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001573

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

2019-05-22

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

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.

Framing

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

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.

Wooden Wall Panel

Ultimate Limit State

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 ⋅ d³

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)

F_{v, Rk} = \sqrt{\frac{2 \times β}{1 + β}} \cdot \sqrt{2 \cdot M_{y, R k} \cdot f_{h, 1, k} \cdot d}

Formula 1

where
d is the diameter of the fastener,
t is the cladding thickness.

Load-bearing capacity of wall:

Equation 4:
Wall width ratio

c_{i} = \{\begin{cases} 1 for b_{i} \geq b_{0} \\ \frac{b_{i}}{b_{0}} for b_{i} \geq b_{0} \end{cases}

Formula 2

Equation 5:
Strength limit state

F_{v, Rk} = \frac{F_{f, Rk} \cdot b_{1} \cdot c_{1}}{a_{v}}

Formula 3

where
b_i is the total wall width,
h is the wall height.
b₀ is

\frac{h}{2}

Formula 4

a_v is a 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 fastener (clamping)

u_{k, inst} = (2 \cdot l 2 \cdot h) \cdot \frac{a_{v}}{k_{ser} \cdot l^{2}} \cdot F

Formula 5

Equation 7:
Yielding of cladding

u_{G, inst} = \frac{F \cdot h}{\frac{5}{6} \cdot G \cdot A}

Formula 6

Equation 8:
Yielding of the ribs

u_{E, inst} = \frac{2}{3} \cdot \frac{F \cdot h^{3}}{E \cdot A \cdot l^{2}}

Formula 7

Conclusion

This article describes 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

Mr. Kuhn is responsible for developing products for timber structures, and provides technical support for our customers.

Links

Structural Analysis and Design Software for Timber Structures

References

Colling, F. Aussteifung von Gebäuden in Holztafelbauart - Grundlagen, Beanspruchungen, Nachweise nach EUROCODE 5, 2. ed.). Karlsruhe: Ingenieurbüro Holzbau, 2018

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