0.533 0.475 0.598 0.764 0.235 0.431 0.595 0.432 0.380 0.377 1.460 0.724 0.620 0.540
B 1.12 1.26 1.31 1.03 1.01 1.01 1.18 1.07 1.16 1.14 1.13 1.11 1.08 1.09 1.06 1.04 1.17 1.10 1.06 1.10 1.11 1.11 0.97 1.04 1.06 1.07
E L = A ⋅ E G1,073 R2 0.63 0.64 0.68 0.79 0.72 0.75 0.95 0.92 0.94 0.78 0.81 0.89 0.77 0.91 0.88 0.93 0.91 0.91 0.97 0.83 0.92 0.74 0.85 0.83 0.84 0.82
A 0.503 0.560 0.536 0.546 0.557 0.551 0.533 0.512 0.523 0.500 0.499 0.499 0.556 0.547 0.551 0.574 0.572 0.573 0.548 0.532 0.542 0.553 0.553 0.552 0.534 0.540
R2 0.63 0.63 0.66 0.79 0.72 0.75 0.94 0.92 0.93 0.77 0.81 0.89 0.77 0.91 0.88 0.92 0.90 0.91 0.97 0.83 0.92 0.74 0.84 0.83 0.84 0.82
TABLE 3 EG = A⋅ E L + B A B R2 0.724 2460 0.82
Linear regression coefficients for all specimens united. E L = A⋅ EG + B EG = A⋅ E L 2 A B R A R2 1.13 -800 0.82 0.935 0.75
E L = A⋅ EG A R2 1.06 0.82
Figures 5 to 12 are based on non-linear regression coefficients from the test results in Table 2. Figure 5 shows the relationship between the local and global moduli of elasticity for all 45x145 mm2 specimens grouped as sub-samples. Figure 6 shows the same relation for material grouped from each institute. High or low density does not seem to affect the EL/EG ratio but the knot size seems to do. From where timber originates, pith or bark, does not have a clear influence. The differences between the curves are large. The material tested at NTI and VTT resulted in a ratio between local and global modulus of elasticity EL/EG > 1, which means that the local modulus of elasticity always is greater than the global. This is not the case for specimens tested at SP and Trätek, where a large amount of low stiffness material has a local modulus of elasticity that is smaller than the global. The general trend is, however, that the ratio between local and global modulus of elasticity increases with increasing stiffness. 1,20
1,10
1,10
EL / E G
1,20
1,00 E L/ EG
1,00 NTI
NTI - close to pith NTI - close to bark
0,90
VTT - close to pith
VTT 0,90
Trätek SP
VTT - close to bark Trätek - small knots
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Local modulus of elasticity, E
12500 L (MPa)
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Trätek - large knots 17500 200 SP - high density
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FIGURE 5 Relation between local and global modulus of elasticity for 45x145 mm specimens.
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Local modulus of elasticity, EL (MPa)
SP - low density
FIGURE 6 Relation between local and global modulus of elasticity for 45x145 mm specimens with united sub-samples.
A non-linear regression analysis on the effect of beam depth (150 mm used as reference) on the relation between EL and EG was performed and the results are presented in Table 4.
TABLE 4
Regression data including timber depth. E L = A ⋅ ( h 150) ⋅ E CG B
NTI SP Trätek VTT All
A 0.525 0.456 0.301 0.259 0.543
B 0.214 0.242 0.133 0.029 0.019
C 1.082 1.083 1.132 1.153 1.072
R2 0.90 0.87 0.93 0.73 0.82
The depth factors (B) in the non-linear regressions of MOE for the specimens tested at NTI and SP are significant and of the same magnitude. The depth factors for specimens tested at VTT and, more importantly, for all specimens taken as one sample are close to zero and the coefficients of determination are quite low. Since the number of timber sizes at each institute is too low to draw any conclusions, the general conclusion on the total material must be that there is no depth effect present.
As can be seen in Figures 7 and 8 the ratio between local and global modulus of elasticity increases with increasing timber dimension. The only exception is the material tested at VTT, where in the 35x70 mm material some extreme values were obtained on the local modulus of elasticity. The reason for this is not clear. It could be, that as the deformation was only measured on one side, twisting of the timber during the test lead to erroneous deformation values. 1,20
1,15
1,15
1,10
1,10
1,05
1,05 EL / EG
1,20
1,00 E L / EG SP 70x220 mm
0,90
VTT 35x70 mm
0,95
SP 45x145 mm
0,95
1,00
VTT 45x145 mm
0,90
NTI 48x123 mm
Trätek 45x145 mm 0,85
0,85
Trätek 45x195 mm
NTI 48x148 mm
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Local modulus of elasticity, EL (MPa)
FIGURE 7 Relation between local and global modulus of elasticity for different specimens sizes with united subgroups.
FIGURE 8 Relation between local and global modulus of elasticity for different specimens sizes with united subgroups.
In Figures 9 to 12 the effect of the different timber characteristics are presented. Figures 9 and 10 show the effect of the location within the log on the EL/EG ratio. This effect was studied at both VTT and NTI. There seems to be a difference between pith and bark, but no clear pattern can be found. 1,20
Samples tested at VTT
1,15
1,15
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1,10
1,05
1,05 EL / EG
EL / E G
1,20
1,00 0,95
35x70 mm - close to pith
0,90
35x70 mm - close to bark 45x145 mm - close to pith
0,85
45x145 mm - close to bark
0,80
Samples tested at NTI
1,00 0,95 48x123 mm - close to pith 0,90
48x123 mm - close to bark 48x148 mm - close to pith
0,85
48x148 mm - close to bark
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Local modulus of elasticity, EL (MPa)
FIGURE 9 Relation between local and global modulus of elasticity for different timber characteristics tested at VTT.
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Local modulus of elasticity, EL (MPa)
FIGURE 10 Relation between local and global modulus of elasticity for different timber characteristics tested at NTI.
Figure 11 shows how the knot size affects the measurements. The tests were performed at Trätek. The material was divided into two sub-samples for each timber size with respect to knot size. Small knots seems to give a higher EL/EG ratio than large knots. Figure 12 shows how the density affects the EL/EG ratio. The tests were performed at SP. The material was divided in two sub-samples with respect to density for each timber dimension. No significant difference in the EL/EG ratio can be seen for the 45x145 mm timber. For the 70x220 mm timber the high density material behaves contrary to the general trend and the EL/EG ratio decreases with increasing stiffness.
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EL / EG
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45x145 mm - large knots
45x145 mm - high density 45x145 mm - low density
0,90
45x195 mm - small knots
0,85
1,00 0,95
45x145 mm - small knots
0,90
Samples tested at SP
70x220 mm - high density
0,85
45x195 mm - large knots
0,80
70x220 mm - low density
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Local modulus of elasticity, EL (MPa)
FIGURE 11 Relation between local and global modulus of elasticity for different timber characteristics tested at Trätek.
FIGURE 12 Relation between local and global modulus of elasticity for different timber characteristics tested at SP.
It was stated in advance that both testing and evaluation for local MOE should be performed according to EN 408 as it is normally done at each institute. As expected from the discussion in the Introduction, there are large differences in results between the participating institutes. Figure 13 presents results NTI and SP, which used basically the same test set-up and evaluation procedure for local MOE. There is a significant difference in the relation between local and global MOE, but as the values were not obtained from the same material, conclusions have to be drawn with care. This is also one reason for the different results in terms of EL/EG ratio between the different participating institutes.
Local modulus of elasticity, E L (MPa)
18000 16000 14000 12000 10000 8000 6000 45x145 mm tested at SP 4000
48x148 mm tested at NTI
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Global modulus of elasticity, EG (MPa)
FIGURE 13
Relation between local and global modulus of elasticity of 45x145 mm2 timber tested at NTI and SP. CONCLUSIONS
A modified test method for determining MOE is presented that has a major advantage compared to the current one. It is comparable to what today is used in the USA and in Australia. The method’s test results are compared to the currently used European method EN 408, but due to differences in method interpretation of the current EN 408 between the participating institutes it is difficult to draw any extensive conclusions. Equations for transferring test results determined according to the current method into the proposed method was however determined. These should be handled with care. The following general conclusions can yet be drawn: • The two methods for determining a modulus of elasticity, based on local respectively global measurement of deformation, give different results. • The ratio between local and global modulus of elasticity, EL/EG, increases with increasing local modulus of elasticity and can obtain values between 0.8 and 1.2.
• The size of defects, in this case knots, seems to affect the ratio between local and global modulus of elasticity. Material with small knots give a somewhat higher EL/EG value than material with large knots. The number of specimens is however small. • The study did not show any consistent effect from either sawing pattern or density on the ratio between local and global modulus of elasticity. No effect of beam depth could either be seen when taking all data into account.
Finally, the test results indicate that it will become very difficult to transfer properties determined using the current EN 408 into the new method. Even though there is a relation between the EL and the EG, these data are difficult to compare since the EL results are differently assessed. Also, the monitored characteristics do not show a consistent pattern and hence will be of little help. REFERENCES • Boström L, Ormarsson S, Dahlblom O (1996): On determination of modulus of elasticity. CIB W18 Meeting 29, Paper 29-10-3 • Boström L (1997): Measurement of modulus of elasticity in bending. CIB W18 Meeting 30. Paper 30-10-2 • Boström L (1999): Measurement of modulus of elasticity in bending of structural timber - comparison of two methods. Holz als Roh und Werkstoff 57, pp 145-149 • Chrestin H, Boström L (1997): The influence of timber origin on machine strength grading yield. IUFRO 5.02 Meeting in Copenhagen, Denmark • Solli K (1996): Determination of modulus of elasticity in bending according to EN 408. CIB W18 Meeting 29. Paper 29-10-2
