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

Figure 01 - Frame Dimensions

Basic velocity  vb  = 25.000   m/s
Basic velocity pressure  qb  = 0.390   kN/m²
Peak velocity pressure  qp(z)  = 0.596   kN/m²
 calculated as follows:
$${\mathrm q}_\mathrm p(\mathrm z)\;=\;1.7\;\cdot\;{\mathrm q}_\mathrm b\;\cdot\;\frac{\mathrm z}{10}^{0.37}\;=\;1.7\;\cdot\;0.39\;\cdot\;\frac{7.5}{10}^{0.37}\;=\;0.596\;\mathrm{kN}/\mathrm m²$$

Force coefficient cf for lattice structures:
$${\mathrm c}_\mathrm f\;=\;{\mathrm c}_{\mathrm f,0}\;\cdot\;{\mathrm\Psi}_\mathrm\lambda$$

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


Solidity ratio:

$$\begin{array}{l}\mathrm\varphi\;=\;\frac{\mathrm A}{{\mathrm A}_\mathrm C}\;\end{array}$$

where

is the sum of the projected area of the members
Ac  is the enclosed area of the examined face calculated as:
$${\mathrm A}_\mathrm C\;=\;\mathrm l\;\cdot\;\mathrm b$$

Area ratio of the lattice:

$$\begin{array}{l}\mathrm A\;=\;2.828\;\mathrm m\;\cdot\;0.1\;\mathrm m\;\cdot\;5\;+\;2.0\;\mathrm m\;\cdot\;0.05\;\mathrm m\;\cdot\;4\;+\;2.0\;\mathrm m\;\cdot\;0.1\;\mathrm m\;\cdot\;2\;+\\+\;10\;\mathrm m\;\cdot\;0.2\;\mathrm m\;\cdot\;2\;=\;6.214\;\mathrm m^2\end{array}$$ $$\begin{array}{l}{\mathrm A}_\mathrm C\;=\;10\;\mathrm m\;\cdot\;2\;\mathrm m\;=\;20\;\mathrm m^2\end{array}$$

Figure 02 - Displaying Parameters for Determination of Solidity in RFEM/RSTAB

Solidity ratio:

$$\mathrm\varphi\;=\;\frac{6.214\;\mathrm m²}{20\;\mathrm m²}\;=\;0.3107$$

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

Figure 03 - Force Coefficient cf,0

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

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

$$\mathrm\lambda\;=\;2\;\cdot\;\frac{10\;\mathrm m}{2\;\mathrm m}\;=\;10\;<\;70\;\rightarrow\;10\;\mathrm{is}\;\mathrm{governing}$$

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

Figure 04 - End-Effect Factor Ψλ

Using this factor, the following force coefficient is obtained:

$${\mathrm c}_\mathrm f\;=\;{\mathrm c}_{\mathrm f,0}\;\cdot\;{\mathrm\Psi}_\mathrm\lambda\;=\;1.6\;\cdot\;0.95\;=\;1.52$$

Calculation of Resulting Wind Load of Lattice Structure

Variant 1: Equivalent static load Fw
$$\begin{array}{l}{\mathrm F}_\mathrm w\;=\;{\mathrm c}_\mathrm f\;\cdot\;{\mathrm q}_\mathrm p(\mathrm z)\;\cdot\;{\mathrm A}_\mathrm{ref}\end{array}$$

where

Aref  is the projected area
$${\mathrm F}_\mathrm w\;=\;1.52\;\cdot\;0.596\;\mathrm{kNm}²\;\cdot\;6.214\;\mathrm m²\;=\;5.63\;\mathrm{kN}$$
Variant 2: Load as Member Loads from Area Load
$${\mathrm F}_{\mathrm w1}\;=\;1.52\;\cdot\;0.596\;\mathrm{kN}/\mathrm m²\;=\;0.91\;\mathrm{kN}/\mathrm m²$$

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.

Reference

[1]   Eurocode 1: Actions on structures - Part 1‑4: General actions - Wind actions; EN 1991‑1‑4:2005 + A1:2010 + AC:2010
[2]   National Annex - Nationally determined parameters - Eurocode 1: Actions on structures - Part 1‑4: General actions - Wind actions; BS EN 1991‑1‑4:2005+A1:2010

Downloads

Links

Contact us

Contact Dlubal Software

Do you have any questions or need advice?
Contact us or find various suggested solutions and useful tips on our FAQ page.

(267) 702-2815

info-us@dlubal.com

RFEM Main Program
RFEM 5.xx

Main Program

Structural engineering software for finite element analysis (FEA) of planar and spatial structural systems consisting of plates, walls, shells, members (beams), solids and contact elements

RSTAB Main Program
RSTAB 8.xx

Main Program

The structural engineering software for design of frame, beam and truss structures, performing linear and nonlinear calculations of internal forces, deformations, and support reactions