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Windlastberechnung für Schilder – IM 1991

A fully worked example of Wind Load Calculation for Signs using EN 1991-1-4

In diesem Artikel, we will be discussing how to calculate the wind loads on signboards using EN 1991-1-4 located in Oxfordshire, Großbritannien. Our references will be the EN 1991-1-4 Aktion auf Strukturen (Windlast) and BS EN 1991-1-4 National Annex. We will be using similar data in IM 1991-1-4 Beispiel für die Berechnung der Windlast.

SkyCiv automatisiert die Windgeschwindigkeitsberechnungen mit ein paar Parametern. Probier unser Signboard Wind Load Calculator:

Strukturdaten

In diesem Beispiel, we will use the data below. We will consider only wind source direction equal to 240°. Außerdem, das ground elevation of the site is 57.35m.

Tabelle 1. The signboard data that are needed for our wind load calculation.

Ort Oxfordshire, Vereinigtes Königreich
Belegung Verschiedenes – Schild
Terrain Flaches Ackerland
Sign Horizontal Dimension, b 12.0 m
Sign Horizontal Vertical, h
12.0 m
Ground to top of signboard, H.
50.0m
Ground to signboard centroid, mite
44.0 m
Reference area of signboard AZeichen
144.0 qm.
Pole diameter, d
1.0 m
Pole surface type
Cast iron
Ground to top of pole, mitG
38.0 m
Reference area of pole APole
38.0 m

 

Zahl 1. Standort (von Google Maps).

 

Zahl 2. Signboard dimensions.

Die Formel zur Bestimmung des Auslegungswinddrucks lautet:

Für die Grundwindgeschwindigkeit:

\({v}_{b} = {c}_{dir} {c}_{Jahreszeit} {c}_{alt} {v}_{b,map}\) (1)

Wo:

\({v}_{b}\) = Grundwindgeschwindigkeit in m / s
\({c}_{dir}\) = directional factor
\({c}_{Jahreszeit}\)= saisonaler Faktor
\({c}_{alt}\)= altitude factor where:

\({c}_{alt} = 1 + 0.001EIN \) zum \( z ≤ 10 \) (2)
\({c}_{alt} = 1 + 0.001EIN ({10/mit}^{0.2}) \) zum \( mit > 10 \) (3)

\({v}_{b,map}\) = fundamental value of the basic wind velocity given in Figure NA.1 of BS EN 1991-1-4 National Annex
\( EIN \) = altitude of the site in metres above mean sea level

Für Grundgeschwindigkeitsdruck:

\({q}_{b} = 0.5 {⍴}_{Luft} {{v}_{b}}^{2} \) (4)

Wo:

\({q}_{b}\) = Auslegungswinddruck in Pa
\({⍴}_{Luft}\) = density of air (1.226kg / cu.m.)
\({v}_{b}\)= Grundwindgeschwindigkeit in m / s

Für Spitzendruck:

\({q}_{p}(mit) = 0.5 {c}_{e}(mit){q}_{b} \) for site in Country terrain (5)
\({q}_{p}(mit) = 0.5 {c}_{e}(mit){c}_{e,T.}{q}_{b} \) for site in Town terrain (6)

Wo:
\({c}_{e}(mit)\) = Belichtungsfaktor
\({c}_{e,T.} \) = exposure correction factor for Town terrain

To calculate the wind force acting on the signboard/pole:

\({F.}_{w} = {c}_{s}{c}_{d}{c}_{f}{q}_{p}({mit}_{e}){EIN}_{ref} \) (7)

Wo:
\( {c}_{s} {c}_{d} \) = structural factor
\({c}_{f} \) = force coefficient of the structure
\({q}_{p}({mit}_{e}) \) = peak velocity pressure at reference height \({mit}_{e} \)
\({EIN}_{ref} = b h\) = reference area of the structure

Geländekategorie

Based on BS EN 1991-1-4 National Annex, the Terrain Categories in EN 1991-1-14 were aggregated into 3 Kategorien: Terrain category 0 is referred to as Sea; Terrain categories I and II have been considered as Country terrain, and Terrain categories III and IV have been considered as Town terrain.

Considering wind coming from 240°, we can classify the terrain category of the upwind terrain as Town terrain.

Directional and Season Factors, \({c}_{dir}\) & \({c}_{Jahreszeit}\)

Um für Gleichung zu berechnen (1), we need to determine the directional and season factors, \({c}_{dir}\) & \({c}_{Jahreszeit}\). From Table NA.1 of BS EN 1991-1-4 National Annex, since the wind source direction is 240°, the corresponding value for directional factor, \({c}_{dir}\), entspricht 1.0.

Andererseits, we want to consider a conservative case for the season factor, \({c}_{Jahreszeit}\), which we will einstellen 1.0.

Altitude Factor \({c}_{alt}\)

For the altitude factor, \({c}_{alt}\), we will only use Equation (2) for a more conservative approach using site elevation \( EIN \) equal to 57.35m. Deshalb:

\({c}_{alt} = 1 + 0.001(57.35) = 1.05735\)

Grundlegende Windgeschwindigkeit und Druck, \({v}_{b}\) & \({q}_{b}\)

The wind speed map for the United Kingdom can be taken from Figure NA.1 of the National Annex for BS EN 1991-1-4.

Zahl 5. Basic wind speed for United Kingdom based on Figure NA.1 of BS EN 1991-1-4 National Annex.

Für unseren Standort, Oxfordshire, England, das berechnete \( {v}_{b,map} \) entspricht 22.7 Frau.

\( {v}_{b} = {c}_{dir} {c}_{Jahreszeit} {c}_{alt} {v}_{b,map} = (1.0)(1.0)(1.05735)(22.7) \)
\( {v}_{b} = 24.0 Frau \)

We can calculate the basic wind pressure, \( {q}_{b,0} \), unter Verwendung von Gleichungen (4):

\( {q}_{b} = 0.5(1.226)({24}^{2}) = 353.09 Gut \)

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Orography Factor \({c}_{Das}(mit)\)

Für diese Struktur, the terrain is relatively flat for the wind coming from 240°, das

altitude factor, \({c}_{alt}\), we will only use Equation (2) for a more conservative approach using site elevation \( EIN \) equal to 57.35m. Deshalb:

Peak Velocity Pressure, \({q}_{p}(mit)\)

For our structure, since the terrain category is classified as Town terrain, the peak Similarly, the peak velocity pressure, \({q}_{p}(mit)\), can be solved using Equation (6):

\({q}_{p}(mit) = {c}_{e}(mit){c}_{e,T.}{q}_{b} \)

Wo:
\({c}_{e}(mit)\) = exposure factor based on Figure NA.7 of BS EN 1991-1-4 National Annex
\({c}_{e,T.} \) = exposure correction factor for Town terrain based on Figure NA.8 of BS EN 1991-1-4 National Annex

To determine the exposure factor, \({c}_{e}(mit)\) , for the signboard, wir müssen die berechnen \(mit – {h}_{dis}\) and the distance upwind to shoreline in km. For simplicity, we will set the the displacement height, \({h}_{dis}\), zu 0. Für die \(mit \) Werte, we will consider it on \(z = 38.0\) und \(z = 44.0\). Außerdem, the distance upwind to shoreline is more than 100km. Deshalb, using Figure NA.7 of BS EN 1991-1-4 National Annex:

Zahl 6. Figure NA.7 of BS EN 1991-1-4 National Annex.

Deshalb:

\({c}_{e}(38.0) = 3.2\)
\({c}_{e}(44.0) = 3.3\)

Andererseits, the exposure correction factor \( {c}_{e,T.} \) for the signboard can be determined from Figure NA.8 of BS EN 1991-1-4 National Annex. Using distance inside town terrain equal to 1km, we can get the exposure correction factor \( {c}_{e,T.} \):

Zahl 7. Figure NA.8 of BS EN 1991-1-4 National Annex.

Deshalb:

\({c}_{e,T.}(38.0) = 1.0\)
\({c}_{e,T.}(44.0) = 1.0\)

Using the values above, we can calculate the peak velocity pressure, \({q}_{p}(mit)\), zum \(z = 38.0\) und \(z = 50.0\):

\({q}_{p}(44.0) = (3.3)(1.0)(353.09) = 1165.20 Gut \)
\({q}_{p}(38.0) = (3.2)(1.0)(353.09) = 1129.89 Gut \)

Structural Factor, \( {c}_{s}{c}_{d} \)

For our signboard, we will use simplified value for the structural factor, \({c}_{s}{c}_{d}\), to be equal to 1.0 basierend auf Abschnitt 6 oder und 1991-1-4.

Force Coefficient, \( {c}_{f}\), for signboard

For signboards, the force coefficient, \({c}_{f}\), entspricht 1.8 basierend auf Abschnitt 7.4.3 oder und 1991-1-4.

Wind Force, \( {F.}_{w,Schild} \), acting on the signboard

The force acting on the signboard can be calculated using Equation (7) basierend auf Abschnitt 5.3(2) oder und 1991-1-4.

\({F.}_{w,Schild} = {c}_{s}{c}_{d}{c}_{f}{q}_{p}({mit}_{e}){EIN}_{ref,Schild} = (1.0)(1.8)(1165.20Gut)(12.0m)(12.0m)\)
\({F.}_{w,Schild} = 302019.84 N\)

Note that the horizontal eccentricity of this wind force acting on the centroid of the signboard is recommended to be equal to 3.0m.

 

The wind calculations can all be performed using SkyCiv Load Generator for EN 1991 (signboard and pole wind load calculator). Benutzer können den Standort eingeben, um die Windgeschwindigkeit und Geländedaten zu erhalten, Geben Sie die Solarmodulparameter ein und generieren Sie die Auslegungswinddrücke. Mit der Standalone-Version, you can streamline this process and get a detailed wind load calculation report for signboards and poles!

 

Wind Force, \( {F.}_{w,Pole} \), acting on the pole

Ähnlich, the force acting on the pole can be calculated using Equation (7) basierend auf Abschnitt 5.3(2) oder und 1991-1-4.

\({F.}_{w,Pole} = {c}_{s}{c}_{d}{c}_{f}{q}_{p}({mit}_{G}){EIN}_{ref,Pole}\) (8)

Wo:

\({c}_{f} = {c}_{f,0}{ψ}_{λ} \)
\({EIN}_{ref,Pole} = {mit}_{G}d \)

Hinweis:
\(ψ_{λ} \) is calculated based on effective slenderness, \( λ \), using using Figure 7.36 der Sektion 7.13 oder und 1991-1-4
\({c}_{f,0}\) is calculated based on Reynolds number \( R_{e} \) mit Abbildung 7.28 oder und 1991-1-4
Wo:
\( {mit}_{G} \) is the height of the pole from the ground in m
\( d \) is the diameter of the pole in m
\( ν = 0.000015 sq.m/s \) is the kinematic viscosity of the air
\( v({mit}_{G}) = (2{q}_{p}({mit}_{G})/r)^{0.5} \) (9)
\( {R.}_{e} = v(z_{G})d/ ν \) (10)

We will dive deep into these parameters on the next sections

Reynolds number, \( {R.}_{e} \), for the pole

Using the calculated values above, we can calculate \( v({mit}_{G}) \) unter Verwendung von Gleichung (9):

\( v({mit}_{G}) = (2{q}_{p}({mit}_{G})/r)^{0.5} = (2(1129.89)/(1.226))^{0.5} \)
\( v({mit}_{G}) = 42.93 m/s\)

Deshalb, the Reynolds number \( R_{e} \) for the pole, unter Verwendung von Gleichung (10) ist:

\( {R.}_{e} = v({mit}_{G})d/ ν = (42.93)(1.0)/(0.000015) \)
\( {R.}_{e} = 2862000 \)

Force coefficient, \( {c}_{f0} \), without free-end flow

The pole material we used is cast-iron which has equivalent surface roughness \( k \) gleich 0.2 basierend auf Tabelle 7.13 oder und 1991-1-4.

Zahl 8. Tabelle 7.13 oder und 1991-1-4 for Equivalent roughness \( k \).

The force coefficient \( {c}_{f0} \) can be determined using the formula from Figure 7.28 of of EN 1991-1-4 mit \( k/d = 0.2\):

\( {c}_{f0}= 1.2 + {0.18log(10 k/d)}/{1 + 0.4log({R.}_{e}/{10}^{6}} = 1.2 + {0.18log(10 (0.2)}/{1 + 0.4log((2862000)/{10}^{6}}\)
\( {c}_{f0} = 1.246 \)

Effective Slenderness, \( λ \)

The effective slenderness, \( λ \), for the pole can be determined from No.4 Table 7.16 oder und 1991-1-4.

\( λ = max(0.7 {mit}_{G}/d, 70) \) zum \( {mit}_{G} \) > 50m
\( λ = max({mit}_{G}/d, 70) \) zum \( {mit}_{G} \) < 15m

Zahl 9. Tabelle 7.16 oder und 1991-1-4 for calculating Effective Slenderness \( λ \).

Schon seit \( {mit}_{G} \) is equal to 38.0m, we need to interpolate the values of \( λ \) for 50m and 15m:

\( {mit}_{G} = 38\)
\( {λ}_{50m} = max(0.7 (38), 70) = 70 \)
\( {λ}_{15m} = max((38), 70) = 70 \)

Deshalb:

\( λ = 70 \)

End-effect Factor, \( {ψ}_{λ} \)

The end-effect factor, \( {ψ}_{λ} \), can be obtained using Figure 7.36 oder und 1991-1-4 requiring the solidity ratio \( Phi \) and effective slenderness \( λ \). We will assume solidity ratio \( Phi \) gleich 1.0 since the pipe column does not have any perforation.

Zahl 10. The corresponding end-effect factor \( {ψ}_{λ} \) for the pole supporting the signboard based on Figure 7.36 oder und 1991-1-4.

Aus der Abbildung 10, we can deduce that the end-effect factor \( {ψ}_{λ} \) for the pole is equal to 0.910.

 

From the calculated parameters above,we can already calculate the Wind Force, \( {F.}_{w,Pole} \):

\({c}_{f} = {c}_{f,0}{ψ}_{λ} = (1.246)(0.910) = 1.134\)

\({F.}_{w,Pole} = {c}_{s}{c}_{d}{c}_{f}{q}_{p}({mit}_{e}){EIN}_{ref,Pole} = (1.0)(1.134)(1129.89)(38.0×1.0) \)
\({F.}_{w,Pole} = 48689.22 N. \)

Zahl 11. The wind forces acting on the signboard and pole.

Zahl 12. The wind forces acting on the signboard and pole for eccentric case.

SkyCiv Lastgenerator

Verwenden des SkyCiv-Lastgenerators, you can get wind loads for signboards and poles with just a few clicks and inputs. Wenn Sie die Standalone-Version kaufen oder sich für ein Professional-Konto anmelden, you will be able to generate the detailed wind report for your signboard project!

You can check the detailed wind load report for the signboard thru these links:

Patrick Aylsworth Garcia Bauingenieur, Produktentwicklung
Patrick Aylsworth Garcia
Statiker, Produktentwicklung
MS Bauingenieurwesen
LinkedIn

Verweise:

  • Im, B.. (2005). Eurocode 1: Aktionen auf Strukturen - Teil 1–4: Allgemeine Aktionen - Windaktionen.
  • BSI. (2005). BS EN 1991-1-4: 2005+ A1: 2010: Eurocode 1. Aktionen an Strukturen. Allgemeine Aktionen. Windaktionen.

 

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