We provide hints and tips to help you get started with the RFEM program.
FAQ 004281 | Does the RF‑LAMINATE program consider the shear correction factor for cross-laminated timber plates?
Video
First Steps with RFEM
Question
Does the RF‑LAMINATE program consider the shear correction factor for cross-laminated timber plates?
Answer
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).
Keywords
Dlubal FAQ Shear correction Factor Shear Frequently Asked Question FAQ about Dlubal Question and Answer about Dlubal
Links
Write Comment...
Write Comment...
Contact us
Do you have any questions about our products or need advice on selecting the products needed for your projects?
Contact us via our free e-mail, chat, or forum support or find various suggested solutions and useful tips on our FAQ page.
