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Analysis of laminated type shell structures became 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. For further theoretical informations about CLT panels click here.

# Panel definition

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 the constituent material of the current layer can be selected. 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 on 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 types a *Display stiffness* option is available to show 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.

# Results

## Analysis

The following analysis results are available for CLT/GLC panels :

- load case
- load combination
- maximum of load combination
- maximum of load groups
- influence line and moving load maximum.

Displacements and internal forces are displayed in the same way as for the existing non-laminated shells.

For displaying stresses some further options are needed due to the laminated structure of these shells:

- a layer has to be selected
*Shell local system*or*Layer local system*coordinate system has to be chosen

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 to 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).

#### Stress detailed results

Two types of detailed result are available for stresses.

*Point based stress detailed result*

User 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 are 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

*Shell based stress detailed result*

Due to the numerous options, finding maximum stresses by components on the shell can be quite time consuming, especially in case of complex loading of the structure. In order to overcome this difficulty and make the maximum finding process much easier a shell based option is also implemented, where User only has to select a shell.

The detailed result the following options are available:

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.

## Deflection check

Deflection check of cross-laminated timber panels can be performed for serviceability limit states. For further information see description of Shell deflection check.

## Design

Cross-laminated timber panels are supported with design calculations for ULS combinations. It is available at Timber design tab, CLT panel design.

The following design checking criteria are available:

- stress checks by EC5
- tension/compression and bending in both grain and perpendicular to grain direction
- transverse shear stresses and rolling shear.

In case of CLT panels these checks are extended by performing them layer by layer (in the current layer's local system), at top and bottom or at parabola maximum in case of transverse shear stresses.

- interaction checks
- shear interaction
- tension/compression and shear.

As these are not included in EC5, in the calculation parameter of the CLT panelUser can specify whether to consider them during the design calculation or not.

- shell buckling check

It is 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.

- torsional check

It is 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.

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