Cross-laminated Timber Plates Research Articles

On the vibroacoustics of cross-laminated timber embedded with acoustic black holes

The adoption of cross-laminated timber (CLT) in building construction is challenged by low-frequency impact noise. Conventional treatments typically involve increasing the mass of the floor assembly or employing structural decoupling techniques, both of which result in increased floor thickness. This study explores an alternative solution by examining the feasibility of embedding acoustic black holes (ABHs) into CLT floors. The ABH acts as a passive waveguide, concentrating vibrational energy in specific regions where it is transferred to damping layers and reduced. Using the finite element method, we investigated the vibroacoustic behavior of CLT plates within the 50–600 Hz frequency range. Our primary focus was on the influence of the ABH’s outer radius and the number of ABH inclusions within a CLT plate. The findings indicate that increasing the outer diameter of the ABH lowers the cut-on frequency and enhances the effective damping of the CLT plate. The increase in damping extends the effectiveness of the ABH to a broader frequency range, with the most noticeable effect above the cut-on frequency. The number of ABH inclusions impacts the structural modes below the cut-on frequency, and the optimal number of inclusions depends on the frequency of interest.

Cross-Laminated Timber (CLT) in Compression Perpendicular to the Plane: Experimental Analysis on the Column below the Wall Load Configuration

This study investigates the load-bearing properties of cross-laminated timber (CLT) under compression perpendicular to the grain. Different series of CLT panels with varying layups, layer thicknesses, and overall depths were tested. Also, the compression perpendicular to the grain properties of CLT plate specimens is compared against clear wood and cubic CLT specimens. The results show a 30% reduction in modulus perpendicular to the grain for cubic samples compared to clear specimens. Increasing the number of layers from three to five leads to a 21% higher modulus, while increasing the overall depth from 105 to 175 mm results (with the same number of layers) in a 17% reduction. The overall depth significantly affects the CLT’s modulus and strength under compression perpendicular to the grain. The study also compares two analytical models for determining the transversal compression factor, kc,90. Although the models showed satisfactory results for thinner CLTs, their accuracy decreased with greater panel depth. These findings enhance the understanding of CLT panels for structural applications.

A finite element for static and dynamic analyses of cross-laminated timber floors

In this paper, a finite plate element for floorings consisting of a cross-laminated timber slab and a floating floor based on linear elastic behavior is presented. Both elemental mass and stiffness matrices are derived, allowing for static and dynamic analyses. For the cross-laminated timber plate, a higher order plate theory is employed, capturing the layer-wise zig-zag deformation of the plate and the stresses derived thereof accurately. It is augmented by an elastic layer representing the footfall sound insulation and an isotropic plate modeling the screed of a floating floor. In total, the finite element exhibits ten nodal degrees of freedom. Hence, larger structures can be analyzed efficiently, which is demonstrated by comparative finite element simulations with a commercial software package based on continuum elements.

The effect of thickness of transverse and longitudinal layers on deformability and stress distribution in three-layer panels made of cross-laminated timber

Introduction. The key feature of timber and materials, made from it, is anisotropy, or a pronounced difference between mechanical properties manifested in different directions. The construction of a cross-laminated timber plate, or a CLT panel, ensures its high strength and rigidity due to the perpendicular arrangement of fibers in mutually perpendicular layers. The article examines the effect of thickness of transverse and longitudinal layers on deformability and stress distribution in three-layer CLT panels. The relevance of the work lies in the need to obtain computational data for analyzing changes in strength characteristics of panels to select the most effective panel configuration.
 
 Materials and methods. Due to the lack of a standardized testing methodology, SCAD+ software package was applied to conduct the studies using numerical methods. The design scheme is identified as a general system whose deformations and principal unknowns are represented by linear displacements of nodal points along the X, Y, Z axes and rotations around these axes. A three–layer plate was selected as the element to be analyzed, the outer layers of which are longitudinal, and the inner one is transverse. Its simplified design scheme is a hinged beam.
 
 Results. The results of the study and calculations made using SCAD+ were applied to make tables and graphs showing dependence of deflection, distribution of normal and shear stresses on thickness of transverse and longitudinal layers of timber.
 
 Conclusions. The data, obtained by the authors, allow evaluating the effect of thickness on deformability and stress distribution in three-layer CLT panels to select the effective design. A change in thickness does not always bring a large difference between mechanical properties, which allows optimizing the panel parameters. The significance of the research lies, among other things, in expanding the scientific and engineering knowledge of timber structures.

Calculating the equivalent elastic moduli and their influence on modelling the sound insulation of softwood cross laminated timber (CLT)

There are characteristics unique to natural materials such as timber that must be dealt with carefully to develop successful sound insulation prediction models. Timber has low internal losses typical of low-density building materials but with material properties that vary according to growth conditions. To study these factors in cross laminated timber (CLT) products, orthotropic thin plate and isotropic thick plate models are investigated. Equivalent elastic moduli are obtained using two methods from values and limits provided in the timber standards and literature, or by the manufacturer. The equivalent moduli are used to calculate the sound insulation of three- and five-layer CLT plates. Appropriate upper and lower limits are calculated from the combined material parameters and compared with sound insulation results measured in accredited laboratories for the first time. EN ISO 10140 test standards require that surface density of the sample be documented in the laboratory; additional precision information such as the fifth percentile of the material density is not required. However, considering the limits on the internal loss factors and elastic moduli only in the thin plate sound insulation model, gives a poor overall prediction performance (23.6% within the upper and lower limits). In this paper we combine the limits on elastic moduli, internal loss factors, and density. With these combined parameters the prediction is improved; less than half of the measured sound insulation values fall within the upper and lower limits of a typical thin plate model (44.0%). The single figure sound reduction index values are underestimated in seven out of nine cases. The prediction is further improved when a thick plate model is considered. There are several layers of complexity in the measurement and modelling conditions that must be carefully considered. The contributions from these compounding factors are discussed, and additional moduli and density parameters are proposed for inclusion in the literature and standards.

Dilatation wave velocities estimated from the plateau in sound insulation of cross-laminated timber (CLT) plates

There are four inherent problems when predicting the airborne sound insulation of cross-laminated timber (CLT) plates. (1) The internal loss factor of wood products is high and therefore difficult to measure using the structural reverberation time technique. (2) Solid wood is a low-density building material compared to reinforced concrete or masonry construction. (3) Timber is orthotropic. (4) Orthotropic behaviour includes low shear moduli. CLT plates, similarly to thick masonry or concrete plates, exhibit thick plate behaviour in the high frequency range (f>1600Hz). The high frequency sound insulation data of nine plates is examined. Transitions to a thick plate seems to occur in all measurements. However, a clearly observable plateau is only visible for six of the nine plates. Simple methods are applied to extract information about the CLT plates from this high frequency (f>1600Hz) measured data. The data extracted from the plate is compared to typical values for equivalent isotropic plates, where the bending stiffness is assumed to be B_iso=√(B_x B_y ). The results are discussed in the context of laboratory measurement of sound insulation.

An efficient analytical method to obtain the homogenised frequency-independent elastic material properties of cross-laminated timber elements

Cross-Laminated Timber (CLT) is a renewable, sustainable, and cost-efficient building element that has been growing in popularity in recent years. To improve one of CLT’s weaknesses, its suboptimal noise and vibration isolation performance, computationally efficient, accessible, and extensible CLT vibro-acoustic models are required. An effective approach to achieve such models is the homogenisation of layered materials. This paper presents a validated homogenisation method based on First-order Shear Deformation Theory (FSDT) that obtains the frequency-independent elastic material properties of CLT. This method is applicable to arbitrary linear elastic material properties, orientations, and stacking sequences of the layers. The homogenised material properties are utilised with FSDT Equivalent Single-Layer (ESL) models that are readily implemented with many finite element method codes to calculate the vibro-acoustic behaviour of CLT elements, even including thickness resonance effects when applied with an appropriate model. The presented homogenisation method for CLT is validated in a numerical study by comparing the mechanical mobilities of ESL models against layerwise dynamic models. The numerical study is conducted based on an experimentally validated 5-ply model for 2- to 7-ply CLT plates with proportionally increasing thicknesses and three idealised boundary conditions. The frequency-independent material properties also allow for the graphical exploration of the anisotropic nature of CLT and the calculation of the universal anisotropic index. The flexibility of the homogenisation method, combined with its ready implementation in already widely implemented FSDT models, can have an application and impact beyond the vibro-acoustic considerations of CLT into the general mechanical modelling of CLT as it is implemented in ever more advanced applications.

Residual stresses in adhesively bonded wood determined by a bilayer flexion reporter system

The application of adhesives in modern timber engineering often introduces moisture into the wood, leading to permanent residual stresses after hardening. This paper proposes a novel approach to assess these residual stresses by using wooden bilayers as a reporter system. For thin bilayers, moisture-induced stresses lead to pronounced visible flexion that can be used to identify the stress-driving parameters of the adhesive’s gelation process. These parameters depend solely on the wood/adhesive combination and are inversely determined by fitting a finite element method model on the experimentally obtained flexion state. In a subsequent step, the determined parameters are used to calculate the residual stresses in the adhesive bondline of cross-laminated timber plates, emphasizing this approach’s scale independence and general applicability to larger scale structures. All combinations of European beech and Norway spruce with the adhesives Melamine–Urea–Formaldehyde (MUF), Phenol–Resorcinol–Formaldehyde (PRF), and Polyurethane (PUR) were investigated.

Bending properties of deconstructable cross-laminated timber-concrete composite floor elements

ABSTRACT Design for disassembly using deconstructable connections facilitates recycling and reusing of building materials and, therefore, reduces waste management problems at the end of service life. In this regard, a deconstructable timber-concrete composite connector using self-tapping screws has been developed at Aalto University. In the presented research, an experimental investigation was performed to further evaluate the effectiveness of this connector in fabricating deconstructable cross-laminated timber (CLT)-concrete composite floors. For this purpose, several CLT-concrete composite beams were fabricated using 5-layer CLT and low-shrinkage concrete. Each beam contained one row of connectors to represent a strip of a full-scale floor. The vibration performance, bending properties, interface slip, failure modes, and ease of disassembly of the beams were investigated. The results were compared with the ones from a reference group of beams fabricated with regular screws. Overall, the deconstructable beams performed exceptionally well by attaining 98.5% of the average bending stiffness of the regular beams. The load-carrying capacity was also similar but governed by the CLT plate. The vibration characteristics were comparable in both groups. After the bending test, the deconstructable beams were disassembled. Although the beams had been exposed to unproportionally large deformations under the bending load, the disassembly process was performed successfully.

Development of Creep Deformations during Service Life: A Comparison of CLT and TCC Floor Constructions

Cross-laminated timber (CLT) slabs in residential buildings need additional weight, e.g., in the form of screeds or gravel layers, to fulfill the criterion for the highest impact-sound class. The additional mass is, however, not exploited for the load bearing behavior, but adds additional weight and leads to an increased height of the floor construction. In this study, such a CLT floor construction with a construction height of 380 mm is compared with a composite slab consisting of a CLT plate with a concrete layer on top with a floor construction height of 330 mm. The timber concrete composite (TCC) slab has a different creep behavior than the CLT slab. Thus, the development of the time-dependent deflections over the service life are of interest. A straightforward hybrid approach is developed, which exploits advanced multiscale-based material models for the individual composite layers and a standardized structural analysis method for the structural slab to model its linear creep behavior. The introduced approach allows to investigate load redistribution between the layers of the composite structure and the evolution of the deflection of the slab during the service life. The investigated slab types show a similar deflection after 50 years, while the development of the deflections over time are different. The CLT slab has a smaller overall stiffness at the beginning but a smaller decrease in stiffness over time than the investigated TCC slab.

Structural Performance of Cross-Laminated Timber Plates in Bending: An Experimental and Numerical Approach

Structural Performance of Cross-Laminated Timber Plates in Bending: An Experimental and Numerical Approach

Bayesian parameter updating in linear structural dynamics with frequency transformed data using rational surrogate models

The identification of parameters of structural models through measurements of the system’s response is of interest in many contexts. In Bayesian system identification the underlying inverse problem is formulated in a probabilistic setting, and Bayes’ rule is applied to update a prior conjecture on the parameters. We apply the Bayesian framework to identify the parameters of structural systems using dynamic measurement data. The likelihood function is formulated in terms of the misfit of the frequency transformed data and the model frequency response function. We introduce a novel formulation that accounts for the correlation of the model error in both spatial and frequency domain. The proposed formulation is able to handle dense data sets in the frequency domain without need to manually select data points. Due to the high computational demands of sampling-based approaches for solving the Bayesian updating problem with expensive structural dynamics models, we resort to surrogate models. We apply a recently introduced rational surrogate model that approximates the complex frequency response as a rational of two polynomials with complex coefficients. Samples of the posterior distribution of the model parameters are then obtained through an adaptive sequential sampling approach using the surrogate instead of the original dynamic model. The proposed method is successfully applied to identify the orthotropic stiffness and damping parameters of a finite element model of a cross laminated timber plate.

Determination of the dispersion relation in cross-laminated timber plates: Benchmarking of time- and frequency-domain methods

The availability of a reliable estimate of the dispersion relation of plates is of great importance for acoustic modelling. Several experimental methods for the extraction of wavenumber and wave velocity information are discussed in the literature. They differ, among other factors, by the sensitivity to noise and multiple reflections, frequency range of application and implementation of the processing algorithm. While for homogeneous thick or thin plates well-established analytical solutions are available, non homogeneous materials would benefit from experimental characterisation. In this framework, our attention is focused on cross-laminated timber (CLT) elements, load-bearing orthotropic layered wood plates that revolutionised the sector of timber construction. The anisotropic and non homogeneous nature of wood suggested testing methods that, though converging for homogeneous materials, could bring different results in their application to CLT elements. The aim of this paper is therefore to benchmark methods for the extraction of wavenumber information on CLT plates, from which the effective elastic properties to model CLT structures as an equivalent homogeneous plate can be derived. This is achieved through a numerical and experimental benchmark of well-established methods for the evaluation of the real component of the propagating wavenumber in CLT elements. Five relevant methods were selected through a literature review, implemented and analyzed: three in the time domain, namely maximum peak, cross-correlation and kurtosis, and two in the frequency domain: phase difference and wave correlation. First, the five methods were benchmarked by numerical simulation on a homogeneous material. In this ideal case, results showed to be consistent for all methods. Then, wavenumber measurements were performed on a cross-laminated timber plate. The results show that the maximum peak, cross-correlation and the wave correlation method provide the lowest dispersion of the data. Considering the time required by the installation of the setup, the wave correlation method seems to be the best alternative among the proposed ones.

Experimental analysis of cross-laminated timber rib panels at normal temperature and in fire

The results of an experimental programme on the structural behaviour, fire behaviour, and fire resistance of CLT rib panels are presented. The floor system consists of cross-laminated timber (CLT) plates rigidly bonded to glued-laminated timber ribs by means of screw-press gluing.The experimental programme comprised ultimate-load tests at normal temperature as reference tests and full-scale fire resistance tests on four cross-sections. In addition to the reference tests, shear tests of the glue line between CLT plate and glued-laminated timber rib were performed for analysis of the cross-sections’ composite action.The results of the reference tests show good agreement with results based on the simplified method according to EN 1995-1-1 [1] and its final draft of CLT design [2]. The importance of the glue line’s quality was confirmed. The fire resistance tests show results on the safe side compared to predictions of the fire behaviour according to EN 1995-1-2 [3] and its actual draft [4]. However, the fire resistance was underestimated due to conservative assumptions about the composite cross-section’s structural behaviour.The experimental programme addressed the fire behaviour and fire resistance of CLT rib panels currently not covered in standards. The project’s overall aim is the development of design rules in fire for EN 1995-1-2.

Effect of cast-in-place concrete application on moisture distribution in timber-concrete composite floors with notched connections, investigated via finite element simulations

Timber-concrete composite (TCC) structures are an efficient way to combine the advantages of cross-laminated timber (CLT) and concrete plates. By cutting notches into the timber part and applying the concrete on top, efficient shear connections can be formed, eliminating the need for additional use of any type of fasteners. However, fresh concrete releases moisture after application, which is absorbed by the highly hygroscopic wood and can lead to a critical reduction in mechanical properties or to problematic situations due to a difference in expansion behavior. Therefore, a separating foil is usually applied between the two materials, which represents an additional time and cost effort and can also negatively influence the connection properties or make the use of notch-only connections impossible. Thus, we investigate numerically what effects the exclusion of such a foil has on the moisture distribution in the CLT plate. Further, the moisture propagation after a fictitious installation on site is analyzed by applying realistic indoor climates to the open wood surface on the bottom of the CLT plate for a period of two years. In addition, the numerical model allows us to study the effect of local sealings of the most critical wooden part, the end-grain surfaces in the notch region. We were able to confirm that, especially in the unsealed case, locally high moisture contents can occur in the critical region next to the notch, where the highest shear stresses are also to be expected. However, by fully sealing the end-grain surfaces in these regions, the moisture levels and thus the risk of failure could be reduced efficiently. The use of such detailed moisture simulations, where moisture uptake due to bleeding of fresh concrete has been calibrated based on experiments, allows the long-term moisture behavior of such critical situations to be studied and effective solutions to be developed.

Three-Dimensional Numerical Calculation Model for Static Behavior Simulation of Cross-Laminated Timber Plates under Thermal Environment

Cross-laminated timber (CLT) is well known as an interesting technical and economical product for modern wood structures. The use of CLT for modern construction industry has become increasingly popular in particular for residential timber buildings. Analyzing the CLT behavior in high thermal environment has attracted scholars’ attention. Thermal environment greatly influences the CLT properties and load bearing capacity of CLT, and the investigation can form the basis for predicting the structural response of such CLT-based structures. In the present work, the finite element method (FEM) is employed to analyze the thermal influence on the deformation of CLT. Furthermore, several factors were taken into consideration, including board layer number, hole conformation, and hole position, respectively. In order to determine the influence, several numerical models for different calculation were established. The calculation process was validated by comparing with published data. The performance is quantified by demonstrating the temperature distribution and structural deformation.

Polynomial chaos based rational approximation in linear structural dynamics with parameter uncertainties

Surrogate models enable efficient propagation of uncertainties in computationally demanding models of physical systems. We employ surrogate models that draw upon polynomial bases to model the stochastic response of structural dynamics systems. In linear structural dynamics problems, the system response can be described by the frequency response function. It is well known that standard polynomial chaos expansions of the frequency response present slow convergence around system eigenfrequencies, due to the highly nonlinear nature of the frequency response for low damping. To overcome this issue, we develop a rational approximation that expresses the system response as a rational of two polynomials with complex coefficients. To estimate the latter, we propose a regression approach that is non-intrusive and can be easily coupled with existing deterministic solvers. We demonstrate the effectiveness of the proposed method with two examples, a two-degree-of-freedom system and a finite element model of a cross laminated timber plate.

Predicting failure of notched cross-laminated timber plates including the effect of environmental stresses

ABSTRACT This paper derives analytical predictions for notched cross-laminated timber (CLT) plate delamination using fracture mechanics for crack propagation from the notch root. The analysis accounts for both CLT heterogeneity and residual stresses caused by seasonal variations in temperature and humidity. The accuracy of predictions coupled with shear corrections, was confirmed by comparison to finite element analysis. The fracture mechanics approach was validated as appropriate by comparison to recent experiments on notched CLT beams. Residual stress effects are significant and depend strongly on notch depth. Environmental changes that promote swelling, such as increases in temperature or moisture content, are more detrimental to plate integrity than are changes that promote shrinkage. Relatively modest levels of swelling stress can potentially cause spontaneous delamination. A new design guide for notched CLT plates that includes effects of heterogeneity and residual stresses is proposed.

Experimental analysis and structural modelling of the punching behaviour of continuous two-way CLT flat slabs

A newly developed bonding technology makes it possible to rigidly connect timber elements parallel to the grain. This technology allows to build two-way and point-supported flat slabs in cross-laminated timber (CLT). In such a structure high loads have to be transferred from the slab into the columns. This paper presents punching tests on different CLT plates. The results of these tests allow for a better understanding of the important parameters of a point-supported CLT slab and should help create the basic design criteria for these connections. To transfer vertical forces from higher storeys through the CLT slab without subjecting it to stresses perpendicular to the grain, the columns are directly connected to each other through an opening in the slab. Even though the opening leads to a stress concentration in the CLT plate, the rolling shear failure was the governing failure mode during the tests. With numerical models the behaviour of the tested plates was simulated and the strains around the opening were calculated. The results show good correlation with the measured strains. After the punching tests, every plate was cut in cubes and the visible failures were recorded. In addition, material samples were cut out of the plates and tested to determine the rolling shear strength of single boards. The achieved shear resistance in the punching tests was 1.4 times higher, than the rolling shear strength determined in shear tests on single boards would allow. An additional rolling shear test series showed that an anchoring effect contributes to the increased rolling shear resistance in punching tests. The results of the punching tests confirm the potential of CLT slabs to be used as biaxial, continuous, point-supported floor slabs.

On the diffuseness of the vibrational field of a cross-laminated timber plate: Comparison between theoretical and experimental methods

The modelling of vibro-acoustic properties of plates usually requires the hypothesis of diffuse conditions of the vibrational field. For heavy-weight homogeneous isotropic plates, this condition is met starting from low frequencies. Nevertheless, the same hypotheses do not hold when applied to stiff, inhomogeneous and non-isotropic materials, like wood, thus its modal behavior needs to be addressed with more detail. The aim of the work is to benchmark theoretical methods and experimental measurements that allow to estimate when the transition from modal to diffuse field occurs in Cross Laminated Timber (CLT) elements. For this purpose, the diffuseness of the vibrational field has been investigated through the experimental evaluation of the mode count and the modal overlap factor on a pilot CLT panel. Measurements of the spatial distribution of modes, impulse responses, dispersion relations and driving point admittance were conducted in laboratory on an 8 m2 CLT plate. The analysis of the results allowed, on the one hand, to directly estimate the two parameters, and on the other, to provide input data necessary to evaluate and compare different theoretical models. Results of direct measurements, performed up to 550 Hz, show that the number of modes occurring in one-third octave bands exceeds the standard threshold of 5 only at 500 Hz, whereas the modal overlap factor is lower than the standard threshold of 1 for most of the modes. This indicates that the vibrational field is mainly non-diffuse in the mid-low frequency range, due to the small number of modes combined with a low damping of the CLT plate. Nonetheless, measurements of modal reverberation time and structural reverberation time in one-third octave band provided consistent results, implying that modal decays are the major contributors to the one-third octave band decay. Furthermore, comparisons with theoretical models show that the driving point admittance proved to be the best method of analysis, requiring simple measurement setup and signal processing, whereas the ISO 10848-4 is affected by the thin plate hypothesis and underestimates the mode count at mid-high frequencies.