Back to FAQ

12/12/2019

004281

Finite Element Analysis

Eurocode 5

CSA O86

ANSI/AWC NDS

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

Shear correction Factor Shear

Downloads

RFEM Model File

Write Comment...

0 Comment

0 0

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

Ask Individual Question

(267) 702-2815

info-us@dlubal.com

Go To:
Events
Videos
Models
Knowledge Base
Screenshots
Product Features
Frequently Asked Questions
Customer Projects

Recommended Events

CSA S16:19 Steel Design in RFEM

Webinar 03/10/2021 2:00 PM - 3:00 PM EST

Eurocode 5 | Timber structures according to EN 1995-1-1

Online Training 03/17/2021 8:30 AM - 12:30 PM CET

Eurocode 3 | Steel structures according to DIN EN 1993-1-1

Online Training 03/18/2021 8:30 AM - 12:30 PM CET

RFEM | Dynamics | USA

Online Training 03/23/2021 1:00 PM - 4:00 PM EST

Plate and Shell Buckling Utilizing Dlubal Software

Webinar 03/30/2021 2:00 PM - 2:45 PM

RFEM for Students | USA

Online Training 04/21/2021 1:00 PM - 4:00 PM EST

RFEM | Timber | USA

Online Training 05/05/2021 1:00 PM - 4:00 PM EST

Eurocode 3 | Steel structures according to DIN EN 1993-1-1

Online Training 05/06/2021 8:30 AM - 12:30 PM

Eurocode 2 | Concrete structures according to DIN EN 1992-1-1

Online Training 05/11/2021 8:30 AM - 12:30 PM

Eurocode 5 | Timber structures according to DIN EN 1995-1-1

Online Training 05/20/2021 8:30 AM - 12:30 PM

RFEM | Structural dynamics and earthquake design according to EC 8

Online Training 06/02/2021 8:30 AM - 12:30 PM

RFEM | Basics | USA

Online Training 06/17/2021 9:00 AM - 1:00 PM EST

The Most Common User Errors With RFEM and RSTAB

Webinar 02/04/2021 2:00 PM - 3:00 PM CET

ADM 2020 Member Design in RFEM

Webinar 01/19/2021 2:00 PM - 3:00 PM EST

Dlubal Info Day Online | December 15, 2020

Webinar 12/15/2020 9:00 AM - 4:00 PM CET

Stability Design in Steel Construction with RFEM and RSTAB

Webinar 12/01/2020 2:00 PM - 2:45 PM CET

FEA Troubleshooting and Optimization in RFEM

Webinar 11/11/2020 2:00 PM - 3:00 PM EST

Soil-Structure Interaction in RFEM

Webinar 10/27/2020 2:00 PM - 2:45 PM CET

NBC 2015 Modal Response Spectrum Analysis in RFEM

Webinar 09/30/2020 2:00 PM - 3:00 PM EST

Documenting Results in the RFEM Printout Report

Webinar 08/25/2020 2:00 PM - 2:45 PM

ACI 318-19 Concrete Design in RFEM

Webinar 08/20/2020 2:00 PM - 3:00 PM EST

How to Be More Productive Using RFEM

Webinar 07/07/2020 3:00 PM - 4:00 PM

$Introduction to Solid Modeling \n in RFEM$

Introduction to Solid Modeling in RFEM

Webinar 06/30/2020 2:00 PM - 3:00 PM EST

Modeling with Solids in RFEM

Webinar 06/09/2020 3:00 PM - 3:45 PM

More Events

Videos

KB 000612 | Considering the Joint Slip in Parametric Timber Cross-Sections

Length 3:41 min

KB 000648 | Changing Boundary Lines of a Surface

Length 0:27 min

KB 000633 | Modeling a Purlin by Using Block Manager

Length 6:36 min

KB 000676 | Adjusting Result Values for Surfaces

Length 1:09 min

KB 000622 | Using Tsai-Wu Material Model (Orthotropic Plastic)

Length 0:39 min

RFEM 5 Tutorial for Students | 014 Dynamics: Natural Vibrations | Results

Length 5:34 min

RFEM 5 Tutorial for Students | 013 Dynamics: Natural Vibrations | Input Data

Length 10:05 min

KB 000480 | Linear and Quadratic Taper Shape

Length 0:37 min

KB 000523 | Using Load Type 'End Prestress'

Length 1:09 min

KB 000799 | User-Defined Colours and Textures for Layer Compositions

Length 0:30 min

KB 000587 | Optimizing Cross-Sections in RF-/TIMBER Pro

Length 1:07 min

KB 000606 | Modeling Downstand Beams in Cross-Laminated Constructions

Length 0:30 min

[DE] CP 001191 | Diemerstein Valley - Free Form

Length 0:04 min

KB 000572 | Optimizing Lateral-Torsional Bracing

Length 0:55 min

KB 000782 | Design of shear connectors of cross -laminated timber structures

Length 0:29 min

KB 000758 | Design of tie rods of cross -laminated timber structures

Length 0:36 min

[PL] CP 001184 | "Terma Bania" Building Extension and Renovation in Białka Tatrzańska, Poland

Length 0:06 min

[DE] CP 001187 | Water Sports Center, Formentera, Spain

Length 0:05 min

Helpful Questions & Answers

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

Answer

Keywords

Downloads