21276x

001491

Dipl.-Ing. (BA) Markus Baumgärtel

2017-11-07

Determining Force Coefficient of Resulting Member Loads for Plane Lattice Structures from Wind Load

This article presents a simple example of a lattice structure to explain how to determine wind loading as a function of the lattice solidity.

Wind Perpendicular to Structure

Frame Dimensions

Basic velocity v_b = 25.0 m/s
Basic velocity pressure q_b = 0.39 kN/m²
Peak velocity pressure

q_{p} (z) = 1, 7 \cdot q_{b} \cdot {(\frac{z}{10})}^{0, 37} = 1, 7 \cdot 0, 39 \cdot {(\frac{7, 5}{10})}^{0, 37} = 0, 596 kN / m ²

Formula 1

Force coefficient cf for lattice structures:

c_{f} = c_{f, 0} \cdot Ψ_{λ}

Formula 2

Determination of Force Coefficient c_f,0 for Lattice Structures Without End-Effect Using Solidity Ratio φ

Solidity ratio:

φ = \frac{A}{A_{C}}

Formula 3

where
A is the sum of the projected areas of members,
A_C = l ⋅ b is the enclosed area of the considered face,

Area ratio of the lattice:

A = 2, 828 m \cdot 0, 1 m \cdot 5 + 2, 0 m \cdot 0, 05 m \cdot 4 + 2, 0 m \cdot 0, 1 m \cdot 2 +

10 m \cdot 0, 2 m \cdot 2 = 6, 214 m ²

A_{C} = 10 m \cdot 2 m = 20 m ²

Formula 4

Display of Parameters to Determine Solidity in RFEM/RSTAB

Solidity ratio:

φ = \frac{6.214 m ²}{20 m ²} = 0.3107

Formula 5

After the solidity ratio is obtained, the force coefficient c_f,0 of 1.6 can be read off the standard EN 1991‑1‑4, Figure 7.33 [1], for example.

Basic Force Factor cf, 0

It is also necessary to define the effective slenderness of the structural component in order to determine the end‑effect factor Ψ_λ.

Effective Slenderness λ (Table 7.16 → BS EN 1991‑1‑4 [2])

λ = 2 \cdot \frac{10 m}{2 m} = 10 < 70 \to 10 is governing

Formula 6

Using the previously calculated values, the end-effect factor Ψ_λ of 0.95 can be read off the diagram in Figure 7.36 of the standard.

Reduction Factor Ψλ

Using this factor, the following force coefficient is obtained:

c_{f} = c_{f, 0} \cdot Ψ_{λ} = 1.6 \cdot 0.95 = 1.52

Formula 7

Calculation of Resulting Wind Load of Lattice Structure

Option 1: Equivalent Static Load F_w

F_{w} = c_{f} \cdot q_{p} (z) \cdot A_{ref}

Formula 8

where
A_ref is the projected area

F_{w} = 1.52 \cdot 0.596 kN / m ² \cdot 6.214 m ² = 5.63 kN

Formula 9

Option 2: Load as Member Loads from Area Load

F_{w 1} = 1.52 \cdot 0.596 kN / m ² = 0.91 kN / m ²

Formula 10

In order to distribute this area load in RFEM/RSTAB to the members only, it is necessary to select the "Empty, on members only" option under Area of Load Application. After entering the load and clicking [OK], the sum of the load to be applied is displayed again in an information window.

Author

Mr. Baumgärtel provides technical support for Dlubal Software customers.

Links

References

Deutsches Institut für Normung e.V. (DIN). (2010). Eurocode 1: Actions on Structures – Part 1-4: General Actions – Wind Actions, DIN EN 1991-1-4:2010-12. Berlin: Beuth Verlag GmbH.
Deutsches Institut für Normung e.V. (DIN). (2010). National Annex – Nationally Determined Parameters – Eurocode 1: Actions on Structures – Part 1-4: General Actions – Wind actions; DIN EN 1991-1-4/NA:2010-12. Berlin: Beuth Verlag GmbH.

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