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.     

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.     

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.     

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.     

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.     

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     

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.     

Evaluation of a modified Iosipescu shear test method for determining the shear properties of clear wood

A modified Iosipescu shear test method is proposed as an alternative for measuring the shear properties of clear wood. The method adopts four-point asymmetric loading procedure in the Iosipescu shear test but with the loading positions shifted to the neutral axis of the specimen. The original V-notched specimen is replaced by a combination of polyvinyl chloride blocks at two ends and a bow-tie-shaped wood specimen in the middle to provide a better stress pattern at failure. The measured shear strength and shear moduli are compared with results from compression test and off-axis tension test. Finite element analysis is also carried out to study the stress distribution in the wood specimen. Results show that the new shear test setup can provide close-to pure shear stress state in the specimen yielding better estimates of the shear properties of wood. The shear strength obtained by the new test setup is slightly lower than that from the off-axis tensile test which is probably due to the relatively thick specimen chosen in this study.     

Structural analysis of tree trunks and branches: tapered cantilever beams subject to large deflections under complex loading

The dimensions, deflections and support costs of tree trunks and branches can be deduced using the structural theory for cantilever beams. However, elementary theory applies only as long as deflections are small, and complex analytical solutions are required to account for complex taper and patterns of loading. This paper describes a method that copes with large deflections, any patterns of taper, and any patterns of distributed loading, point loading or externally applied bending moments. A beam is considered to be composed of a series of short segments, such that each has only a small deflection, and each can have specified dimensions, Young's modulus and loading. The transport matrix method of structural analysis is used to determine the end conditions of each segment and of the whole beam. The method is verified by comparing predicted deflections with deflections (a) calculated using an analytical solution by Bisshopp and Drucker (1945), (b) calculated and measured for sapling tree trunks by Leiser and Kemper (1968), and (c) measured on tapered and untapered plastic rods.     

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.     

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.     

Cooling set and its recovery in water-saturated bamboo under large bending deformation

To clarify the bending properties and cooling set for bamboo under large deformation, the relationship between applied deflection and residual deflection was investigated, and comparison was made with the results of thermal recovery and anatomical changes due to deformation. No clear effect of initial deflection on set measured after a long time was found for wood and bamboo loaded on the epidermis side (Bepi). On the other hand, set for bamboo loaded on the endodermis side (Bendo) increased with deformation level. Recovery from the deformation with time for Bendo was almost complete at around 1000 min after unloading in the three-point bending method. This recovery behavior was not seen for Bepi or wood. It was considered that no failure was caused in the bent specimen, because most of the deformation was completely recovered by reheating to the temperature at which the specimens were deformed before cooling. The recovery from deformation for B_endo loaded by the four-point bending method continued even after 1000 min. From microscopic observations, shearing deformations were seen for Bendo loaded by the three-point bending method. From these results, it can be considered that shearing deformations between the two loaded points effectively contribute to decreased recovery force from deformations for B_endo. Part of this report was presented at the 54th Annual Meeting of the Japan Wood Research Society in Sapporo, August 2004     

Defect detection in lumber including knots using bending deflection curve: comparison between experimental analysis and finite element modeling

A new method has been developed for detecting localized defects such as edge knots using a bending deflection curve. The coordinates of a bottom edge (edgeline) of an unloaded piece of lumber are extracted from a digital image, and a bending deflection curve is obtained from the displacement of the edgeline of the lumber using a digital image correlation (DIC) technique. Depending on the knots within the beam, the bending deflection curve is shifted from the curve of a defect-free beam. The measured bending deflection curve is regressed to a theoretical curve by elementary beam theory. A finite element method (FEM) model of the beams including defects as simplified knot structure has been performed. Comparison between the bending experiment and FEM analysis shows that cross-sectional reductions cause characteristic variations in the bending deflection curves depending on the position of encased knots, and local grain distortions cause variations in the curves depending on the direction of spike knots. Using the residual variance between the measured deflection curve and a polynomial regression curve, it is possible to detect knots at which failures initiate. Part of this article was presented at the 57th Annual Meeting of the Japan Wood Research Society, Hiroshima, Japan, August 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。     

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     

Cell wall thickness and tangential Young's modulus in coniferous early wood

To investigate the effect of wall thickening around cell corners on the tangential Young's modulus of coniferous early wood, tapered beam cell models in which the variation of the cell wall thickness in the axial direction was taken into account were constructed for seven species. Their tangential Young's moduli were compared with the experimental results. The calculated Young's moduli of tapered beam cell models were larger than those of the models composed of the cell walls with uniform thickness, although both models showed almost the same density. For some species the calculated Young's moduli of the models in which the cell wall thickness increased curvilinearly in the axial direction were much closer to the experimental values. The reduction of the radial cell wall deflection due to the increase of the stiffness around cell corners was considered to increase the tangential Young's modulus of a wood cell.This report was presented at the 49th annual meeting of the Japan Wood Research Society, Tokyo, April 1999     

Evaluation of rolling shear strength of plywood by flexural vibration method

The rolling shear strength of plywood was evaluated using a flexural vibration test. Test specimens were lauan and Douglas fir three-ply plywoods made from thick veneers. The dynamic shear and Young's moduli were determined using the flexural vibration method, which involved in-plane and out-of-plane flexural vibration. The rolling shear strength was determined using the static destructive method, which is dependent on the direction of the lathe check in the core veneer. Before and after accelerated aging treatments were conducted, there were relations between out-of-plane dynamic properties (out-of-plane shear and Young's moduli) and its rolling shear strength. It was concluded that the rolling shear strength is related not only to the shear property of the core but the flexural stiffness of two faces when the deformation of out-of-plane plywood was not restrained.Part of this work was presented at the 47th Annual Meeting of The Japan Wood Research Society, Kochi, April 1997     

Shear deflection of two species laminated wood beams

Summary In addition to the deflection due to pure bending in a beam, there is a shear force in all cases of non-uniform bending and a further deflection, due to shear stresses. This additional shear deflection usually is assumed to be negligible and is not considered in computing the total deflection of a beam. In the case of two-species laminated wood beams, due to the development of greater shear stresses, the percentage of shear deflection further increases and failure to take it into consideration may introduce errors of considerable magnitude in determining the distortion of the beam. It is shown here that the percentage of shear deflection can be considerable, approaching the amount due to pure bending. Furthermore it is shown that the magnitude of shear deflection depends on both the span to depth ratio of the beam and the elastic properties of the species involved. It increases as the effective span to depth ratio of the composite beam decreases and as the core ratio of pure modulus of elasticity to modulus of rigidity increases.

---

Zusammenfassung Zu der Verformung eines Balkens unter reiner Biegung tritt bei der Einwirkung ungleichförmiger Biegekräfte eine zusätzliche Verformung, die durch eine Schubkraft und die daraus resultierenden Schubspannungen verursacht wird. Von dieser zusätzlichen Schubverformung nimmt man gewöhnlich an, daß sie vernachlässigt werden kann. Sie wird daher bei der Berechnung der Gesamtverformung eines Balkens nicht mit berücksichtigt. Im Falle von Schichtholzbalken aus zwei verschiedenen Holzarten erhöht sich der Anteil der Schubverformung, verursacht durch das Auftreten größerer Schubspannungen noch weiter, und die Vernachlässigung kann bei der Bestimmung der Gesamtformveränderung zu beträchtlichen Fehlern führen. Es wird gezeigt, daß der Anteil der Schubverformung hoch sein und sich der Größe der reinen Biegeverformung deutlich nähern kann. Es wird ferner nachgewiesen, daß die Größe der Schubverformung vom Verhältnis der Stützweite zur Dicke des Balkens und von den elastischen Eigenschaften der verwendeten Holzarten abhängt. Die Schubverformung erhöht sich, wenn das wirksame Verhältnis von Spannweite zu Dicke des Schichtholzbalkens ansteigt und wenn das Verhältnis zwischen reinem E-Modul und Schubmodul ansteigt.

---

---

The experimental work of this study was conducted at the Yale School of Forestry in cooperation with the Office of Naval Research. Department of the Navy, under contract No. 609 (13), Project NR 330-001, Properties of Tropical Woods.     

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.     

Effect of loading frequency on fatigue life and dissipated energy of structural plywood under panel shear load

Wood-based panels are subjected to cyclic panel shear load caused by wind and seismic forces in such an application as the sheathing of bearing walls. The fatigue behavior of structural plywood under panel shear load with two different loading frequencies was examined. Pulsating panel shear load with a triangular waveform and loading frequency of 0.5 or 5 Hz was applied to the plywood specimens. Stress−strain hysteresis loops were measured throughout the fatigue tests. Fatigue life was highly dependent on loading frequency at more than 0.5 stress level. The deterioration of mechanical property and damage accumulation in plywood specimen was observed to be slower at higher loading frequency at more than 0.5 stress level. Analyses based on energy loss suggest that panel shear load with higher loading frequency causes less damage to the plywood specimen during one loading cycle at higher stress level, and that the fatigue damage accumulation causing failure might be dependent on stress level although it seems to be unaffected by loading frequency. Based on these results, a new fatigue failure model for plywood specimen was qualitatively developed by combining Weibull’s weakest link model and Daniels’ fiber bundle model.