Measurement of the shear modulus of wood by static bending tests

When measuring the shear modulus of wood by static bending tests, the basic theory is dependent on Timoshenko's bending theory. The shear modulus obtained by static bending is a much smaller value than that derived by other methods. We examined the applicability of Timoshenko's theory and propose an empirical equation that can derive the shear modulus properly. Three softwoods and three hardwoods were used for the tests. First, the Young's modulus and shear modulus were measured by free-free flexural vibration tests. Then the three-point static bending tests were undertaken, varying the depth/span ratios. Additionally, the bending tests were simulated by the finite element method (FEM). The shear moduli obtained by these methods were then compared. The deflection behaviors in static bending were not expressed by the original Timoshenko bending theory because of the stress distortion near the loading point. Based on the experimental results and numerical calculations, we modified the original Timoshenko bending equation. When using our modified equation the stress concentration must be carefully taken into account.     

Influence of loading point on the static bending test of wood

We conducted three-point bending tests by changing the condition at the loading point and then examined the influence of the loading point on the test data. Yellow poplar (Liriodendron tulipfera L.) was used for the tests. First, using loading noses with various radii, static bending tests were conducted by varying the depth/span ratios. Deflections were measured from the displacement of the cross head and at the point against the loading nose: Young's and shear moduli were obtained from the modified Timoshenko's bending equation proposed in a previous paper. Then a similar testing procedure was undertaken by inserting cushion sheets of Teflon between the specimen and the nose. After the measuring these moduli, bending strengths were measured using the loading noses and cushion sheets. The following results were obtained: (1) When the deflection was measured from the displacement of the cross head, the radius of the loading nose had an influence on the additional deflection when the depth/span ratio was high, causing the dependence of the shear modulus on the radius. In contrast, the radius had little influence on the measurement of Young's modulus. By placing cushion sheets between the nose and the specimen, the effect of the radius was moderated. When the deflection was measured at the point against the loading nose, the radius of the nose had little influence on the additional deflection; hence the loading nose had little influence when obtaining Young's and shear moduli. This tendency was commonly observed regardless of whether the cushion sheets were in place. (2) When the specimen had a high depth/span ratio, the bending strength increased with the increase in the radius of the loading nose. However, the influence of the radius was small when the specimen had a low depth/span ratio. There was no significant effect of the cushion sheets used here on the measurement of bending strength.Part of this paper was presented at the 48th annual meeting of the Japan Wood Research Society, Shizuoka, April 1998     

Influence of span/depth ratio on the measurement of mode II fracture toughness of wood by end-notched flexure test

The influence of the span/depth ratio when measuring the mode II fracture toughness of wood by endnotched flexure (ENF) tests was examined. Western hemlock (Tsuga heterophylla Sarg.) was used for the specimens. The ENF tests were conducted by varying the span/depth ratios; and the fracture toughness at the beginning of crack propagation G_IIc was calculated by two equations that require the load-deflection compliance or Young's modulus. Additionally, the influence of the span/ depth ratio on the load-deflection compliance was analyzed by Timoshenko's bending theory in which additional deflection caused by the shearing force is taken into account. The following results were obtained: (1) When the span/depth ratio was small, the fracture toughness calculated with the data of load-deflection compliance was large. In contrast, the fracture toughness calculated with the equation containing Young's modulus tended to be constant. (2) In the small span/depth ratio range, the load-deflection compliance was estimated to be larger than that predicted by Timoshenko's bending theory. (3) To obtain the proper fracture toughness of wood with a single load-deflection relation, the span/depth ratio should be larger than that determined in several standards for the simple bending test method of wood, 12:16.     

Bending and shear properties of compressed Sitka spruce

We examined the bending and shear properties of compressed wood using small and clear specimens of Sitka spruce (Picea sitchensis Carr.). For measuring the bending properties, three-point bending tests were conducted under the span/depth ratio of 14, which is standardized in the American Society for Testing and Materials [ASTM D143-94 (2005a)] and Japanese Industrial Standards [JIS Z2101-94 (1994)]. In the bending test, the load, deflection at the midspan, and strain at the bottom of the midspan were simultaneously measured, and Young’s modulus and bending strength were obtained by elementary beam theory. For obtaining the shear modulus and shear strength, asymmetric four-point bending tests were conducted using the specimens with rectangular and side-grooved cross sections, respectively, and the influence of the compression ratio on the shear properties was examined. The results are summarized as follows: (1) Young’s modulus increased with increasing compression ratio when it was determined by the load–strain relation. Nevertheless, this tendency was rather obscured when Young’s modulus was determined by the load–deflection relation. Hence, it is preferable that Young’s modulus is measured from the load–strain relation. (2) The shear modulus in the longitudinal–tangential plane was maximum at the compression ratio of 50%, whereas that in the longitudinal–radial plane was minimum at the compression ratio of 50%. (3) The influence of the compression on the bending and shear strength ratio was not significant.     

Shear strengths of wood measured by various short beam shear test methods

We conducted three types of short beam shear tests of western hemlock (Tsuga heterophylla Sarg.) under various span/depth ratios, and examined whether the maximum shear stress was used as the shear strength. The following results were obtained. (1) In the short beam shear tests under the three-point loading method, it was difficult to have the specimen failing by horizontal shear. We thought that this method should not be recommended for determining the shear strength of wood. (2) In the short beam shear tests under the asymmetric four-point loading of the specimen with a rectangular cross-section, the failure caused by horizontal shear occurred under some span/depth ratio range. Nevertheless, this range was dependent on the specimen geometry and was quite restricted. We therefore think that this method should not be recommended for determining the shear strength of wood. (3) In the short beam shear tests under the asymmetric four-point loading of the I-shaped specimen, failure caused by horizontal shear occurred under the span/depth ratio range wider than that applicable for the asymmetric four-point loading of the specimen with a rectangular cross-section. The maximum shear stress was stable in a certain span/depth ratio range and the value of the maximum shear stress is effective as a parameter for comparing the shearing strength of materials with each other.     

Measurement of bending properties of wood by compression bending tests

We measured Young's modulus, proportional limit stress, and bending strength by the compression bending test and examined the applicability of the testing method by comparing it with conventional bending test methods. Long columns of todomatsu (Japanese fir,Abies sachalinensis Fr. Schmidt) with various length/thickness ratios were the specimens. A compressive load was axially applied to the specimen supported with pin ends. Young's modulus, the proportional limit stress, and the bending strength were obtained from the load-loading point displacement and load-strains at the outer surfaces until the occurrence of bending failure. Four-point bending tests were also conducted, and the bending properties obtained were compared with the corresponding properties obtained by the compression bending tests. Based on the experimental results, we believe that when the stress-strain relation is measured by the load-loading point displacement relation using specimens whose length/thickness ratio is large enough, the bending properties can be obtained properly using the compression bending test.     

Determination of Young's modulus for spruce, fir and isotropic materials by the resonance flexure method with comparisons to static flexure and other dynamic methods

Summary Dynamic methods provide rapid and accurate means to determine Young's modulus, i.e. the modulus of elasticity, of wood. For dry, clear specimens of épicéa commun (Norway spruce, picea excelsa) and sapin pictiné (silver fir, abies amabilis) we present a comparison of results from tests by a resonance flexure method with results obtained from four-point static flexure tests. For a wide range of specimen size the resonance flexure method provides a simpler, more rapidly performed alternative to the classical static flexure method, giving Young's modulus values which are for the spruce and fir specimens of this study, nearly identical to those calculated from the static flexure tests. Results are also presented which show that a resonance longitudinal method yields higher values of Young's modulus and an ultrasonic method yields still higher values. We provide also a comparison of the four test methods applied to isotropic materials.The authors wish to thank Pierre Michel and André Perrin for preparing the test specimens and components of the test apparatus for this study     

Applicability of the losipescu shear test on the measurement of the shear properties of wood

We examined the applicability of the Iosipescu shear test for measuring the shear properties of wood. Quarter-sawn board of sitka spruce (Picea sitchensis Carr.) and shioji (Japanese ash,Fraxinus spaethiana Lingelsh. were used for the specimens. Iosipescu shear tests were conducted with two types of specimen whose longitudinal and radial directions coincided with the loading direction. The shear modulus, yield shear stress, and shear strength were obtained and were compared with those obtained by the torsion tests of rectangular bars. The results are summarized as follows: (1) The Iosipescu shear test is effective in measuring the shear modulus and the yield shear stress. (2) To measure the shear strength properly by the Iosipescu shear test, the configuration of specimen and the supporting condition should be examined in more in detail.     

Estimation of shear moduli of wood by quasi-simple shear tests

A quasi-simple shear test, which is the most direct method for examining the shear properties of sheet metals, has been applied to measure the shear moduli of wood. Buna (Fagus crenata Blume) with variously sized shear regions was used for the test specimens. Strain gauges were mounted in the center of the shear regions to measure the shear strains. The shear tests were carried out to determine the shear moduli in the radial and tangential planes. Apparent shear moduli obtained from the experimental results were corrected by finite element method (FEM) simulation of the shear region, where both shearing and bending are produced. It was found that the corrected shear moduli are roughly independent of test conditions, and their values are in good agreement with the data obtained from bending-shear tests. This suggests that the method employed here can effectively estimate the shear moduli of wood.Part of this research was presented at the 50th Annual Meeting of the Society of Materials Science, Osaka, May 2001     

Measurement of the shearing properties of wood by in-plane shear test using a thin specimen

In this research, in-plane shear tests were conducted for obtaining the shearing properties of wood. Thin strips of western hemlock (Tsuga heterophylla Sarg.) were used for the specimens. Two circular holes were cut along the axial centerline of the wider surface (longitudinal-tangential plane), and then two slots were cut from the holes asymmetrically to each other by varying the inclined angle of the slot with respect to the axial centerline. Shear stress was induced in the area between the holes, which is called the shear zone, by applying a tension load along the long axis of the specimen; the shear modulus, shear strength, and principal strain angle were measured from the shear stress/shear strain relation obtained. Independently of the in-plane shear tests, Iosipescu shear tests were conducted, and the validity of the in-plane shear tests was examined by comparing the test results with those obtained by the Iosipescu shear tests. In addition to the tests, stress distribution in the in-plane shear test was calculated by the finite element method, and the results were compared with those obtained by the actual in-plane shear tests. The following three results were obtained. First, the shear moduli obtained by the in-plane shear tests were close enough to those obtained by the Iosipescu shear tests throughout the range of inclined angle examined here. Additionally, the calculated result of the finite element method also verified the validity of the in-plane shear test for measuring the shear modulus. Thus, the in-plane shear test method examined was effective for measuring the shear modulus. Second, a failure was initiated at the hole edge because of the stress concentration, which was also confirmed by the finite element calculation, and it immediately propagated along the grain in the early stage of the test. Thus, it was difficult to obtain the proportional limit stress and realistic shear strength by the in-plane shear test because of the catastrophic failure in the early stage of the test. Third, since it is desirable that the stress field in the shear zone is close to the pure shear stress condition, we recommend that the slot runs outward from the hole when conducting the in-plane shear test in spite of the independence of the shear strength on the inclined angle.     

Simultaneous evaluation of bending and shear moduli of wood and the influence of knots on these parameters

Summary This paper presents a method of simultaneous evaluation of bending and shear moduli of wooden beams. The method, which is based upon the measurement of two natural frequencies of a beam, is simple to perform. Existing techniques for determining shear moduli of wood based materials are either too cumbersome to carry out or prone to measurement errors. Using this method tests were conducted on matched groups of clear and knotty specimens. It was found that for clear specimens a value of 20 can be assumed for the E to G ratio. For specimens which contain knots the variation was so large that no corresponding figure can be suggested with confidence. But the ratio for knotty materials is though to be higher than 20.Symbols A cross sectional area - E modulus of elasticity in bending - G shear modulus - I second moment of area - K shear shape factor - L span - P load - m mass per unit lenght - t time - x distance along the length of a beam - v transverse displacement - angular natural frequency This work was undertaken with financial support from the Natural Sciences and Engineering Research Council of Canada under Special Support for Forestry Grant No. FRP0030800. Thanks are also due to Dr. I. Smith for his contructive comments and permission to use the test facilities at the Wood Science and Technology Centre, and to Miss L. J. Hu for conducting the tests.     

Derivation and application of an equation for calculating shear modulus of three-ply laminated material beam from shear moduli of individual laminae

In a detailed study of the relation between the deflection caused by shear force and the constitution of a laminated material beam, we derived an equation for calculating the shear modulus of a laminated material beam from the shear moduli of individual laminae. The validity of the derived equation was investigated using crosslaminated wood beams made with five species. The calculated shear moduli parallel to the grain of face laminae ranged from 48.3 MPa to 351 MPa, while those perpendicular to the grain of face laminae ranged from 58.0 MPa to 350 MPa. The calculated shear moduli increased markedly with increasing shear modulus in a cross section of perpendicular-direction lamina of a cross-laminated wood beam. The calculated apparent modulus of elasticity (MOE) of cross-laminated wood beams agreed fairly well with the measured apparent MOE values. This fact indicated that the apparent MOE of cross-laminated wood beam was able to be calculated from the true MOE values and shear moduli of individual laminae. The percentage of deflection caused by shear force obtained from the calculated apparent MOE (Y _sc) was close to that obtained from the measured apparent MOE (Y _s) and there was a high correlation between both values. From the above results, it was concluded that the derived equation had high validity in calculation of shear modulus of a cross-laminated wood beam.     

Vibrational properties of Sitka spruce heat-treated in nitrogen gas

Sitka spruce (Picea sitchensis Carr.) wood was heated for 0.5–16.Oh at temperatures of 120°–200°C in nitrogen gas or air. The values for Young's modulus, shear modulus, and loss tangent were measured by free-free flexural vibration tests. X-ray diffractometry was carried out to estimate the crystallinity index and crystallite width. The results obtained are as follows: (1) Density decreased at higher temperatures and longer heating times. The specific Young's modulus, specific shear modulus, crystallinity index, and crystallite width increased during the initial stage and were constant after this stage at 120°C and 160°C, whereas they increased during the initial stage and decreased later when the temperature was high. Loss tangent in the longitudinal direction increased under all conditions, whereas that in the radial direction increased at 120°C and decreased at 160°C and 200°C. (2) From the relation between Young's modulus and moisture content, it can be safely said that Young's modulus is increased by the crystallization and the decrement in equilibrium moisture content, and that crystallization (rather than degradation) is predominant at the initial stage of the heat treatment, whereas the latter is predominant as the heating time increases. (3) It is implied that the specific Young's modulus, specific shear modulus, crystallinity index, and crystallite width decreased more in air than in nitrogen gas because of oxidation in air.This study was presented in part at the 43th Annual Meeting of Japan Wood Research Society at Morioka, August 1993, the 44th Annual Meeting of Japan Wood Research Society at Nara, April 1994, and the 45th Annual Meeting of Japan Wood Research Society at Tokyo, April 1995     

Shear modulus of several kinds of Japanese bamboo obtained by flexural vibration test

The vibrational properties of Japanese bamboo were examined. To obtain the Young’s modulus and shear modulus, a flexural vibration test and a longitudinal vibration test were conducted. The Young’s modulus with vibration in the R-direction was smaller than that measured in the longitudinal vibration test E _l . This was due to the shift of the neutral axis to the outer layer. On the other hand, the Young’s modulus with vibration in the T-direction was close to E _l . Hence, an adequate Young’s modulus should be used for each use of bamboo. The shear moduli of the LR and LT planes of bamboo were similar to those of beech. There were high correlations between shear moduli of the LR and LT planes and density.     

Elastic modulus of lignin as related to moisture content

The Young's and shear moduli of two lignins have been measured at several moisture contents. Cylindrical test specimens moulded from periodate and Klason lignin powders were conditioned to the required moisture contents and tested in tension and torsion. The Young's modulus of periodate lignin increased linearly from 3.1x10⁹ to 6.7x10⁹ Pa, and the shear modulus from 1.2x10⁹ to 2.1x10⁹ Pa as the moisture content of the lignin decreased from 12 to 3.6%. Klason lignin showed similar behaviour but its moduli were always much lower. This was probably a consequence of the more drastic alteration undergone by the Klason lignin during its isolation from the wood cell wall.I am indebted to Messrs M. B. Forsyth and L. P. Lowe for assistance with the design and construction of the testing equipment used in this work.     

Shear tests of double shear plate connector joints in sugi—Japanese larch composite glulam beams

To study the shear strength of structural joints in sugi (Cryptomeria japonica D. Don) — Japanese larch (Larix kaempferi Carriere) composite glulam beams using structural connectors with double shear plates, shear tests were conducted on two types of joint (post-beam and girder-beam). Two types of the composite beam (240 and 300 mm depth) were prepared for the tests. Ordinary sugi glulam beam and Japanese larch glulam beam were also used as control specimens. The load—displacement curves of joints in composite beams were somewhere between those of sugi and Japanese larch glulam beams. The shear strength of joints in composite beams was higher than that in the sugi glulam beam control. However, the allowable loads of the joints in composite beams were lower than those in the sugi beam with 240 mm depth. Large variation of maximum load of the joints in the composite beams resulted in lower allowable load.     

Bending strength and toughness of heat-treated wood

The load-deflection curve for static bending and the force-time curve for impact bending of heat-treated wood were examined in detail. The effect of oxygen in air was also investigated. Sitka spruce (Picea sitchensis Carr.) was heated for 0.5–16.0h at a temperature of 160°C in nitrogen gas or air. The dynamic Young's modulus was measured by the free-free flexural vibration test, the static Young's modulus and work needed for rupture by the static bending test, and the absorbed energy in impact bending by the impact bending test. The results obtained were as follows: (1) The static Young's modulus increased at the initial stage of the heat treatment and decreased later. It decreased more in air than in nitrogen. (2) The bending strength increased at the initial stage of the heat treatment and decreased later. It decreased more in air than in nitrogen. (3) The work needed for rupture decreased steadily as the heating time increased. It decreased more in nitrogen than in air. It is thought that heat-treated wood was more brittle than untreated wood in the static bending test because W₁₂ was reduced by the heat treatment. This means that the main factors contributing to the reduction of the work needed for rupture were viscosity and plasticity, not elasticity. (4) The absorbed energy in impact bending increased at the initial stage of the heat treatment and decreased later. It decreased more in air than in nitrogen. It was concluded that heat-treated wood became more brittle in the impact bending test becauseI ₁₂ andI ₂₃ were reduced by the heat treatment.     

Determination of Young’s and shear moduli of common yew and Norway spruce by means of ultrasonic waves

Despite the exceptional position of yew among the gymnosperms concerning its elastomechanical properties, no reference values for its elastic constants apart from the longitudinal Young’s modulus have been available from literature so far. Hence, this study’s objective was to determine the Young’s moduli E _L, E _R and E _T and the shear moduli G _LR, G _LT and G _RT of yew wood. For that purpose, we measured the ultrasound velocities of longitudinal and transversal waves applied to small cubic specimens and derived the elastic constants from the results. The tests were carried out at varying wood moisture contents and were applied to spruce specimens as well in order to put the results into perspective. Results indicate that E _L is in the same order of magnitude for both species, which means that a high-density wood species like yew does not inevitably have to have a high longitudinal Young’s modulus. For the transverse Young’s moduli of yew, however, we obtained 1.5–2 times, for the shear moduli even 3–6 times higher values compared to spruce. The variation of moisture content primarily revealed differences between both species concerning the shear modulus of the RT plane. We concluded that anatomical features such as the microfibril angle, the high ray percentage and presumably the large amount of extractives must fulfil important functions for the extraordinary elastomechanical behaviour of yew wood which still has to be investigated in subsequent micromechanical studies.     

Effect of element type on the internal bond quality of wood-based panels determined by three methods

Three mechanical tests with different loading modes were conducted to evaluate the effect of element type on the internal bond quality of wood-based panels. In addition to the internal bond test, which is commonly used for mat-formed panels, interlaminar and edgewise shear tests were used to test oriented strandboard (OSB), particleboard, medium-density fiberboard (MDF) of two thicknesses, and plywood. The following results were obtained. Epoxy resin proved to be suitable for determining the interlaminar shear modulus instead of hot-melt glue. There was a linear relation between panel density and interlaminar shear modulus and a linear correlation between the interlaminar shear strength and internal bond (IB) strength for the mat-formed panels tested. OSB had the highest edgewise shear modulus, and MDFs had the highest edgewise shear strength in this study. The modulus/strength ratio also depended on both panel type and loading mode. The relation between the shear moduli determined from the edgewise and interlaminar tests indicated the characteristics of the shear properties of panels made of different elements.Part of this paper was presented at the Fourth International Wood Science Symposium, Serpong, Indonesia, September 2002     

Resistance curve for the mode II fracture toughness of wood obtained by the end-notched flexure test under the constant loading point displacement condition

 The measurement method of mode II fracture toughness-crack propagation length relation (i.e., the resistance curve, or R-curve) was examined by end-notched flexure tests on sitka spruce (Picea sitchensis Carr.). The tests were conducted by varying the span/depth ratios under the constant loading point displacement condition. The fracture toughness was measured from the load-crack shear displacement (CSD) and load-longitudinal strain relations. The crack length was determined by a combination of load-CSD and load-strain compliances and Williams's end correction theory, as well as the observation of crack propagation. When the specimen had an appropriate span/depth ratio, the fracture toughness and crack propagation length were measured from the load-CSD compliance and combined load-CSD and load-strain compliances, respectively, and the R-curve could be determined properly under the constant loading point displacement condition. Received: March 15, 2002 / Accepted: July 25, 2002