Calculating Timber Panel Walls | 1. Determining the Ultimate Limit State and Stiffness

Technical Article

The stiffening of timber structures is usually carried out by means of timber panels. For this purpose, structural components consisting of slabs (chipboards, OSB) are connected with members. Several articles will describe the basics of this construction method and the calculation in the RFEM program. This first article describes the basic determination of the stiffnesses as well as the calculation.

Figure 01 - Timber Panel Construction

Structure of the Timber Panel

The ultimate limit state of a timber panel is determined according to standards such as Eurocode 5 or NDS 2018. In many countries, the shear panel theory is generally used for the design.

As mentioned in the beginning, the design of the timber panels is not the main focus of this analysis. Therefore, it is described in the following only briefly according to the method regulated in Eurocode 5. Furthermore, these articles will not provide comprehensive information about the geometric rules or minimum distances of the fasteners.

A timber panel wall consists of the following elements:

  • Head rib
  • Inner rib, if applicable
  • Cladding
  • Fasteners
  • Edge rib
  • Foot rib
The cladding can be carried out on both sides or only on one side. For outer walls, calculations are usually performed with a cladding on one side due to structural-physical reasons.

Figure 02 - Timber Panel Wall

Ultimate Limit State

The cladding consisting of OSB is usually connected with the ribs my means of staples.

Ultimate limit state of a fastener:

Equation 1:
Yield moment My,Rk = 150 ⋅ d3

Equation 2:
Hole bearing resistance fh,k = 65 ⋅ d-0,7 ⋅ t0,1

Equation 3:
Ultimate limit state ${\mathrm F}_{\mathrm f,\mathrm{Rk}}\;=\;1.1\;\cdot\;\sqrt{2\;\cdot\;{\mathrm M}_{\mathrm y,\mathrm{Rk}}\;\cdot\;{\mathrm f}_{\mathrm h,1,\mathrm k}\;\cdot\;\mathrm d}$
where
d = diameter of the fastener
t = thickness of the cladding

Ultimate limit state of the wall:

Equation 4:
Ratio wall width ${\mathrm c}_{\mathrm i}\;=\;\left\{\begin{array}{l}1\;\mathrm{for}\;{\mathrm b}_{\mathrm i}\;\geq\;{\mathrm b}_0\\\frac{{\mathrm b}_{\mathrm i}}{{\mathrm b}_0}\;\mathrm{for}\;{\mathrm b}_{\mathrm i}\;\geq\;{\mathrm b}_0\end{array}\right.$

Equation 5:
Ultimate limit state ${\mathrm F}_{\mathrm v,\mathrm{Rk}}\;=\;\frac{{\mathrm F}_{\mathrm f,\mathrm{Rk}}\;\cdot\;{\mathrm b}_1\;\cdot\;{\mathrm c}_1}{{\mathrm a}_{\mathrm v}}$
where
bi = total wall width
h = wall height
b0 = $\frac{\mathrm h}2$
av = distance of the fastener

Further important designs include, for example, the buckling analysis of the edge ribs, the design of the anchorage and the buckling design of the cladding.

Deformation

Equivalent to the ultimate limit state design, the four elements of a timber panel are important to calculate the deformation when determining the stiffness:

  • Flexibility of the fastener
  • Flexibility of the cladding
  • Flexibility of the ribs
  • Flexibility of the anchorage

Equation 6:
Flexibility of the fastener (staple) ${\mathrm u}_{\mathrm k,\mathrm{inst}}\;=\;\left(2\;\cdot\;\mathrm l\;+\;2\;\cdot\;\mathrm h\right)\;\cdot\;\frac{{\mathrm a}_{\mathrm v}}{{\mathrm k}_{\mathrm{ser}}\;\cdot\;\mathrm l^2}\;\cdot\;\mathrm F$

Equation 7:
Flexibility of the cladding ${\mathrm u}_{\mathrm G,\mathrm{inst}}\;=\;\frac{\mathrm F\;\cdot\;\mathrm h}{\displaystyle\frac56\;\cdot\;\mathrm G\;\cdot\;\mathrm A}$

Equation 8:
Flexibility of the ribs ${\mathrm u}_{\mathrm E,\mathrm{inst}}\;=\;\frac23\;\cdot\;\frac{\mathrm F\;\cdot\;\mathrm h^3}{\mathrm E\;\cdot\;\mathrm A\;\cdot\;\mathrm l^2}$

Summary

This article described the determination of the ultimate limit state and the stiffness of a timber panel. In the following articles about timber panels, these basics will be used to describe the consideration of these stiffnesses in a two- or three-dimensional calculation.

Keywords

Timber panel Timber panel wall Chipboard OSB

Reference

[1]   Colling, F.: Aussteifung von Gebäuden in Holztafelbauart - Grundlagen, Beanspruchungen, Nachweise nach EUROCODE 5, 2. Auflage. Karlsruhe: Ingenieurbüro Holzbau, 2018

Links

RFEM Main Program
RFEM 5.xx

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Structural engineering software for finite element analysis (FEA) of planar and spatial structural systems consisting of plates, walls, shells, members (beams), solids and contact elements

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RFEM Timber Structures
RF-TIMBER AWC 5.xx

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Design of timber members according to the American standard ANSI/AWC NDS

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1,120.00 USD
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RF-TIMBER CSA 5.xx

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Design of timber members according to the Canadian standard CSA 086-14

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RF-TIMBER NBR 5.xx

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Design of timber members according to the Brazilian standard NBR 7190:1997

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RFEM Timber Structures
RF-TIMBER Pro 5.xx

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Timber design according to Eurocode 5, SIA 265 and/or DIN 1052

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RFEM Timber Structures
RF-TIMBER SANS 5.xx

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Design of timber members according to the South African standards SANS 10163-1:2003 and SANS 10163-2:2001

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RSTAB Main Program
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The structural engineering software for design of frame, beam and truss structures, performing linear and nonlinear calculations of internal forces, deformations, and support reactions

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TIMBER AWC 8.xx

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Design of timber members according to the American standard ANSI/AWC NDS

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1,120.00 USD
RSTAB Timber Structures
TIMBER CSA 8.xx

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Design of timber members according to the Brazilian standard NBR 7190:1997

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RSTAB Timber Structures
TIMBER NBR 8.xx

Add-on Module

Design of timber members according to the South African standards SANS 10163-1:2003 and SANS 10163-2:2001

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1,120.00 USD
RSTAB Timber Structures
TIMBER Pro 8.xx

Add-on Module

Timber design according to Eurocode 5, SIA 265 and/or DIN 1052

Price of First License
1,120.00 USD
RSTAB Timber Structures
TIMBER SANS 8.xx

Add-on Module

Design of timber members according to the South African standards SANS 10163-1:2003 and SANS 10163-2:2001

Price of First License
1,120.00 USD