# Cross laminated timber

Contents

The calculation of CLT panels is based on the laminated shell theory, which is a general way of calculating any kind of laminated shells, regardless on the material of the components. However, in the civil engineering practice the most popular application area is definitely the timber shells. Keep in mind this, in FD user interface the CL(T) feature strictly connects to timber panels, including the possibility for both analysis (internal forces/stresses) and design options. Moreover, to the make the best of the applied mechanical theory, general composite laminated shells are also implemented, with any kind of constituent material. As the design of these general composite shells are not supplemented by the standard, only analysis results are available of them.

# Definition on User interface

For the definition of CLT panels the currently existing *Timber plate* and *Timber wall* tools are used:

All the tool window options (Define, Properties, Hole, Edge connection, Physical extent, Panels) are valid and applied for both original and CLT timber panels.

On the General tab the *Eccentricity* on General tab is also modified (improved). So far it was only a display option, without any effect on the calculation. This limitation has no real technical obstacles, thus it will be the choice of the User with a new checkbox here.

On the Material tab of properties dialog, we can set the mechanical model of the plate. The original orthotropic shell model is supplemented with two new types, so User can select from the following options:

- Orthotropic shell
- Cross laminated timber
- General laminated composite

For the sake of uniformity, *Display stiffness* is available for all three kind of mechanical models. This matrix is calculated to the middle surface of the element (independently on the eccentricity of the General tab), it should be noted in the tooltip of this button.

Independently on the selected type, the *General*, *Border* and *Panel* tabs are the same for all the three options, only the Material tab changes according to the selection.

## Orthotropic shell

Within this feature, there is not change on the Material tab of orthotropic timber shell (picture taken after the separation of creep factors and library displaying change to tree view item)

## Cross laminated timber (CLT)

CLT panels consist of individual timber layers. As there are several typical panels, they need a new a library, which can be managed from the Material tab, similarly to the orthotropic shells. For the analysis and design the following parameters are necessary:

- mechanical properties: E
_{x}, E_{y}, G_{xy}, G_{xz}, G_{yz}(G_{rolling}), nu_{xy}, Unit mass, Alpha - limit stresses: f
_{b0k}, f_{b90k}, f_{t0k}, f_{t90}, f_{c0k}, f_{c90k}, f_{xyk}, f_{vk}, f_{Rk}

It is assumed by default that the grain runs in x direction. The directions by the layers for the CLT panels are: 0 or 90 degrees. As the constituent layers are not general timber materials (in the specification of producers it is stated that the timber material properties are taken according to EN338, but they clearly use different values), a new timber library should be created as constituent materials for CLT panels. According to these specifications even the E_{0,mean} value can be different for C24 types, the library should differentiate them by producers. This library needs to store the following data:

There are some values which not specified by the Eurocode, these can be assumed from the existing ones according to the following (if producer does not give exact values for them):

- G
_{rolling}= G_{mean}/ 10 - nu
_{0.90}= 0.2 - f
_{Rk}= f_{vk}/ 2 - f
_{xyk }= f_{vk}

The Material tab of the CLT plate/wall with the existing library (left) elements and necessary application data (right):

The library elements are grouped by the producers, our aim is to implement many manufacturers’ product by default, it would mutually beneficial for both the producers and for FEM-Design. We can edit the new CLT library elements with the *New/Modify* buttons:

The library elements are basically consisting of a list of Timber materials (Timber library elements). User can add a new layer by clicking to an empty Material cell (or change one by clicking on the filled row’s cell Material). By this, the new special Timber library pops up. After selecting one (e.g. C24), the row is automatically filled with the Mechanical properties and Limit stresses, only the Thickness and Alpha angle should be defined by the User (the mechanical properties and limit stresses are NOT modifiable in the table). If Limit stresses is selected at the top, the table is changing according to the following:

The preview and Information sections are automatically updating themselves after inserting/modifying/deleting a layer. On the preview picture, layers with the same Alpha are filled with the same colour, moreover layers with 0 angle are displayed with sign of grain direction.

## General laminated composite

As these composite shells are general and can be made of any material, they are strictly for analysis purpose only, they are not supported with design calculations (User get displacement, internal force and stress results for them). As in case of CLT, the *General*, *Border* and *Panel* tabs are the same, only the *Material* tab is different:

Because of this generality, a new library is needed for these laminated composite shells, which has similar appearance as CLT library, with slight modifications:

In this case, only mechanical properties are needed for a library element (as no design for them), and these values should be manually defined by the User (instead of selecting an existing material from the Concrete/Steel/Timber library).

# Analysis and results

Analysis of laminated type shell structures become available by a new mechanical model implemented into FEM-Design, based on the laminated shell theory. From civil engineering point of view, the most popular field of application is the cross laminated timber (CLT) panel, although the theory in itself is more general, it is applicable for any kind of laminated composite surface structure. As the main purpose of this feature is to calculate and design CLT panels, the currently existing Timber plate and Timber wall tools are supplemented with this calculation model.

Although, the theory used for the calculation of displacements and stresses is general, the application data (e.g. deformation factor, service class, etc.) and design methods for CLT panels are very specific and standard dependent. In order to preserve the possibility of general application, two new options are added to the original mechanical model used for the calculation of timber shell structures (Orthotropic shell): Cross laminated timber and General laminated composite (GLC).

For CLT panels, both analysis results (displacements and stresses) and design calculations are available, while for GLC panels only the first one is provided. These panel types are stored in different libraries, but their definition is very similar, we can define them layer by layer. In case of CLT, adding a new layer is possible by clicking on the material cell of the table, by this the original timber material library pops up, where we can select the constituent material of the current layer. After the selection, the program automatically fills all necessary data of the current layer, including mechanical properties (for analysis results) and limit stresses (for design calculations).

It is very important that among the required layer data, there are some properties not specified by the Eurocode, these can be assumed based on the existing ones according to the following (in case the manufacturer does not specify different values for them):

• G_{yz} (G_{rolling}) = G_{mean} / 10

• nu_{xy} = 0.2

• f_{Rk} = f_{vk} / 2

• f_{xyk} = f_{vk}

Of course, every value can be overwritten by demand. Besides the layers, the default deformation factors by service classes and stiffness reduction factors also need to be specified for a CLT library element. The new cross laminated timber library is filled up with the products of many famous manufacturers by default, new elements can be easily created based on them. The definition of GLC library elements is very similar, except that only the mechanical properties are necessary to define. For all the three mechanical type a display stiffness option is available to see the element stiffness matrix (refer to mid-plane) of the panels used in the calculations (and/or check its singularity), including the "B" submatrix responsible for the coupling effect.

Models containing CLT/GLC panels offering both model space and detailed analysis results for load case, load combination, maximum of load combination, maximum of load groups, influence line and moving load maximum results. The first group contains the displacements, internal forces and stresses, where the former two are displayed in the same way as for the existing non-laminated shells, while the stresses need some further options due to the laminated structure of these shells. A layer in which we would like to see the top/center/bottom stresses and a coordinate system also need to be selected the plot the well-known stress result types. As the shell itself has a local system and all layers in the shell have a local system, the understanding of the stress components is not obvious, therefore the coordinate system is also an option it can be either "Shell local system" or "Layer local system". For example, the physical direction of a displayed Sigma x' stress varies according to the selected system, if shell and layer local system is not identical, which means the angle Theta defined in the library for the layer is not zero.

It is worth to mention that in contrary with the non-laminated shells, the transverse shear stresses (Tau y'z' and Tau x'z') can be also displayed at the top and bottom of layers besides the center, as in case of some intermediate layer they are not necessarily zero (for non-laminated shells, due to the parabolic stress distribution the top and bottom values are always zero, only the center value can be selected from the shell stresses list). Due to the numerous options, finding maximum stresses by components on the shell can be quite time consuming, especially in case of the complex loading of the structure. In order to overcome this difficulty and make the maximum finding process way easier, besides the point based detailed result (e.g. for RC shells, Footfall calculation) a shell based option is also implemented. At the first option we can select an arbitrary point on the CLT/GLC panel, in the detailed result the geometry of the shell and the five stress components are displayed. As the whole section of the shell can be seen here, the coordinate system selector is supplemented with each layer's local system options. In case of maximum result (maximum of load combinations, etc.) plenty of maximum criteria available, which can be grouped by the following:

• All components maximum (e.g. All components+): search for the combination(s) component by component which results the largest positive value of the stress component along all the layers at the selected point, on the stress figures the result of the combinations belonging to the components is displayed (note that there can be five different combination displayed in the detailed result)

• All layer maximum by stress type (e.g. All layer, Sigma x+): search for the combination which results the largest positive x directional normal stress along all the layers at the selected point, on all the five stress figures the result of this combination is displayed

• Layer maximum by stress type (e.g. 2. layer, Sigma x+): search for the combination which results the largest positive x directional normal stress in the second layer at the selected point, on all the five stress figures the result of this combination is displayed

The second option to query a detailed result is the shell based option, where only a CLT/GLC panel need to be selected, without defining an exact point on it.

PICTURE

It is only available for maximum type results, the maximum criteria are the same as for the point based detailed result, except one significant difference: in this case the searching is not limited to a node, the program checks all node on the shell according to the selected criteria. For the first criteria group (All components maximum) the five stress component maximums may arise at five different nodes on the shell (also possibly from five different combinations), this result is excellent to see the overall maximum stresses on the shell considering simultaneously all nodes and all combinations. These nodes are displayed with position and node number on the geometry figure. In case of the second (All layer maximum by stress type) and third (Layer maximum by stress type) maximum criteria group the search focuses on one stress component, thus all stress figures display the result of the same node that provides the maximum for the selected component with simultaneous stress figures at this node for the other components. In the display options the scale/size of the figures and display/font of the values can be specified.

The cross-laminated timber panels are supported with design calculations for ULS combinations and deflection check for serviceability limit states. The latter one can be performed on the analysis tab with the deflection check feature (further information can be found in the description of Shell deflection check). By setting different deformation factors in the application data of the panel for characteristic and quasi-permanent combination types, both the instantaneous and long-term deflections can be checked properly according to the EC, respectively. In terms of the ultimate combinations, several checking criteria is available, some of them is optional (can be specified in the calculation parameter) as the EC itself does not contain them. Design check is available at Timber design tab, CLT panel design.

The first group of design formulas are the well-known stress checks from the Eurocode, extended to CLT panels: tension/compression and bending in both grain and perpendicular to grain direction, transverse shear stresses and rolling shear. The extension means that these checks are performed layer by layer (in the current layer's local system), at top and bottom or at parabola maximum in case of transverse shear stresses. The second group are three interaction formulas: shear interaction and tension/compression and shear. As these are not included in the EC5, in the calculation parameter of the CLT panel it can be specified that these checks should be considered during the design calculation or not. The third group are the buckling and torsional check. The shell buckling check of CLT panels are performed only for those buckling regions, which has non-zero buckling factor, also for those layers, which are less than 45° from the buckling direction. For the torsional check, typically applied for walls (in plane loaded structures), the "no glue at narrow sides" option must be checked in the application data. These methods are based on different standards and scientific papers, further information about the detailed checking process can be found in the theory manual of this feature: Theory of Laminated Composite Shells - CLT application. In the detailed result of the CLT panel the performed design calculations together with a geometry figure showing the critical nodes are displayed.