Helpful Questions & Answers

Back to FAQ

Video 01 - FAQ Explanatory Video

Figure 01 - Layer Structure in RF-LAMINATE

Figure 02 - Stiffness Matrix in LAMINATE

New

FAQ 004281 EN-US

12/12/2019

Bastian Kuhn Calculation RFEM RF-LAMINATE Timber Structures Finite Element Analysis Eurocode 5 CSA 086 ANSI/AWC NDS

Does the program RF-LAMINATE consider the shear correction factor for cross-laminated timber slabs?

Answer

The shear correction factor is taken into account in the RF-LAMINATE program 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 the shear stiffness itself can be found on page 15 of the English version to the manual of RF-LAMINATE as follows:

For the 10 cm thick plate in Figure 1, the calculation of the shear correction factor is shown. The equations used here are only valid for the simplified symmetrical plate structures!

Layer	z_min	z_max	E_x (z) (N/mm²)	G_xz (z) (N/mm²)
1	-50	-30	11000	690
2	-30	-10	300	50
3	-10	10	11000	690
4	10	30	300	50
5	30	50	11000	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$}_{i,min}^3}3$

$=11000\left(\frac{-30^3}3+\frac{50^3}3\right)+300\left(\frac{-10^3}3+\frac{30^3}3\right)$

$+11000\left(\frac{10^3}3+\frac{10^3}3\right)+300\left(\frac{30^3}3-\frac{10^3}3\right)+11000\left(\frac{50^3}3-\frac{30^3}3\right)$

$=731,2\times10^6Nmm$

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

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

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

$k_z=\frac{43,4}{{(731,2e^6)}^2}6,713284\;e^{13}=5,449\;e^{-3}$

$D_{44}=\frac{{\displaystyle\sum_i}G_{xz,i}A_i}{k_z}=\frac{43,4}{5,449\;e^{-3}}=7964,7N/mm$

This corresponds to the value output in RF-LAMINATE (Figure 2).