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  2. 载入中
  3. 标志的风荷载计算 – 在 1991

标志的风荷载计算 – 在 1991

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

在这篇文章中, we will be discussing how to calculate the wind loads on signboards using EN 1991-1-4 located in Oxfordshire, 英国. Our references will be the EN 1991-1-4 对结构的行动 (风荷载) and BS EN 1991-1-4 National Annex. We will be using similar data in 在 1991-1-4 风荷载计算实例.

请注意,基本风速值是从最近的风等值线内插的. 试试我们的 Signboard Wind Load Calculator:

结构数据

在这个例子中, we will use the data below. We will consider only wind source direction equal to 240°. 此外, 的 ground elevation of the site is 57.35m.

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

位置 Oxfordshire, 英国
占用 各种各样的 – 招牌
地形 平坦的农田
Sign Horizontal Dimension, b 12.0 米
Sign Horizontal Vertical, H
12.0 米
Ground to top of signboard, H
50.0米
Ground to signboard centroid, 与Ë
44.0 米
Reference area of signboard A标志
144.0 平方米.
Pole diameter, d
1.0 米
Pole surface type
Cast iron
Ground to top of pole, 与G
38.0 米
Reference area of pole Apole
38.0 米

 

数字 1. 地点坐标 (从Google地图).

 

数字 2. Signboard dimensions.

确定设计风压的公式为:

对于基本风速:

\({v}_{b} = {C}_{给你} {C}_{季节} {C}_{alt} {v}_{b,map}\) (1)

在哪里:

\({v}_{b}\) = 以 m/s 为单位的基本风速
\({C}_{给你}\) = directional factor
\({C}_{季节}\)= 季节性因素
\({C}_{alt}\)= altitude factor where:

\({C}_{alt} = 1 + 0.001一个 \) 对于 \( z ≤ 10 \) (2)
\({C}_{alt} = 1 + 0.001一个 ({10/与}^{0.2}) \) 对于 \( 与 > 10 \) (3)

\({v}_{b,map}\) = fundamental value of the basic wind velocity given in Figure NA.1 of BS EN 1991-1-4 National Annex
\( 一个 \) = altitude of the site in metres above mean sea level

对于基本速度压力:

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

在哪里:

\({q}_{b}\) =设计风压Pa
\({⍴}_{空气}\) = density of air (1.226公斤/立方米)
\({v}_{b}\)= 以 m/s 为单位的基本风速

对于峰值压力:

\({q}_{p}(与) = 0.5 {C}_{Ë}(与){q}_{b} \) for site in Country terrain (5)
\({q}_{p}(与) = 0.5 {C}_{Ë}(与){C}_{Ë,Ť}{q}_{b} \) for site in Town terrain (6)

在哪里:
\({C}_{Ë}(与)\) 雪地装载
\({C}_{Ë,Ť} \) = exposure correction factor for Town terrain

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

\({F}_{w} = {C}_{s}{C}_{d}{C}_{F}{q}_{p}({与}_{Ë}){一个}_{ref} \) (7)

在哪里:
\( {C}_{s} {C}_{d} \) = structural factor
\({C}_{F} \) = force coefficient of the structure
\({q}_{p}({与}_{Ë}) \) = peak velocity pressure at reference height \({与}_{Ë} \)
\({一个}_{ref} = b h\) = reference area of the structure

地形类别

Based on BS EN 1991-1-4 National Annex, the Terrain Categories in EN 1991-1-14 were aggregated into 3 类别: 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, \({C}_{给你}\) & \({C}_{季节}\)

为了计算方程 (1), we need to determine the directional and season factors, \({C}_{给你}\) & \({C}_{季节}\). 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, \({C}_{给你}\), 等于 1.0.

另一方面, we want to consider a conservative case for the season factor, \({C}_{季节}\), which we will 设置 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 \( 一个 \) equal to 57.35m. 因此:

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

基本风速和压力, \({v}_{b}\) & \({q}_{b}\)

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.

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

对于我们的站点位置, Oxfordshire, 英国, 计算的 \( {v}_{b,map} \) 等于 22.7 小姐.

\( {v}_{b} = {C}_{给你} {C}_{季节} {C}_{alt} {v}_{b,map} = (1.0)(1.0)(1.05735)(22.7) \)
\( {v}_{b} = 24.0 小姐 \)

We can calculate the basic wind pressure, \( {q}_{b,0} \), 使用方程 (4):

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

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Orography Factor \({C}_{的}(与)\)

对于这种结构, the terrain is relatively flat for the wind coming from 240°, 的

altitude factor, \({C}_{alt}\), we will only use Equation (2) for a more conservative approach using site elevation \( 一个 \) equal to 57.35m. 因此:

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

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

\({q}_{p}(与) = {C}_{Ë}(与){C}_{Ë,Ť}{q}_{b} \)

在哪里:
\({C}_{Ë}(与)\) = exposure factor based on Figure NA.7 of BS EN 1991-1-4 National Annex
\({C}_{Ë,Ť} \) = exposure correction factor for Town terrain based on Figure NA.8 of BS EN 1991-1-4 National Annex

To determine the exposure factor, \({C}_{Ë}(与)\) , for the signboard, 我们需要计算 \(与 – {H}_{dis}\) and the distance upwind to shoreline in km. For simplicity, we will set the the displacement height, \({H}_{dis}\), 至 0. 为了 \(与 \) 价值观, we will consider it on \(z = 38.0\) 和 \(z = 44.0\). 此外, the distance upwind to shoreline is more than 100km. 因此, using Figure NA.7 of BS EN 1991-1-4 National Annex:

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

因此:

\({C}_{Ë}(38.0) = 3.2\)
\({C}_{Ë}(44.0) = 3.3\)

另一方面, the exposure correction factor \( {C}_{Ë,Ť} \) 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 \( {C}_{Ë,Ť} \):

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

因此:

\({C}_{Ë,Ť}(38.0) = 1.0\)
\({C}_{Ë,Ť}(44.0) = 1.0\)

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

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

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 可以假设为 6 或AND 1991-1-4.

Force Coefficient, \( {C}_{F}\), for signboard

For signboards, the force coefficient, \({C}_{F}\), 等于 1.8 可以假设为 7.4.3 或AND 1991-1-4.

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

The force acting on the signboard can be calculated using Equation (7) 可以假设为 5.3(2) 或AND 1991-1-4.

\({F}_{w,signboard} = {C}_{s}{C}_{d}{C}_{F}{q}_{p}({与}_{Ë}){一个}_{ref,signboard} = (1.0)(1.8)(1165.20出色地)(12.0米)(12.0米)\)
\({F}_{w,signboard} = 302019.84 N\)

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). 我们将插入已知值, 我们将插入已知值. 我们将插入已知值, 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

相似地, the force acting on the pole can be calculated using Equation (7) 可以假设为 5.3(2) 或AND 1991-1-4.

\({F}_{w,pole} = {C}_{s}{C}_{d}{C}_{F}{q}_{p}({与}_{G}){一个}_{ref,pole}\) (8)

在哪里:

\({C}_{F} = {C}_{F,0}{ψ}_{λ} \)
\({一个}_{ref,pole} = {与}_{G}d \)

注意:
\(ψ_{λ} \) is calculated based on effective slenderness, \( λ \), using using Figure 7.36 的部分 7.13 或AND 1991-1-4
\({C}_{F,0}\) is calculated based on Reynolds number \( R_{Ë} \) = 考虑到高于当地地形高度时加速减少的因素 7.28 或AND 1991-1-4
在哪里:
\( {与}_{G} \) 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
\( v({与}_{G}) = (2{q}_{p}({与}_{G})/ρ)^{0.5} \) (9)
\( {[R}_{Ë} = v(z_{G})d/ ν \) (10)

We will dive deep into these parameters on the next sections

Reynolds number, \( {[R}_{Ë} \), for the pole

Using the calculated values above, we can calculate \( v({与}_{G}) \) 使用方程式 (9):

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

因此, the Reynolds number \( R_{Ë} \) for the pole, 使用方程式 (10) 是:

\( {[R}_{Ë} = v({与}_{G})d/ ν = (42.93)(1.0)/(0.000015) \)
\( {[R}_{Ë} = 2862000 \)

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

The pole material we used is cast-iron which has equivalent surface roughness \( ķ \) 我们将插入已知值 0.2 基于表 7.13 或AND 1991-1-4.

数字 8. 桌子 7.13 或AND 1991-1-4 for Equivalent roughness \( ķ \).

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

\( {C}_{f0}= 1.2 + {0.18日志(10 千/天)}/{1 + 0.4日志({[R}_{Ë}/{10}^{6}} = 1.2 + {0.18日志(10 (0.2)}/{1 + 0.4日志((2862000)/{10}^{6}}\)
\( {C}_{f0} = 1.246 \)

有效的纤细度, \( λ \)

有效的细长, \( λ \), for the pole can be determined from No.4 Table 7.16 或AND 1991-1-4.

\( λ = max(0.7 {与}_{G}/d, 70) \) 对于 \( {与}_{G} \) > 50米
\( λ = max({与}_{G}/d, 70) \) 对于 \( {与}_{G} \) < 15米

数字 9. 桌子 7.16 或AND 1991-1-4 for calculating Effective Slenderness \( λ \).

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

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

因此:

\( λ = 70 \)

End-effect Factor, \( {ψ}_{λ} \)

The end-effect factor, \( {ψ}_{λ} \), can be obtained using Figure 7.36 或AND 1991-1-4 requiring the solidity ratio \( 披 \) and effective slenderness \( λ \). We will assume solidity ratio \( 披 \) 我们将插入已知值 1.0 since the pipe column does not have any perforation.

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

从图 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, \( {F}_{w,pole} \):

\({C}_{F} = {C}_{F,0}{ψ}_{λ} = (1.246)(0.910) = 1.134\)

\({F}_{w,pole} = {C}_{s}{C}_{d}{C}_{F}{q}_{p}({与}_{Ë}){一个}_{ref,pole} = (1.0)(1.134)(1129.89)(38.0×1.0) \)
\({F}_{w,pole} = 48689.22 ñ \)

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

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

SkyCiv负载生成器

使用 SkyCiv 负载生成器, you can get wind loads for signboards and poles with just a few clicks and inputs. 使用 SkyCiv 负载生成器, 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 结构工程师, 产品开发
帕特里克·艾尔斯沃斯·加西亚
结构工程师, 产品开发
土木工程硕士
领英

参考资料:

  • 在, 乙. (2005). 欧洲规范 1: 对结构的操作 - 第 1-4 部分: 一般作用——风作用.
  • BSI. (2005). BS EN 1991-1-4: 2005+ A1: 2010: 欧洲规范 1. Actions on structures. General actions. 风动作.

 

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