Answer:
The shear correction factor is considered in the RF‑LAMINATE add-on module 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 Image 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 | 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$}_{i,min}^3}3$
$=11,000\left(\frac{-30^3}3+\frac{50^3}3\right)+300\left(\frac{-10^3}3+\frac{30^3}3\right)$
$+11,000\left(\frac{10^3}3+\frac{10^3}3\right)+300\left(\frac{30^3}3-\frac{10^3}3\right)+11,000\left(\frac{50^3}3-\frac{30^3}3\right)$
$=731.2\times10^6 Nmm$
$\int_{-h/2}^{h/2}\frac{\left(\int_z^{h/2}E_x(z)zd\overline z\right)^2}{G_{xz}(z)}\operatorname dz=\sum_{i=1}^n\frac1{G_{i;xz}}\left(χ_i^2(z_{i,max}-z_{i,min})\;χ_iE_{i,x}\frac{z_{i,max}^3-z_{i,min}^3}3+E_{i,x}^2\frac{z_{i,max}^5-z_{i,min}^5}{20}\right)$
$χ_i=E_{i;x}\frac{z_{i,max}^2}2+\sum_{k=i+1}^nE_{k;x}\frac{z_{k,max}^2-z_{k,min}^2}2$
| 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 (Image 02).
.png?mw=512&hash=4e74affa9ad0c7b703151c5085ac9b8e59171c23)
.jpg?mw=350&hash=8f312d6c75a747d88bf9d0f5b1038595900b96c1)
.png?mw=600&hash=49b6a289915d28aa461360f7308b092631b1446e)