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

Technical Article

This article was translated by Google Translator

View original text

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 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 trusses:
${\mathrm c}_\mathrm f\;=\;{\mathrm c}_{\mathrm f,0}\;\cdot\;{\mathrm\Psi}_\mathrm\lambda$

Determination of the basic force coefficient c f, 0 for trusses with infinite slenderness with the degree of solidity φ

Solidity ratio:
$\begin{array}{l}\mathrm\varphi\;=\;\frac{\mathrm A}{{\mathrm A}_\mathrm C}\;\\\mathrm{mit}\\\mathrm A\;=\;\mathrm{Summe}\;\mathrm{der}\;\mathrm{projizierten}\;\mathrm{Flächen}\;\mathrm{der}\;\mathrm{Stäbe}\\{\mathrm A}_\mathrm C\;=\;\mathrm l\;\cdot\;\mathrm b\;=\;\mathrm{umschlossene}\;\mathrm{Fläche}\;\mathrm{des}\;\mathrm{betrachteten}\;\mathrm{Bereichs}\end{array}$

Area ratio of the truss:
$\begin{array}{l}\mathrm A\;=\;2,828\;\mathrm m\;\cdot\;0,1\;\mathrm m\;\cdot\;5\;+\;2,0\;\mathrm m\;\cdot\;0,05\;\mathrm m\;\cdot\;4\;+\;2,0\mathrm m\;\cdot\;0,1\;\mathrm m\;\cdot\;2\;+\\+\;10\;\mathrm m\;\cdot\;0,2\;\mathrm m\;\cdot\;2\;=\;6,214\mathrm m²\\{\mathrm A}_\mathrm C\;=\;10\;\mathrm m\;\cdot\;2\;\mathrm m\;=\;20\;\mathrm m²\end{array}$

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

Solidity ratio:
$\mathrm\varphi\;=\;\frac{6,214\;\mathrm m²}{20\;\mathrm m²}\;=\;0,3107$

Once the degree of completeness is known, the basic force coefficient c f, 0 can be read as 1.6 , for example, in Figure 7.33 of the standard DIN EN 1991-1-4 [1] .

Figure 03 - Force Coefficient cf,0

Furthermore, the effective slenderness of the structural component must be determined to determine the reduction factor des λ .

Effective slenderness λ (Tab. 7.16 → DIN EN 1991-1-4 [2] )

$\mathrm\lambda\;=\;2\;\cdot\;\frac{10\;\mathrm m}{2\;\mathrm m}\;=\;10\;<\;70\;\rightarrow\;10\;\mathrm{ist}\;\mathrm{maßgebend}.$

With the previously calculated values, the reduction factor Ψ λ can be read as 0.95 in the diagram shown 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

Option 1: static equivalent load F w
$\begin{array}{l}{\mathrm F}_\mathrm w\;=\;{\mathrm c}_\mathrm f\;\cdot\;{\mathrm q}_\mathrm p(\mathrm z)\;\cdot\;{\mathrm A}_\mathrm{ref}\\\mathrm{mit}\\\;{\mathrm A}_\mathrm{ref}\;=\;\mathrm{projizierte}\;\mathrm{Fläche}\\\;{\mathrm F}_\mathrm w\;=\;1,52\;\cdot\;0,596\;\mathrm{kN}/\mathrm m²\;\cdot\;6,214\;\mathrm m²\;=\;5,63\;\mathrm{kN}\end{array}$

Option 2: Load as Member Loads from Surface Load
${\mathrm F}_{\mathrm w1}\;=\;1,52\;\cdot\;0,596\;\mathrm{kN}/\mathrm m²\;=\;0,91\;\mathrm{kN}/\mathrm m²$

To ensure that this area load in RFEM/RSTAB is only distributed to the members, it is necessary to select the area of the load application to "Not filled, only on members". After entering the load and clicking [OK], the sum of the load to be applied is displayed once more in an info window.

Reference

[1]   Eurocode 1: Actions on structures - Part 1-4: General actions - Wind loads; 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 loads; DIN EN 1991-1-4/NA: 2010-12

Downloads

Links

Contact us

Contact Dlubal Software

Do you have questions or need advice?
Contact our free e-mail, chat, or forum support 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

Price of First License
3,540.00 USD
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

Price of First License
2,550.00 USD