Measurement of the shear modulus of wood by asymmetric four-point bending tests

We conducted asymmetric four-point bending tests of wood and obtained the shear moduli on the basis of Timoshenko's theory of bending. Akamatsu (Japanese red pine,Pinus densiflora D. Don) and shioji (Japanese ash,Fraxinus spaethiana Lingelsh.) were used for the tests. Asymmetric four-point bending tests were undertaken by varying the depth/span ratios; and Young's modulus and the shear modulus were calculated by Timoshenko's bending theory. Independent of the asymmetric bending tests, we also conducted three-point bending tests, free-freeflexural vibration tests, and numerical calculations by the finite element method. Young's and shear moduli obtained by these methods were compared with those derived from the asymmetric bending tests. Based on these comparisons, we concluded that the shear modulus can be properly obtained by the asymmetric four-point bending tests when the span is 20 times larger than the depth.     

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.     

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.     

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.     

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.     

定向刨花板剪切模量和弹性模量动态测试

【目的】研究定向刨花板(OSB)的各向异性,探讨OSB面内剪切模量动态和静态测试方法,以提供一种快速、简便、重复性好、精度高的动态测试方法测量和分析OSB弹性常数。【方法】应用ANSYS程序计算OSB自由板和悬臂板试件的振形系数,给出振形系数依赖于板长宽比和宽厚比的关系式,通过仿真计算、动态试验和方板静态扭转试验验证其正确性。动态试验测试OSB剪切模量试件从一块整张OSB上下料制作,分为3个方向,即沿整板纵向下料制作的试件(0°或x向)、横向方向下料制作的试件(90°或y向)和沿与纵向呈45°方向下料制作的试件;方板扭转试验测试OSB剪切模量试件沿整板纵向或横向下料制作;动态测试OSB纵向、横向和45°方向弹性模量以及面内剪切模量和45°方向剪切模量。【结果】OSB实测纵向弹性模量是横向弹性模量的2.89倍,45°方向剪切模量小于面内剪切模量。正交各向异性材料方板扭转试验测试剪切模量推算公式需用±45°方向应变测量值的差值进行推算,将其用于OSB,测得的静态剪切模量与动态测试的剪切模量相当吻合。【结论】OSB弹性模量具有方向性,纵向最大,横向最小,45°方向介于二者之间;自由板扭转振形法和悬臂板扭转模态法适用于动态测试OSB面内剪切模量,其正确性得到方板扭转试验验证;0°和90°OSB动态测得的剪切模量几乎相等,可作为OSB面内剪切模量Gxy的估计值;OSB不宜按单向复合材料处理,在理论分析时宜按正交各向异性处理,OSB45°方向的剪切模量G45°相似文献   

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.     

Study on the estimation of the strength properties of structural glued laminated timber I: determination of optimum MOE as input variable

There have been many attempts to predict the performance of glulam beams. Several approaches have been taken, from early empirical techniques to more sophisticated stochastic methods. In recent years, more emphasis has been placed on the modeling of material properties. Generally, the modulus of elasticity (MOE) has been used as a criterion of laminar strength for the prediction of glulam performance in the traditional models. Most of the current models are based on MOE that was measured using the long span test; that is, they account only for variability between pieces of lumber. Therefore, these models do not account for the variation of material properties within a given piece of lumber. Five methods were considered to choose the appropriate one that could effectively predict the performance of glulam in this study. Prediction of glulam performance was done by the transformed section method. MOEs measured with the five methods were applied to a strength prediction program to compare the actual test results and the predicted results. MOEs used as input variables are as follows: long span MOE of the static bending test, localized MOE of the static bending test, long span MOE of the stress wave test, localized MOE of the stress wave test, and MOE of the machine stress rating (MSR) test. Results of the localized test showed excellent signification compared to those of the long span test. The MSR method, when used as input variable, obtained the most approximate result, so it is considered adequate for predicting the strength of glulam.An outline of this paper was presented at the 48th annual meeting of the Japan Wood Research Society, Shizuoka, April 1998     

Estimation of the shear strength of wood by uniaxial-tension tests of off-axis specimens

To determine shear strength we conducted uniaxial-tension tests of off-axis specimens and examined the proper off-axis angles. Sitka spruce (Picea sitchensis Carr.) and katsura (Cercidiphyllum japonicum Sieb. and Zucc.) were used for the studies. Uniaxial tension tests of the specimens with various off-axis angles were conducted, and the shear stress at failure was obtained. Independent of the tension tests, torsion tests were conducted, and the shear strengths were obtained. Comparing the data of the uniaxial tension and torsion tests, we examined the validity of estimating shear strength by the off-axis tension test. The shear strengths obtained from the tension tests coincided well with those measured by the torsion tests when the specimen had an off-axis angle of 15°–30°. In this off-axis angle range, the tensile stress perpendicular to the grain might have a serious influence on the shear strength, and we thought that the shear strength predicted by uniaxial tension tests should be treated as an approximate value despite the simplicity of the tension test. Other test methods should be adopted to obtain the precise shear strength of wood.     

An alternative solution for the determination of elastic parameters in free–free flexural vibration of a Timoshenko beam

An alternative inversion solution is presented to compute the elastic parameters based on the Timoshenko equation of motion in free flexural vibration. The interest of this solution was its relatively simple formulation and its validity domain, which was not restricted to the initial frequencies and a certain range of length-to-height ratio. The uniqueness of the solution was verified numerically, and the best optimization strategy was deduced. It was underlined that the shear modulus determination depended on the length-to-height ratio coupled with the number of resonance frequencies involved in the computation. The accuracy of the computed elastic modulus values was in the same scale as that for the measurement errors of frequency. However, the sensitivity of the shear modulus was found to be very high and depended on the number of frequencies taken into account. The theoretical model was found to be more accurate and to better estimate the frequency values than a classic solution of the Timoshenko equation. Furthermore, the inversion procedure gave equivalent elastic property values to those obtained with a classic solution (in the validity range of the classic solution) and was more robust when the number of frequencies taken into account was low.     

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.     

Evaluation of quality indexes of bending performance and hardness for hardwoods

The mechanical properties of 613 small clear specimens of 35 species (11 ring-porous hardwoods, 19 diffuse-porous hardwoods, and 5 softwoods) were evaluated. The aim of the study was to examine indexes of wood quality that are easy to measure and that exhibit a high correlation with bending performance and hardness that are essential properties of hardwood products. The modulus of rigidity, dynamic modulus of elasticity, bending properties (modulus of elasticity, modulus of rupture, stress at the proportional limit, absorbed energy, Tetmajer’s modulus), dynamic energy absorption by an impact bending test, compressive strength parallel to the grain, shear strength, partial bearing strength, and Brinell’s hardness were measured. A high correlation was found between dynamic modulus of elasticity and static modulus of elasticity. Bending stress at the proportional limit was found to be approximately equivalent to the compressive strength parallel to the grain. Static energy absorption correlated with dynamic energy absorption. Tetmajer’s modulus was found to be closely related to the ratio of the initial stiffness within the elastic range to the secant modulus at the maximum load. A high correlation was observed between Brinell’s hardness and partial bearing strength. The difference in the regression coefficients obtained for these correlations between the species groups was small. Part of this study was presented at the All Division 5 Conference of IUFRO, Taipei, October 2007     

用高阶剪切理论研究竹木复合空心板的弯曲性能

运用高阶剪切理论对竹木复合空心板的弯曲性能进行分析与研究。结果表明 :在跨高比较小时 ,横向剪切效应对板的弯曲性能有显著影响 ;预测的变形与一阶剪切理论基本相当 ;预测的强度能够反映出横向剪切效应的影响 ,其影响只与载荷大小有关 ,而与跨高比无关 ;描述横截面上的应力分布与一阶剪切理论显著不同 ,尤其是剪应力 ,不仅在跨中截面上存在较大差异 ,而且还随截面的位置而变。     

大跨度竹质方梁的制备与抗弯性能研究

为了探究木质材料在大型建筑应用的可行性,以竹材为原料,利用层积热压组坯的方式制备长度为3 m和6 m的竹质方梁,对其进行四点抗弯测试,观察其在测试过程中的弯曲变形及破坏特征,分析弹性模量、静曲强度,根据其破坏形式分析竹质方梁结构及组坯方式对其抗弯性能的影响。结果表明:6 m竹质方梁弹性模量达10261.24 MPa,跨中竖向位移至86.97 mm而不破坏;3 m竹质方梁静曲强度达85.51 MPa。竹质方梁破坏均出现在弯曲的受拉面,且裂纹通过竹节处、胶合界面以及竹纤维排布方向蔓延,这与竹材本身结构特性有关。通过对3 m和6 m竹质方梁抗弯实验及分析,以期为竹质方梁在大跨度下的应用提供数据支撑。     

Characterisation of the bending stiffness components of MDF panels from full-field slope measurements

This paper deals with the characterisation of bending stiffness components of medium density fibreboard (MDF) by carrying out a single plate bending test. The approach couples full-field slope measurements with an inverse identification method. MDF panels manufactured with different fractions of Eucalyptus fibres and sugarcane bagasse particles were used. The slope maps generated across the plate surface were measured by the deflectometry technique. The curvature fields of the deformed plate were reconstructed by numerical differentiation afterwards. The virtual fields method was then implemented for material parameter identification under the framework of Kirchhoff–Love plate bending theory. The elastic properties obtained from the proposed data reduction (i.e. simultaneous identification of modulus of elasticity, Poisson’s ratio and shear modulus) were compared with values determined from classical three-point bending tests and reported in the literature. The set of properties were found in relatively good agreement.     

柳桉立木力学分析

以柳桉立木为研究对象,重点分析不同状况下桉树应力和弯矩分布情况。结果表明：柳桉立木随着树高的增加,树干断面积呈指数迅速减少,而树干材积和质量均呈一元二次方程的增加。柳桉立木随着树高的增加,树干各截面的应力呈线性降低,而所受弯矩呈非线性减少。外力载荷下作用点与树干基部间各截面的应力会迅速增加,也使得其间的弯矩（绝对值）急剧增大。外力载荷随着树高上移,相对而言不会增加树高基部的应力,但会显著增加作用力位点截面的应力,也显著提高树干基部的弯矩。柳桉在树高3.9 m以上树干部位,由于惯性矩产生的抗弯矩应力能力趋于减少,而小于弯矩应力,易使树干发生变形导致树干折断。     

基于横向振动法对樟子松木材进行应力分等的研究

以樟子松木材为试验对象,分别运用横向振动法和静态弯曲法得出其动态弹性模量和静态抗弯弹性模量,重点对二者的关系以及尺寸、节子等因素对动态弹性模量的影响进行了研究.其结论是：动态弹性模量与静态抗弯弹性模量以及抗弯强度都有很好的相关关系;尺寸对动态弹性模量没有显著性的影响;节子的个数对木材动态弹性模量有显著性影响.     

A static analysis of two-shaft columns spaced by gussets

The paper focuses on timber constructions. It analyses two-shaft columns spaced by gussets made of timber, plywood, particleboard or fibreboard. Based on the theory authored by Timoshenko and Gere, some formulae, defining the column critical force, its slenderness ratio, the shear force applied to the column and the maximum shear force that a column can carry, were derived. Next, based on the derived formulae and those applied in the literature (Standard EN-1995 Eurocode 5), a comparative analysis was conducted on the load-bearing capacity and gusset calculation for the columns. The calculations demonstrate that there are substantial discrepancies between the static values being compared and both calculation methods lead to partially divergent results.     

Comparison between modulus of elasticity values calculated using 3 and 4 point bending tests on wooden samples

Several data banks on wooden properties of different species contain mechanical characteristics of which the bending modulus of elasticity. This modulus can be calculated using different test methods, the more ordinary used are the 3 point and 4 point bending tests. The values obtained by one method cannot be directly compared with those of other methods. So the bending properties read in a data bank have to be converted before using them and correctly compared with other data from different references. The aim of this study is to make an analytic formula of a crossing coefficient between 3 point and 4 point bending concerning the longitudinal modulus of elasticity measured following the French standards (NF 1942; NF 1987). This formula includes a study of the shear force influence, and a study of supports and loading head indentation effect, in a 3 point bending test. The analytical study and the experiences have shown that the supports and loading head indentation effect are not negligible but have the same influence as the shear effect. The indentation is the result of the competition between two physical phenomena which are the wood stiffness and the load level applied on the piece of wood during a bending test. The practical result of this study is the development of a crossing analytic formula from a 3 point bending modulus of elasticity to a 4 point bending one, verified by the experimentation. Received 26 June 2000 The C.I.R.A.D.-Forêt team and especially M. Bernard Thibaut, M. Gilles Calchera, and M. Joseph Grill from Laboratoire de Mécanique et de Génie Civil (L.M.G.C.) are gratefully acknowledged for their precious help during this research.