Mechanical and geometric data for each tested panel.
-->of full-height wall segments and inversely proportional to the openings height;
From Eqs. (1) and (2), the ratio between
The beams above and below the opening contribute in transferring load;
All the panels have the same height and similar openings.
Therefore, the following analytical formulation is proposed: where
The geometrical dimensions for the tested panels are reported in Table 3. Table 4 shows the application of the proposed analytical expression for the four panels that have been tested in Tsukuba. The ratio between the ultimate strength of two panels determined during the experimental session is compared with the value obtained by comparing the geometrical conditions.
The error given by the analytical value never exceeds 8%, showing therefore that the mathematical formulation can predict fairly closely the ultimate strength of panels with the same geometry, characteristics and boundary conditions. However, it must be noted that this relationship gives acceptable results when panels are similar. If configuration of the openings or dimensions of the compared panels such as height and thickness change and, for example, the openings are not symmetrical, the proposed equation is too simple and it will not lead to reliable results.
Moreover, no tests on no-fenestrated panels have been conducted, so it was not possible to compare the results with a common value
The tested panels were modelled in SAP2000 by using a two-dimensional (2D) schematization with
|Modulus of elasticity—lower value (N/mm2)||4200|
|MOE—average value (N/mm2)||5200|
|Maximum bending strength (N/mm2)||11,6|
|Modulus of elasticity—outer layers (N/mm20)||173.33|
|Modulus of elasticity—inner layer (N/mm2)||5200|
|Rolling shear modulus (N/mm2)||100|
|Longitudinal shear modulus (N/mm2)||400|
|Tensile strength—minimum value (N/mm2)||6.1.1. ||12|
|Tensile strength—average value (N/mm2)||16|
Under lateral loads, the connectors exhibit two different mechanisms of deformation. In the vertical direction, the anchors are subjected to tension, while in the horizontal one they experience shear deformation. These two deformation mechanisms are incorporated into the model by using individual springs for each of it, which act in unison. To find the stiffness and ultimate strength, tests on single-anchor elements should be conducted. In the present case, only the tensile connector (UT) has been previously subjected to monotonic load tests to correctly define its behaviour when subjected to tension.
The stiffness, strength and ductility of the steel connections are determined according to the Yasumura and Kawai procedure . This procedure was initially proposed for the evaluation of wood-framed shear walls. The ultimate strength
A pushover analysis was performed with a control of imposed displacement.
Confirming the experimental observation, the break occurs in the inner-cross layer due to the maximum tension attained in the corner of the opening of panel A (Figure 11). The maximum strength of 12 MPa is attained for a corresponding displacement of 17mm and 83-kN force.
The force-deformation response obtained matches quite good to the experimental response for the elastic behaviour. When the panel starts to break and the behaviour became plastic, the CLT shear wall is subjected to large displacement for small increments of load.
For panel B, the upper left corner is the one where the break occurred, as seen in the experimental test (Figure 12a). Figure 12b shows the pushover curve obtained for the shear wall B. Panel B, contrary to panel A, has a very brittle behaviour. In this case, the yielding point is near the breaking point and an overall acceptable accuracy in terms of elastic stiffness was obtained. The presence of the sub-window increases the global stiffness of the panel and highlights again the relevant role of the boundary conditions (contact and friction). The overall behaviour of panel C, due to the absence of the sub-windows, depends strongly from the UT and US connectors.
In this case, the maximum tension is concentrated in both the external and internal corners as shown in Figure 13a. Due to the eccentric position of the load joint (located not in the geometrical centre of the panel but in the centre of the right window), the maximum tension that brought to failure occurred in the inner corner. Figure 13b shows the comparison between the backbone curve and the pushover curve with the observation that the numerical model results approximate the experimental ones quite well.
As shown in Figure 14a, the stress concentration occurs in the corners of the windows and the breaking point corresponds with the inner corner of the left window confirming the experimental results. Also in this case, the sub-window contributes to increase the overall stiffness behaviour. In contrast with the other cases, for panel D, the pushover curve does not approximate exactly the stiffness of the panel (Figure 14b). The main reason of this result can be founded both in the general errors that occurred in the experimental session and in the general approximation of the boundary conditions. Other numerical analyses could be aimed at evaluating the energy dissipated by panels during cycles as done for masonry buildings .
The main results obtained from experimental tests on CLT panels with openings have been compared and interpreted through analytical and numerical models. Concerning the experimental tests, failure occurred at the upper corner of the opening for all the specimens. The general behaviour was brittle for all the panels with the exception of the panel with a one-door opening, the most ductile and also the one with maximum dissipation of energy and deformation. The maximum strength was obtained for the sample with two windows but in this case the bending and sliding of the panel affected the results. Anyway, the maximum strength of the window type (panels B and D) was observed to be higher than that for the door type (panels A and C). An analytical model was adopted to predict the ultimate strength of panels similar to the tested ones, knowing the ultimate strength of one of two panels and the panels have the same height. The error given by the analytical method never exceeded 8%, showing therefore that the mathematical formulation can predict fairly closely the ultimate strength of panels with the same geometry, characteristics and boundary conditions. Finite element models confirmed, in terms of failure type and crack position, the experimental results. Moreover, the pushover curve obtained from the finite element procedure generally matched the experimental one quite well. Further analyses could be addressed to evaluate the out-of-plane resistance of the timber panels, by means of rocking analysis with proper boundary conditions, applying analogous concepts adopted for masonry panels [19, 20].
An experimental campaign aimed at evaluating the ultimate behaviour of CLT panels with openings was here described and interpreted with both analytical and numerical models. The four-wall panels were shown to exhibit a prevalent brittle behaviour, except for the specimen with one-door opening, more ductile. This response was reproduced quite well in the multilayered finite element model. The position of the cracks at the ultimate limit state was correctly obtained from the numerical procedure, highlighting that the failure occurs at the corner of the openings, in different position depending on their size and configurations. The analytical model was capable to correctly evaluate the values of ultimate limit strength of walls with cut-out openings, with errors lower than 8%.
The research presented in this paper was funded by the Japanese company
The authors would like to thank the Timber Structure Laboratory members (Department of Human and Social System, Institute of Industrial Science of the University of Tokyo) and Prof. Massimo Fragiacomo who provided technical expertise for the experimental testing.
Submitted: May 30th, 2016 Reviewed: July 26th, 2016 Published: March 1st, 2017
© 2017 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.