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     

胶合木-钢夹板螺栓连接滞回性能试验

[目的]为探明胶合木-钢夹板螺栓连接的动力性能和抗震性能,确保连接件在车辆、机械振动等动力荷载下的可靠性.[方法]针对胶合木-钢夹板螺栓连接的构造特点,考虑胶合木厚度和螺栓直径之比(厚径比)、螺栓顺纹间距、螺栓并列和错列布置方式等参数的影响,设计制作了4类13组共39个胶合木-钢夹板螺栓连接件,在低周反复荷载作用下进行...     

现代木结构螺栓连接性能及其影响因素研究现状

螺栓类连接具有简洁、可靠、美观、防火等特点, 是木结构中常用的一种连接方式, 被广泛应用于现代木结构。深入研究螺栓连接性能及其影响因素, 对现代木结构的结构设计及其性能优化具有重要意义。文中详细阐述了国内外螺栓连接性能及其影响因素的研究现状, 以期为我国木结构螺栓连接性能研究提供借鉴。     

An application of the Tsaï criterion as a plastic flow law for timber bolted joint modelling

Summary This paper describes a modelling approach to predict the behaviour of an elementary thin timber bolted joint. The application concerns principally joints with steel side members; bolts have a constant 12 mm diameter with two ratios of end distance to bolt diameter and two bolt clearances. The behaviour of the bolted joints is characterized by a double non linearity; the first one is due to the contact area evolution between the bolt and the hole of the jointed elements. The second one is owing to the evolution of plasticity on the wood. A spring element compatible with isoparametric plane finite elements represents the contact evolution. The elastic-plastic wood is provided with a plastic flow rule according to the Tsa? criterion. This study allows an investigation on the parameters characterizing the Tsa? criterion, particularly F₁₂ which represents the interaction between the principal axis of orthotropy. A two-dimensional model is used. It permits the assessment of the clearance bolt, joint dimensions, wood plasticity and wood grain angle effect on the joint behaviour. The wood grain angle has a non negligible effect on the plastic strains distribution and it can create a parasite loading because the joint tends to rotate even for an axial loading. The results showed a good agreement between experimental values given by some authors and numerically-predicted stresses on the joint. So, the applications concern a two-dimensional joint with anisotropic plastic material. The generalization in the three-dimensional modelling is desirable to take into account the interaction between the wood and a metallic fastener in thick joints with different geometric characteristics.     

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     

Three-dimensional finite element analysis of the Japanese traditional post-and-beam connection

A three-dimensional finite solid element model for Japanese traditional post-and-beam connections was developed using the wood foundation method, which employed the concept of a beam on a nonlinear foundation. The wood foundation in the model was a three-dimensionally prescribed zone surrounding a nail shank in order to address the intricate wood crushing behavior induced by nail slip. Material models for the wood members and the foundation were developed based on the transversely isotropic plasticity from the software package ANSYS. The Japanese post-and-beam connection modeled was a ten-nail multiple connection with a mortise and tenon joint and is called the CPT (Corner Plate, T-shaped) connection. Details of the model development are presented. As a feasibility study, blind predictions of the model were compared with available connection test data and showed good results for predicting the progress of the load-deformation relations in three dimensions. However, the limitation of the model was found in simulating fracture failures such as wood splitting or nail tear-out from the wood. Model applications and the need for model improvement are discussed.     

Lateral strength of nailed timber connections with decay

Loading tests were conducted on nailed connections with decay due to a brown rot fungus. The effect of the decay on the lateral strength of nailed connections was investigated. After loading tests, the sound and decayed regions of a nailed connection were observed in the cross section, which was cut parallel to the grain through the nailed point. The nailed connections with decay showed a low load during initial deformation when the main and side members had a decayed region in the boundary between them. The nailed connections showed low load after yielding when the sound region in the main member decreased. The yield load of nailed connections with decay was calculated based on the yield theory. The model of calculations had sound and decay regions within a member. The yield load of nailed connections obtained by the calculation based on the yield theory agreed with the results obtained by experiments when significant decay in a direction parallel to the grain was observed in the main and side members. This result indicates that the yield theory can estimate the yield load of nailed connections not only with a sound member, but also a member that is partly or wholly decayed.     

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.     

Fracture analysis of perpendicular to grain loaded dowel-type connections using a 3D cohesive zone model

The strength and fracture behavior of dowel-type connections with stiff dowels loaded perpendicular to grain was studied by nonlinear 3D finite element (FE)-analysis. A cohesive zone model was used to model the perpendicular to grain fracture of the wood, i.e., failure by wood splitting along the grain. The influence of load eccentricity and dowel-to-loaded-edge distance was studied for a plate type of geometry loaded in tension and for a simply supported beam loaded in bending. The strength found from the FE-analysis is compared to strength from experimental tests with centric loading, showing overall good agreement. Numerical results for centric loading are further compared to strength predictions according to the linear elastic fracture mechanics (LEFM)-based design criterion present in Eurocode 5 (EN 1995-1-1:2004). The comparison showed good agreement regarding the relative influence of connection geometry, but the design criterion appears, however, to yield unconservative strength predictions. The results of the FE-analyses regarding dowel load eccentricity showed that such loading conditions may yield significantly lower strengths compared to centric loading. An approximate engineering method to account for the strength reduction due to load eccentricity is, furthermore, presented.     

Numerical analysis on tensile performance of bolted glulam joints with initial local cracks

Under varying climate conditions, cracks are commonly observed in bolted joints, owing to the shrinkage of wood and confinement from slotted-in steel plates and bolts. A three-dimensional finite element model was developed to investigate the mechanical behavior of bolted glulam joints with initial cracks. Wood foundation was prescribed in the model to simulate the local crushing behavior of wood surrounding the bolts. The behavior of wood in compression and the foundation were defined as transversely isotropic plastic in the software package ANSYS. Cohesive zone model was applied in the numerical analysis to consider the propagation of initial cracks and brittle failure of wood in the bolted joints under tension load. The numerical model was validated by the experiments conducted on full-scale specimens and it is indicated that the numerical model has good ability in predicting the failure modes and capacity of tension joints with local cracks. To further investigate the influence of crack number, length and locations, a parametric study was conducted with the verified model. Moreover, to study the effects of cracks on the behavior of bolted joints with different failure modes, another bolted joint including bolts with different strength grades and diameters was designed and analyzed in the parametric study, which was expected to have bolt yielding failure mode. It was found that the initial cracks can decrease the capacity and initial stiffness of tension joints by up to 16.5 and 34.8%, respectively.     

Thermal degradation modeling for single-shear nailed connections

The load-carrying capacity of a timber structure is highly dependent on the strength of its connections. Very limited information exists on the thermal degradation, or the properties at elevated temperatures, of such connections. This insufficient information is one of the major impediments for modeling elevated temperature performance for wood-frame structures. The objective of this study was to characterize thermal degradation of yield load capacity of single-shear nailed connections between wood and oriented strand board (OSB) as a function of time and temperature. The mechanism of degradation was explained using first order kinetics. Using the principles of time–temperature superposition (TTS), predictive models for connection capacity degradation were developed. A total of 450 wood-to-OSB connections were tested laterally after exposure to nine different elevated temperature regimes. The degradation of yield load strength over time occurred at a constant linear rate. Temperature dependence of this rate was modeled using the Arrhenius activation energy theory. Using Arrhenius activation energy theory and principles of TTS, a master curve was developed to predict the performance of connections after exposure to a temperature of 150°C. The predictions matched well with independent experimental observations. The master curve developed using TTS provides predictive estimates of residual capacity in a connection as well as its failure times.     

Evaluation of embedding strength on Uruguayan wood to apply the European yield theory for double shear bolted joint

The main objective of this study was to evaluate embedding strength on Uruguayan wood to apply the European yield theory (EYT) for double shear bolted joints’ on Eucalyptus grandis H.(EGH). To introduce the dowel-type connection performance, double shear tests were conducted. The embedding tests were conducted to calculate the yield strength of bolted joint by EYT and the compression test, to estimate the embedding strength. The yield strength obtained from the experiments showed a good agreement with the yield strength calculated by EYT method. The yield strength of double shear bolted joint evaluated from compressive strengths is a very close to the yield strength calculated by EYT. The average value and variability of the yield strength of double shear bolted joint calculated by EYT applying the embedding strengths of experimental results were very close to the yield strength or 5 % offset method of experimental results. The results from this study showed a good behavior to structural design with EGH in accordance to the Japanese standard code.     

Theoretical models for creep slip of nailed joints between wood and wood-based materials

Summary Applying modern methods of analyzing floor, wall, and connection subsystems in light-frame wood buildings requires information on the stiffness of nailed joints under long-term loads. Because this information can best be derived by testing nail-joint specimens under constant loads, theoretical procedures were developed that use test data for constant loads to predict stiffness under variable in-service loads; five nonlinear, viscous-viscoelastic models were develpoed on the basis of existing formulations of creep and mechanisms of load transfer between nails and wood. The models incorporated the modified superposition and strain-hardening principles in describing responses to discrete or continuous loading functions. Tests have shown that the models closely predict creep slip of typical nailed joints.This research was jointly supported by the Forest Research Laboratory, Oregon State University, and the Cooperative State Research Service, U.S. Department of Agriculture, Special Grant 85-CRSR-2-2553. This is Paper 2288 of the Forest Research LaboratoryFormerly Graduate Research Assistant Forest Research Laboratory     

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     

Study of mechanical properties of wooden bolt-nut connector I: effect of size and shape of thread on withdrawal strength

The withdrawal strength of a bolt-nut connector made from wood-based material was evaluated. The thread strength of the wooden bolt-nut connector was tested to select various parameters of the connector and the type of wood material; the wood materials tested were hard maple, white oak, ebony, glue-laminated bamboo, and densified Japanese cedar. A plane model of wooden threads with various thread angles was also evaluated. The results showed that the maximum failure load of the thread increased with increasing bolt density and connection area, which was calculated from the diameter of the bolt and the thickness of the nut. The withdrawal resistance after reaching the maximum load underwent a graded decrease because the bolt threads were broken one by one. In addition, the thread strength depended on the thread angle. In the model with a thread angle of 90°, compressive deformation in the transverse direction occurred prior to shear deformation along the root of the threads; the model with this thread angle thus had higher strength than those with other angles.     

Load-carrying capacity of steel-to-timber joints with a pretensioned bolt

Previous experimental studies reported that bolt pretensioning greatly increases the initial stiffness and load-carrying capacity of bolted joints. It is also a matter of great importance to structural designers to understand the effect of pretension on the load-carrying capacities of bolted joints, and this study presents an extended yield model that considers the fastener’s pretension force. In the extended yield model, the load-carrying capacity was defined as the load at a slip of 15 mm. The ultimate fastener bending angle at the yielded cross section equivalent to this joint slip, which was affected by the fastener’s axial force, was iteratively evaluated in numerical analyses. The introduction of bolt pretensioning largely increased the joint slip resistance at initial loading, but it decreased the ultimate fastener bending angle. This decrease of fastener bending angle resulted in a relatively low stiffness hardening (or secondary stiffness), which is caused by secondary axial forces associated with embedment of steel plates into the wood member. Prediction was verified by the tests of 36 steel-to-timber joints under three different pretension forces and two loading directions relative to the grain. Some of the observed load-carrying capacities of the joints, particularly in loading perpendicular to the grain, however, were not as high as those expected by the numerical analyses considering the given pretension forces.     

应用变参数Maxwell模型拟合中密度纤维板蠕变

在研究木质材料的流变性质时，广泛采用多个弹簧和阻尼单元的各种组合形式的力学模型。但其多个常流变参数不易求解，本文提出一种变参数流变模型的概念，并以两单元的变参数Maxwell模型拟合了MDF的蠕变性质。结果表明，上述作法是可行的，采用变参数Maxwell模型不仅能以较少的弹，粘单元组合代替常参数的多个弹，粘单元组合模型。使流变参数便于求解，而且该模型还可方便地应用Boltzmann叠加原理拟合MDF在变荷下的蠕变变形。     

Investigation of the structural performance of glulam beam connections using self-tapping screws

The characteristic strength properties of structural glulam connections assembled with self-tapping screws were examined following the ASTM testing procedure in the study. Four screw types with various numbers were designated at each connection of the beam–girder structure with different nailing schedules. The results indicated that the maximum load capacity and dissipated energy of a connection fastened with 10-mm self-tapping screws were higher than those with 8-mm screws. And, the screws with both double-threaded sections and fully threaded shanks were higher than those of single-threaded screws. An improvement on the initial stiffness of a connection was found when the number of self-tapping screws increased. The connections assembled with the toe-nailing approach from the beam’s bottom surface provided higher maximum loading capacity, medium initial stiffness, and a larger ductility factor, resulting in higher dissipated energy with less fragile failure. The derived allowable loading values for a beam–girder connection fastened with self-tapping screws using the face-nailing approach were close to the code values for bolted and pinned connections. And, a toe-nailing approach provided higher allowable loads for connections than using a face-nail approach.     

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.     

The variable parameter rheological model of wood

How to establish the rheological model to simulate creep behavior of wood and wood-based composites under change-load has not been solved in research of wood rheology. This paper presents a new model—variable parameter rheological model. The bending creep behavior of small clear poplar specimens under different constant load levels were examined. The load levels within 50% of rupture load of the specimens, and the experimental creep behavior were simulated by the variable parameter Maxwell model. The results show that using only one model of variable parameters may simulate the creep behavior of wood under different constant load levels very well. Applying the generalized Boltzmanns superposition principle, the variable parameter rheological model can be used to simulate the creep behavior of wood under change-loads conveniently and accurately.