《木结构 Timber Engineering》课程教学资源（参考文献）Three-dimensional finite solid element model for Japanese post and beam connection.pdf_大学文库

Three-dimensional finite solid element model for Japanese post and beam connection Jung-Pyo HONG Post Doctoral Fellowship Department of Wood Science, University of British Columbia Vancouver, Canada David BARRETT Professor Emeritus Department of Wood Science, University of British Columbia Vancouver, Canada Summary A three-dimensional finite element (3D FE) model for Japanese post and beam connection was developed using a newly-developed 3D FE wood foundation model. This is the pioneering FE model for multiple nail connections. Details of model development were presented. Simulated results were compared with available experimental data. Limitations of the model and needs for model improvement were discussed. 1. Introduction The Japanese CP-T connection is a standard connection for attaching a post to a beam in traditional Japanese post and beam construction. This connection consists of a CP-T steel plate connector with ten Japanese standard ZN65 nails. Often, a mortise and tenon joint is combined with the CP-T plate to strengthen the joint. In this study, based on the 3D FE single nailed connection model using wood foundation method which was newly developed by Hong [1], a 3D FE analysis for the CP-T connection with mortise and tenon joint was conducted. To validate the connection model, the experimental data of the CP-T connection tests available from Stefanescu [2] were cited. 2. Model description Fig. 1 The reference test setup by Stefanescu [2] (units: mm) Fig. 1 and Fig. 2 show the configuration of Stefanescu’s CP-T connection test and the corresponding 3D FE connection model. Dimensions of the connection and the boundary conditions of the model conformed to the Stefanescu’s tests [2]. Any influence from loose or tight wood-to-wood contact in the mortise and tenon joint was not considered. The CP-T plate was installed on one side, which is a typical connection detail. The connection was loaded by pulling a steel pin through the post. Stefanescu used Canadian coastal Western Hemlock for the post and beam, which had a 105 mm × 105 mm cross section and a range of specific gravity (SG) from 0.39 to 0.47; however, since the single nailed connection model was developed with Douglas-fir, the CP-T connection model used also the material models of Douglas fir employed in the single connection model

Fig. 2 Three-dimensional FE CP-T connection model and the boundary conditions To embody the connection brick elements (SOLID45 from ANSYS) that are eight-noded, quadrilateral isoparametric element are used. The surface-to-surface contact elements were defined on every contact interface with frictional coefficient of 0.7 for wood involved contact and 0.3 for steel-to-steel contact (CONTA174 and TARGE170 from ANSYS). Table 1 shows the material parameters used for the CP-T connection model. Details of the procedures to determine the material parameters and the rationale of wood foundation method can be found in companion paper [3]. The wood foundation was chosen to have a square cross section with width of 4.5×nail diameter, d (= 3.3mm) as shown in Fig. 3. Since the nail spacing of the connection was too narrow to accommodate the two adjacent the 4.5×d foundations, overlap of the foundations was inevitable. Wood foundation with square cross section facilitated meshing work on this overlapped regions. Table 1 Material parameters of three-dimensional finite element models for wood, wood foundation and steel used for the CP-T connection model. Material parameters * For wood material model For wood foundation material model Elastic modulus: L (MPa) 16900 740 Elastic modulus: R=T (MPa) 830 140 Elastic shear modulus: RL= LT (MPa) 1740 140 Elastic shear modulus: RT (MPa) 301 50 Poisson’s ratios: RL, LT, RT ( ) 0.018, 0.37, 0.38 0.07, 0.37, 0.38 Compressive, tensile yield stress: L, R (=T) (MPa) 44.3, 4.5 18.1, 5.7 Compressive, tensile tangent modulus : L, R (=T) (MPa) 169, 8.3 7.4, 1.4 Shear yield stress : RL (=LT), RT (MPa) 43.2, 1.3 3.2, 3.2 Shear tangent modulus : RL (=LT), RT (MPa) 17.4, 3.0 1.4, 0.5 For nail, elasto-perfectly plastic model was assumed with the yield stress of 360 MPa, modulus of 200 GPa and Poisson’s ratio of 0.3. For CP-T plate, an elasto-perfectly plastic model was assumed with the yield stress of 250 MPa, modulus of 200 GPa and Poisson’s ratio of 0.3. * L = longitudinal, R = radial and T = tangential direction

Fig. 3 The square wood foundations incorporated in wood member models 3. Results 3.1 Excerpts from Stefanescu’s experimental reports Stefanescu [2] reported that one-side attachment of the CP-T plate to the post made the connection eccentric during loading; and eventually, the connection was tilted toward the plate side, due to the twisted beam and post, as shown in Fig. 4-A. This tilting behaviour was observed for all eight tests with an average tilting angle (θ) of 2.8 degrees between post and beam. This phenomenon necessitated deliberation on the loading scheme and boundary condition for the FE model. For an original model, the boundary condition was set with all fixed nodes on the side surfaces of the 400 mm-long beam conforming to the fixtures of bolted connections in the real test; and, for the loading scheme, an incremental displacement-controlled loading method was used at first, then, the force (pressure)-controlled loading method was tried. Failure modes of the connection, which were photographed by Stefanescu [2], are shown in Fig.4-B and C. Perpendicular to grain tension splitting of the beam member, nail pull-out and plate shear were the major failure modes. However, during the process of model development, it was discovered that the most influential failure on model prediction was end-tearout of nail in the tenon. More details of end-tearout effect on the simulated results will be presented in section 3.4. Fig.4 Actual deformations observed by Stefanescu [2]; (A) a tilted CP-T connection under loading, θ was the tilting angle, (B) failure mode; perpendicular to grain tension splitting, (C) failure mode; nail pull-out and the CP-T plate in shear 3.2 Simulated deformation of the CP-T connection Fig. 5 and Fig. 6 show the progress of the simulated deformation when displacement-controlled, and force (pressure)-controlled loading were applied to the connection model. It was found that the model using an incremental displacement-controlled loading scheme could not simulate the tilting behaviour of the connection. It provided only a uniformly vertical translation of the post. Although the force (pressure)-controlled loading scheme represented the tilting behaviour, it did not agree with actual tilting behaviour because it was due to the rotation of the post only and the bottom sill was not twisted

embedment on the wood post. These discrepancies between the model and the real test resulted in highly stiff predictions of the load-deformation response compared to experimental observations. Therefore, assuming that the real connection tests were conducted under ideally rigid constraints, the deformation simulated by the displacement-controlled method was deemed reasonable. Fig. 4-C appears the case of deformation under ideally rigid constrains. 3.3 Simulated deformation of nails and CP-T plate Fig. 7 shows the simulated deformation of nails and CP-T plate under displacement-controlled loading. Judging from Stefanescu’s results, deformation simulated by the displacement-controlled loading method agreed more closely with the experimental observations than the force-controlled loading method. The flexural deformation of the three nails penetrating the tenon showed nail pullout from the bottom sill and intensively plastic bending. Simulated Y-directional plastic strain contours in the CP-T plate appears good agreement with the experimental observation. Compared to Fig. 4-C, the contour showed a good indication of the plate shear failure that was observed in the real tests. Fig. 7 The Y-directional plastic strain contour in the nails (left) and the CP-T plate under displacement-controlled loading (right) 3.4 Load-deformation curve of the CP-T connection 3.4.1 Initial model Fig. 8 Simulated load-deformation curves of the initial and the modified CP-T model Simulated load-deformation curves under displacement-controlled loading are superimposed on Stefanescu’s experimental curves in Fig. 8. Simulated curve of the initial model showed high load-carrying capacity compared to the experimental curves. Although causes of this poor load-deformation prediction may be due to many sources such as different wood species, the rigid boundary conditions and the tilting member. The inability of the model to predict fractures was suspected as one of the major causes. In the CP-T connection, the three middle nails out of the five nails in the bottom sill penetrated into the tenon. The typical failure type of nails penetrating into the tenon is shown in Fig. 9

Fig. 9 Typical failure types of the three nails penetrating the tenon: nail edge splitting (off) in the side nails and nail end-tearout in the centre nail Since these connections had narrow end and edge distances in the configurations, it is most likely that the failures occurred in a brittle manner, including the edge splitting (off) in the side nail connections and the end-tearout of the centre nail in the tenon. These kinds of failures may occur at the initial deformation level or at the time when the nail was driven. Once the nail was off the tenon, the loadcarrying ability of the nail connection vanished. The model used in this study, however, could not simulate the process of the endtearout. As shown in Fig. 10, the wood elements surrounding the nail could not split off, unless a fracture algorithm or an intentional cleavage for allowing the endtearout was introduced into the model. As long as the nail was surrounded by the wood elements, the load-carrying ability of the connection would remain in the model. In order to investigate the influence of these fracture failures on model prediction, the model was modified and re-run with the assumption that the edge wood in the side nails were split in the beginning, thus eliminating the load-carrying ability of the two side nail connections in the tenon. No contact element-the side nail connection did not transfer loads in the tenon. Fig. 10 Simulated load-deformation curves of the initial and the modified CP-T model 3.4.2 Modified model The original CP-T connection model was modified so as to remove the load-carrying ability of the side nail connections in the tenon, by eliminating the contact elements between the side nails and the tenon. The nails could then move independently, regardless of the surrounding wood elements in the tenon. The centre nail connection model remained without any modifications. Fig. 10 shows the deformed shape of the nail connection in the tenon with the modified CP-T joint model. As expected, the side model nails did not deform within the tenon. The goal of zero-load carrying capacity of the side nail connections, due to the edge split, was achieved. Compared to the real failure of the centre nail connection, the bulging of the wood elements under the centre nail would have progressed to the nail eventually slipping off the tenon. However, the plasticity-based model could not predict this fracture failure. This shows the limitations of the

model in this study. For further study, it may be useful to introduce a fracture algorithm to this kind of failure prediction. As shown in Fig. 8 the simulated load-deformation curve of the modified model revealed that the influence of the nail end-tearout on model prediction was significant. Although the influences of the initial edge split on the real connection were unknown, the model did react with sensitivity to this influence, so that the prediction of the load-deformation curve was highly improved. If this influence was also true for the real CP-T joint, reinforcing the connections within the tenon may be useful for improving the load-carrying capacity of a traditional CP-T joint. 4. Conclusions Three-dimensional finite element model of Japanese traditional post and beam connection, called CP-T connection was developed using the wood foundation method that enabled creation of FE nail connection model with solid elements. As a pioneering model for 3D FE multiple nail connection, although the model showed needs for improvements, the simulated results provided in threedimensions was able to disclose the inside behaviour of the connection that complicated with interactions of nail, mortise and tenon. Findings from this study would be helpful to improve the performance of Japanese traditional post and beam connection. 5. References [1] Hong J., Three-dimensional nonlinear finite element model for single and multiple dowel-type wood connections, Ph.D dissertation, Department of wood science, The University of British Columbia, Vancouver, BC, Canada, 2007. [2] Stefanescu M., Lateral resistance of traditional Japanese post-and-beam frames under monotonic and cyclic loading conditions, Master thesis, Department of Wood Science, The University of British Columbia, Vancouver, BC, Canada, 2000. [3] Hong J. and Barrett D., “Wood material parameters of numerical model for bolted connections-Compression properties and embedment properties” 10th World Conference on Timber Engineering, Miyazaki, Japan, 2008