Modeling wood pole failure

Summary This is the first of two papers designed to describe the most recent efforts in using contemporary technology to predict strength and failure location in wood poles. In this report, a three-dimensional finite element model is presented which was developed to provide a rational stress analysis tool for wood poles. Due to practical considerations, only critical pole segments were subjected to stress analyses. Twelve-inch (30.5 cm) segments were selected for analysis which contained knots or knot clusters deemed consequential.The linear elastic model assumes small-deflection theory, and exploits linear strain, 15-node wedge and 20-node parallelepiped, isoparametric finite elements. Element geometry was selected to reflect knot size distribution found in full-size wood poles used in North America. Boundary conditions represented both applied loading and support considerations.Model verification studies were conducted on poles with isotropic (steel) and anisotropic (wood) material properties with and without spiral grain and variable longitudinal elastic properties along the pole radius. The results showed excellent agreement between theoretical and numerically-predicted pole stresses. The effect of boundary conditions on predicted stress distribution was defined, and the element geometry was appropriately modified. The developed model proved to be a rational basis for a more enhanced version to predict the mechanical behavior of wood poles with several inherent growth characteristics.     

Modeling wood pole failure

Summary In part 1 of this series, a three-dimensional, structural analysis, finite element program has been developed to predict the stress distribution in wood poles with and without spiral grain and variable material properties. This program serves as a basis for a model to predict the strength and failure location in full-size wood poles. Fundamental to this model is the ability to quantify the effects of key material and geometric properties of the pole. This paper deals with the enhancement of the program to quantify the effect of knots and their associated cross grain on the stress distribution of wood poles. The technique is based on the theoretical behavior of laminar fluid flow around an elliptical obstruction. The flow-grain analogy was employed to develop empirical relationships between knot diameter and pertinent variables (grain deviation angle near the knot and area of influence of the knot). Prior to the development of the empirical relationships, a study was conducted to determine the size and distribution of knots in Douglas-fir and western redcedar poles.The validity of the technique to describe knot behavior is reflected in the ability of the finite element model to predict the strength and failure location of wood poles. The results suggested that the flow-grain analogy is a rational mechanism to quantify the fiber orientation near a knot. Furthermore, this technique could have meaningful implication in improving visual grading methods for wood poles.The authors would like to recognize the contributions of Engineering Data Management, Inc. of Ft. Collins, Colorado for their contribution of test materials and facilities for this study.     

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.     

Relationship between branch-scar parameters and knot features of oriental beech (Fagus orientalis Libsky)

The classification of roundwood is inextricably linked to the measurement of a particular single wood defect. The appearance, location, and number of defects are important in the quality evaluation of logs and sawn timber, and the most important defects are knots. The purpose of this study was to investigate the relationship between the appearance of branch scars and features of the related knot inside oriental beech logs, and to model the relationship between well-defined branch-scar and knot parameters. One hundred and fifty knots in 15 stems of oriental beech trees were studied. Image analysis software was used to measure the branch-scar and knot features. The results showed a significant positive correlation between the branch-scar parameter “moustache length” and the knot length. The ratio of branch-seal length to width was found to be a good estimator of the stem diameter at the time of knot occlusion and the amount of clear wood between the knot occlusion and the bark. The relationship obtained for the oriental beech stem radius at time of knot occlusion confirms relationship reported for European beech (Fagus sylvatica L.).     

扭叶松实木板材三种动态弹性模量和静态弹性模量比较研究(英文)

采用Pundit、Metriguard、FFT等三种无损检测方法和常规弯曲法对加拿大扭叶松(lodgepole pine)蓝变与非蓝变实木板材的动态及静态弹性模量进行检测和比较研究。结果表明,蓝变材三种动态弹性模量及静态弹性模量均高于非蓝变材;对比分析表明,蓝变材和非蓝变材的动态及静态弹性模量存在差异,其中动态弹性模量差异均达到0.01显著性水平,静态弹性模量差异达到0.05显著性水平,并且心、边材及密度值不同是导致以上差异的主要原因。相关性分析表明,动态与静态弹性模量间相关性达到0.01显著性水平;尽管三种无损检测方法测量结果存在差异,但它们之间仍存在密切相关性,FFT 技术测量的准确性高于Pundit和Metriguard;板材中结子数影响木材动态和静态弹性模量,随着板材结子数增加弹性模量相应地降低。     

A comparison between three different methods of measuring knot parameters in picea abies

Both foresters and sawmillers are interested in the knot structure of trees; in particular, position and number of knots, knot diameter, knot length and dead knot border. For research purposes, it is possible today to carry out non‐destructive measurements using computer tomography (CT) and image analysis. The aim of this study was to measure knot parameters on Norway spruce (Picea abies (L.) Karst.) using a non‐destructive method developed for Scots pine (Pinus sylvestris L.), and to compare the results of this method with the results of two different destructive methods. In order to do this, two Norway spruce stems were scanned by CT. Then five logs from one stem were cut into flitches 20 mm thick and the defects on the sawn surfaces were scanned manually. The other stem was cut just above every whorl and then each knot was split through its centre and the knot parameters were measured manually. The study showed that the CT method compares well with the destructive methods. It is a reasonably fast, non‐destructive method which measures position and diameter of knots and detects larger knots with acceptable accuracy. The study also showed that a large number of smaller knots were not found by the CT method and that the CT method measured knot length and dead knot border with low accuracy. This means that the CT method has to be adjusted to Norway spruce in order to improve its ability to measure knot length and dead knot border and to detect smaller knots.     

Knots in trees: strain distribution in a naturally optimised structure

Electronic speckle pattern interferometry was applied to directly measure the distribution of longitudinal, tangential, and shear strains in small boards of Norway spruce (Picea abies (L.) Karst.) exposed to tensile load in longitudinal direction. A sample with a central intergrown knot and one with an equivalent loose knot were compared with reference samples made of clear wood with an artificial central circular or square hole, respectively. The observed measurements were compared with a finite element (FE) simulation. The FE model was based on a geometric model to quantify the local fibre orientation and a micromechanical model to estimate elastic constants of clear wood and knot tissue. Both the measurements and simulation clearly illustrate a rather homogenous strain distribution around the intergrown knot. In comparison, the natural optimisation of dispersing strain peaks is less efficient in the case of loose knots. The artificial circular and square holes in samples with parallel fibre orientation lead to high gradients in the strain field and peak values in vicinity of the disturbance.     

基于振动模态分析的落叶松节子定位的无损检测

木材作为结构材使用时,节子的存在影响木材的强度,降低了木材的利用价值.为了节约木材,提高木材的使用率,人们一直在研究木材缺陷无损检测的方法.Beall(2000)首次使用表面传感器研究人造板的力学性能和内部缺陷,收到良好效果.日本学者小玉泰羲(2000)用连续小波变换分析处理利用敲击木材所获得的声信号,对气干木材的节子缺陷进行检测,研究发现,当木材含有节子缺陷时,声信号的共振频率降低、声信号共振的持续时间缩短.     

Shape and distribution of knots in a sample of picea abies logs

In an attempt to develop a better understanding of the effect of knottiness on the yield of logs for sawn timber products, the present study examines the position and geometrical characteristics of 429 knots found in seven Norway spruce (Picea abies (L.) Karst) middle logs from southern Finland. The raw data used in this study were in the form of coordinates of points located on the knot surface recorded in a cylindrical (R, L, T) reference frame. The data were smoothed using a non linear three‐dimensional model. A curvature analysis of the knot pith was used to differentiate the curved and straight portions of the knots. This analysis made possible calculation of knot angles, symmetry, ovality and volume. The major finding of this study is the uneven distribution of knots around the log circumference. Nearly 50% of the total knot volume was concentrated in one‐third of the log facing the south‐east. Knots were also more prominent in higher portions of the logs studied. These observations support the argument that the uneven distribution of knots offers potential for improving the grade yield of timber sawn from trees harvested in high‐latitude countries.     

Effects of commercial thinning,log position in the stem,and cutting width on the surface quality of cants produced by a chipper-canter

Fifteen stems of jack pine (Pinus banksiana Lamb.) of 3 commercial thinned plots (control, moderate, and intensive thinning) and 15 stems of black spruce (Picea mariana (Mill.) B.S.P), both coming from the Abitibi-Témiscamingue region – Canada, were cross-cut into three 2.4?m length sections: bottom, middle, and top logs. Logs were processed with a chipper-canter at three cutting widths (12.7, 19.1, and 25.4?mm), producing chips and a three-faced cant. The middle section of the cant was used to evaluate surface quality across the grain on each face. Roughness and waviness parameters and depth of torn grain were recorded. Knot characteristics were assessed in the three cant faces. Poorer surface quality was found in the lower part compared to the upper part of the cant for both species. At larger cutting widths, jack pine logs coming from a natural stand showed lower surface quality compared to logs from thinned stands. Black spruce waviness increased with the cutting width and stem height. These results were attributed to the increase of forces and vibration when cutting at larger cutting widths, which was worsened by the presence of bigger, more numerous knots at the control plot and in the top logs. Black spruce had deeper torn grain compared to jack pine. Their differences in knot characteristics resulted in a maximum torn grain depth favored by the presence of more knots rather than by bigger knot size. Other knot characteristics, such as the position of the knots in the cant face, the insertion angle of the branch and the distribution of the knots around the log, should be studied to better understand the relationship between torn grain formation and knottiness.     

A three-dimensional paradigm of fiber orientation in timber

Knowledge of the three-dimensional orthogonal directions of wood material at any position within a tree is necessary for the understanding of strength reducing effects of knots and essential for the continuation of research in areas which relate small clear wood specimen behavior to the behavior of full size structural timber. A complete three-dimensional paradigm describing the geometry of knots and related fiber distortion, initially derived to predict the strength-reducing behavior of knots in structural timber of Norway Spruce with the finite element method, is presented in this article. Besides strength prediction analyses, it is believed that the paradigm may be useful in other areas of research on structural timber that are effected by fiber orientation, such as drying and form change of structural timber. The paradigm generates fiber orientation in any position within a log or lumber from assumed fiber patterns in planes parallel to the longitudinal direction of the original tree. Fiber patterns in the radial and tangential directions are derived from physical restraints related to fiber production within the annual increase surfaces of the tree and from theories of knot formation. The adaptability of the paradigm allows practically any softwood knot to be modeled with an accuracy that is limited only by input-data. The knot-axis may be non-linear, and the knot cross-section oval with its vertical and horizontal axis increasing from the pith of the stem at chosen rates. Spiral grain may also be included in the paradigm and vary with the annual growth layers. Investigations presented in this article showed that generated fiber orientations for Picea abies complied well with measured fiber distortions, and that the general trends of fiber orientation, explained by the applied knot formation theory, is reflected in the measured specimens. Received 12 May 1999     

世界节子研究进展

通过对大量文献的整理分类,从节子自身研究状况、对木材加工利用的影响和节子的无损检测技术几个方面,对截至目前世界上对节子研究的进展状况进行了综述,并提出了今后的一些研究发展方向。     

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.     

Estimating the influence of knots on the local longitudinal stiffness in radiata pine structural timber

A theoretical model is developed to evaluate the negative effect of knots on the local longitudinal stiffness (elastic modulus) in radiata pine structural timber. The parameters in the compliance matrices for knotwood in branches are estimated by extending the mechanical formula for clearwood also to knotwood, assuming a structural similarity for stem and branch. The stiffness of knots in the longitudinal direction of sawn boards is then obtained by coordinate transformation. The effective local longitudinal stiffness in a mixture of wood (a combination of knotwood and stem wood) is estimated in terms of the elastic moduli and volume fractions of all phases using a modified rule of mixtures. The effects of branch angle and volume fraction of a knot on the local longitudinal stiffness of structural timber are simulated under different scenarios. Experimental observations also demonstrate similar trends to those shown in the simulations. Received 5 December 2000 The author is grateful to Prof. John Walker (The New Zealand School of Forestry), Dr. Huawu Liu (Wool Research Organisation of New Zealand), Dr. Ian Cave (Department of Chemistry, Canterbury University) and Dr. Dave Cown (New Zealand Forest Research) for their comments and advice during the preparation of this paper.     

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     

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.     

Anatomical observations of Pseudomonas savastanoi on Rhamnus alaternus

Buckthorn (Rhamnus alaternus) was recently reported as a new host of Pseudomonas savastanoi. The main symptom on buckthorn is the formation of knots on stems, branches and occasionally on leaves. Knot formation and anatomical changes in host tissues induced by P. savastanoi were studied macroscopically and by light microscopy. Inoculation of buckthorn shoots with P. savastanoi initiated small green swellings that developed into normal size knots. The pathogen invades intercellular spaces of parenchyma tissues degrading cell walls and resulting in extensive cavities filled with bacterial cells. Many host cells contiguous to such cavities were plasmolysed and necrotic. Depending on the depth of the inoculation wound, parenchyma, cambium, ray parenchyma, and pith cells close to bacterial cavities enlarge and proliferate forming the fully grown knots. At later stages of knot development, the cambium appears dispersed in the knot and forms unoriented vascular tissues. Periderm surrounds bacterial cavities and outer layers of knots. These findings on buckthorn are compared with those reported to be caused by the same pathogen on ash, oleander and olive.