Quasi-non-linear fracture mechanics analysis of the splitting failure of single dowel joints loaded perpendicular to grain

A quasi-non-linear fracture mechanics model based on beam on elastic foundation theory is applied for analysis of dowel joints with a single dowel loaded perpendicular to grain. The properties of the elastic foundation are chosen so that the perpendicular-to-grain tensile strength and fracture energy properties of the wood are correctly represented. It is shown that this particular choice of foundation stiffness makes a conventional maximum stress failure criterion lead to the same solution as the compliance method of fracture mechanics. Results of linear elastic fracture mechanics are obtained as a special case by assuming an infinitely large value of the foundation stiffness. Results of tests on so-called plate joints are compared with theoretical predictions, showing good agreement for variations in initial crack length as well as edge distance.     

Estimation of yield and ultimate strengths of bolted timber joints by nonlinear analysis and yield theory

A finite element nonlinear analysis was conducted on bolted timber joints under lateral loads parallel and perpendicular to the grain. The results obtained from this analysis were compared with the experimental results and calculated values based on the yield theory. The analysis and experiment were performed on double shear bolted joints parallel and perpendicular to the grain with steel side plates and a slotted-in steel plate. It was found from the analysis that the yielding of wood and bolt occurred before the overall yielding of the bolted joint. Shear strength of bolted joints calculated from the yield theory using the embedding yield strength of wood and the yield moment of the bolt showed comparatively good agreement with the shear strength evaluated by 5% offset of the load–slip curve in the experiment and analysis. The shear strength of the bolted joint calculated from the yield theory using the embedding ultimate strength of wood and the ultimate moment of the bolt agreed quite well with the shear strength evaluated by the maximum load up to 15mm slip in the analysis. The former, parallel and perpendicular to the grain, were 11% and 34%, on average smaller than the latter in the experiment.Part of this paper was presented at the 52nd Annual Meeting of the Japan Wood Research Society, Gifu, April 2002; the Annual Meeting of Architectural Institute of Japan 2002, Ishikawa, August 2002; and the World Conference on Timber Engineering 2002, Shah Alam, Malaysia, August 2002     

Quasi-non-linear fracture mechanics analysis of splitting failure in simply supported beams loaded perpendicular to grain by dowel joints

A quasi-non-linear fracture mechanics model based on beam on elastic foundation theory is applied for analysis of the splitting failure of dowel joints loaded perpendicular to grain. Simply supported beams symmetrically loaded by two dowels are considered, and the effects of edge distance, dowel spacing, and distance between dowels and supports are accounted for. The foundation modulus used in the beam on elastic foundation model is chosen so that the perpendicular-to-grain tensile strength and fracture energy properties of the wood are correctly represented. This ensures that a conventional stress analysis and failure criterion lead to the same solution as the compliance method of fracture mechanics. A semiempirical efficiency factor is proposed to account for the influence of the total beam depth, which does not enter the beam on elastic foundation model, but the effect of which is evident from tests. It is shown that the so-called Van der Put/Leijten model, which recently has been adopted in Eurocode 5, appears as a special case of the model presented. Tests on simply supported beams with a single dowel joint at midspan are compared with the theoretical predictions. Various edge distances, beam depths, and spans were tested.     

A stress transformation approach to predicting the failure mode of wood

Summary A simple model, based on the use of transformations of second-order tensors, is presented in this paper to predict the failure mode of wood members stressed in various degrees of parallel-and perpendicular-to-grain tension and parallel-to-grain shear. This type of loading is indicative of structural wood members with cross grain or grain deviations in the vicinity of knots subjected to bending or tension. The model is based on the assumptions that failure is dictated by the presence of any of the aforementioned stresses that exceed the clear wood strength in that mode and that failure does not result from stress interactions. The magnitudes of the applied stresses are normalized relative to the wood strength in that mode. The ratio of applied stress to material strength that is greatest at any particular angle of load to grain is presumed to be the failure mode at that angle. To verify model predictions, optical and microscopic analyses of surfaces of failed specimens loaded in uniaxial tension at angles between 0° and 90° to grain were compared to previously obtained, or otherwise known, surfaces of specimens tested in tension and shear. Specimens tested at various angles to grain demonstrated failed surfaces very much like those associated with specimens loaded in the modes predicted by the model.     

Nonlinear superposition model for the behavior of bolted joints

Summary A previously developed model to predict the load-slip relationship for mechanical joints using one bolt subjected to lateral loading (Part 1) was extended to incorporate the rotational resistance of joints containing two bolts. The rotation is about the long axis direction of the bolts, and considers the wood members oriented at arbitrary angles to the grain. The model utilizes nonlinear translational springs to represent the parallel and perpendicular to grain components of the reaction force present on each bolt resisting the applied moment. A series of experiments were conducted to determine the spring constants of bolted joints in axial loading and to verify the predictions of the mathematical model. Bolted joints subjected to a pure rotation were tested using combinations of steel plates and wood side members experiencing bolt reaction forces at various angles of load to grain. The results indicated an excellent agreement between theoretical predictions and experimentally obtained data.The authors wish to extend thanks to the Colorado State Agricultural Experiment Station for their financial support and to the Fulbright-Hayes Foundation for the educational scholarship and research funding provided to the project     

人工林杉木、马尾松木材的断裂特性

使用扫描电子显微镜观察杉木、马尾松横纹拉应力、顺纹拉应力及冲击载荷作用下的破坏表面，结果表明不同的加载方式、加载速率对木材的断裂过程有影响；木材的微观构造影响其断裂过程。     

Bearing properties of Shorea obtusa beneath a laterally loaded bolt

Empirical equations to determine the bearing strength have been proposed by many researchers and design standards. Because these equations have been developed mainly based on test results of softwood species, it is a matter of great importance (to ASEAN structural engineers) to verify the applicability of these equations for tropical hardwood species, which are commonly used in many ASEAN countries. In this study, wood specimens of Shorea obtusa (a tropical hardwood species) were used and the bearing test under full-hole confi guration was carried out for fi ve different loading angles to the grain. The bearing stress-embedment curve obtained from the test was approximated by a linear elastic-plastic diagram indicating the initial and fi nal stiffness of the curve. Testing showed that the average bearing strength parallel to the grain was 7.25% lower than the prediction given in Eurocode 5. The bearing strength perpendicular to the grain evaluated based on bearing load at initial cracking was substantially different from any predictions given by previous studies or design standards. It was also found that the bearing strength and initial stiffness from the bearing stress-embedment curve for loading at intermediate angles to the grain could be satisfactorily predicted with Hankinson’s formula.     

Prediction of the load carrying capacity of bolted timber joints

Failure of bolted timber joints is analyzed experimentally and numerically. In this study, the prediction of the load-carrying capacity of dowel-type joints with one dowel under static loading is based on the analysis of fracture in wood contrarily to most engineering methods that are based on the yield theory. Mechanical joints consist of glued laminated spruce members and steel dowels. In the different analyzed tests, the bolt loads the wood parallel or perpendicular to the grain. The wood member thickness is chosen sufficiently thin to avoid the fastener from presenting plastic hinges. The influences of different structural parameters such as the dowel diameter, the edge- and end-distances are investigated. The fracture propagation analysis is carried out with the Finite Element (FE) method in the framework of Linear Elastic Fracture Mechanics (LEFM). The only identified parameter is the critical energy release rate in mode I (G_Ic). The comparison between experimental and numerical results shows that the fracture must be considered for a correct prediction of the ultimate load and that LEFM can help to improve design codes. Received 11 August 1997     

Nonlinear superposition model for the behavior of bolted joints

Summary A nonlinear superposition model was developed to assess the load-slip behavior of bolted joints consisting of a single bolt subjected to lateral loading at angles of load to grain. This model characterizes the bolted joint as a pair of orthogonal nonlinear springs aligned parallel and perpendicular to the grain of the wood members. The spring stiffnesses are quantified by a logarithmic or exponential function depending upon whether the connection softens or stiffens with increasing slip. The spring deformations are superimposed to determine the movement of each component of the connection. Deformations of connected members are added vectorially to determine their relative displacement. Spring constant were determined experimentally using metal-to-wood connections. Thick steel side plates were employed to limit the system deformation to the wood component. Wood members were evaluated at angles of load to grain ranging from zero to ninety degrees. Once the spring constants had been determined, the model was executed to predict the load-slip behavior of wood-to-wood connections. These predictions were compared to experimentally obtained load-slip values. The results indicate that the nonlinear superposition concept is a valid approach to predict joint deformation at angles of load to grain.The authors express their gratitude to the Fulbright-Hays Foundation and the Colorado State Agricultural Experiment Station for their financial support of this study     

Fracture of multiply-bolted joints under lateral force perpendicular to wood grain

The crack initiation and propagation of multiplybolted joints subjected to lateral forces perpendicular to the grain were analyzed. Two types of bolted joint were subjected to lateral loads perpendicular to the grain. One had joints of two bolts aligned with the wood grain (type H), and the other had joints of two or three bolts aligned perpendicular to the grain (type V). The crack initiation and propagation were analyzed by means of the average stress method (ASM) and linear elastic fracture mechanics (LEFM), respectively. The maximum loads calculated by LEFM agreed comparatively well with the experimental results, and it was proved that the LEFM was an appropriate tool to analyze the fracture of multiply-bolted joints subjected to a force perpendicular to the grain. It was also found that the multiply-bolted joints failed with the fracture of the wood before the joints yielded, and that it caused a considerable decrease of the maximum loads. The reduction of strength should be considered in the design of multiply-bolted joints subjected to lateral forces perpendicular to the grain.Part of this work was presented at the annual meeting of the Architectural Institute of Japan, Hikone, September 1996     

Determination of embedding strength of wood for dowel-type fasteners

Embedding tests parallel and perpendicular to the grain were conducted to produce a database of embedding strength of wood for the design of dowel-type joints. Dowel diameters were 8,12,16, and 20mm. Embedding strength was evaluated by the 5% off-set method and a maximum load up to 5mm displacement according to EN383. The embedding strength parallel to the grain evaluated by the former method showed values close to those obtained with the latter method, but they showed a significant difference in tests conducted perpendicular to the grain. The embedding strength parallel to the grain was 0.9 times as large as the compressive strength parallel to the grain regardless of the evaluation method. The embedding strength perpendicular to the grain evaluated by the 5% off-set method was four times as large as the compressive strength perpendicular to the grain. When the embedding strength perpendicular to the grain was evaluated by a maximum load up to 5mm displacement according to EN383, the ratio of embedding strength perpendicular to the grain to the compressive strength perpendicular to the grain decreased as the dowel diameter increased.Part of this paper was presented at the annual meeting of the Architectural Institute of Japan 1999, Hiroshima, September 1999; the 50^th annual meeting of the Japan Wood Research Society, Kyoto, April 2000; and the World Conference on Timber Engineering 2000, Whistler, Canada, July–August, 2000     

An experimentally validated fatigue model for wood subjected to tension perpendicular to the grain

This study presents an experimental investigation of fatigue in wood subjected to tension perpendicular to the grain. The study has been designed with special reference to the influence of the frequency of loading. The investigation reveals an interaction between number of load oscillations and accumulated time under load to failure. This interaction corresponds to frequency dependent fatigue. Current models for damage accumulation and failure modelling are screened with respect to their ability to account for such “two-source” damage. The Damaged cracked viscoelastic material model proved to give a good basis.     

正交胶合木横纹承压性能研究现状

正交胶合木（CLT）在木结构建筑中应用越来越广泛,特别是在中高层建筑物中。CLT作为楼盖构件使用时,承受柱或墙体施加的垂直荷载,因此CLT产品的设计及应用需要其横纹承压弹性模量和强度方面的参数;改善CLT横纹承压性能,也可以提高整体结构强度和建筑安全系数。文中主要介绍目前CLT横纹承压性能测试方法,总结CLT横纹承压性能影响因素方面的研究进展,以期为国内CLT研究提供参考。     

温度对人工林落叶松材物理力学性能的影响

探讨在不同的干燥温度状态下,木材抗弯强度,抗弯弹性模量、横纹抗压强度的变化规律。试验结果显示,在中、低温区域,随着温度的升高,抗弯弹性模量、横纹抗压强镁呈降低趋势;在高温区域,随着温度的升高,抗弯强度被明显削弱,而纹抗压强度则得到增强。     

Effect of grain angle on shear strength of glued end grain to flat grain joints of defect-free softwood timber

To evaluate the effect of grain orientation on the adhesive bond strength, three-layered Norway spruce wood specimens were tested in shear. The two axial-oriented outer layers were jointed with the middle layer using three typical glues for load bearing constructions, i.e. one-component polyurethane (PUR), melamine–urea–formaldehyde (MUF) and phenol–resorcinol–formaldehyde (PRF). The grain orientation of the middle layers was varied from 0° (parallel to grain of the surface layer) to 90° (perpendicular to grain of the surface layer) in incremental steps of 10°. Samples with middle layers oriented parallel to the outer layers showed shear values in the range of solid spruce wood. Decreased shear strength values were expected for increased grain angles of the middle layer. However, no explicit tendency was observed for the shear strength in dependence of the grain direction. In general, MUF-bonded samples showed slightly higher shear strength values compared with PUR- and PRF-bonded specimens.     

Effect of fatigue and annual rings’ orientation on mechanical properties of wood under cross-grain uniaxial compression

The mechanics of fresh wood with and without a fatigue pre-treatment that mimics a mechanical pulping process was experimentally studied. The mechanical properties of Norway spruce samples under compression are considered with the macroscopic stress–strain data and from local strain properties via digital image correlation technique. The results highlight the effects of the orientation of the wood annual rings compared to the loading direction and of the pre-fatigue. The wood presents a low yield point when the annual rings are tilted compared to the load axis, but the Young’s modulus and yield stress are higher when the annual rings are either parallel or perpendicular to the load direction. In the last case, buckling of softest layers occurs. The fatigue treatment makes the wood less stiff as deduced from the decreases of Young’s modulus and yield stress, whatever the orientation of annual rings. Secondly, it creates a thin and localized softened layer.     

Effects of semi-isostatic densification of wood on the variation in strength properties with density

The variation in strength properties with density was compared between semi-isostatically densified and non-densified wood. Strength properties were compared with published data from earlier studies using other methods for densification. Small clear specimens of eight species were analysed for compression strength in axial, radial and tangential direction, three-point bending and Brinell hardness. After densification, all tested strength properties increased with density, but especially strength perpendicular to grain became lower than expected from the density of non-densified wood. Strength of densified wood relative to what could be expected for non-densified wood of similar density was denoted as ‘strength potential index’. For axial compression strength and bending strength, strength potential index of individual wood species varied between 0.7 and 1.0, i.e. densified wood is slightly weaker than what could be expected from its density. Strength potential index was lower for properties much determined by strength perpendicular to grain. In radial direction, densified wood was rubbery with low modulus of elasticity and nearly no proportional limit or modulus of rupture. Generally, wood was apparently weakened in proportion to the degree of compression in respective direction. Strength potential index also increased with increasing original density of the species.     

Axially loaded glued-in hardwood dowels

The failure load of axially loaded hardwood dowels glued-in parallel to the grain direction of the jointed timber parts is considered. Two simple theoretical solutions using linear elastic fracture mechanics/ideal plasticity and linear elastic stress analysis, taking into account the finite shear stiffness of the bond line are, presented and compared with experimental results. Theory shows that bond line shear strength is the governing strength property for ductile joints and fracture energy is the governing strength property for brittle joints. Bond line shear strength and fracture energy are determined by means of curve-fitting. Received 24 April 1997     

木材横纹理断裂及强度准则

以杉木为研究对象从宏观和微观上研究了木才横纹断裂的性质，并阐述了木才的强韧机理。研究表明：木材横纹Ⅰ型裂纹扩展方式是先沿纤维开裂伸展，然后再沿横截面作韧性断裂，其扩展过程分线性、稳定和非稳定性3个阶段；顺纹启裂时的断裂韧性与试件尺寸无关，是木材的固有属性；木材因其多胞及纤维增强的多层胞壁结构，而具有很强的抗横断韧性，不会因裂尖应力奇异性而发生低工作应力破坏，故在对含横纹理裂纹的木构件作安全设计时，建议仍采用传统的强度准则，考虑净尺寸上的常规强度即可。     

Splitting strength of beams loaded perpendicular to grain by dowel joints

A linear elastic fracture mechanics model for calculation of the splitting strength of dowel-type fastener joints loaded perpendicular to grain (Van der Put/Leijten model) has previously been presented, and now forms the basis for design in Eurocode 5. The original Van der Put/Leijten model was derived using a number of simplifying assumptions, e.g., that the normal forces in the cracked parts of the beam can be ignored, leading to a solution that does not involve the effect of an initial crack. In the present article an extended version of the Van der Put/Leijten model is derived without any simplifying assumptions, and it is shown that the original Van der Put/Leijten model appears as a special case, namely by assuming that only contributions from shear deformations are significant. The model presented here involves the effect of an initial crack and may be characterized as a generalized linear elastic fracture mechanics model. Results of tests showing the influence of initial cracks of various lengths are presented and compared with the predictions.