Shear Modulus and Shear Strength Evaluation of Solid Wood by a Modified ISO 15310 Square-Plate Twist Method

Square-plate twist (SPT) tests were conducted to measure the shear modulus and shear strength using the method, which was a modifi cation of the International Organization for Standardization (ISO 15310) standardized method. In the SPT test, the length/thickness ratio varied. In addition, asymmetric four-point bending (AFPB) tests were conducted, and the shear modulus and shear strength obtained were compared with those obtained by the SPT tests. The shear modulus was obtained effectively by the SPT test when the specimen was thin enough. Although the shear strength was evaluated as higher than that obtained by the AFPB tests, it might be regarded as an apparent value of shear strength when the range of length/thickness is limited. To obtain the actual shear strength by the SPT test, some modifi cation of the equation is required.


Ključne riječi: smicajna čvrstoća, test uvijanja kvadratne ploče (SPT), test asimetričnog savijanja u četiri točke (AFPB test)
1 INTRODUCTION 1. UVOD Various testing methods have been proposed for determining the shear properties of solid wood (Yoshihara, 2006).Among them, torsion testing is attractive because a rather pure shear stress condition can be induced in the material (Timoshenko and Goodier, 1987).Square-plate twist (SPT) testing is an application of torsion testing, and it has been standardized as a way of measuring the edgewise shear modulus of plywood and fi ber-reinforced plastics in ASTM D3044-94 (ASTM, 2005) and ISO 15310-99 (ISO, 1999), respectively.These standards determine the measurement of shear modulus alone.If the SPT enables the proper measurement of shear strength as well as that of shear modulus, however, it will be applied frequently because it is an application of torsion testing and can be conducted easily.In the present research, we examined the validity of a modifi ed ISO 15310 method for the measurement of shear strength using Sitka spruce.

MATERIJALI I METODE
Sitka spruce (Picea sitchensis Carr.) lumber was used for the tests.The density was 400 kg/m 3 at 12 % moisture content.The specimens cut from the lumber were side matched.During cutting the specimens, the defects such as knots, grain distortion, and grain orientation were removed, so the specimen could be regarded as "small and clear."Seven specimens were used for each test condition.
Figure 1 shows a diagram of the SPT test according to the modifi ed ISO 15310 method.Specimen B was 140 long and 140 mm wide; its thickness, H, varied from 3 to 15 mm at intervals of 3 mm.The x, y, and z directions coincided with the longitudinal (L), tangential (T), and radial (R) directions, respectively, so the shear stress and shear strain in the LT plane are designated τ LT and γ LT , respectively.In the ASTM D 3044 method, a metal plate must be attached to each corner of the specimen for applying the loads just at the corners.The corner plates may restrict the saddle-like deformation in the specimen, and a combined stress condition induced at the corners may distribute widely in the specimen.In contrast, these plates are not required in the ISO 15310 method, so the saddle-like deformation is not restricted.The ISO 15310 method was, therefore, adopted in this experiment.Figure 2(a) shows the photograph of the ISO 15310 SPT test actually conducted in this investigation.
The specimen was supported and loaded at the moment arm, W, of 130 mm (Fig. 1).The radius of the support and loading points was 15 mm.Load P was applied at a crosshead speed of 5 mm/min until the specimen separated into two pieces.The loading-line defl ection, δ, was obtained from the crosshead movement.The total testing time was about 5-10 min.The shear stress at the center of the LT plane, τ LT , in the SPT test was obtained from the following equation (Timoshenko and Goodier, 1987): Using δ, γ LT was also obtained as follows (ISO 15310 1999): where K is the correction factor for the shifted position of the loading points, which is derived as follows (ISO 15310 1999): The shear modulus in the LT plane G LT was determined from the initial slope of the τ LT -γ LT relationship.The shear strength in the LT plane, S LT , was determined by substituting the maximum load into Eq.( 1).
The asymmetric four-point bending (AFPB) test, the validity of which was verifi ed in a previous study (Yoshihara, 2009), was conducted using a notched specimen, and G LT and S LT obtained were compared with those obtained from the SPT method.Figure 2(b) shows the photograph of the AFPB test.A beam specimen with the dimensions of 340 (L) × 30 (T) × 12 (R) mm 3 was initially prepared.Straight-through notches were cut at mid-span of the top and bottom surfaces of the specimen, which corresponded to the LR planes, by a circular saw (thickness = 3 mm).The depth of the notch was 10 mm, so the distance between the notch roots was 10 mm.A biaxial strain gauge, which was similar to that used in the SPT test, was bonded at both centers of the side surfaces (LT plane) to measure the shear strain γ LT .The total span length was 300 mm, and the specimen was supported eccentrically at two trisected points.Load P was applied to the remaining two trisected points at the crosshead speed of 2 mm/min until the load markedly decreased.The total testing time was about 5 min.τ LT in the AFPB test was obtained using the following equation: where b is the width of the specimen and h is the distance between the notches.γ LT was obtained from the strain gauge output.Similar to the SPT twist method, G LT was measured from the initial slope in the τ LT -γ LT relationship, whereas S LT was derived from the maximum stress.

REZULTATI I RASPRAVA
Figure 3 shows typical τ LT -γ LT relationships obtained by the SPT and AFPB tests.In the SPT test, τ LT continuously increases with the increase of γ LT .This tendency is different from that obtained from the AFPB test, which is convex.It is attributed to the geometrical nonlinearity in loading.Equation ( 1) is derived on the basis that the load is applied vertically to the specimen.When the specimen has a small thickness, however, the defl ection increases so markedly that the load is applied obliquely to the surface of the specimen.The shear stress obtained using Eq. ( 1) is therefore larger than that actually induced and the concavity in τ LT -γ LT relationship is induced.
Figure 4 shows a comparison of G LT obtained from the SPT and AFPB tests.Statistical analysis of the difference between the G LT values obtained using the SPT and AFPB tests revealed that the G LT value was signifi cantly smaller than the results obtained by the AFPB test, except for that with H = 3 mm, at the signifi cance level of 0.01.In addition, the G LT value obtai-ned using the SPT test decreases with the increase of thickness of specimen.The statistical analysis also revealed they are different from each other at the significance level of 0.01.These tendencies, which were similar to the results obtained in a previous work (Yoshihara and Sawamura, 2006), are the consequence of the three-dimensional effect.When the global defl ection is measured, the shear stress in the radial-tangential plane τ RT is signifi cant and it reduces the measured value of G LT as the plate gets thicker.
Figure 5(a) shows a comparison of S LT values obtained from the SPT and AFPB tests.The statistical analysis for the S LT values obtained from the SPT and AFPB tests reveals that the values of S LT obtained from the SPT test are signifi cantly larger than those obtained from the AFPB test at the signifi cance level of 0.01 except for that of H = 6 mm.The large value of S LT obtained by the SPT is because of the large defl ection during the test.Due to large defl ection, the load is applied obliquely to the specimen surface.The torsional moment induced by oblique loading is smaller than that induced by vertical loading, so the shear stress actually induced may be smaller than that derived by Eq. ( 1).As shown in Figure 5(b), which shows the maximum defl ection δ max corresponding to the specimen's thickness H, the value of δ max of H = 3 mm is significantly larger than those of the specimen with the larger thickness, so the defl ection may infl uence the measurement of S LT .According to the previous study (Yoshihara and Sawamura, 2006), the edgewise shear modulus can be measured appropriately by the modifi ed ISO 15310 AFPB test when the specimen is thin enough.Nevertheless, the result described above suggests that  When conducting the statistical analysis for the S LT values obtained using the SPT tests, there are no differences among the values of S LT of H = 6, 9, 12, and 15 mm.The statistical analysis for the δ max values also reveals that there are no differences among the values of δ max in this range of H.The shear strength of solid wood is often evaluated by the shear-parallel-to-grain test method standardized in the ASTM D143 (ASTM 2005) although the shear strength obtained is regarded as an apparent property and is not the actual strength of the material.The results obtained here suggest the feasibility that the S LT value obtained from the SPT test might be regarded as an apparent value of shear strength when the range of length/thickness is limited while reducing the large defl ection during the test.
In many shearing tests, including the ASTM D143 test, specimen often fails at the loading and/or supporting points of the specimen where the combined stress condition is induced.In the SPT test, however, it should be noted that the specimen failed along the fi ber direction at the mid-plane of wider surface, which is far from the loading and supporting points.This issue indicates the advantage of the SPT test over the other tests, and shows why it is attractive to conduct the SPT test.Further research should be conducted to modify Eq. ( 1) for obtaining the shear strength of solid wood more properly while considering the large defl ection.

CONCLUSIONS 4. ZAKLJUČCI
A modifi ed ISO 15310 square-plate twist test of Sitka spruce was conducted to obtain the shear strength in the longitudinal-tangential plane using specimens with various thicknesses.In addition to the square-plate twist test, the asymmetric four-point bending test was performed, and the results were compared with those of the square-plate twist tests.It is feasible that shear strength obtained from the square-plate twist method could be regarded as an apparent value of shear strength, which is larger than that obtained by the asymmetric four-point bending test because of the large defl ection.To increase the accuracy of the measurement, further research should be undertaken to modify the equation for obtaining the shear strength while considering the large defl ection.

Figure 4 4 .
Figure 4 Shear modulus corresponding to the thickness of the specimen obtained by the square-plate twist test, and comparison with results obtained by the asymmetric fourpoint bending tests Slika 4. Ovisnost smicajnog modula o debljini uzorka dobivena testom uvijanja kvadratne ploče i usporedba s rezultatima dobivenim testom asimetričnog savijanja u četiri točke

SFigure 5 5 .
Figure 5 (a) Shear strength corresponding to the thickness of the specimen obtained by the square-plate twist test, and comparison with results obtained by the asymmetric four-point bending tests, and (b) Maximum defl ection corresponding to the thickness of the specimen obtained by the square-plate twist test Slika 5. Ovisnost smicajne čvrstoće o debljini uzorka dobivena testom uvijanja kvadratne ploče i usporedba s rezultatima dobivenim testom asimetričnog savijanja u četiri točke, b) ovisnost maksimalne deformacije o debljini uzorka dobivena testom uvijanja kvadratne ploče