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     

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.     

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 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     

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.     

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.     

Effects of pretension in bolts on hysteretic responses of moment-carrying timber joints

The adoption of a concept similar to the prestressing technique used in laminated wood decks of bridge structures might increase the initial stiffness or ultimate resistance of dowel-type timber joints by applying pretension to their bolts. This study investigated the effect of pretension in bolts on hysteretic responses and ultimate properties of moment-carrying timber joints with steel side plates. A pretension of 20 kN that yielded a prestress level of 1600 kPa or about 90% of the allowable long-term end-bearing strength of spruce species was applied to the bolts of prestressed joints. The superiority of the prestressed joint over the non-pre-stressed joint was proved by very high hysteretic damping, equivalent viscous damping ratio, and cyclic stiffness. At any given rotation level, hysteretic damping reduction and moment resistance decrement due to continuously reversed loads were found to be small because bolt pretensioning minimized the pinching effect. This study showed that the hysteresis loop of the prestressed joint can be obtained by adding the frictional hysteresis loop due to pretension force into the hysteresis loop of the non-pre-stressed joint. Despite a great increase of initial stiffness, only slight increments in ductility coefficient and ultimate moment resistance were found in the prestressed joint.     

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滞回性能试验。【结果】试验结果表明:在单螺栓连接中,连接部位的破坏模式逐渐由"螺栓刚直"向"双铰"转化,胶合木销槽破坏模式逐渐由销槽整体承压破坏向两端部挤压破坏转变,试件滞回曲线基本都呈现饱满的弓形和棱形,具有良好的耗能能力和抗震性能,但其承载能力较低。在多螺栓连接中,螺栓和胶合木的破坏模式分别以"双铰"破坏和销槽端部挤压破坏为主,试件滞回曲线均呈现饱满棱形,该类试件在承载能力、抗震性能和耗能能力上均有大幅提升;随着螺栓顺纹间距的增大,试件的承载能力不断增大,但螺栓顺纹间距在200 mm时,极限荷载增幅趋于平缓,初始刚度增涨大幅放缓,且整体刚度退化与螺栓顺纹间距为250 mm时基本相同;螺栓并列布置滞回曲线饱满程度好于错列布置;螺栓双排布置承载能力比单排布置的承载能力更高,刚度退化更小。【结论】胶合木-钢夹板螺栓连接具有较好的耗能能力、抗震性能及延性性能;螺栓顺纹间距在200 mm时,抗震性能最佳;螺栓错列布置的抗震性能比并列要好,螺栓双排布置的抗震性能更优越。     

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     

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     

Development of LVL frame structures using glued metal plate joints II: strength properties and failure behavior under lateral loading

In past years high priority was given to developing a seismic design for wood structures, including research on the response of wood structures to earthquakes. In this study a new type of portal frame with relatively large span was developed for the traditional Japanese wooden houses with large openings at the front to strengthen the structure. Stainless steel plates coated with zinc and glued with epoxy adhesives on laminated veneer lumber (LVL) members, composed of Douglas fir veneer and bonded with phenolformaldehyde resin, were used. The connection between the frame's beam and columns and between the columns and groundsills was mechanical, with bolts. The subject of this research was to analyze strength properties and failure behavior of glued LVL metal joints used as structural components and to evaluate the response of LVL portal frames under cyclic lateral loading. The results show that portal frames using glued LVL metal plates have a good multiplier for the shear walls and may be applied to traditional Japanese structures. The equivalent viscous damping provided good energy dissipation in the frames. The joints displayed good mechanical behavior during tests; moreover, the structures demonstrated high strength, stiffness, and ductility, which are necessary for a seismic design.Part of this paper was presented at the 47th annual meeting of the Japan Wood Research Society, Kouchi, April 1997; and at the 5th world conference on timber engineering. Montreux, Switzerland, August 1998     

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.     

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.     

Lateral resistance of anchor-bolt joints between timber sills and foundations III: numerical simulations of the effect of sill thickness on the effective lateral resistance of multiple anchor-bolt joints

Effective lateral resistance of multiple anchorbolt joints was estimated by considering sill thickness or length/diameter ratios of anchor bolts. Load-slip relationships of single anchor bolt joints were analyzed by the stepwise linear approximation based on the generalized theory of a beam on an elastic foundation and the criterion of “fracture bearing displacement” for several sill thicknesses or length/diameter ratios of anchor bolts. Monte Carlo simulations of the effective lateral resistance of multiple anchor-bolt joints were conducted using the analyzed load-slip curves of single anchor-bolt joints. Effective resistance ratios of multiple anchor-bolt joints were simulated for some combinations of length/diameter ratios of anchor bolts, lead-hole clearances, and number of anchor bolts. The simulated results are: (1) the influence of lead-hole clearance becomes more apparent as length/diameter ratios of single anchor-bolt joints decrease; (2) there is no obvious effect of number of anchor-bolts over the range of 5 to 15; (3) average effective resistance ratios can be adopted for allowable stress design; and (4) reduction of effective resistance ratios should be considered particularly for small length/diameter ratios of anchor-bolt joints.     

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.     

Feasibility of improved slotted bolted connection for timber moment frames

This note examines the feasibility of an improved slotted bolted connection for timber moment frames. In the improved connection, steel tubes are inserted into drill holes in glulam and fixed to the glulam with resin injection. Aluminum splice plates with curved slots, or curved elongated holes, are fastened mechanically by using high-strength bolts that go through the steel tubes. Since the compression due to bolt tension is fully supported by the steel tubes, the reduction of bolt tension due to shrinkage of the glulam can be avoided. The use of slotted aluminum splice plates allows stable energy dissipation due to smooth sliding between the aluminum splice plates and the end surfaces of the steel tubes within the specified range of rotation angle. Through quasistatic cyclic loading tests of two connection specimens, it was demonstrated that stable and nearly rigid-plastic hysteresis loops were obtained whose equivalent viscous damping ratio was more than 30% in the range of rotation angle close to or greater than 1/50 radian. Although further improvement is necessary, the experimental results demonstrate the feasibility and potential of the present connection.     

Effect of decay on shear performance of dowel-type timber joints

Monotonic and reversed cyclic loading tests were conducted on dowel-type timber joints with varying degrees of wood decay due to Fomitopsis palustris (Berk. et Curt.), a brown rot fungus, and the effect of decay on various shear performances of dowel-type joints was investigated. For joints affected by the brown rot fungus, the initial stiffness, yield load, and maximum load of dowel-type joints were significantly decreased, even with a small mass loss of wood. The reductions in shear performance were the largest for initial stiffness, followed by yield load and maximum load, in that order. For a 1% reduction of the yield load, initial stiffness and maximum load showed reductions of 1.15% and 0.77%, respectively. When dowel-type joints that had been exposed to the brown rot fungus were subjected to reversed cyclic loading, the gap between the dowel and the lead hole of the wood was increased and equivalent viscous damping was decreased. These results indicate that decay around the dowel lead hole especially affects the load-displacement behavior at small displacement level, and dowel-type joints under cyclic loading have very low resistance to forces acting on the wooden structure. Part of this report was presented at the 5th Symposium on Timber Bridges of the Japan Society of Civil Engineers, Tokyo, July 2006; the 56th Annual Meeting of the Japan Wood Research Society, Akita, August 2006; and the Annual Meeting of the Architectural Institute of Japan, Fukuoka, August 2007     

One-year stress relaxation of timber joints assembled with pretensioned bolts

In our previous study, great increases of hysteretic damping and initial slip resistance of timber joints were attained by applying axial pretension to the steel fasteners. To evaluate the effectiveness of this method, 1-year stress-relaxation measurement was carried out. Nine prestressed joints were prepared and three of them were restressed after 3 and then 6 months after the initial prestressing. All joints were exposed to indoor conditions, and relaxation of the pretension was regularly measured from time-dependent decreases of axial strain of the bolts. After measurement, the joints were subjected to cyclic and monotonic loading tests until failure. The average ratio of residual stress to the initial prestress after 1 year was about 0.23 and 0.66, respectively, for joints without restressing and those with restressing. A simulated stress-relaxation curve developed from the four-element relaxation model predicted 3% of the initial stress after 5 years. Without a regular restressing program, the initial prestressing effect therefore must be considered negligible. However, about 20% of the pre-stress level can be reasonably assumed if restressing is carried out annually. This small residual stress was found to introduce suffi cient frictional damping to signifi cantly increase the equivalent viscous damping ratio of the joints. Part of this study was presented at the 10th World Conference on Timber Engineering, Miyazaki, June 2008     

Effect of moisture content of members on mechanical properties of timber joints

To investigate the effect of moisture content (MC) of members on the mechanical properties of timber joints, bending tests of precut joints and shear tests of dowel-type joints were carried out using timbers of Japanese cedar (Cryptomeria japonica D. Don) with three moisture conditions: green, kiln-dried with a MC target of 15%, and over-kiln-dried with a MC target of 5%. For the bending test, timbers were processed with a precut processing machine into “koshikake-ari” (a kind of dovetail joint) and “koshikake-kama” (a kind of mortise and tenon joint). A pair of members was jointed together without mechanical fasteners. Bolts (diameter = 12 mm) and nails (diameter = 2.45 mm) were used as dowels in the shear test. Bolted joints were constructed with one bolt and two metal side plates. Two nails and two metal side plates were used for the nailed joint. For precut joints, no clear effect of MC was recognized on maximum moment and initial stiffness. The maximum strength of mechanical joints assembled with kiln-dried wood was changed by the degree of drying. Stiffness of the joints assembled with kiln-dried specimens was larger than that of the joints assembled with green specimens.Part of this study was presented at the 7th International IUFRO Wood Drying Conference, Tsukuba, July 2001     

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.