《木结构 Timber Engineering》课程教学资源（参考文献）Contact-free measurements and numerical analyses of the strain distribution in the joint area of steel-to-timber dowel joints.pdf_大学文库

DOI 10.1007/s00107-006-0112-1 ORIGINALARBEITEN · ORIGINALS Holz als Roh- und Werkstoff (2006) 64: 497–506 Johan Sjodin · Erik Serrano · Bertil Enquist ¨ Contact-free measurements and numerical analyses of the strain distribution in the joint area of steel-to-timber dowel joints Published online: 12 April 2006 © Springer-Verlag 2006 Abstract Two different dowel-type joints of differing size were loaded in tension parallel to the grain. The strain distribution in the joint area was studied using a contact-free measurement system. The results were compared with those of numerical analysis. The measurement system was found to be a valuable complement to traditional measurement techniques and also to numerical analyses performed in parametric studies. The measurements obtained were shown to be particularly useful for studying the highly nonlinear behavior of timber that is of special importance in characterizing timber dowel joints. Several observations of considerable interest were made on the basis of numerical results in combination with results of the contact-free measurement system. A non-uniform strain distribution in the joint area was detected, for example, and shear strains and tensile strains, both parallel and perpendicular to the grain were found to be concentrated in the areas most likely to influence the failure mode of the joint. A general observation made was that the larger size joint failed in brittle manner, an observation supported by previous research. Beruhrungslose Messung und numerische Analyse der ¨ Dehnungsverteilung in Stahl-Holz-Stabdubelverbindungen ¨ Zusammenfassung Zwei verschiedene Stabdübelverbindungen unterschiedlicher Größe wurden auf Zug in Faserrichtung belastet. Die Dehnungsverteilung im Bereich der Verbindung wurde mittels eines berührungslosen Messsystems untersucht und mit den Ergebnissen aus einer numerischen Analyse verglichen. Das Messsystem erwies sich als wertvolle Ergänzung zu herkömmlichen Messtechniken sowie zu den Ergebnissen von Parameterstudien. Die Messungen erwiesen sich als besonders hilfreich zur J. Sjödin (✉) · B. Enquist School of Technology and Design, Växjö University, Lückligs plats 1, 351 95, Växjö, Sweden E-mail: johan.sjodin@vxu.se E. Serrano SP Swedish National Testing and Research Institute, Borås, Sweden E. Serrano Division of Structural Mechanics, Lund University, Lund, Sweden Untersuchung des stark nicht-linearen Verhaltens von Holz, das für die Charakterisierung von Holzdübelverbindungen große Bedeutung hat. Die numerischen Ergebnisse führten zusammen mit den berührungslosen Messungen zu einigen interessanten Erkenntnissen. So wurde zum Beispiel eine ungleichmäßige Dehnungsverteilung im Verbindungsbereich festgestellt. Darüber hinaus fand man heraus, dass Schubdehnungen und Zugdehnungen parallel und senkrecht zur Faser konzentriert in den für den Bruch maßgebenden Bereichen vorkamen. Generell wurde in Übereinstimmung mit früheren Untersuchungen festgestellt, dass bei den größeren Verbindungen ein Sprödbruch auftrat. 1 Introduction The design rules contained in the European timber code EC5 (Eurocode 5 2004) for multiple dowel-type joints loaded parallel to the grain are based on the Johansen yielding theory (Johansen 1949), which assumes a rigid plastic behavior of the timber and the dowels. Restrictions related to spacing, end and edge distances and timber thickness are also included in EC5 in order to help avoid brittle failure modes. In addition, the current version of EC5 contains informative design rules aimed at reducing occurrence of the block-shear/plug-shear failure mode at which attention has been directed in recent investigations. According to Schmid et al. (2002), most timber design codes are based on the experience of craftsmen and the results of joint tests conducted in the laboratory. Theoretical methods that have been employed in this area include the approach of Jorissen (1998), which is based on the theory of beams on an elastic foundation, for analyzing stresses perpendicular to the grain as well as shear stresses in dowel-type joints. Brittle failures in dowel-type joints (or bolted joints) in contradiction to what design codes predict are reported in the literature; see e.g. the experimental results of Quenneville and Mohammad (2000). The failure of a large glulam structure was described as being brittle (Ranta-Maunus and Kevarinmäki 2003). This exemplifies the need for more adequate knowledge of the behavior of multiple dowel-type joints

498 There is a gap between investigations involving experiments and those based on a theoretical approach. Despite the fact that theoretical methods can provide detailed results it is still rather unusual in experimental studies of joints to gather data other than that of a joint’s global load-displacement response. Modern contact-free measurement techniques should be possible to employ in order to fill this gap. Some studies in which measurement techniques of this type have been used for timber joints have been reported in the literature. For example, Masuda and Tabata (2001) studied single-bolt joints by use of a digital image correlation method, comparing the results with those of theoretical analyses. A close correlation between results of the measurements and of the theoretical analyses was obtained, but the results were limited to the area close to the bolt. In order to gain a better understanding of the overall performance of timber joints, a larger area around the joint needs to be studied. This is possible today thanks to advanced contact-free measurement systems often commercialized and frequently used as established techniques in areas other than timber engineering. Advantages of these new systems include the possibility of determining deformations and strains within large areas, and of maintaining a high level of accuracy and spatial resolution in a large number of separate instances during loading. Also, such systems can simultaneously record data such as load and displacement readings from the loading machine. In systems of this sort, which in addition are user-friendly, strong efforts have been directed at making it easy to evaluate the measurement data. In the present paper, one such commercial contact-free measurement system is used for studying the joint area in two types of dowel joints loaded in tension parallel to the grain. The aim is to evaluate the results from a general point of view and also to illustrate the advantages and the possibilities of such a measurement system, which does not appear to have been used previously for dowel-type joints. This will involve comparing the results with those of traditional measurement methods and also with those of numerical analysis. Fig. 1 Joint geometries used Abb. 1 Art und Abmessung der untersuchten Verbindung 2 Experimental 2.1 Specimens The two types of joints used in this study are shown in Fig. 1. The type 1 joints, made of Norway spruce, had a mean density of about 450 kg/m3 at 12% moisture content. For type 2 joints, spruce glulam beams manufactured by Moelven Töreboda Limträ AB (L40 quality according to Swedish regulations, approximately the same as the European GL32 quality) were employed. All specimens were stored in a standard climate of 20 ◦C and 65% relative humidity (RH) until 12% moisture equilibrium (±0.6%) was reached, prior to further preparation. The distances a3,t, a4,c and a1 were set according to the minimum values as given in EC5. For type 1, the dowel spacing perpendicular to the grain was twice the minimum distance prescribed by EC5, whereas the minimum distance was used for type 2. The side members were 20 mm thick for type 1 and 30 mm for type 2. The dowels were 12 mm in diameter with a tolerance of ±0.2 mm. The holes in the steel plates, which were cut out by laser, were set to 12.2 mm, with a tolerance of ±0.1 mm. The steel plates were used as templates for drilling the holes in the timber. 2.2 Test setup Eight and five replicates for types 1 and 2, respectively, were loaded in tension. The slotted-in steel plate for both types of joints was connected to the loading system by a fork connection, see Fig. 2. For type 1 joints, the other end was first reinforced with plywood and was then connected to a similar fork. For type 2 joints, a wedge device was used for the other end where the specimens were inserted about 1 m into the grip of the testing machine, see Fig. 2. During the loading procedure, the joints were subjected to a displacement-control rate of 0.5 mm/min for type 1 and 0.9 mm/min for type 2 joints. Failure was usually reached within

499 Fig. 2 a Load-setup for type 1 joints, b load-setup for type 2 joints, c application of inductive gauges (similar in the case of both types) and d type 2 joint, into which random patterns are applied, and the CCD-cameras used Abb. 2 a Versuchsanordnung für Prü- fungen des Typs 1, b siehe a für Typ 2 c Anordnung der Induktionswegaufnehmer (für beide Typen ähnlich) und d Verbindung vom Typ 2 mit aufgebrachten stochastischem Muster und eingesetzten CCD-Kameras 5–15 minutes for type 2. For type 1, the time to failure was usually longer and in some cases, owing to large deformations in the contact zone between the dowels and the timber, the loading procedure was ended before a complete failure by tearing the test specimen apart occurred. During the tests, the load was recorded and the relative displacement between the plate and the timber was measured by two inductive gauges attached on opposite sides of the joints, see Fig. 2. 2.3 Contact-free measurement system The measurement system ARAMISTM manufactured by the company GOM was employed. The system is based on evaluating a random or regular pattern, which is applied to the surface and deforms along with the material. The placing of two CCD cameras (1280 by 1024 resolution) in front of the specimen at different angles enables stereoscopic pictures of the patterned surface, at different occasions during loading, see Fig. 2. The first digital-image processing step defines macro-image facets in the image pair in the original, unloaded state. For each stage of loading, the 3D coordinates of these facets on the specimen’s surface are calculated accurately using image correlation and photogrammetric principles. On the bases of these 3D coordinates, the 3D displacements, rotations and in-plane strains as well as the shape of the specimen can be calculated with a high degree of spatial resolution. The test arrangements for all the joints were similar. The CCD cameras were calibrated to a measurement volume that included the joint area and part of the steel plate; see the area inside the dashed lines in Fig. 2. A random pattern was achieved in two steps. First a matt light-colored paint was sprayed on the area around the dowels. This was done in order to obtain better contrast of the gray scale defining the facets and also to reduce the shininess of the timber. After this, small black dots were applied by spraying black paint on the surface from a distance. The cameras were triggered every five seconds, also logging analog signal readings of displacement and force from the loading machine. The test images were then processed by the software, which is included in the ARAMIS-system. For each pair of images, 3D coordinates for a large number of facets could be determined and be converted to relative displacements and strains. The calibration volume selected results in a spatial resolution of approximately 3.0 mm for type 1 joints and 4.2 mm for type 2. According to the manufacturer, the strain accuracy is approximately 0.02%. 3 Numerical analyses The FE-software ABAQUS (ABAQUS Inc. 2003) was used for the 2D numerical analyses of the joints. The element subdivision in the joint area, shown in Fig. 3, consists of approximately 8200 elements in the case of type 1 joints and 19 000 elements in the case of type 2. In both cases, 6-node second-order triangular elements were employed. Linear-elastic behavior was assumed for the wood, which for the area close to the dowels is an approximation. The moduli of elasticity and the shear moduli for defining the orthotropic wood material were set to EL = 15 160, ET = 505 ER = 505, GL R = 950, GLT = 950 and GRT = 95 MPa, being estimated from the European EN 338 standard. The indices L, R and T denote the longitudinal, radial and tangential directions of the timber, respectively (Fig. 3). No consideration was taken of the difference between the radial and the tangential direction. Thus, T in Fig. 3 represents any transverse direction in the timber. The Poisson’s ratios used were set to vL R = 0.50, vLT = 0.50 and vRT = 0.70. The load was applied as a uniform deformation (u) of the dowels (Fig. 3). Elastic springs were used for type 2 to simulate the stiffness of the steel plate in the L-direction. The elastic stiffness, K, of these springs was calculated using the expression K = (Eplate × Aplate)/Ldowelspacing. The interaction between the dowels, which was assumed to act as rigid bodies, and the wood material were modeled by contact elements involving friction in the tangential direction of the dowels. The coefficient of friction was set to 0.4. Because of these various approximations in the modeling, the evaluation of the numerical results will be restricted mainly to a qualitative discussion of them

501 present, only a single crack develops located centric in relation to the dowels. Two developing cracks have the effect of reducing the embedment capacity due to the area between the initial cracks are taking most of the load, since after the cracks have been initiated, the dowels can more easily push the wood aside (Rodd 1973). This seems to be a plausible explanation for the fact that the load usually decreased after the ultimate load was reached. The development of the two cracks, as described above, in type 1 joints, was usually followed by the final failure mode, usually by splitting (Fig. 4). This caused the load to drop. Note that in some joints the initial cracks in front of the dowels seemed to be propagating up to the final failure, whereas in some cases the final failure seemed to be initiated from the end grain. For type 2 joints, almost no ductile behavior could be observed. Instead, failure occurred at the ultimate load suddenly and the specimens could then no longer transmit load. The primary failure mode was the so-called block-shear failure, but usually in a combination with the so-called row-shear-out failure mode (Fig. 4). Note that prior to final failure the general tendency was Fig. 5 Load-displacement results measured by both the ARAMIS-system and the inductive gauges Abb. 5 Vergleich der mittels ARAMIS-System und Induktionswegaufnehmern bestimmten Kraft-WegDiagramme that an initial crack developed; see Fig. 4, followed almost directly by final failure. 4.2 Comparing load-displacement results of the ARAMIS-system and of the inductive gauges The load-displacement behavior for a type 1 and a type 2 joint is presented in Fig. 5. The results for each of the two gauges are presented there instead of the mean value, in contrast to Fig. 4, allowing possible rotation and eccentricity in the joint area to be studied. In order to compare results of the traditional measurement method with those of the contact-free method, Fig. 5 also presents the load-displacement results as registered by the ARAMIS-system. This involves calculating the change in length in the load direction between points located on the steel plate and points located on the timber close to the respective gauges, see the upper picture in Fig. 5. The results shown in Fig. 5 indicate no marked rotation or eccentricity in the joint area between the steel plate and the timber

502 for type 1 joint, whereas such behavior is observed in the type 2 joint. Hole clearances in the joint area or material defects in the timber are possible explanations for this, but it is also possible that installation of the joints in the wedge device of the loading machine generates this behavior to some extent. The possible in- fluence of eccentricity should not be ignored. In experimental testings, Pedersen et al. (1999) showed eccentricity to affect the load-bearing capacity of similar joints, also finding that increasing the eccentricity produced more brittle behavior. The two measurements systems show a close correlation. For the type 1 joint, the results for both systems being almost identical, wheras there is a slight deviation of the two for type 2 on the lower side of the joint (Fig. 5). This latter deviation is difficult to explain. One possible explanation is that rotation in the joint area may to some extent generate it if one bears in mind the fact that the two systems do not measure the displacement at exactly the same position. 4.3 Comparing results of the strain distribution in the joint area found by the ARAMIS-system and by numerical analysis The strain distributions in the joint area for the two types of joints are presented below. The results obtained by the ARAMISsystem were taken in the elastic region just before the joints indicated plastic behavior in the global load-displacement response involving a total load of approximately 28 kN for type 1 and 270 kN for type 2 (compare this with the load-displacement results obtained for these two joints of the ARAMIS-system as presented in Figs. 8 and 11). For comparing these results with those of the numerical analyses, the same load levels were then simulated. The results were not compared in the plastic range since the numerical analyses dealt only with elastic behavior. It should be emphasized that only the surface on one side of the joints was studied with the ARAMIS-system. Due to that it is possible that, for example, cracks may have occurred on the opposite side of the joints. 4.4 Type 1 joints The results the ARAMIS-system provided and those of the numerical analyses of the strain distribution in the joint area are presented in Fig. 6, which indicates close correlation between the measured and the theoretical values. For example, large tensile strains perpendicular to the grain can be seen to have developed (red areas) in the area between the dowels and the end-grain surface at the free end in both cases. This can be observed more clearly if the strains along a path extending from the dowel towards the end of the grain surface are plotted as shown in Fig. 7, where strains perpendicular to the grain along two different paths are presented both in terms of the numerical analyses and of the measured values obtained using the ARAMIS-system. There is a rather close correlation, both the measured and theoretical results showing very similar tendencies. As can be seen in Figs. 6 and 7, some areas close to the dowels and to the end grain cannot be evaluated using the ARAMIS-system. This can be solved by Fig. 6 Results for the strain distributions in the joint area at 28 kN: a numerical results, b results for the ARAMIS-system Abb. 6 Dehnungsverteilung im Verbindungsbereich bei 28 kN: a numerische Ergebnisse, b mit dem ARAMIS-System ermittelte Ergebnisse Fig. 7 Strain distributions perpendicular to the grain along two paths Abb. 7 Dehnungsverteilung senkrecht zur Faser entlang der Linien 1 und 2 studying only a smaller part of the joint although this would be at the expense of missing the overall picture of the strains in the joint area as a whole. Jorissen (1998) has described the influence of shear stresses and tensile stresses perpendicular to the grain on the cracking tendencies of dowel-type joints. The shear strains and strains perpendicular to the grain along the line where the final crack later occurred were studied with these findings in mind. The results as obtained by the ARAMIS-system at several different stages are shown in Fig. 8. It can be seen that the tensile strains perpendicu-

503 Fig. 8 Strains perpendicular to the grain as well as shear strains at several loading stages along the line where the final crack later developed. The load displacement results in the picture at the upper left indicate the load levels chosen for evaluation Abb. 8 Dehnungen senkrecht zur Faser und Schubdehnungen bei verschiedenen Lastzuständen entlang des entstehenden Bruchverlaufs. Im Kraft-Weg-Diagramm im oberen linken Bild sind die gewählten Lastzustände angegeben lar to the grain increase between stages 3 and 4 in the area close to the dowel. The same tendency can also be noted for the shear strains. It is likely, therefore, that the initial crack shown in Fig. 4 was initiated at these stages and was propagated further during stages that remained. The tendency, as discussed above, for the final failure mode for some of the specimens to apparently be initiated at the end grain could not be verified for this particular specimen. 4.5 Type 2 joints Note that the results shown in Fig. 9 indicate a greater discrepancy in the measured and the calculated results in the case of the type 2 joint than of the smaller type 1 joint. A possible explanation for this is that further parameters are involved, ones not taken into account in the analysis. For instance, due to hole clearances, variations in stiffness between different parts of the timber, and material defects of other types there may be a nonuniform load distribution between the dowels, see for example Cramer (1968), Lantos (1969) and Wilkinson (1986). One example of this is the influence of knots shown in Fig. 9, indicating large strains to develop in the area around the knot. There are also certain marked similarities when one compares the results of the numerical analyses with the measured results. In studying the strains parallel to the grain and the shear strains as shown in Fig. 9, one can note that large tensile strains parallel to the grain develop in the column of dowels farthest from the end grain and that large shear strains develop in the rows of dowels closest to the edges. This is clearly of interest in considering the block-shear failure mode observed during testing and mentioned in the introduction, see Fig. 10. The authors are not aware of findings of this type having been reported in the literature. The presence of tensile strains perpendicular to the grain is of considerable importance. As discussed above, the ARAMISsystem indicated tensile strains to be found in the area close to the end grain. It is possible that cracks are initiated there and are propagated further, leading to the block-shear failure mode. In order to study this, strains perpendicular to the grain as well as shear strains, were studied with use of the ARAMIS-system at several different stages in the area where the initial crack later occurred (Fig. 11). The results indicate tensile strains perpendicular to the grain to increase at every stage in the area closest to the end grain. By using the same estimated modulus of elasticity perpendicular to the grain that was used in the numerical analyses, the tensile stresses in this area can be estimated to about 1.5 MPa. This value is larger than the characteristic tensile strength perpendicular to the grain in glulam (according to EN 1194). However, the shear strains also increase to a higher level at each stage, especially close to the dowel, at the x = 0 position. Thus, it is just as likely that a crack either was initiated by the shear strains or by the tensile strains discussed above. With these results and considerations in mind, one can ask whether a stress interaction criterion may be needed in order to accurately predict

504 Fig. 9 Results for the strain distributions in the joint area at 270 kN: a numerical results, b results for the ARAMIS-system and presence of knots in the areas inside the dashed lines Abb. 9 Dehnungsverteilungen im Verbindungsbereich bei 270 kN: a numerische Ergebnisse, b mit dem ARAMISSystem ermittelte Ergebnisse und Darstellung von Ästen in den gestrichelten Bereichen Fig. 10 The block-shear failure mode Abb. 10 Blockscherversagen the block-shear failure mode. At present, the EC5 code considers the shear capacity and the tension capacity parallel to the grain separately, assuming in connection with this that the joint capacity is governed by the maximum value for the two. 5 Conclusions General observations: • The results for the type 2 joint confirm the brittle failure tendencies for multiple dowel joints loaded in tension parallel to the grain, that have been reported in other studies. • The results of both the ARAMIS-system and the numerical analyses indicate shear strains and tensile strains parallel to the grain to be concentrated to areas that generate the blockshear failure mode. This is a finding which has not been reported previously in the literature. • The results of the ARAMIS-system indicate a non-uniform load distribution in the joint area for type 2 joints. Although this behavior has been taken up in the literature earlier, see e.g. Cramer (1968), Lantos (1969) and Wilkinson (1986), attention there has been directed at single row joints. On the basis of the load distribution obtained in the present study, a possible negative effect of there being several dowel rows should not be ignored. In the Canadian timber design code (CSA O86.1. 2001), in contrast to EC5 code, reduction factors for this are included. Advantages and disadvantages of the contact-free measurement system employed: • The comparisons of the load-displacement results obtained through measurements by the gauges and by the ARAMISsystem showed that the latter technique not only can be a complement, but also replace traditional measurement techniques. This can especially be the case if it is difficult to apply gauges

505 Fig. 11 Strains perpendicular to grain and shear strains at several stages in the area along the line where the initial crack later occurred. The load displacement results in the picture at the upper left show which stage is chosen for evaluation Abb. 11 Dehnungen senkrecht zur Faser und Schubdehnungen bei verschiedenen Lastzuständen im Bereich des später entstehenden ersten Risses. Im KraftWeg-Diagramm im oberen linken Bild sind die gewählten Lastzustände angegeben • Contact-free measurement techniques appear to be valuable tools for calibration in theoretical analyses. They also allow the user to study which parameters are of greatest interest and also make it possible to study non-uniform load distribution within a joint. • It is difficult at present to model the non-linear behavior of timber, a matter which is of interest in studying timber joints. Using contact-free measurement techniques might be one way to study this behavior. • A great advantage in the use of a contact-free measurement system as compared to other measurement techniques is that the user does not have to know which area is of greatest interest before performing a test. Instead, the user can first carry out a test and then evaluate which areas one should devote greater attention to. This is very useful, for example, when studying the initiation of a crack, since it allows the strain, which is present prior to the crack being initiated, to be analyzed. • One problem which is obvious here is that only one side of a joint was studied in each case, meaning that possible cracks on the other side of it could not be detected. The solution to this problem would be to use two measurement systems, acting as a master and slave pair. Then both sides of the joints can be detected at the same instants. • Using two systems could be a possible solution to another type of problem, noted for the larger type 2 joint. The problem was the rather weak resolution obtained, due to the fact that a large area was being studied. This meant that some areas of the joint could not be studied adequately, especially areas in the close vicinity of the dowels. Using two measurement systems of differing resolution could have avoided this. Acknowledgement This research was made possible thanks to financial support obtained from the Development Fund of the Swedish Construction Industry (SBUF), the Wood Science Program at Växjö University (WDATWood Design and Technology) and Skanska AB. The work was carried out at Växjö University and at SP Swedish National Testing and Research Institute. Special thanks to GOM GmbH in Germany and Cascade Computing AB in Sweden for use of the contact-free measurement equipment, to Mo-