# 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 (chipboard, 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.

#### Timber Panel Structure

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 text 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

#### Load-Bearing Capacity

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

Ultimate limit state of a fastener:

Equation 1:

Yield moment M_{y,Rk} = 150 ⋅ d^{3}

Equation 2:

Hole bearing resistance f_{h,1,k} = 65 ⋅ d^{-0.7} ⋅ t^{0.1}

;f_{h,2,k} = 0.082⋅ρ_{k} ⋅ d^{-0.3}

Equation 3:

Load-bearing capacity (NA.109 DIN EN 1995-1-1)

${\mathrm{F}}_{v,\mathrm{Rk}}=\sqrt{\frac{2\times \beta}{1+\beta}}\xb7\sqrt{2\xb7{M}_{y,Rk}\xb7{f}_{h,1,k}\xb7d}$

where

d = diameter of fastener

t = thickness of cladding

${\mathrm{c}}_{\mathrm{i}}=\left\{\begin{array}{l}1\mathrm{for}{\mathrm{b}}_{\mathrm{i}}\ge {\mathrm{b}}_{0}\\ \frac{{\mathrm{b}}_{\mathrm{i}}}{{\mathrm{b}}_{0}}\mathrm{for}{\mathrm{b}}_{\mathrm{i}}\ge {\mathrm{b}}_{0}\end{array}\right.$

Equation 5:

Load-bearing capacity

${\mathrm{F}}_{\mathrm{v},\mathrm{Rk}}=\frac{{\mathrm{F}}_{\mathrm{f},\mathrm{Rk}}\xb7{\mathrm{b}}_{1}\xb7{\mathrm{c}}_{1}}{{\mathrm{a}}_{\mathrm{v}}}$

where

b

_{i}= total wall width

h = wall height

b

_{0}=

$\frac{\mathrm{h}}{2}$

a

_{v}= 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 in calculating the deformation when determining the stiffness:

- Flexibility of the fastener
- Flexibility of the cladding
- Yielding of the ribs
- Flexibility of the anchorage

Equation 6:

Yielding of the fastener (clamping)

${\mathrm{u}}_{\mathrm{k},\mathrm{inst}}=\left(2\xb7\mathrm{l}2\xb7\mathrm{h}\right)\xb7\frac{{\mathrm{a}}_{\mathrm{v}}}{{\mathrm{k}}_{\mathrm{ser}}\xb7{\mathrm{l}}^{2}}\xb7\mathrm{F}$

Equation 7:

Yielding of the cladding

${\mathrm{u}}_{\mathrm{G},\mathrm{inst}}=\frac{\mathrm{F}\xb7\mathrm{h}}{{\displaystyle \frac{5}{6}\xb7\mathrm{G}\xb7\mathrm{A}}}$

Equation 8:

Yielding of the ribs

${\mathrm{u}}_{\mathrm{E},\mathrm{inst}}=\frac{2}{3}\xb7\frac{\mathrm{F}\xb7{\mathrm{h}}^{3}}{\mathrm{E}\xb7\mathrm{A}\xb7{\mathrm{l}}^{2}}$

#### 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.

#### Author

#### Dipl.-Ing. (FH) Bastian Kuhn, M.Sc.

Product Engineering & Customer Support

Mr. Kuhn is responsible for the development of products for timber structures and provides technical support for our customers.

#### Keywords

Timber panel Timber panel wall Oriented strand board OSB

#### Reference

#### Links

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