Derivation and application of an equation for calculating shear modulus of three-ply laminated material beam from shear moduli of individual laminae

In a detailed study of the relation between the deflection caused by shear force and the constitution of a laminated material beam, we derived an equation for calculating the shear modulus of a laminated material beam from the shear moduli of individual laminae. The validity of the derived equation was investigated using crosslaminated wood beams made with five species. The calculated shear moduli parallel to the grain of face laminae ranged from 48.3 MPa to 351 MPa, while those perpendicular to the grain of face laminae ranged from 58.0 MPa to 350 MPa. The calculated shear moduli increased markedly with increasing shear modulus in a cross section of perpendicular-direction lamina of a cross-laminated wood beam. The calculated apparent modulus of elasticity (MOE) of cross-laminated wood beams agreed fairly well with the measured apparent MOE values. This fact indicated that the apparent MOE of cross-laminated wood beam was able to be calculated from the true MOE values and shear moduli of individual laminae. The percentage of deflection caused by shear force obtained from the calculated apparent MOE (Y _sc) was close to that obtained from the measured apparent MOE (Y _s) and there was a high correlation between both values. From the above results, it was concluded that the derived equation had high validity in calculation of shear modulus of a cross-laminated wood beam.     

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.     

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.     

Shear resistance and failure modes of nailed joints loaded perpendicular to the grain

Shear tests were conducted on nailed joints in wood that were loaded perpendicular to the grain; these joints had 21 specifications depending on different combinations of wood species, nail dimensions, number of nails, and edge distances of the main members, and their effects on the shear resistance of the nailed joints were also investigated. The nailed joints with CN75 nails had higher initial stiffness than the joints with CN50 nails, provided the initial stiffness of nailed joints connected with 3 or 5 nails was not always a simple product of the number of nails and the initial stiffness of nailed joints connected with a nail, and instead depended on the combination of wood species of the main member and nail dimensions. When the edge distance decreased, the maximum load and energy capacity decreased, thereby affecting the energy capacity. The maximum load of the nailed joints with CN75 nails may be smaller than those with CN50 nails depending on the combination of wood species and nail dimensions. When the edge distance of the nailed joints was less than 26 mm, the energy capacity of the nailed joints with CN75 nails was less than or similar to those with CN50 nails.     

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.     

Theoretical and experimental deflections of glued laminated timber beams made from a tropical hardwood

Abstract

Nondestructive testing (NDT) can play an important role in improving the quality and reliability of tropical hardwood as an engineering material. By means of these methods, the stiffness of the material can be determined and the information used to improve its structural performance. Although, it is a usual approach for qualifying the material used to manufacture engineered wood products made mainly from softwoods, it is not so common for tropical hardwoods. Additionally, the lack of information regarding properties of glulam beam made from these kinds of wood is evident. In this context, the paper aimed at evaluating the theoretical and experimental deflection of glulam beams made from the Brazilian hardwood louro-vermelho (Sextonia rubra). Initially, the stiffness of each lamina was determined nondestructively using transverse vibration method (E _dtv), which has been demonstrated to be the most suitable method for this wood species. Then, ten 5-lamina glulam beams were assembled according to descending lamina E _dtv values. The experimental evaluation was performed using a four-point bending schedule. In general, the theoretical values of deflection were 2% higher than the experimental ones. The transverse vibration showed to be a suitable method to both measure lamina stiffness and predict glulam beam deflection.     

Plywood frame corner joints with glued-in hardwood dowels

This paper presents research on plywood frame corners jointed to glulam beams and columns by means of glued-in hardwood dowels. The frame corner was made of a solid block of ordinary plywood of the same width as the glulam beams and with plies parallel to the plane of the frame to avoid splitting due to stress perpendicular to the grain. Hardwood dowels with a diameter of 12mm and a maximum glued-in length of 120mm were glued into drilled holes in the plywood corner and glulam beam ends parallel to the grain direction of the beams to form a momentresisting joint. Static bending tests were conducted of frame corners with 100 X 200mm² and 120 X 420mm² beam cross sections. Bending capacities of the joints corresponding to a modulus of rupture of the jointed glulam beams of about 30MPa were obtained for both closing and opening moments for the small cross sections, and about 22MPa was obtained for the large cross sections. Simple design models for calculation of joint strength and rotational stiffness are also presented.     

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.     

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。     

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     

Influence of accessory substances,wood density and interlocked grain on the compressive properties of hardwoods

Wood samples of nine tropical hardwoods from Peru and sugar maple wood from Quebec were selected to perform moisture sorption tests associated with parallel-to-grain and tangential compression tests using a multiple step procedure at 25°C. Cold-water and hot-water extractives, sequential cyclohexane (CYC), acetone (ACE) and methanol (MET) extracts, ash content (ASH), wood density and interlocked grain (IG) were evaluated on matched samples too. Wood density corrected for the accessory substances was by far the major factor positively affecting the compressive properties of tropical hardwoods. The total amount of accessory substances is required in order to establish better relationships between physico–mechanical properties and density of tropical hardwoods. For a given wood density, the ultimate stress in parallel-to-grain compression was higher in tropical hardwoods than in temperate hardwoods. However, the compliance coefficients for both types of woods were quite similar. Sequential extraction with organic solvents was the most suitable method for evaluating the effect of extractives on compressive properties of tropical hardwoods. The CYC and ACE fractions did not contribute to variation in these mechanical properties. The substances dissolved in MET affected positively the compliance coefficient s ₁₁ in parallel-to-grain compression and negatively the compliance coefficient s ₃₃ in tangential compression. The IG decreased the compliance coefficient s ₁₁ but also decreased the ultimate stress in parallel-to-grain compression. Finally, variations in compressive properties that were due to changes in equilibrium moisture content (EMC) were clearly influenced by wood density; denser woods were more sensitive to changes in EMC than lighter woods.     

Variations in compression strength and surface roughness of heat-treated Turkish river red gum (Eucalyptus camaldulensis) wood

This article reports the effects of heat treatment on compression strength parallel to the grain, the surface roughness [average roughness (R_a)], and the air-dry den-sity of wood from the river red gum tree (Eucalyptus camaldulensis Dehn.) planted in Turkey. Eucalyptus wood was heat-treated at temperatures varying from 120° to 180°C for durations of 2–10 h. Samples cut from the heat-treated wood were tested for air-dry density, compression strength parallel to grain, and surface roughness properties. Roughness measurements by the stylus method were made in the direction perpendicular to the fiber. Based on the findings in this study, the results showed that density, compression strength, and surface roughness values decreased with increasing treatment temperature and treatment times. Eucalyptus wood could be utilized by using proper heat treatment techniques without any losses in strength values in areas where working, stability, and surface smoothness, such as in window frames, are important factors.     

Critical discussion of perpendicular to grain tension testing of structural timber – case study on the European hardwoods ash,beech and maple

ABSTRACT

Knowledge about perpendicular to grain tension behavior of wood is essential, since in construction tension stresses perpendicular to grain cannot be avoided completely. Especially for hardwoods, the data basis is scarce. EN 338 design values are with 0.6 N/mm² characteristic strength set very low. The US-American National Design Specifications even set this value to zero and make local reinforcements mandatory. This paper compares strength and stiffness values attained with newly-designed, little, prismatic specimens and EN 408 structural timber specimens to evaluate the current European design values. Little specimen’s characteristic strength values range from 7.2 to 10.6?N/mm² and are assumed to be real material properties. EN 408 specimen values are with approximately 4.0?N/mm² lower. These lower values are mainly due to stress peaks introduced by the force introduction. Strength values attained for the medium-dense European hardwoods beech, ash and maple exceed EN 338 design values by a factor of six to seven. Adaptation of the EN 338 design value is not recommended, though. The abundance of influencing factors makes clear that the design value and the ensuing design code have to be synchronized carefully by tedious testing in order to make use of the perpendicular to grain tension strength potential of the selected hardwoods.     

Bending creep performances of three-ply cross-laminated woods made with five species

To improve the performance of cross-laminated woods, 30 types of three-ply parallel-laminated and cross-laminated woods were prepared from five species with various densities and shear compliances in cross section, and their bending creep performances were investigated on the basis of our previous research in cross-laminated wood made with sugi (Japanese cedar). The creep deformation perpendicular to the grain was decreased by cross laminating. The creep deformation perpendicular to the grain of parallel-laminated woods (P_⊥ type), that perpendicular to the grain of face laminae of cross-laminated woods (C_⊥ type), and also that parallel to the grain of face laminae of cross-laminated woods (C_║ type) tended to decrease with increasing density of species used for perpendicular-direction lamina. It was found that the extent of the decrease was greater in creep deformation than in initial deformation. The degrees of anisotropy for both deformations of laminated wood were markedly decreased by cross laminating. The extent of the decrease was much greater in creep deformation than in initial deformation and considerably smaller in buna with higher density than in sugi with lower density. The measured values of initial deformation and creep deformation of C_⊥ type were almost equal to the calculated values obtained from the measured values of parallel-laminated woods, whereas the measured values of both deformations of C_║ type were much greater than their calculated values and increased markedly with increasing shear compliance in cross section of perpendicular-direction lamina used for core. The ratios of the average of measured values to the calculated value of C_║ type ranged from 1.05 (katsura) to 1.50 (sugi) in initial deformation and from 1.30 (katsura) to 3.69 (sugi) in creep deformation. This result can be explained as the effect of deflection caused by shear force.     

Comparison of wood,fibre and vessel properties of drought-tolerant eucalypts in South Africa§

Three drought-tolerant eucalypt genotypes have been investigated for a broad spectrum of properties to provide a basis for comparison on their suitability for various end-uses. The genotypes included were a Eucalyptus grandis × E. camaldulensis hybrid, E. gomphocephala and E. cladocalyx, selected based on previous studies that indicated good potential to tolerate arid conditions, reasonably good volume growth and straightness of stems. In this study, information was added on differences between species and parts of stems in growth (volume and biomass) and properties of wood (density and stiffness), fibres (dimensions and microfibril angle) and vessels (size and numbers). We found high wood densities and stiffness values for E. cladocalyx and E. gomphcephala, making them suitable for construction wood. Logs from the mid-part of the stem had the best timber properties, as the butt logs showed the highest microfibril angle and lowest wood stiffness due to longitudinal juvenility. Such juvenility was also to some degree observed for wood density and fibre length. The information gained will be especially helpful for selecting species and processing options for small farm and community plantations for producing higher-value products that may be sold to generate much-needed income as well as for local uses, such as fuelwood and charcoal.     

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     

Ultrastructural analysis of softwood fracture surfaces

Summary The ultrastructural characteristics of fracture surfaces from southern pine and Douglas-fir specimens tested in tension at various angles to grain were examined. The fracture surace morphology was inspected using scanning electron microscopy. Three anatomical failure types were recognized: intercell failure, transwall failure, and intrawall failure. Certain failure characteristics were ascribed as a function of the magnitudes of paralleland perpendicular-tograin tension and parallel-to-grain shear present in the specimen. In specimens tested in paralleland perpendicular-to-grain tension, the thick-walled latewood cells were found to fail in a combination of transwall and intrawall failure. The intrawall failures were usually at the S₁–S₂ interface. The more thin-walled earlywood cells were more likely to exhibit abrupt, transwall failures. At intermediate angles of load to grain, surfaces indicative of the type found in pure shear tests were predominant. Perpendicularto-grain tension failures resulted in mostly intercell failures. Ray cells consistently exhibited transwall failures. The failure surface frequently changed planes in all loading modes. This path transfer was inevidably associated with material discontinuities in the wood. When the path did transfer, all three failure types were observed. No significant species effect was observed.     

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.     

Nondestructive test and prediction of modulus of elasticity of veneer-overlaid particleboard composite

The effects of grain angle, thickness of face veneer, and shelling ratio on dynamic modulus of elasticity (E) of veneer-overlaid particleboard composite (VOP) were examined by using nondestructive test. In this study, the possibility that E of VOP can be predicted by means of some empirical formula was also discussed. This study has shown that grain angle, thickness of face veneer, and shelling ratio have substantial effects on E of VOP. The E at 0° of grain angle of face veneer was the largest, decreasing rapidly with increase in the grain angle. The lowest value of E occurred at 90° of grain angle of face veneer. The relationship between grain angle of face veneer and E of VOP can be expressed in the form of Jenkin’s and Hankinson’s equations. The orthotropic properties of wood and VOP defined as the ratio E ₀/ E ₉₀ were 25.7 for wood and 4.7 for VOP. When the grain direction of face veneer was parallel to the length of the specimens, the E of VOP increased with increasing shelling ratio. VOP increased E from 125 to 179% over that of the particleboard and veneer thickness from 2.1 upto 3.6 mm. However, when the grain direction of face veneer was perpendicular to the length of the specimens, the E of VOP decreased with increasing shelling ratio. VOP decreased E from 23 to 41% over that of the particleboard and veneer thickness from 2.1 upto 3.6 mm. The relationship between E of VOP and face veneer thickness can be expressed in the form of a second-order parabolic equation. Rule of Mixture (ROM) can be used to predict E of VOP from the E of wood element and particleboard element.     

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.