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• Is it possible to perform fire resistance design of cross-laminated timber panels in RF‑LAMINATE?

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FAQ 004349 EN-US

Fire resistance design is not implemented in the RF‑LAMINATE add-on module by default.

However, you can calculate the charring rates yourself and consider them accordingly in the module. In the following example, this is explained on a simple plate.

Structural system (Figure 01):

• Span 5 m
• Plate width 2 m
• LC2 (medium) 2.5 kN/m²
• 3 layers
• S1 35 mm C24
• S2 20 mm C24
• S3 35 mm C24
The information regarding the correction factors and stiffnesses can be found in the attached file.

Factors for fire resistance:

• Charring rate ß0 = 0.65 mm/min
• Pyrolysis zone k0d0 = 7 mm
• Charring time t = 30 min
• Effective thickness def=t ß0+k0d0=30 min × 0.65 mm/min+7 mm = 26.5 mm
Remaining thickness of Layer 3 = 35 − 26.5 = 8.5 mm > 3 mm → thickness may be applied. (Figure 02)

Because of the modified layer thicknesses, a new stiffness matrix results, which is applied in RFEM for accidental combinations with the characteristic stiffness values. For the ultimate limit state, the design values are calculated here (Figure 03).
• Is it possible to perform a detailed analysis of connections, supports, or reinforcements of cross‑laminated timber plates in RF‑LAMINATE?

In principle, it is also possible to perform detailed analysis in RF‑LAMINATE. In the case of a very high shear distortion, for example, it can be reasonable to use orthotropic solids for modeling. The video shows a simple modeling and result evaluation of a layer structure by using solids.

A criterion, as of when is the modeling using solids useful, is the shear correction factor. Further information and other criteria can be found in the following FAQ:

• How can I consider the flexibility of a continuous beam with slotted dowel connections?

The easiest way to consider this is to use the RF‑/JOINTS Timber - Steel to Timber add-on module. For this purpose, the module decomposes the original connection, and creates a new structural system that considers the flexibility accordingly. In this case, the ultimate limit state, the serviceability limit state, and the accidental design situations are considered separately.
• Does the RF‑LAMINATE program consider the shear correction factor for cross-laminated timber plates?

The shear correction factor is considered in the RF‑LAMINATE add-on module by using the following equation.

$k_{z}=\frac{{\displaystyle\sum_i}G_{xz,i}A_i}{\left(\int_{-h/2}^{h/2}E_x(z)z^2\operatorname dz\right)^2}\int_{-h/2}^{h/2}\frac{\left(\int_z^{h/2}E_x(z)zd\overline z\right)^2}{G_{xz}(z)}\operatorname dz$

with $\int_{-h/2}^{h/2}E_x(z)z^2\operatorname dz=EI_{,net}$

The calculation of shear stiffness can be found in the English version of the RF-LAMINATE manual, page 15 ff.

For a plate with the thickness of 10 cm in Figure 01, the calculation of the shear correction factor is shown. The equations used here are only valid for simplified symmetrical plate structures!

 Layer z_min z_max E_x(z)(N/mm²) G_xz(z)(N/mm²) 1 -50 -30 11,000 690 2 -30 -10 300 50 3 -10 10 11,000 690 4 10 30 300 50 5 30 50 11,000 690

$\sum_iG_{xz,i}A_i=3\times0.02\times690+2\times0.02\times50=43.4N$

$EI_{,net}=\sum_{i=1}^nE_{i;x}\frac{\mbox{$z$}_{i,max}^3-\mbox{$z$}_{i,min}^3}3$

$=11,000\left(\frac{-30^3}3+\frac{50^3}3\right)+300\left(\frac{-10^3}3+\frac{30^3}3\right)$

$+11,000\left(\frac{10^3}3+\frac{10^3}3\right)+300\left(\frac{30^3}3-\frac{10^3}3\right)+11,000\left(\frac{50^3}3-\frac{30^3}3\right)$

$=731.2\times10^6 Nmm$

$\int_{-h/2}^{h/2}\frac{\left(\int_z^{h/2}E_x(z)zd\overline z\right)^2}{G_{xz}(z)}\operatorname dz=\sum_{i=1}^n\frac1{G_{i;xz}}\left(χ_i^2(z_{i,max}-z_{i,min})\;χ_iE_{i,x}\frac{z_{i,max}^3-z_{i,min}^3}3+E_{i,x}^2\frac{z_{i,max}^5-z_{i,min}^5}{20}\right)$

$χ_i=E_{i;x}\frac{z_{i,max}^2}2+\sum_{k=i+1}^nE_{k;x}\frac{z_{k,max}^2-z_{k,min}^2}2$

 χ1 13.75 106 χ2 8.935 106 χ3 9.47 106 χ4 8.935 106 χ5 13.75 106

$\sum_{i=1}^n\frac1{G_{i;yz}}\left(χ_i^2(z_{i,max}-z_{i,min})-χ_iE_{i,y}\frac{z_{i,max}^3-z_{i,min}^3}3+{E^2}_{i,y}\frac{z_{i,max}^5-z_{i,min}^5}{20}\right)=$

 8.4642 1011 3.147 1013 2.5 1012 3.147 1013 8.4642 1011

Total 6.7133 x 1013

$k_z=\frac{43.4}{{(731.2e^6)}^2}6.713284\;e^{13}=5.449\;e^{-3}$

$D_{44}=\frac{{\displaystyle\sum_i}G_{xz,i}A_i}{k_z}=\frac{43.4}{5.449\;e^{-3}}=7,964.7 N/mm$

This corresponds to the resulting value in RF‑LAMINATE (Figure 02).
• What is the meaning of 'Shear Failure in Glued Contact Surface' in the details of the RF-LAMINATE add-on module?

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FAQ 004206 EN-US

In the case of cross laminated timber panels not glued to the narrow sides and a wall-like structural behaviour, the torsion stress in the glued joints is often decisive. This design is performed according to the explanations in the literature reference below according to the following equation.

$\eta_x=\frac{\tau_{tor,x}}{f_{v,tor}}+\frac{\tau_x+\tau_{xz}}{f_R}=\frac{\displaystyle\frac{3\ast n_{xy}}{b(n-1)}}{f_{v,tor}}+\frac{{\displaystyle\frac{\frac{\partial n_x}{\partial x}}{n-1}}+\tau_{xz}}{f_R}\leq1$

Values:
• b board width
• n number of board layers
• nxy shear in pane plane
• $\frac{\partial n_x}{\partial x}$ shear of board layers
• $\tau_{xz}$ shear in thickness direction
• fR rolling shear strength
• fv,tor torsional shear strength
For the y-direction, the design is analogous but with the values for the y-direction.
• What are the stiffness reduction factors k33 and k88 in RF‑LAMINATE?

These factors reduce the torsional stiffness D33 as well as the shear stiffness D88 of the corresponding stiffness matrix elements of a surface. Since cross-laminated timber is generally not glued at the narrow side, it is also not possible to transfer shear stresses to the timber narrow sides. Thus, the stiffness would be overestimated in this case. For this reason, the stiffness must be reduced accordingly.

Some manufacturers have already provided us these values when delivering the layer structures. They result from the internal analysis. The explanation for determining the correction factors is covered in [1]. The analysis of this work has also been included in the Austrian Annex to EN 1995‑1‑1 [2]. The result is shown in Figure 02. The ratio of the timber width (a) to the timber thickness (ti) can be taken from the respective approval.
• Is it possible to import the effective lengths from RF-STABILITY or RSBUCK in RF-/TIMBER Pro?

Yes, that is possible.

First, RF-STABILITY (or RSBUCK in RSTAB 8) can be used to determine the effective lengths for a particular structure and loading.

They can then be imported in the 'Effective Lengths' of the RF-/TIMBER Pro dialog box.

• How to display the primary load-bearing direction graphically in RF-LAMINATE?

While entering data in the RF-LAMINATE add-on module, there is an option to control the orthotropic direction of each individual layer graphically. To do this, simply place the cursor in the desired row of the corresponding position. Then, a coordinate system is displayed in the surface in the RFEM model (see Figure 01). This is to be interpreted as follows:

red axis = x-axis = β-value of the corresponding layer

Generally, the outer layers specify the main load-bearing direction, which is why it is sufficient to consider only the first layer. The red axis specifies the primary load-bearing direction (see Figure 01).

Displaying the primary load-bearing direction in RFEM
However, the primary load-bearing direction can also be interpreted directly in RFEM. The local axis systems of the surfaces can be displayed in detail (see Figure 02). The orthotropic direction β refers to the local x-axis of the surface. For the example shown in Figure 03, it has a consequence that the primary load-bearing direction for the left surface runs from one support to another and the secondary surface direction to the right surface. If you want to change the supporting direction for the right surface, it is possible to either rotate the local surface axis system (see Figure 04) or create a new structure and rotate the orthotropic direction β by 90° (see Figure 05).

If the primary load-bearing direction is not clearly evident, it is worth taking a look at the stiffness matrix of the surface (see Figure 06). There, it is possible to find the 'decisive' load-bearing direction, e.g. by means of the bending stiffness. The element D11 refers to the local x-axis of the surface and the element D22 refers to the local axis y of the surface.

If not, contact us via our free e-mail, chat, or forum support, or send us your question via the online form.

First Steps

We provide hints and tips to help you get started with the main programs RFEM and RSTAB.

Wind Simulation & Wind Load Generation

With the stand-alone program RWIND Simulation, wind flows around simple or complex structures can be simulated by means of a digital wind tunnel.

The generated wind loads acting on these objects can be imported to RFEM or RSTAB.

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