Determining Force Coefficient of Resulting Member Loads for Plane Lattice Structures from Wind Load
Technical Article
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
Basic velocity v_{b} = 25.0 m/s
Basic velocity pressure q_{b} = 0.39 kN/m²
Peak velocity pressure ${\mathrm q}_\mathrm p(\mathrm z)\;=\;1.7\;\cdot\;{\mathrm q}_\mathrm b\;\cdot\;\frac{\mathrm z}{10}^{0.37}\;=\;1.7\;\cdot\;0.39\;\cdot\;\frac{7.5}{10}^{0.37}\;=\;0.596\;\mathrm{kN}/\mathrm m²$
Force coefficient cf for lattice structures:
${\mathrm{c}}_{\mathrm{f}}={\mathrm{c}}_{\mathrm{f},0}\xb7{\mathrm{\Psi}}_{\mathrm{\lambda}}$
Determination of Force Coefficient c_{f,0} for Lattice Structures Without End-Effect Using Solidity Ratio φ
$\mathrm{\phi}=\frac{\mathrm{A}}{{\mathrm{A}}_{\mathrm{C}}}$
where
A = sum of projected areas of members
A_{C} = l ⋅ b = enclosed area of considered face
$\mathrm{A}=2.828\mathrm{m}\xb70.1\mathrm{m}\xb752.0\mathrm{m}\xb70.05\mathrm{m}\xb742.0\mathrm{m}\xb70.1\mathrm{m}\xb72\phantom{\rule{0ex}{0ex}}10\mathrm{m}\xb70.2\mathrm{m}\xb72=6.214\mathrm{m}\xb2\phantom{\rule{0ex}{0ex}}{\mathrm{A}}_{\mathrm{C}}=10\mathrm{m}\xb72\mathrm{m}=20\mathrm{m}\xb2$
Image 02 - Displaying Parameters for Determination of Solidity in RFEM/RSTAB
$\mathrm{\phi}=\frac{6.214\mathrm{m}\xb2}{20\mathrm{m}\xb2}=0.3107$
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.
Image 03 - Force Coefficient c_{f,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])
$\mathrm{\lambda}=2\xb7\frac{10\mathrm{m}}{2\mathrm{m}}=1070\to 10\mathrm{is}\mathrm{governing}$
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.
Image 04 - End-Effect Factor Ψ_{λ}
Using this factor, the following force coefficient is obtained:
${\mathrm{c}}_{\mathrm{f}}={\mathrm{c}}_{\mathrm{f},0}\xb7{\mathrm{\Psi}}_{\mathrm{\lambda}}=1.6\xb70.95=1.52$
Calculation of Resulting Wind Load of Lattice Structure
Option 1: Equivalent static load F_{w}
${\mathrm{F}}_{\mathrm{w}}={\mathrm{c}}_{\mathrm{f}}\xb7{\mathrm{q}}_{\mathrm{p}}\left(\mathrm{z}\right)\xb7{\mathrm{A}}_{\mathrm{ref}}$
where
A_{ref} = projected area
${\mathrm{F}}_{\mathrm{w}}=1.52\xb70.596\mathrm{kN}/\mathrm{m}\xb2\xb76.214\mathrm{m}\xb2=5.63\mathrm{kN}$
Option 2: Load as Member Loads from Area Load
${\mathrm{F}}_{\mathrm{w}1}=1.52\xb70.596\mathrm{kN}/\mathrm{m}\xb2=0.91\mathrm{kN}/\mathrm{m}\xb2$
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.
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