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

2020-07-13

Calculating Timber Panel Walls | 4. Wall Design

This article describes the design of timber panel walls due to generated horizontal loads.

The wall design refers to the third article of this series.

KB | Calculating Timber Panel Walls | 3. Floor Plan

Structural System

Wall 4 at the bottom right will be designed in this article. The position of the wall is indicated in Image 01. You can download the corresponding model with the forces at the end of this article.

1 Forces per Wall

The system values are already included in Part 2; the most relevant ones are listed below.

KB | Calculating Timber Panel Walls | 2. Stiffness and Flexibility of Wall

Beam material = C24
Beam cross-section = 6/12 cm
Sheathing material = OSB 3
t = 18 mm one-sided
ρ_m,O = 439 kg/m³
G = 108 kN/cm²
k_ser = 159 N/mm
b_E = b + t = 12 cm + 1.8 cm = 13.8 cm
Staples d = 1.5 mm, t = 45 mm
Clamping distance a_v = 60 mm (single row)
Grid = 62.5 cm
Tie rod with 10 nails
Diameter = 4.2 mm
Fully nailed
Wall length = 1 m (no intermediate rib)
Wall height = 2.75 m
Force = 5.67 kN

The calculation is performed at the characteristic level without partial safety factors. The design is performed according to Section 9.2.4.2 of Eurocode 5. Design requirements such as the minimum thickness of sheeting, and so on, are met.

Ultimate Limit State of Staples

M_{y, Rk} = 150 \cdot d^{3} = 150 \cdot 1 . 5^{3} = 506 Nmm

Formula 1

f_{h, 1, k} = 65 \cdot d^{- 0.7} \cdot t^{0.1} = 65 \cdot 1 . 5^{- 0.7} \cdot 18^{0.1} = 65.3 N / {mm}^{2}

Formula 2

f_{h, 2, k} = 0.082 \cdot ρ_{k} \cdot d^{- 0.3} = 0.082 \cdot 350 \cdot 1 . 5^{- 0.3} = 25.4 N / {mm}^{2}

Formula 2b

β = \frac{f_{h, 2, k}}{f_{h, 1, k}} = \frac{25.4}{65.3} = 0.4

Formula 2c

F_{v, Rk} = \sqrt{\frac{2 \times β}{1 + β}} \cdot \sqrt{2 \cdot M_{y, Rk} \cdot f_{h, 1, k} \cdot d} = \sqrt{\frac{2 \cdot 0.4}{1 + 0.4}} \cdot \sqrt{2 \cdot 506 \cdot 65.3 \cdot 1.5} = 238 N = 0.24 kN

Formula 3

Ultimate Limit State of Timber Frame Wall

For brackets F_v,R,k x 2 due to 2 nails.

F_{v, Rk} = \frac{F_{v, Rk} \cdot b_{1} \cdot c_{1}}{a_{v}} = \frac{2 \cdot 0.24 kN \cdot 100 cm \cdot 1}{6 cm} = 8 kN

Formula 4

\frac{5, 67 kN}{8 kN} = 0, 71 < 1

Formula 5

Ultimate Limit State of Anchorage

External forces to be introduced

2 Forces Anchor

F_{\max} = \frac{F \cdot h}{b} = \frac{5.67 kN \cdot 275 cm}{100 cm} = 15.6 kN

Formula 6

Fully nailed with 12 ribbed nails, the ultimate limit state is 20.5 kN > 15.6 kN according to the manufacturer's table values.

The design is thus fulfilled.

Timber Design

Buckling design in the wall plane is not necessary, because the timber is held by paneling.

For design with RF-TIMBER Pro, see Model 3 and Image 03.

3 Buckling Analysis

Compression Perpendicular to Grain

f_{c, 90, k} = 0.2 kN / cm ²

Formula 7

σ_{c, 90, k} = \frac{F_{c, 90, k}}{A_{ef}} = \frac{15.6 kN}{12 cm \cdot (6 cm + 3 cm)} = 0.14 kN / {cm}^{2}

Formula 8

\frac{σ_{c, 90, k}}{k_{c, 90} \cdot f_{c, 90, k}} = \frac{0.144}{1.25 \cdot 0.2} = 0.576 < 1

Formula 9

Buckling Analysis

\frac{b_{net}}{t} = \frac{100 cm - 6 cm}{1.8 cm} = 52.2 < 100

Formula 10

Conclusion

The design of the timber panels is shown in this last article of this series. You can calculate the stiffening of the building very well with the program using the analysis per story. Together with simple manual formulas, the design of wood-based panels is quick and easy.