Tension strength capacity of finger joined beech lamellas

Tension strength capacity of finger joined beech lamellas

Barbara Fortuna

_{*, Mitja Plos}

_{, Boris Azinović}

_{, Tamara Šuligoj}

_{and Goran Turk}

1_{University of Ljubljana}

Faculty of Civil and Geodetic Engineering Ljubljana, Slovenia

2_{Slovenian national Building and} Civil Engineering Institute

Ljubljana, Slovenia

ABSTRACT

Beech wood has high mechanical properties, therefore the production of high quality beech glulam beams is one of our main objectives. Finger joints with standard geometries and adhesives used for joining coniferous wood are not sufficient in terms of strength when gluing beech wood. A hybrid glulam beam was produced and tested in a standard four point bending test. The beam was produced from finger joined beech lamellas on the outer sides and finger joined spruce lamellas in the middle. The results from the bending test showed a lack of tensile strength of the finger joints of beech lamellas on the bottom middle part of the beam, where the rupture occurred. We prepared a numerical model of finger joined beech lamellas and simulations of tension tests, parallel to the lamella. We performed parametric studies with multiple variables referring to geometrical properties of finger joints and two different types of applied adhesives. The results showed a high influence of the finger joint geometrical parameters. Experimental tests on the tension strength of the finger joints were performed. Two finger joint lengths were tested, 10 and 20 millimetres. The results showed a clear influence of the finger joint geometry where highest strengths were obtained with longer and thinner fingers.

1. INTRODUCTION

Finger joints were primarily designed for use in softwood bonding. Since hardwoods usually have higher mechanical properties than softwood, the currently used finger joint design might pose a problem for joining beech. This was observed during the hybrid glulam bending test and also in other research (Ehrhart et al., 2018). To address the issue, we decided to perform analytical and numerical calculations and try to find a finger joint design better suited for beech wood. To evaluate the simulations, samples were made and tested using different adhesives and finger joint lengths .,

The strength of a finger joint is essentially determined by three factors, the strength of the joined boards, the quality of the production and the finger joint profile (Aicher and Radovic, 1999; Collin and Ehlbeck, 1992). The type of glue used also plays an important role in the strength of the finger joint (Konnerth et al., 2006). We tried to take into account as many of the significant variables as we could, excluding the production process. The main focus was the finger joint profile. We expected that the finger joint length would play a major role in the strength of the joints. This was shown in the study of Franke, Schusser and Müller (2014), where longer (50 mm) finger joints resulted in a higher flat-wise bending strength and in the study of Tran, Oudjene and Méausoone (2014) where maximal finger joint length and minimal pitch produced the best results in edge-wise bending tests.

Our primary focus was to find a solution for finger joints in beech wood, that could withstand the higher tension strengths. This could enable the glulam producers to manufacture beech or hybrid glulam with a much higher strength than the most commonly used softwood glulam.

2. METHODS

In the first part of the study, a preliminary assessment of finger joint tension strength was made based on simple equilibrium equations for scarf joints that are, in terms of achieving the highest strength, known as the most effective

in Figure 1 (left). The shear stress σξη and normal stress σηη in the inclined plane were calculated by the following Equations (1) 0 sin cos       and 0 2 sin     , (1)

where σ0 is the normal stress in the longitudinal direction (



were calculated based on the assumption of the quadratic strength criteria by the Equation (2) (Aicher and Klöck, 2001) and the assumed ratio τ1/σu = 6

2 2 1

1















_

_















With the determined strength properties, the obtained nominal tension strength ft was observed. When calculating

the effective length of the glue line, the tip width bt was neglected.

Figure 1: Scarf joint (Aicher, 2003) (left) and finger joint geometry (right).

In the second part of the study, a numerical model was used to estimate the response of the finger joints in tension. The main aim of the parametric studies was the optimization of the finger joint geometry for beech boards.

The tension test was simulated with a 2D numerical model in Abaqus. The model takes into account the symmetrical response along the longer axis of the lamination. Therefore, only a small section of the lamination with one half of the finger was analyzed (Figure 2). The lamination was fixed at one end, while on the other end, a displacement (ux) was induced until failure. The model is supported in transverse direction (uy) due to the symmetry. The eight node biquadratic plane stress quadrilateral elements were used in the finite element. The mesh is condensed in the local area next to the cohesive elements and the cohesive surface (the maximum size of the element was approximately 0.5 × 0.5 mm2).

Figure 2: 2D numerical model of the finger joint.

The model consisted of parts with linear elastic and orthotropic behavior for beech, where the wood fibers were oriented in the longitudinal direction. The mean values for the elastic behavior of beech (Table 1) were assumed according to the literature (Desch and Dinwoodie, 2016; Sandhaas, 2012). The nonlinear behavior was presumed in the finger’s adhesive layer (failure of the joint, modelled by a cohesive surface) and along the weakened area of the pitch (wood failure, modelled by cohesive elements). To model the adhesive layer a cohesive zone model (CZM) approach was used, where the input parameters were based on experiments with melamine urea formaldehyde adhesive (MUF) and beech performed by Khelifa et al. (2016) and Tran et al. (2014). Damage initiation was assumed by a quadratic traction criterion and the evolution of damage was considered according to the energy law.

Table 1: Mean elastic properties of beech.

E1

[MPa] [MPa] E2 ν[-] 12 [MPa] G12

13700 11400 0.51 1060

Note: E1, E2… elastic moduli in the longitudinal and radial directions of the wood; ν12…Poisson’s ratio, where the first index refers to the direction of the applied stress and the second index to the direction of lateral deformation; G12… shear moduli in the 12 plane.

Table 2: Cohezive zone model properties used for the cohesive surface and cohesive elements.

σu τ1 K_nn Ktt,₁ G_f η

[MPa] [MPa] [MPa/mm] [MPa/mm] [mm] [-]

Timber adhesive bond-line

(cohesive surface) 1.6 9.6 default contact enforcement method (high stiffness) 0.50 0.001 Beech along the pitch

(cohesive elements) 70 100 13700 1610 10 5 ∙ 10-6

Note: σu … strength in the normal direction, τ1 … shear strength; Knn … stiffness in the normal direction; Ktt,1 … stiffness in the

shear direction;Gf … fracture energy (mode independent);η … viscosity coefficient

In the parametric study, three different parameters were varied; pitch (p), tip thickness (bt) and length of fingers (l).

Parameters were changed in the range of; (i) α = 2 – 6 º, (ii) bt = 1 - 2 mm and (iii) l= 10 – 50 mm. 3. MATERIAL

The experiments were carried out on beech wood gathered from Southeastern part of Slovenia. Boards were air dried and then sawn and planned to the nominal cross sections of 70 × 20 mm2 _{for the 10 mm long finger joints and 120} × 20 mm2 _{for the finger joints with the length of 20 mm. The density was determined measuring the weight and actual} dimension of each board. The average density of the material was 695 kg/m3_{. The moisture content was measured with} the resistance moisture meter Brookhuis FME. The average moisture content was 9.6 %.

Finger joints were produced in two production companies. The shorter length of 10 mm was produced by a Slovenian window and door manufacturer M Sora d.d. The profile of the finger joints isn’t in compliance with the EN 14080:2010+A1:2012 demands for structural finger joints, where self-interlocking is required. Nevertheless, we decided to include the geometry in the testing program to evaluate the influence of the adhesive type on the strength properties. The geometry is illustrated in Figure 3A. The pitch is p = 6 mm and tip width is bt = 2 mm. The application

of the glue and the joining of the boards were handled manually. Joined boards were then placed in a press for curing for 24 hours. The longer finger joints (20 mm) were produced in a Slovenian glulam producer Hoja d.d., using the cutting knives that are otherwise used for longitudinal joining of spruce lamellas. The configuration is in accordance with the standard for structural finger joints. The pitch was p = 6 mm and the tip width bt = 1 mm. The cutting, glue application

and pressing were automatized. The majority of the joints were pressed under a pressure of 5 MPa while one third of the specimens were joined under 10 MPa of pressure.

Two types of adhesives were used. Melamin-urea formaldehyde (MUF) as one of the most commonly used adhesive for spruce timber among the Slovenian glulam producers and Phenol-resorcinol Formaldehyde (PRF) as one of the adhesives with the highest tensile shear strength (Konnerth et al. 2016).

The length of the boards before gluing was 1.2 m for the 10 mm and 1.5 m for the 20 mm finger joints. The boards were selected in a way that there were no knots within 300 mm from the joint line. Before cutting the finger joint, all the boards were non-destructively tested. The dynamic modulus of elasticity (Edyn) from longitudinal vibrations was

determined with the STIG strength grading machine. The measurements were carried out with a microphone, capturing sound oscillations from a hammer impact on the board’s end. In order to assess the influence of joining on the non-destructive testing, the measurements of Edyn were repeated after the cutting and gluing process.

Glued specimens were then tested in tension. The experiments were carried out according to the EN 408:2010+A1:2012 standard. The test length, clear of the clamping, was 1.20 m and the finger joint was positioned in the middle, between the clamps. For the 10 mm finger joints, only the tension strength was measured, while for the longer finger joints the static modulus of elasticity was also determined. Deformations of the glue line are rather difficult to measure since it is hard to exclude the timber deformation within the length of the measurement. Therefore, we decided to measure the deformations in the same way as it is usually done in tension tests, that is with linear variable displacement transformers (LVDTs) and at a reference length l0 = 600 mm. Knowing that the obtained deformations are a combination of glue and timber deformation, we wanted to assess the quality of the whole joint. In our previous measurements of moduli of elasticity, we observed increased accuracy of the measurements if the loading cycle was repeated three times. When calculating the modulus of elasticity, the last displacement measurement was taken into account. Before further loading, the LVDTs were removed and the specimen was tested to failure. The position of the clamping system remained the same.

A pilot hybrid beech-spruce-beech glulam beam was produced at HOJA d.d. with a cross section of 140 × 300 mm2 and a length of 5 m. The glulam had two layers of 6 lamellas of beech wood and 8 spruce lamellas in the middle with a thickness of 13 mm and 18 mm, respectively. MUF glue was used. The beam was tested in bending according to EN 408:2010+A1:2012. Bending strength, modulus of elasticity and shear modulus were measured.

Figure 5: Bending test on hybrid glued laminated timber made of spruce and beech.

4. RESULTS

For preliminary calculations, a reference shear strength of 8.8 MPa and normal peel strength of 1.5 MPa were used. Both were determined from the average tension strength of the 20 mm finger joints according to the quadratic strength criteria. For a series of different finger joint profiles, we made the estimation of tension strength, shown in Figure 6. The tension strength is linearly correlated to the effective glue line area. On the graphs, the pitch p is expressed indirectly through the slope of the fingers and the influence of each geometry parameter can be seen. The graphs show that longer finger joints produce higher tension strength. The increase of the strength can also be achieved by decreasing the slope α and decreasing the tip width bt. In order to achieve higher strengths, for example 80 MPa which is about 10 % above

the average tension strength of Slovenian beech wood, it would be necessary to increase the length to at least 30 mm, having a rather small slope and tip width compared to the most common geometry profiles (Aicher, 2003).

Figure 6: Graphical demonstration of the influence of the geometrical parameters on the tension strength of finger joints - analytical model.

4.1. NUMERICAL MODEL

Although the obtained strengths were lower, the results from the numerical simulations were similar. The results of the parametric study are shown in Figure 7. An optimal pitch dimension (p) can be found for each curve on the graphs (with a constant bt and l). In the first part of the curve (low values of p), the ultimate load capacity of the joint increases until the optimal p is reached. For smaller values of p (smaller slope of the fingers), the failure occurs in the cohesive elements simulating the failure of wood. After reaching the optimal pitch, the failure mode changes and the load capacity decreases with further increase of p since the area of the glued surface decreases correspondingly. The optimal slope of the fingers proved to be approximately 3-4° for the analyzed numerical model with MUF adhesive and the assumed failure mechanisms. One can observe that the results from the numerical simulation are always lower than those from the analytical analysis. The differences increase with increased length. We believe that tension strength is considerably overestimated by the analytical analysis. This stems from the stresses distribution along the glue line which were assumed to be constant in the analytical model and is not the case in reality, where peaks of the shear stresses occur at the beginning and the end of the glue line.

Figure 7: Ultimate capacity of the finger joint dependent on different geometric parameters - numerical model.

4.2. EXPERIMENTAL TESTING

The results from the tension tests of the 10 mm finger joints showed a significant difference in tension strength between both adhesives. The PRF adhesive clearly had a higher strength than MUF. On average, the ratio between the adhesives was approximately 1:2.25. The obtained tension strengths were very low, which can be explained with the lack of finger joints interlocking in this type of the profile and lack of control of the applied pressure in the curing time. The statistical values are shown in Table 3. In general, the rupture of the specimens occurred along the glue line (Figure 8A), only two specimens, glued with PRF, failed in wood (Figure 8B).

Figure 8: Failiures of finger joints (10 mm) glued with PRF (A) and MUF (B).

As expected, the 20 mm long finger joints proved to have a much higher tension strength (Table 3). The average value for all specimens was 51.0 MPa and the 5th _{percentile was 15.9 MPa. The values are still relatively low compared} to another study (Aicher, Hoffelin and Behrens, 2014) where they tested 20 mm long finger joints on beech wood with Melamin type of adhesive. One of the reasons for the difference could be in the different production precision and applied pressure. In our study, quite a few of the specimens cracked in the joint area during the gluing and pressing procedure. Though boards weren’t visually graded, we observed the obvious slopes of grain and some discolorations, therefore the boards were of a rather low quality and more exposed to cracking.

When comparing the two types of the adhesives, the mean tension strength is no longer higher for joints glued with PRF as was the case with the short joints. The average value was almost 15 % lower than in the case of the MUF adhesive. In the case of PRF adhesive, a high percentage of wood failure was observed. This means that the measured strengths represent the timber tension strength and one can notice they are quite low. Previous research indicates much higher strength properties for European beech timber (Ehrhart et al. 2018; Fortuna et al. 2018). In Figure 8 the strengths for the specimens that failed in the glue line are shown separated by groups of joint length, glue and pressure used. The PRF specimens have the highest values, but the difference is not statistically significant as in the case of 10 mm finger joints. This confirms the results from the preliminary assessment of tension strengths with numerical simulations, where the influence of the adhesive type decreased with the increasing length of the finger joints and the selected finger joint profile became the influential parameter for increasing the strength.

Table 3: Statistical values for tension strength, modulus of elasticity in tension and dynamic modulus of elasticity for specimens divided into six groups by the type of adhesive, assembling pressure and type of failure.

ft [MPa]

10 mm 20 mm

Joint failure Wood failure Joint failure

MUF

(-) PRF (-) (5 MPa) MUF (10 MPa) MUF (5 MPa) PRF (5 MPa) MUF (10 MPa) MUF (5 MPa) PRF 5th _{percentile 3.6 8.1 20.2 13.7 9.8 20.6 32.0 36.1} Mean 6.5 14.1 36.8 31.1 28.1 41.5 43.9 46.4 St. Deviation 1.4 3.8 10.6 12.7 13.0 14.1 7.0 9.0 N 28 25 13 9 17 14 17 9 Et,mean [MPa] - - 17500 16600 16500 17900 18300 17800 Edyn,mean [MPa] - - 15900 14500 15300 16900 16300 16900

The dynamic modulus of elasticity was measured on each board separately and then on joined boards with the STIG. The correlation between the measured Edyn and the tension strength was analyzed. With all the specimens

included, the correlation factor R was 0.40 for tension strength ft and 0.48 for the static modulus of elasticity Et. When

Figure 9: Box plots of tension strengths for five groups of finger joints that failed in the glue line.

In the case of the joint failure group, the correlation factor was not significant and negative. In the case of wood failure, the correlation factor was 0.52 which is a relatively high correlation for a non-destructive measured property, that can be easily and quickly obtained and could possibly be included into the glulam production as part of the manufacturing process of structural elements.

Figure 2: Correlation of dynamic modulus of elasticity measured on joined boards and tension strength of all boards. The hybrid glulam beam was tested in bending. As expected, the rupture occurred in the finger joint in the lower beech lamella. The static global modulus of elasticity Em,g was 14900 MPa. The ultimate force Fmax was 133 kN,

corresponding to a bending strength fm of 47.6 MPa. A shear modulus G = 630 MPa was also measured between the

loading point and the supports. Since beech was only on the outer part of the beam, mostly spruce lamellas were influential on the shear modulus.

5. CONCLUSIONS

The results of experimental tension testing of the finger joints are highly influenced by the specimens that failed in wood. However, based on the studies performed on European beech (Ehrhart et al. 2018) and also specifically on Slovenian beech (Fortuna et al. 2018), higher tension stresses can be expected. The results showed, that with the use of standard finger joint cutting heads used in spruce glulam production, it is not possible to achieve the high strengths that

Méausoone (2014), where the best results were obtained with the maximal length and minimal pitch within the selected optimization limits. In order to achieve a strength of at least 80 MPa, which is around 10 percent above the mean value for Slovenian beech, some suitable profiles would be l = 30 mm, p = 5.8 mm and bt = 1 mm; l = 40 mm, p = 7.1 mm and

bt = 1 mm or l = 50 mm, p = 8.4 mm and bt = 1 mm. The production of the proposed cutting head has its limits and would

be somewhat challenging. Another finger joint profile that could be used and was presented in EN 385:2001 with l ∙ p ∙ bt = 32 ∙ 6.2 ∙ 1.0 mm. According to the analytical model, a tension strength of approximately 70 MPa could be

expected, where the strength parameters were obtained from the experiments with the assumption of the quadratic strength criteria. The numerical model exhibits somewhat lower strengths (approximately 55 MPa) then the analytical model, but we have to emphasize that the strength parameters were obtained from the literature and are probably slightly underestimated. The expected tension strength for a 32 mm finger joint is higher than the strength that was obtained with the hybrid glulam beam where 20 mm finger joints were used. Using finger joints that can withstand 55 to 60 MPa in tension will have a considerable influence on the bending strength of the glued laminated beam made of beech wood.

6. ACKNOWLEDGEMENTS

We would like to acknowledge the national TIGR4smart project funded by the Slovenian Ministry of education, science and sport and the Cohesion fund of the European Commission.

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