# Calculating Timber Panel Walls | 2. Stiffness and Slip of a Wall

## Technical Article on the Topic Structural Analysis Using Dlubal Software

• ### Technical Article

The calculation of timber panels is carried out on simplified member or surface structures. This article describes how to determine the required stiffness.

The calculation of the deformation is based on this first article of this series.

#### Wall Stiffness

The stiffness of a wall is calculated under a unit load for 1 kN. You can find more information about the equations used here in the given literature , as well as in the aforementioned earlier article of this series.

#### Example:

The calculation of the stiffness is performed for a simple example with the dimensions shown in Figure 01.

Structure:

• Length of wall l = 2.50 m
• Height of wall h = 2.75 m
• Stand C24 6/12 cm, ρm, T = 350 kg/m³
• Cladding OSB 3, t = 18 mm (one-sided), ρm, O = 439 kg/m³, G = 108 kN/cm²
• kser = 159N/mm
• bE = b + t = 12 cm + 1.8 cm = 13.8 cm
• Clamping d = 1.5 mm, t = 45 mm
• Clamping distance av = 60 mm (single row)
• Grid = 62.5 cm
• Tie rod with 10 nails of diameter 4.2 mm nailed
• FE mesh size is 1.3 m. (4 elements per panel)

Stiffness:

Yielding of fastener (clamping)

Formula 1

$$uk,inst = 2 · l 2 · h · avkser · l² · F= 2 · 2,500 mm 2 · 2,750 mm · 60 mm159 N/mm · (2,500 mm)² · 1.000 N= 0.634 mm$$

Formula 2

$$uG,inst = F · h56 · G · A = 1,000 N · 2,750 mm56 · 1,080 N/mm² · 18 mm · 2,500 mm = 0.068 mm$$

Yielding of ribs

Formula 3

$$uE,inst = 23 · F · h3E · A · l2 = 23 · 1,000 N ·(2,750 mm)³11,000 N/mm² · 60 mm · 120 mm · (2,500 mm)² = 0.028 mm$$

Yielding of anchor

Formula 4

$$kser = 10 · ρm1.5 · d0.880 = 10 · (350 kg/m³)1.5 · (4.2 mm)0.880 = 2,579.95 N/mmuK,DF = h · sin α = 2,750 mm · sin (0.0195) = 0.94 mmα = F · h · 180KDF · π = 1,000 N · 2,750 mm · 1808.06 · 109 · π = 0.0195°KDF = l2 · kser2 = (2,500 mm)² · 2.579.95 N/mm2 = 8.06 · 109$$

Sum of yieldings (calculated without tie rod)

Formula 5

$$uinst = uE,inst 1∑1uG,inst 1∑1uk,inst = 0.028 0.07 0.63 = 0.728 mm$$

Conversion into effective area:

The calculated stiffness is converted into an effective orthotropic panel stiffness. Read this technical article for background information about the orthotropic material model.

Normal stiffness component

Formula 6

$$Eeq = F · h³3 · uE,inst · l³ · b12=1 kN · (275 cm)³3 · 0.0028 cm · (250 cm)³ · 12 cm12 = 158.45 kN/cm²D66/77 = E · d1 - ν = 158.45 kN/cm² · 12 cm = 1901.4 kN/cm$$

Shear stiffness in panel plane

Formula 7

$$Geq = F · h(uG,inst uk,inst) · 56 · bE · l = 1 kN · 275 cm0.07 cm · 56 · 13.8 cm · 250 cm = 1.37 kN/cm²D88 = Geq · bE = 1.37 kN/cm² · 13.8 cm = 18.86 kN/cm$$

The tie rod can be defined directly in RFEM as a linear elastic spring with the calculated spring stiffness of 2,579.95 N/mm. The comparison of the deformations is shown in Figure 1. The differences can also be seen in model 1 attached to this article.

For a three-dimensional calculation, this method shows the problem of defining the panel bending stiffnesses. This is described in more detail in the technical article on orthotropic material models mentioned above.

Instead of displaying the stiffness of the timber panel wall by means of surfaces, a method for converting the calculated yielding into a line release is shown below.

Formula 8

$$F = C · uC = Fu = 1 kN0.73 mm = 1.3699 kN/mmc = Fl · C = 1 kN2.5 m · 1.3699 kN/mm = 0.5479 N/mm$$

The advantage here is that the surface properties of the model can be assumed to be rigid.

#### Summary

In this article, the calculation of a timber panel was shown using an effective orthotropic surface. The tie rod can be defined directly as spring stiffness. For a linear two-dimensional calculation of the system, the results correspond very well with the manual calculations in . Thus, a real design with the loads from a stiffening calculation can be performed. The model for the example calculation can be found below, under Downloads.

Another option was the conversion of yielding into a linear spring of the line. For spatial models, this method is more suitable because it largely excludes the influence of plate bending as well as bending in the panel plane. The model can also be found under Downloads.

The next article will show the stiffening of a floor plan in 2D as well as the design of wall panels in 3D.

#### 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.

#### Reference

  Technische Dokumentation der Lignum: Erdbebengerechte mehrgeschossige Holzbauten, 2010

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• Updated 26 August 2021 