Capacity of a traditional timber mortise and tenon joint

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2 Table 1. Average values of density (one specimen for each timber element). Density (kg/m 3 ) Brace Rafter Average Std. Dev. Group Figure 1. Details of typical tenon and mortise joints. a visual survey, can also be the support of maintenance decisions. Non-destructive evaluation is already widely applied to the control of structural integrity, due its characteristics of reliability, simplicity and low cost. For the purpose of numerical analysis wood is often considered as a homogenous and isotropic material. This is certainly not the case as: (a) wood exhibits anisotropic elastic and inelastic behaviour; (b) natural growth characteristics such as knots, slope grain and other defects are always present. Defects can be included in numerical simulations but this requires a thorough investigation of the specimens and fine tuning, being of moderate interest for practical purposes. On the contrary, the usage of orthotropic failure criteria is essential for accurate numerical simulations. Failure criteria that describe orthotropic inelastic behaviour offer the opportunity to perform adequate analyses of wood elements and structures, beyond the elastic limit. This can be especially valuable in the detailed analysis of timber joints and other details with complex stress distribution. Here, the finite element method (FEM) is adopted to simulate the structural behaviour and obtain a better understanding of the failure process. Calculations are performed using a plane stress continuum model, which can capture different strengths and softening/hardening characteristics in orthogonal directions. The failure criterion is based on multi-surface plasticity, comprising an anisotropic Rankine yield criterion for tension, combined with an anisotropic Hill criterion for compression. The failure criterion from Lourenço (1996) is used in the analysis. The influence of compression perpendicular to the grain and elastic stiffness on the response is addressed in detail. 2 DESCRIPTION OF THE TEST SPECIMENS Chestnut is usually present in historical Portuguese buildings and all the wood used in the specimens came from the North of Portugal. The 8 specimens were divided in two groups: New Chestnut Wood (NCW), obtained from recently sawn timber, and Old Chestnut Wood (OCW), obtained from structural elements belonging to old buildings (date and precise origin unknown). The old logs were obtained from a specialist J_ NCW J_ J_ J_ J_ OCW J_ J_ J_ contractor claiming that the wood has been in service for over years. The OCW specimens were made using original beams obtained from rehabilitation works carried out in the Northern of Portugal, using specimens with the least possible damage. The NCW specimens were prepared using new wood with minor defects. Attention was paid to the conditioning of the timber before and after the manufacture of the joints. The conditioning was conducted in such a way that the test conditions correspond in a realistic manner to adequate in situ conditions as regards the influence of moisture content and the occurrence of gaps induced by shrinkage. Each specimen consists of two timber elements, with a cross section of mm 2, connected with a mortise and tenon joint without any pins. The angle between the elements is CHARACTERIZATION OF PHYSICAL AND MECHANICAL PROPERTIES 3.1 Density Given the conditioning of the specimens, the average density ρ m is determined for a moisture content of 12%. Table 1 presents the results for the average density organized according to two group types (wood element and age). The density tests were carried out in samples removed from the specimens ends. Even if the sample size is very low, the NCW group presents slightly higher values of average density ( 4%) than OCW group, with an average of kg/m 3 for NCW and kg/m 3 for OCW. 3.2 tests A test set-up was built to test the specimens under compression. One hydraulic jack was used to apply a compression force aligned with the rafter, with a programmed loading cycle. The system includes a support plate with stiffeners, able to rotate and ensure 834

7 Numerical (k n =.5) Numerical (k n =1.) Numerical (k n =2.) Figure 7. Minimum principal stresses (values in N/mm 2 ). marginal. The usage of infinite stiffness for the interface (rigid joint) results in an increase of the slope of the first part of the response, from 3 kn/mm to kn/mm (+266.7%). The ultimate strength of the joint, given by an offset of the linear stretch by 2% in terms of strain values, also changes from 13 kn to 152 kn (+17%), once the joint becomes fully rigid. Figure 7 shows the contour of minimum principal stresses at the end of the analysis. It is possible to observe a concentration of stresses in a narrower band with peak stresses at the joint (zone where the interface elements were placed). With this concentration of stresses one may say that failure is clearly governed by wood crushing where, for a late stage of the analysis, the compressive strength of the wood in the joint is completely exhausted. This situation is also confirmed in the experiments. 7 EFFECTS OF THE MATERIAL PARAMETERS A strong benefit of using numerical simulations is that parametric studies can be easily carried out and the sensitivity of the response to the material data can be assessed. There are a total of six key parameters in the present model and the effect of each parameter on the global response will be analyzed separately. It is noted that moderate variations (±25%) are considered for the strengths and large variations (division/multiplication by two) are considered for the stiffness values. These assumptions are rooted in the fact that strength is usually better known than stiffness. 7.1 Normal stiffness of the interface Figure 8a shows a comparison between the results of the variation of the k n parameter: with a reduction of 5% in k n, the ultimate strength of the joint, given by an offset of the linear stretch by 2%, decreases from kn to kn ( 6%); multiplying k n byafactor of two the ultimate strength of the joint, given by (a) Numerical (k s =.5) Numerical (k s =1.) Numerical (k s =2.) (b) Figure 8. Effect of the variation of parameter: (a) k n, and (b) k s on the model response. an offset of the linear stretch by 2%, increases from kn to 135. kn (+7%). The reduction/increase of the normal stiffness of the interface also affects the global stiffness of the joint: the global stiffness of the joint decreases as the normal stiffness of the interface decreases, being more sensitive to this variation when compared with the ultimate strength. The reduction of 5% of the k n parameter, results in a decrease of the slope of the first part of the response, from 32 kn/mm to 26 kn/mm ( 23%). On the other hand, the multiplication by a factor of 2 of this parameter results in an increase of the slope of the first part of the response, from 32 kn/mm to 41 kn/mm (+28%). Because this parameter sets the relation between the normal traction and the normal relative displacement, the obtained results were expected a priori. 7.2 Tangential stiffness of the interface Figure 8b shows a comparison between the results of the variation of the k s parameter. The ultimate strength is insensitive to a k s variation, whereas the reduction/increase of the k s parameter affects the global stiffness of the joint: the global stiffness of the joint 839

8 Numerical (E x=.5) Numerical (E x =1.) Numerical (E x =2.) Figure 9. Effect of the variation of the elastic modulus of elasticity (E x ) on the model response. decreases as the k s parameter decreases. The reduction of 5% of the k s parameter, results in a decrease of the slope of the first part of the response, from 32 kn/mm to 28 kn/mm ( 14%). On the other hand, the multiplication by a factor of 2 of this parameter results in an increase of the slope of the first part of the response, from 32 kn/mm to 37 kn/mm (+16%). 7.3 Elastic modulus The effect of the variation of the elastic modulus of elasticity parallel and perpendicular to the grain was considered individually. Figure 9 indicates that the ultimate strength is almost insensitive to the variation of the elastic modulus of elasticity for wood (± 4%). The inclusion of the effects of the elastic modulus of elasticity does change significantly the elastic stiffness of the joint. Therefore, decreasing the parameter E decreases the global stiffness of the joint. The reduction of 5% of the E x parameter, results in a decrease of the slope of the first part of the response, from 32 kn/mm to 28 kn/mm ( 14%). On the other hand, the multiplication by a factor of 2 of this parameter results in an increase of the slope of the first part of the response, from 32 kn/mm to 36 kn/mm (+13%). 7.4 Compressive strength The ultimate strength and the global stiffness of the joint are insensitive to the variation of the compressive strength of wood in the parallel direction. Figure 1 indicates higher sensitivity of the ultimate strength of the joint to the variation of the compressive strength of wood in direction perpendicular to the grain, as expected: with a reduction of 5%, the ultimate strength of the joint, given by an offset of the linear stretch by 2, decreases from 13 kn to kn ( 3%); multiplying by a factor of 2 the ultimate strength of the joint, given by an offset of the linear stretch by 2, increases from 13 kn to kn Numerical (f c,y =.75) Numerical (f c,y =1.) Numerical (f c,y =1.25) Figure 1. Effect of the variation of the compressive strength (f c,y ) on the model response. (+23%). However, the global stiffness of the joint is insensitive to the variation of the compressive strength perpendicular to the grain. 8 CONCLUSIONS Despite the wide use of mortise and tenon joints in existing timber structures scarce information is available for design and in situ assessment. The objective of the present study was to quantify its strength capacity by physical testing of full-scale specimens. Also, the performance of different NDT for assessing global joint strength is evaluated. Finally, the adequacy of an anisotropic failure criterion to represent the behaviour of a traditional mortise and tenon joint was assessed from the comparison between experimental and numerical results. The difference in the results for the ultimate load between the two groups is very low, which is in agreement with the values of density found for the sample. Thus, safety assessment of new and existing timber structures can be made with similar mechanical data. With respect to the usage of NDT for the prediction of the ultimate strength, the dispersion found for the density, Resistograph and Pilodyn do not recommended the usage of the related parameters for quantitative mechanical assessment. On the contrary, ultrasonic testing provides good correlations. Novel linear regressions have been proposed in this study. The different failure mechanisms observed in the experiments are well captured by the model, which is the most important validation of any simulation. It is striking that such excellent agreement is obtained also in the load-displacement diagrams. A preliminary analysis considering an infinite stiffness of the interface, assuming a fully rigid connection, indicates that such an assumption provides too stiff results. Another conclusion is that the normal stiffness of the interface elements has considerable influence in the yield strength of timber joints. The numerical 8

9 results, in terms of force-displacement diagrams, with the adjusted stiffness for the interface elements, provide very good agreement with the experimental results both in the linear and nonlinear parts. The influence of the experimental horizontal restraint, simulated by a linear spring, is only marginal. It has been shown that the parameters that affect most the ultimate load are the compressive strength of wood perpendicular to the joint and the normal stiffness of the interface elements representing the contact between rafter and brace. The tangential stiffness of interfaces and the Young s moduli of wood have only very limited influence in the response. The compressive strength of wood parallel to the grain has almost no influence in the response. REFERENCES Ross, R., DeGroot, R., Nelson, W., Lebow, P., 1997 The relationship between stress wave transmission characteristics and the compressive strength of biologically degraded wood. Forest Products Journal, Vol. 47(5), pp CEN; 1991 EN Timber structures. Joints Made With Mechanical Fasteners General principles for the determination of strength and deformation characteristics. Office for Official Publications of the European Communities. Brussels, Belgium. Feio, A., Machado, J., Lourenço, P., 5 Compressive behaviour and NDT correlations for chestnut wood (Castanea sativa Mill). Lourenço, P., 1996 Computational strategies for masonry structures. PhD thesis, Delft University of Technology. 841

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