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Tensile-strength incidence mechanism of structural finger-jointed laminae.

Abstract

The mechanism of tensile-strength incidence of structural finger-jointed laminae was investigated. Tensile Young's moduli and strains at the finger joint (FJ) and the solid members near the FJ were measured using strain gauges. Sugi (Cryptomeria japonica D. Don) lumber was used. All failures occurred at the FJ, mostly at the base of the FJ with a lower tensile Young's modulus. The values of the tensile Young's moduli and strains at the FJ were almost equal to the average of the values of the solid members near the FJ. With a linear elastic theory of stress, the tensile Young's moduli, strains, and tensile strengths at the FJ were calculated. The theoretical values accurately agreed with the test data. From correlation to the tensile strength of the FJ, maximum strain energy, instead of maximum strain, was considered to be a better failure criterion for characterizing the behavior of the FJ.

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Solid lumber used for structural finger-jointed laminae are graded by strength before finger-jointing by machine stress-rating based on the average bending Young's modulus along the length of the solid lumber. However, it is known that there are relatively large variations in bending Young's modulus along the length of solid lumber (Kass 1975, Samson 1985). The strength of a finger joint (FJ) is considered to be influenced by the solid member strengths near the FJ. Therefore, the relationship between the FJ strength and solid member strengths near the FJ should be investigated in detail.

Other researchers (Burk and Bender 1989, Hoshi and Hayashi 1991) have investigated the strength properties of finger-jointed laminae using solid members with different bending Young's moduli. However, the relationship between the FJ strength and solid member strengths near the FJ, and the incidence mechanism of the FJ strength, have not been investigated in detail. Although finite element methods have been applied to FJ strength analysis (e.g., Aicher and Klock 1991, Pellicane 1994), these analyses were mainly aimed to predict a stress distribution in FJ and optimize the FJ profile, and their practical applications were not sufficient.

In this study, we actually measured the tensile Young's moduli and strains at the FJ and the solid members near the FJ using strain gauges. The relationship between the FJ strength and solid member strengths near the FJ was investigated. The tensile-strength incidence mechanism of the FJ was analyzed with a linear elastic theory of stress. Failure criteria for describing the performance were also investigated.

Experimental

Materials

The test material was sugi (Cryptomeria japonica D. Don) lumber grown in the Kyushu region of Japan. The kiln-dried sugi members were finger-jointed and were finished into 30-mm-thick, 120-mm-wide, and 1,800-mm-long members with the FJ at the center. Forty laminae were fabricated. The bending Young's moduli of the members were measured by a grading machine before jointing, and the members with a wide difference of bending Young's modulus (provide range) were selected for the laminae. The geometry of the FJ was: vertical, 25 mm long, 7 mm pitch, 0.8 mm tip width, 8 degrees slope. Adhesive was a phenol-resorcinol formaldehyde (Aica Kogyo Co. Ltd., PRX-350AM), which was radio-frequency heated for about 30 seconds after jointing. The specimens were conditioned for more than 1 week before testing. The average density and moisture content of the specimens were 0.38 g/[cm.sup.3] and 10.1 percent, respectively.

Methods

In the tension test, four and six strain gauges (Kyowa Electronic Instruments Co. Ltd., KFG-10-120; 10 mm long) were attached on the center of the FJ (two strain gauges per wide face) and on the solid members near the FJ (two per wide face and one per narrow face), respectively (Fig. 1). For each specimen, a total of 16 strain gauges were attached parallel to the load axis and on the glueline for the FJ. The strain gauges were bonded using a cyano-acrylatebased adhesive (Kyowa Electronic Instruments Co. Ltd., CC-35). The stresses and strains at the FJ and the solid members were measured to the failures of each specimen and recorded with a data logger. The maximum capacity of the testing apparatus (Maekawa Testing Machine Co. Ltd., HZS-50) was 500 kN, and the distance between the chucks was 600 mm. The times to failure ranged from 1 to 2 minutes. The strains at the FJ and the solid members were obtained by averaging each strain value from the attached strain gauges.

Results and discussion

The test results are summarized in Table 1 and Figure 2. A typical ([sigma]) strain ([epsilon]) diagram is shown in Figure 3. The relationships between stress and strain were approximately linear to the maximum stress for all test data. All failures occurred at the Fl, mostly at the base of the Fl with a lower tensile Young's modulus. The values of the tensile Young's moduli and strains at the FJ were almost equal to the average of the values of the solid members near the FJ.

To investigate the tensile Young's modulus and tensile strength of the Fl, the FJ was modeled using the test data (Fig. 4). At the cross section of the FJ in this model, a tensile load (P) was divided into [P.sub.1] and [P.sub.2] at the glueline for each tensile Young's modulus. The tensile Young's modulus ([E.sub.alpha]), strain ([[epsilon].sub.[alpha]]), and strain energy ([W.sub.[alpha]]) at a normalized area, [alpha] (defined as A1 I [[A.sub.1] + [A.sub.2]), were calculated using the ratio of tensile Young's modulus at each solid member, [beta] (defined as [E.sub.high] / [E.sub.low]) (see Eqs. [1], [2], and [3]). Here, the strain in the FJ at each normalized area is constant, and the shear strength of the glueline is ignored. The effects of stress concentrations at the finger tip gaps are also ignored in this calculation, because the calculation is for locations far from the finger tips.

P = [P.sub.1] + [P.sub.2] [E.sub.[alpha]] x [[epsilon].sub.[alpha]] x ([A.sub.1] + [A.sub.2]) = [E.sub.low] x [[epsilon].sub.[alpha]] x [A.sub.1] + [E.sub.high] x [[epsilon].sub.alpha] x [A.sub.2] [alpha] = [A.sub.1] ([A.sub.1] + [A.sub.2]) [E.sub.[alpha]] = [E.sub.tow] x [alpha] [E.sub.high] x (1 - alpha]) [beta] = [E.sub.high] / [E.sub.tow] [E.sub.[alpha]] = [E.sub.tow] x [alpha] + [E.sub.tow] x (1 - [alpha]) x [beta] [E.sub.[alpha]] = {(1 - [beta])[alpha] + [beta]} [E.sub.tow] [1]

P = [P.sub.1] + [P.sub.2] [E.sub.tow] x [[epsilon].sub.[alpha] x [A.sub.1] + [E.sub.high] x [[epsilon].sub.[alpha]] x [A.sub.2] = [E.sub.tow] x [[epsilon].sub.1] x ([A.sub.1] = [A.sub.2]) [alpha] = [A.sub.1] / ([A.sub.1] + [A.sub.2]) [[epsilon].sub.[alpha] {[alpha] x [E.sub.tow] + (1 - [alpha]) x [E.sub.high]} = [E.sub.tow] x [[epsilon].sub.1] [beta] = [E.sub.high / [E.sub.tow] [[epsilon].sub.[alpha]] {[alpha] + (1 - [alpha])[beta]} = [[epsilon].sub.1] therefore [[epsilon].sub.[alpha]] = {(1 - [beta])[alpha] + [[beta]}.sup.-1] [epsilon].sub.1] [2]

[W.sub.alpha] = ([E.sub.a] x [[epsilon].sub.[alpha] x [[epsilon].[alpha].sup.2])/2 [3]

An example of the theoretical values of [E.sub.[alpha] [[epsilon].sub.[alpha] calculated from Equations [1], [2], and [3] is graphed in Figure 5. The tensile Young's modulus ([E.sub.alpha]) at a normalized area, [alpha], varied linearly in the FJ. The strain ([epsilon].sub.[alpha]) and strain energy ([W.sub.alpha]) at a normalized area, [alpha], increased gradually from the higher to the lower tensile Young's modulus (E[alpha]). The tensile Young's modulus (EFJ-cal) and strain ([epsilon]FJ-cal) for the entire FJ (10 mm long, in this calculation) are calculated by in-

tegrating [E.sub.[alpha]] and [[epsilon].sub.[alpha]] from [alpha] = 0 to 1 (Eqs. [4] and [5]). The tensile strength of the FJ ([TS.sub.FJ-cal]) can be calculated by Equation [6].

[E.sub.FJ-cal] = [[integral].sup.1.sub.0] [E.sub.[alpha]] d[alpha]

= [[integral].sup.1.sub.0] [{(1 - [beta])[alpha] + [beta]} [E.sub.low]]d[alpha]

= (0.5 + 0.5[beta]) [E.sub.low] ([beta] = [E.sub.high] / [E.sub.low]) [4]

[[epsilon].sub.FJ-cal] = [[integral].sup.1.sub.0] [[epsilon].sub.[alpha]][d.sub.[alpha]]

= [[integral].sup.1.sub.0] [[{(1 - [beta])[alpha] + [beta]}.sup.-1] [[epsilon].sub.1]]d[alpha] =

{ln[beta] / ([beta] - 1)}[[epsilon].sub.1] ([beta] = [E.sub.high] / [E.sub.low]) [5]

[TS.sub.FJ-cal] = [E.sub.FJ-cal] x [[epsilon].sub.FJ-cal] [6]

Comparisons of the test data ([E.sub.FJ], [[epsilon].sub.FJmax], [TS.sub.FJ]) and the theoretical values ([E.sub.FJ-cal], [[epsilon].sub.FJ-cal], [TS.sub.FJ-cal] from Eqs. [4], [5], and [6]) for the FJ part are shown in Figure 6. A high correlation between the test data and the theoretical values was obtained for both the tensile Young's modulus and strain. The tensile strength of the FJ, therefore, was calculated accurately with Equations [4], [5], and [6]. The suitability of these calculation methods to other FJ, e.g., other slope angles of FJ, species, or composites, must still be investigated.

In this test, the correlation between the tensile strength ([TS.sub.FJ]) and the tensile Young's modulus ([E.sub.FJ]) of the FJ was weak (Fig. 7). This is important for considering the present Japanese Agricultural Standards (JAS), in which the strengths of finger-jointed laminae are graded using their bending Young's moduli. To investigate the correlation between the tensile strength and tensile Young's modulus of FJ, Fujita et al. (200_) measured the tensile Young's moduli in a distance of 200 mm with the FJ positioned at the center. In their experiment, a regression curve, [TS.sub.FJ] = 9.5[E.sub.FJ.sup.0.5] ([r.sup.2] = 0.401), was obtained from 365 specimens (79 for sugi and 286 for Douglas-fir [Pseudotsuga menziesii Franco]). This regression curve was based on maximum strain energy ([W.sub.Fjmax]) as a failure criterion of the FJ; [TS.sub.FJ] [infinity] [E.sub.FJ.sup.0.5] ([W.sub.FJmax] = [TS.sub.FJ] X [[epsilon].sub.FJmax] / 2 = [TS.sub.FJ.sup.2] / 2 [E.sub.FJ] = const.). Using the regression curve, th e test data in the present experiment were compared for the tensile Young's moduli at the FJ ([E.sub.FJ]) and the solid members ([E.sub.low], [E.sub.high]), and each standard error (se) from the regression curve was calculated (Fig. 8). From the result, the value of standard error for the data at the FJ was the smallest (3.99 vs. 4.16 and 5.01). Therefore, the relationship between the tensile strength and tensile Young's modulus of the FJ is characterized with the regression curve.

Failure criteria for the FJ were investigated using the test data for maximum strain energy ([W.sub.Fjmax]) and maximum strain ([[epsilon].sub.FJmax]). The results are shown in Figure 9. The correlation between the tensile strength of the FJ and maximum strain energy was greater than maximum strain ([r.sup.2] = 0.867 vs. 0.576). Thus, maximum strain energy, instead of maximum strain, is a better failure criterion for characterizing the behavior of the FJ.

Summary

From the experimental results using strain gauges, the values of the tensile Young's moduli and strains at the FJ were almost equal to the average of the values of the solid members near the FJ. To characterize this mechanism, a linear elastic theory of stress was used, and the tensile Young's moduli, strains, and tensile strengths at the FJ were calculated. These parameters were accurately represented with the theoretical values. From correlation to the tensile strength of the FJ, the failure criterion for the FJ was predicted better by the maximum strain energy theory than the maximum strain theory.

[FIGURE 3 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]
Table 1

Summary of the test results. (a)

n = 40 [TS.sub.FJ] [E.sub.low] [E.sub.FJ] [E.sub.high]
 (MPa) (GPa)

[micro] 21.6 4.88 5.68 6.62
COV(%) 16.4 13.27 12.51 17.47
Maximum 31.0 6.54 7.13 9.17

Minimum 14.7 3.33 4.54 5.02


n = 40 [E.sub.high]/[E.sub.low] [[epsilon].sub.1]
 (GPa) ([10.sup.-3])

[micro] 1.38 4.65
COV(%) 22.89 22.47
Maximum 2.14 7.51
 (9.17/4.28)
Minimum 1.01 2.49
 (5.73/5.70)

n = 40 [[epsilon].sub.FJ].sub.max] [[epsilon].sub.2]
 ([10.sup.-3])

[micro] 4.03 3.42
COV(%) 19.30 24.25
Maximum 5.59 5.21

Minimum 2.13 2.06


n = 40 [W.sub.FJ].sub.max]
 (kPa)

[micro] 44.60
COV(%) 33.05
Maximum 84.41

Minimum 15.66


(a)[TS.sub.FJ] tensile strength at the FJ (maximum stress: maximum
load/cross-sectional area of member [30 x 120 [mm.sup.2]])

[E.sub.low], [E.sub.high]=tensile Young's modulus at each solid member

[E.sub.FJ] = tensile Young's modulus at the FJ

[[epsilon].sub.1], [[epsilon].sub.2] = maximum strain at each solid
member ([[epsilon].sub.1]: maximum strain of solid member with
[E.sub.1ow], [epsilon.sub.2]: maximum strain of solid member with
[E.sub.high])

[[epsilon].sub.FJ].sub.max] = maximum strain at the FJ

[[W.sub.FJ].sub.max] = maximum strain energy at the FJ ([TS.sub.FJ] X
[[epsilon].sub.FJ].sub.max]/2)

n = number of specimens

[micro] = mean

COV = coefficient of variation. Tensile Young's moduli are obtained from
slope of stress-strain curve between 10 and 40 percent of maximum
stress.


Literature cited

Aicher, S. and W. Klock, 1991. Finger joint analysis and optimization by elastic, nonlinear and fracture mechanics finite element computations. In: Proc. International Timber Engineering Conference, London, 3, pp.66-76.

Burk, A.G. and D.A. Bender. 1989. Simulating finger-joint performance based on localized constituent lumber properties. Forest Prod. J. 39 (3): 45-50.

Fujita, K., H. Yoshimura, C. Goto, T. Morita, T. Hayashi, K. Komatsu, and Y. lijima. 200_. A study on the tensile-strength properties of laminae for glulam beams (in Japanese).M. Gakkaishi (to be published).

Hoshi, T. and T. Hayashi. 1991. Strength properties of finger-jointed lumber for structural use I. Bending and tensile strength of sugi finger-jointed lumber (in Japanese). M. Gakkaishi 37, 194-199.

Kass, A.Y. 1975. Middle ordinate method measures stiffness variation within pieces of lumber. Forest Prod. J.25 (3): 33-41.

Pellicane, P.J. 1994. Finite element analysis of finger-joints in lumber with dissmilar laminate stiffnesses. Forest Prod. J.44(3): 17-22.

Samson, M. 1985. Potential of finger-joined lumber for machine stress-rated lumber grades. Forest Prod. J. 35 (7/8): 20-24.

The authors are, respectively, Research Fellow, Institute of Wood Technology, Akita Prefectural Univ., Noshiro 016-0876, Japan (current address: Researcher, Kochi Prefectural Forest Technology Center, Tosayamada 782-0078, Japan); Researcher, Hiroshima Prefectural Forestry Research Center, Miyoshi 728-0015, Japan; Chief, Forestry and Forest Products Research Institute, Tsukuba 305-8687, Japan; Professor, Wood Research Institute, Kyoto Univ., Uji 611-0011, Japan; Lecturer, Institute of Wood Technology, Akita Prefectural Univ.; and, Professor, Institute of Wood Technology, Akita Prefectural Univ. The results of this work were presented at the 19th Annual Meeting of the Japan Wood Technological Assoc., October 26-26, 2001, Tokyo, Japan. The authors would like to thank Yamasa Mokuzai Co. Ltd. for supplying test specimans. This paper was received for publication in January 2002. Article No. 9426.

Tomoyuki Hayashi *

* Forest Products Society Member.

[C] Forest Products Society 2003.

Forest Prod. J. 53(6):58-62.
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Author:Morita, Takao; Fujita, Kazuhiko; Yoshimura, Hideyuki; Goto, Chizuko; Hayashi, Tomoyuki; Komatsu, Koh
Publication:Forest Products Journal
Geographic Code:9JAPA
Date:Jun 1, 2003
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