Derivation of tensile strength ratio by second-order theory

Summary Tension members with edge knots or edge knotholes deflect laterally when they are loaded by a tensile force. In order to consider this behavior for determination of tensile strength ratio (TSR), second-order theory is applied. A matrix displacement method of structural analysis developed from the slope deflection method is used to implement the second-order theory. The method reveals that in a member with a single edge knot the lowest TSR is obtained when the lateral deflection is negligible, and when the ends are hinged. For a stiffness value (EI/L) that is small, both end conditions (hinged and fixed) yield the same TSR; for large stiffness value, fixed end condition always gives a higher TSR than a hinged end condition because the moment is reduced at the defect as a result of the fixed ends. The method further reveals that the maximum moment for two edge knots on the same edge is lower than when they are on opposite edges.The findings are important because they can provide guidance in planning tensile testing methods for lumber, in interpretation of results of tests, and in design considerations. These findings help to develop better relationships between TSR, which is an index of tensile strength (T), and apparent modulus of elasticity, E_a, which are so important for the determination of the best predictor of T.Maintained at Madison, Wis., in cooperation with the University of Wisconsin.     

SPF规格材蠕变特性研究

以轻型木结构建筑常用的SPF规格材为研究对象,采用简支梁中部集中加载的方式进行短期弯曲蠕变试验。结果表明:在不同试验条件下蠕变经过瞬态蠕变阶段、相对稳定蠕变阶段。试件在不同持续负载水平下的蠕变应变-时间曲线具有几何相似性,其曲线的形状和走向趋势大致相同。蠕变变形量和曲线上的跳跃点随着应力水平的增加有增大的趋势。相比于侧弯受力,平弯蠕变速率更大,承载强度损耗较大。     

Quantification of visual inducement of knots by eye-tracking

Knots have been considered an undesirable visual feature of lumber. To clarify the essence of this visual undesirability, eye-tracking data from 20 subjects, who freely observed 55 images of wood wall panels, were recorded and distribution maps of eye-fixation pauses were composed. These maps were compared with the arrangement of knots on each knotty wall panel image and the visual inducement of knots was evaluated using a new numerical index of pausing probability. The present study is the first to objectively quantify the visual inducement of knots. In addition, the subjective noticeability of knots and ten visual impressions of each wood panel image were investigated by a sensory evaluation. There was a very clear linear relationship between the visual inducement of knots and the subjective noticeability of knots. A correlation analysis suggested that many visual impressions of wood wall panels were influenced by a complementary effect between the subjective noticeability of knots and the visual inducement of knots. The visual impact of knots was masked to some extent by special visual stimuli such as deep red grooves on the wood wall panels. This study was presented at the 56th and 57th Annual Meetings of the Japan Wood Research Society, Akita and Hiroshima, August 2006 and August 2007, respectively     

无损检测技术评估规格材的性质

采用两种应力波设备对北美黄杉规格材进行抗弯强度性质的预测,分析规格材破坏模式,并讨论木材节子对规格材强度的影响。测试结果表明,动态与静态测试结果之间的相关程度较高。结构材的破坏模式主要为纹理断裂和脆性断裂;在规格材中间部位节子较多,且节子在规格材横断面上投影面积较大时,易发生脆性断裂。     

Strength properties of glued laminated timber made from edge-glued laminae I: strength properties of edge-glued karamatsu (Larix kaempferi) laminae

The object of this study was to investigate the strength properties of edge-glued laminae and to propose a suitable grading method based on the lamina modulus of elasticity (MOE). Edge-glued laminae composed of lumber with similar MOEs (uniform laminae) and edge-glued laminae produced by randomly gluing lumber independent of MOE (random laminae) were made from karamatsu (Larix kaempferi) lumber having the same thickness and length, but various widths. For both the uniform and random laminae, there was a strong correlation between MOE values measured using the longitudinal vibration technique, the static bending test, and a grading machine. The average values of bending, tensile, and compressive strengths of the uniform laminae were similar to those of the random laminae. On the other hand, the average strength of laminae without end joints was significantly higher than that of finger-jointed laminae for both uniform and random laminae. Finger-joints and knots played a significant role in the failure of specimens, but the edge-gluing and the difference in MOE within an edge-glued lamina did not appear to affect the strength properties. The bending, tensile, and compressive strengths of edge-glued laminae were strongly correlated to the lamina MOE.     

钢琴音板木材的杨氏模量动态法测量及其评价

以钢琴音板用西加云杉锯材试件为研究对象,依据梁的纵向、横向弯曲原理及其动力学理论,采用振动频率法和声学频率法,测量该批试材在自由支承状态下的基频值,得到杨氏弹性模量值,并对其性能进行评价。     

图像分割技术在木材表面缺陷识别中的应用

阐述了图像分割技术在图像处理及分析中重要意义,以及主要的图像分割技术。以木材表面缺陷为主要研究对象,利用微分算子边缘检测、最优迭代阈值分割及形态学方法针对具有代表性缺陷死节和虫眼进行分割处理。     

Differences of tensile strength distribution between mechanically high-grade and low-grade Japanese larch lumber I: Effect of length on the strength of lumber

An experimental study was conducted to evaluate the effect of length on the parallel-to-grain tensile strength of Japanese larch (Larix kaempferi, Carriere) lumber. Six hundred pieces of mechanically graded lumber were tested at gauge lengths of 60, 100, and 180 cm. The lumber was sorted into matched groups according to the dynamic Young's modulus measured by the longitudinal vibration method before the lumber was cut to the particular length. The averages of the dynamic Young's modulus of high-grade (H) and low-grade (L) specimens were 12.8 and 7.5 GPa, respectively. Using nonparametric estimates, the estimated length effect parameters of H and L were 0.268 and 0.304 for the 50th percentile and 0.121 and 0.256 for the 5th percentile, respectively. We then concluded that the different length effect factors between H and L could be used when using the lumber for practical purposes. The parameters of L were larger than those for H, and the parameters for 5th percentiles were smaller than the parameters for 50th percentiles. When two-parameter Weibull distribution functions were fitted to the strength data, the estimated shape parameters of the Weibull distribution by the parametric method were almost identifical to the inverse of nonparametric parameters except the 5th percentiles for H. The influence of defects such as knots on the lower tail of the strength distribution in H may be different from that in L.Part of this paper was presented at the 48th annual meeting of the Japan Wood Research Society, Shizuoka, April 1998     

落叶松锯材目测分级与力学性能相关性的研究

以落叶松锯材为试验对象,依据GBS0005—2003《木结构设计规范》中外观分等的相关规则。对人工林落叶松锯材进行了以节子为检量对象的外观分等试验,并对分等后的锯材进行了弯曲破坏试验,分析比较了外观分等结果与其弯曲破坏检测结果的相关关系。     

Effects of thinning and pruning on knots and lumber recovery of Taiwania (<Emphasis Type="Italic">Taiwania cryptomerioides</Emphasis>) planted in the Lu-Kuei area

This study investigated the effects of various thinning and pruning methods on the knots (number and size) and lumber recovery from Taiwania (Taiwania cryptomerioides Hay.) plantation trees. The results showed that heavy thinning caused more knots and larger-diameter knots than medium or no thinning; moreover, pruning caused fewer numbers of knots and smaller-diameter knots than no pruning. Better-quality Taiwania trees occurred with the no-thinning/no-pruning treatments, as shown by analyzing the knots, although the results also showed that the healing process seemed to have produced not completely clear wood during the 9 years after the pruning treatment. The thinning intensity slightly enhanced the lumber recovery of logs. Pruning did not affect lumber recovery from taiwania trees and logs. Thinning increased the lumber recovery per tree due to an increase in the diameter at breast height.     

Differences of tensile strength distributions between mechanically high-grade and low-grade Japanese larch lumber III: effect of knot restriction on the strength of lumber

It is well known that the presence of knots in structural lumber is one of the most important strengthreducing factors. For practical purposes, visual grading including knot restriction is an effective method for nondestructive evaluation of strength. Edge knot restriction for not only visually graded lumbers but also mechanically graded lumbers is specified in the Japanese agricultural standards for glued laminated lumber. We conducted experimental studies on differences of tensile strength distributions between mechanically high-grade and low-grade Japanese larch (Larix kaempferi, carriere) lumbers daily used for manufacturing glued laminated timbers in Nagano, Japan. We then examined the additional visual grading of mechanically graded lumbers for nondestructive evaluation. We visually graded the prepared mechanically graded lumber by focusing on the knots' area ratio of grouped knots. We confirmed that the higher visual grade related to the stronger tensile strength, similar to our present knowledge; but the effects of knot restriction were reduced when the length of the lumber increased in view of nonparametric 5th percentiles of tensile strength. The differences in the strength/elasticity ratio between mechanically high-grade and low-grade lumber were negligible. It was clear that the length effect on the ratio in visually graded high-grade lumber was smaller than that of visually graded low-grade lumber. It was thus concluded that knot restriction should have little effect on the tensile strength of mechanically graded lumber.     

Variation of tensile strength with annual rings for lumber from the Japanese larch

To examine the effectiveness of long rotation forestry and the potential of complete utilization of Japanese larch (Larix kaempferi Carriere), we designed a tensile test using the lumber from six 87-year-old sample trees. Results showed that strength properties of lumber varied greatly in the radial direction within trees, but all sample trees showed a similar trend. There was little difference in dynamic Young's modulus but a large difference in tensile strength (TS) between the lumber and small clear specimens from undestroyed parts of the lumber. These differences decreased with an increase in ring number and became constant after 30 years. The presence and distribution of knots markedly affected the TS; and among the knot indices, the knot number (Kn) and knot area ratio of a maximum single knot (Km) proved to be effective for explaining the effect of knots. The distribution of Kn and Km in the radial direction agreed with the variation of TS in the radial direction. By investigating the variation patterns of lumber and small clear specimens in the radial direction, it was found that the strength properties of both required a long time, about 30 years, to reach a relatively constant state.Part of this report was presented at the 49th annual meeting of the Japan Wood Research Society, Tokyo, April 1999     

Strain fields around knots in Norway spruce specimens exposed to tensile forces

Two-dimensional strain fields around knots in two Norway spruce specimens subjected to tension loading were detected using a contact-free measuring technique based on white-light digital image correlation. The first specimen included a traversing Edge knot, and the second one, a Centric knot. The development of strain fields as a function of load level was measured by consecutive cyclic load tests where one side of the specimen was studied during each test. The objectives were to examine to what extent the strain fields could be detected, to investigate the correlation between strain fields measured on different sides of a specimen and to analyse the strain distributions around the knots. The results show that the applied technique is useful for catching both overall and detailed information about the behaviour of knots in wood members exposed to loading. Clear wood defects that could not have been detected by neither visual inspection nor scanning were observed, and conclusions could be drawn regarding the release of internal stresses. The correlations between strain fields on different sides of the specimens were excellent, and the correspondence between measurement results and comparative finite element calculations was surprisingly good considering the fact that the employed FE models were fairly simple.     

Strain-softening behavior of wood under tension perpendicular to the grain

Three softwood samples and one hardwood sample were tested under a tension load applied along the radial direction using small clear specimens and the local tension strain was measured using the digital image correlation method. We successfully obtained a stress-strain curve with a strain-softening branch by calculating the stress using the strain distributions in the vicinity where the specimen ruptured. The continuous digital imaging of the specimen proved to be very effective for measuring the strain in quasi-brittle materials such as wood under tension. The nonlinearity of the stress-strain curve was quantified using two parameters representing the deviation from linear elasticity, and the formula of the stress-strain curve was deduced from the interrelation between these parameters. This formula is expressed quite simply by using the modulus of elasticity along the radial direction and another constant that is unique to the material. Part of this article was presented at the 56th Annual Meeting of the Japan Wood Research Society, Akita, Japan, August 2006     

Radial variations of wood properties of an endangered species, <Emphasis Type="Italic">Pinus armandii</Emphasis> var. <Emphasis Type="Italic">amamiana</Emphasis>

A dead tree of Pinus armandii Franch. var. amamiana (Koidz.) Hatusima (abbreviated to PAAm) was obtained from a natural habitat on Tanega-shima Island and various properties of its wood were investigated. Grain angle was measured and soft X-ray analysis was undertaken to obtain the density in each annual ring. Unit shrinkage and dynamic properties were measured by shrinkage, bending, and compression tests. Variations of wood properties in the radial direction, relationships of wood properties to density, and annual ring width were examined. Roughly speaking, variations in the radial direction of the grain angle, twist angle by drying, Young’s modulus and strength in static bending, absorbed energy in impact bending, compressive Young’s modulus, compressive strength, and compressive proportional limit corresponded to the variation of annual ring width. As a result, it was determined that if PAAm is afforested artificially for the purposes of lumber production and conservation, the annual rings of logs should not be too widely spaced. Wood properties of PAAm were similar to those of Japanese black pine (Pinus thunbergii Parl.), which is another representative pine on Tanegashima Island. This study was presented in part at the 56th Annual Meeting of the Japan Wood Research Society, Hiroshima, August 2007     

Development of structural composite products made from bamboo II: fundamental properties of laminated bamboo lumber

This experiment explored the technical feasibility of using bamboo zephyr mat with pre-hot-pressed treatment for the manufacture of laminated bamboo lumber (LBL), which is similar in construction to that of laminated veneer lumber (LVL). Six LBL boards (made from four-ply bamboo zephyr mats) with approximate dimensions of 2×42× 42cm were fabricated using resorcinol-based adhesive. The experimental design involved three combinations of layered structures (types I, II, and III) and two LBL loading positions (H-beam and V-beam) during the bending test. These materials were then compared to ordinary LVL. Results indicated that the bending properties (moduli of rupture and elasticity) of LBL were comparable to those of LVL, but there was no significant effect on the physical and mechanical properties among the three types of LBL beam. Interestingly, orienting the glue line to the vertical direction (V-beam) could maximize the ultimate strength of the LBL.Part of this research was presented at the 49th Annual Meeting of the Japan Wood Research Society, Tokyo. April 1999, and at the Pacific Timber Engineering Conference, Rotorua, New Zealand, March 1999     

Location of the neutral axis in wood beams: A preliminary study

Abstract

It is commonly accepted in the analysis of wood beams that the neutral axis coincides with the beam's centroid. However, wood is not an isotropic material, has different elastic properties in the tangential, radial and longitudinal directions, and is non-homogeneous, as it contains characteristics such as knots. Therefore, there is need for an analysis of the neutral axis for anisotropic, non-homogeneous materials, such as wood, to predict deformations and strains. Specifically, digital imaging correlation, a non-contact technique to measure deformation of an object's surface, is used to examine how knots influence neutral axis location. Output from digital imaging correlation software provides a clear image of the location of the neutral axis. The neutral axis in a clear wood beam remains close to the centroidal axis throughout loading, while the location of a knot determines the size of the compression and tension zones as well as the location of the neutral axis.     

Strain analysis of lumber containing a knot during tensile failure

We analyzed the strain distribution of lumber containing a knot under a tensile load. The local tensile strain near the knot was measured using the digital image correlation method. Fracture often initiated near the knot where the fiber orientation changed in a three-dimensional manner. The fiber direction in this zone was different from that in the clear part, coinciding with the thickness direction and not with the longitudinal direction of the specimen. Our results disagree with those of previous models that assumed the longitudinal direction of lumber as the direction of crack propagation. Strain analysis showed that a nonlinear region existed around the knot just before ultimate fracture occurred. The results indicated that nonlinear characterization is necessary to determine the failure mechanism of lumber containing a knot, despite the brittleness fracture at the macroscopic scale.     

Differences of tensile strength distribution between mechanically high-grade and low-grade Japanese larch lumber 11: Effect of knots on tensile strength distribution

The tensile strength (TS) test results of Japanese larch (Larix kaempferi, Carriere) lumber of varying length have shown that the length effects on TS were different between high-grade (H) and low-grade (L) lumber. In this paper, we examined the effect of knots on the TS distribution by measuring the number of knots and the knot area ratio of each specimen. There were more knots in L than in H; and the knot area ratio in L distinctly increased as the length increased compared to that in H. The correlation coefficients between physical properties and TS indicated that knots were the most influencial factor for TS among several physical properties: annual ring width, distance from pith, density, dynamic Young's modulus, and knots. We attempted to estimate the length effect parameters by introducing the concept of assumed knot strength. We thought that the length effect parameters for 50th percentiles of TS could be estimated well with fitted 3P-Weibull, and that the parameters for 5th-percentiles could be estimated well with 2P-Weibull fitted to lower-tail 10% data by the likelihood method. The differences of length effect on TS between H and L should be governed by the presence of knots. The independent model based on the concept of assumed knot strength may express the TS of structural lumber of various lengths.     

Modelling of knots in logs

A geometrical model was derived to describe knots in logs and on the surface of lumber beams sawn from those logs. Each knot is defined by 7 parameters related to the shape and position in the stem. A computer simulation program was written to study knot shapes on a variety of observation planes.An initial investigation on the shape of knots in Scots pine logs and lumber beams suggests that the model is sufficiently accurate to describe knottiness in this species. Potential applications of this model include automated lumber grading, computerized log reconstitution and yield optimization studies.This research was carried out when the author was a Visiting Scientist at the Technical Research Centre of Finland (VTT), Forest Products Laboratory, P.O. Box 207, SF-02151 Espoo, Finland. Technical assistance of U. Saarelainen, A. Usenius and C. O. Sommardahl from VTT is gratefully acknowledged. This work was partially supported by Forestry Canada and the Natural Sciences and Engineering Research Council of Canada