Proposal for an equivalent frame model for the analysis of multi-storey monolithic CLT shearwalls

Highlights

• A simple yet robust model for the analysis of multi-storey CLT shearwalls is presented.

• The mechanical interaction between wall segments and lintels is studied.

• Pushover analyses are conducted on the proposed equivalent frame model.

• The proposed EFM is compared with published test results on CLT shearwalls.

Abstract

The paper presents a simple yet robust frame model to be used as an alternative to continuous 2D or 3D finite element models for the purpose of analyzing multi-storey cross-laminated timber (CLT) shearwalls with openings when subjected to lateral loads. The proposed model is applicable to monolithic CLT walls and takes into account the mechanical interaction between wall segments and lintel/parapet elements as well as the non-linear behaviour of the mechanical anchors, while the contribution of the vertical load is omitted. Pushover numerical analyses were conducted on the proposed equivalent frame model (EFM) and 2-D finite element model, and the results showed good agreement between the two models along the entire force-displacement curves. The failure conditions were found to be consistent in all cases, and the distribution of the internal forces were found to be reasonable. The proposed EFM was also compared with published test results on CLT shearwalls and the fit was deemed reasonable, with a slight tendency to underestimating the ultimate capacity of the shearwalls.

Introduction

Cross Laminated Timber (CLT) panels are multi-layered structural assemblies, where each layer consists of parallel boards oriented in the same direction and at ninety-degrees relative to the two adjacent layers ([1], [2]). The interface between the laminates is typically glued, although other connection types (e.g. nails, screws or wood dowels) can also be used. The alternating layers yield an assembly with a very high in-plane stiffness that is particularly suitable for use as part of a shearwall system. Such shearwalls comprise of CLT panels that are typically connected to each-others through mechanical fasteners that are capable of dissipating inelastic energy, and to the foundation or the storey below through hold-down and angle bracket connections to transfer the shear and overturning forces. Fig. 1 shows a representative two-storey platform construction of CLT shearwall system and highlights its key structural components.

This system is inherently appropriate for seismic design, where dissipative zones (e.g. connections in vertical joints) are identified and detailed to absorb the energy imparted on the structural system, and non-dissipative zones (e.g. CLT panels) are designed to remain elastic. This behaviour is relatively easy to attain in segmented CLT shearwalls with no openings due to the high strength and stiffness of the CLT panels. Even when openings are introduced during the erection process by installing header beams and parapets separately following the installation of the wall segments, the behaviour of the shearwall system may resemble that of segmented CLT shearwalls, due to inability of the joints connecting the elements to transfer moments. A fundamentally different behaviour is observed when window and door openings are introduced into the CLT shearwall by means of cuts in the CLT panels. This creates monolithic wall systems, which introduces areas that are susceptible to high stress concentrations and could lead to premature and brittle failure in the CLT panels prior to the strength and ductility in the mechanical joint are attained [3]. In such structural typologies, the behaviour of the wall could be significantly affected by the relative dimensions of the lintel beams and parapets to that of the vertical wall segments, and as such the influence of the elements above and below the openings cannot be ignored in the analysis. Studies have attempted to characterize the behaviour of CLT walls with openings by developing stiffness and strength reduction coefficients that takes into account the opening dimensions [4], [5], [6]. These are useful preliminary design tools, however, they do not account for the stress state in the CLT panel. For this reason, designers and researchers have typically resorted to employing complex 2D or even 3D continuous models with multi-layer shell elements [7]. Spring or link elements are used typically to incorporate the uni-axial [8], [9] or bi-directional [10], [11], [12], [32] behaviour of the connections into the overall behaviour of the shearwall system.

Blass and Fellmoser [13] proposed an equivalent orthotropic approach to describe the behaviour of the panel elements. This approach was adopted by Rinaldin and Fragiacomo [14] in a numerical model to compare with experimental results obtained from a shake-table test on 3- and 7-storey full-scale CLT buildings. The model approach was also used by Susterisc et al. [15] to investigate the influence of panel size and connection ductility in the seismic analysis of multi-storey CLT buildings. Anisotropic shell elements and non-linear spring elements were used in the study carried out by Yasumura et al. [3] with the aim to predict the mechanical behaviour of two full-scale tests on CLT shearwalls.

In order to avoid intricate numerical analysis, and to provide reasonably simplified modelling approaches to be used in design practice, Mestar et al. [16] proposed an equivalent frame model (EFM) to describe the elastic behaviour of a single-storey wall with centrally placed window or door opening. The concept of using EFM has also been successfully used in masonry structures [17], [18], [19], [20]. The basic premise of the approach is that the wall segments and the lintels (and parapets) are assumed to be flexible, while the intersection zones connecting these elements are characterized by high stiffness. Of particular interest to the current proposed model is the work by Siano et al. [21], where it was shown that the assumptions related to the flexible length of the wall segments and lintels, as well as the dimension of nodes, have a significant effect on the results of the analyses. The implications of these aspects will be particularly investigated and discussed in this paper.

The current study aims to develop a simple yet robust frame model that would be used as an alternative to the 2D or 3D continuous models for the purpose of analyzing multi-storey CLT shearwalls with openings when subjected to lateral loads. This approach is expected to significantly simplify the analysis and reduce both run time and errors typically associated with more complex continuous models. The proposed model is applicable to monolithic CLT walls and takes into account the mechanical interaction between wall segments and lintel/parapet elements. The main contribution of the proposed model is that it provides modelling tools to determine the distribution of internal forces in the frame element that accurately represents the internal stresses obtained from an area model analysis. The main limitation of the proposed model is that it does not consider the contribution of the vertical load. This is attributed to the lack of developed analytical expressions to determine the internal force distribution in the CLT shearwalls in the presence of a vertical gravity load. This limitation is the subject of future research effort by the authors.