# 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.

#### 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:

• Inner rib, if applicable
• 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.

#### 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 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.

#### Reference

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