Derivation of Wind Loads to Signage Structures | Worked Example

This article explores the considerations necessary for accurately calculating wind loads on signage structures, with a focus on the guidelines provided by the Eurocode.

Signage structures play a vital role in conveying information and advertising, often standing prominently in outdoor environments where they are exposed to various environmental forces. Among these forces, wind presents a significant challenge due to its dynamic and unpredictable nature. The impact of wind on signage structures can lead to potential hazards if not adequately addressed during the design phases. Thus, understanding how wind loads affect signage structures is fundamental to ensuring their stability, safety, and longevity.

This article explores the considerations necessary for accurately calculating wind loads on signage structures, with a focus on the guidelines provided by the Eurocode.

Derivation of Wind Loads to Eurocode

Given the variability and intensity of wind forces, it is essential for structural designers to be as precise as possible when assessing the potential wind loads that signage structures may encounter. Wind loads depend on several factors, including wind speed, terrain characteristics, and the height and shape of the structure. Improper calculation of these loads can lead to structural failures, posing risks to public safety.

The Eurocode stands as a fundamental reference in the European construction industry, providing standardized procedures for ensuring the safety and durability of structures under different environmental conditions. Specifically, EN 1991-1-4:2005 (Eurocode 1: Actions on structures – Part 1-4: General actions – Wind actions) outlines the principles and methods for calculating wind actions on buildings and other structures.  In a previous article (See: Derivation of Wind Load on Buildings) this subject was covered extensively within context of Eurocodes; however, references were only made to building structures. Thus, article explores the application in the context of signage structures, guiding readers through the process of deriving wind loads and highlighting the critical factors that influence these calculations. It is advised that the reader review’s the above-mentioned article at this point before proceeding with this.

Steps to Derive Wind Load on Signage Structures

1. Determine the Basic Wind Velocity

The first step in calculating wind load is to determine the basic wind velocity (v_b ​). This is derived from the fundamental wind speed (v_b,0​), which is provided for different regions in the National Annexes of the Eurocode. The basic wind velocity considers the effects of wind direction and seasonal variations, and is calculated using the following equation:

v_b=c_{alt}.c_{dir}.c_{season}\times v_{b,0}

Where:

• c_alt is the factor which accounts for the altitude of the structure above the mean sea level.
• c_dir is the directional factor, which accounts for the predominant wind direction in a specific region. This factor is usually 1.0 unless specified otherwise by local guidelines.
• c_season is the seasonal factor, which considers seasonal variations in wind speed. This factor is typically 1.0 unless specified otherwise.
• v_b,0 is the fundamental wind speed provided in the National Annexes.

2. Calculate the Mean Wind Velocity

Once the basic wind velocity is determined, the next step is to calculate the mean wind velocity (v_m(z) at a specific height z. The mean wind velocity is influenced by the roughness of the terrain and the presence of any significant topographical features. It is calculated using the equation:

v_m(z)= v_b.c_r(z). c_0

Where:

• c_r(z) is the roughness factor, which depends on the terrain category and height above ground level. Terrain categories range from open sea (category 0) to urban areas with dense buildings (category IV) See Clause () of BS EN 1991-1-4.
• c₀ is the orography factor, which accounts for the influence of topographical features such as hills and valleys.

3. Determine the Turbulence Intensity

Turbulence intensity (I_v(z) is a measure of the fluctuations in wind speed at a specific height. It is an important factor in determining the dynamic effects of wind on a structure. Turbulence intensity is calculated using the equation:

I_v(z)=\frac{k_I}{In (z/z_0)}

Where:

• k_I ​ is a terrain-dependent constant that varies based on the roughness of the terrain.
• z₀ ​ is the roughness length, which is a measure of the height at which the wind speed theoretically becomes zero.

4. Compute the Peak Velocity Pressure

The peak velocity pressure (q_p(z) at a specific height z represents the maximum pressure exerted by wind on a structure. It is a key parameter in determining the wind load. The peak velocity pressure is calculated using the equation:

q_p(z)=(1+7.I_v(z))\times 0.5\rho v_m^2(z)

Where:

• ρ is the air density, which is typically taken as 1.25 kg/m³.

The peak wind velocity v_e(z) considers both the mean wind velocity and the turbulence intensity, providing a comprehensive measure of the wind’s impact on the structure.

5. Apply the Force Coefficients

For signage structures, the force coefficients (c_f) need to be applied and this depends on the shape and orientation of the signage structure. The Eurocode provides detailed tables and guidelines for determining these coefficients for various shapes, such as rectangular, circular, or elliptical signs (See Clause of BS EN 1991-1-4). The force coefficient accounts for the aerodynamic effects of the sign’s shape and orientation, ensuring that the wind load calculation accurately reflects the actual forces exerted on the structure.

6. Calculate the Wind Load

Finally, the wind load (F_w) on the signage structure is calculated using the following equation:

F_w=c_f.q_p(z).A

Where:

• A is the projected area of the sign perpendicular to the wind direction.
• c_f ​ is the force coefficient determined in the previous step.

The wind load calculation combines the peak velocity pressure, the force coefficient, and the projected area to provide a comprehensive measure of the forces exerted by wind on the signage structure.

Worked Example

A billboard of size 8m wide and 4m high is required to be elevated 10m above the ground in a city centre (Figure 1). Assuming the fundamental wind speed of the location is 40m/s, and the force coefficient is 1.2. Determine the total wind force applied on the billboard and the unfactored over-turning moment arising from the load on the billboard stanchions. (Take site altitude = 100m above msl)

1. Calculate the basic wind velocity (v_b)

c_{alt} = 1+(0.001\times100)=1.1

c_{dir}=1.0

c_{season}=1.0

v_b=c_{alt}.c_{dir}.c_{season}\times v_{b,0}\\1.1\times1.0\times1.0\times40=44m/s

2. Calculate the mean wind velocity (v_m(z))

Since the billboard is located in a city center then a Category II terrain applied; therefore, c_r(z) = 1.0 and also there is no mention of the influence of orography, so c₀ = 1.0

v_m(z)= v_b.c_r(z). c_0\\27.5\times1.0\times1.0=44m/s

3. Calculate the turbulence intensity (I_v(z))

I_v(z)=\frac{k_I}{In (z/z_0)}

The roughness length z₀ and the minimum height z_min are specified in EN1991-1-4 Table 4.1 as a function of the terrain category. And for category II terrain the corresponding values are z₀ = 0.050 m. Assume k_I = 1.0)

I_v(z)=\frac{1.0}{In (10/0.05)}=0.215

4. Calculate the peak velocity pressure (q_p(z))

q_p(z)=(1+7.I_v(z))\times 0.5\rho v_m^2(z)

q_p(z)=(1+7\times0.215)\times 0.5\times1.25\times44^2\\ 3.0kN/m

5. Calculate the wind load F_w

F_w=c_f.q_p(z).A

A=8\times4=32m^2

c_f=1.2

F_w=1.2\times3.0\times32= 115.2kN

6. Determine overturning moment M

EN1991-1-4 §7.4.3 specifies that the resultant force acting perpendicular to the signboard must be applied at the center of the signboard’s height. Consequently, the total overturning moment M​ at the base of the structure equals:

M= F_w\times (z_g+h/2)\\115.2\times(10+4/2) =1382.4kN.m

To design the billboard, ensure the base can resist the factored value of this overturning moment.

Additional Considerations

Aside from the static wind calculation steps presented above, there are some additional considerations. The designer must sometimes consider with respect to the effect of wind on signage structures. These include:  

Dynamic Response of the Structure

In addition to the static wind load calculation, it is sometimes necessary to consider the dynamic response of the structure. Signage structures, especially those that are tall and slender, can experience dynamic effects due to wind-induced vibrations. The Eurocode provides guidelines for calculating the dynamic response of structures, which include the following considerations:

• Natural Frequency of the Structure: The natural frequency of the structure depends on its stiffness and mass distribution. Structures with lower natural frequencies are more susceptible to dynamic effects.
• Damping Ratio: The damping ratio represents the energy dissipation characteristics of the structure. Higher damping ratios result in lower dynamic amplification.
• Wind Spectrum: The wind spectrum represents the distribution of wind energy across different frequencies. The Eurocode provides guidelines for calculating the wind spectrum based on the terrain category and height above ground level.

Fatigue Analysis

Wind-induced vibrations can cause fatigue damage to the structure over time. Fatigue analysis involves calculating the cumulative damage due to repeated wind load cycles. The Eurocode provides guidelines for performing fatigue analysis, which include the following considerations:

• Stress Range: The stress range represents the difference between the maximum and minimum stress experienced during a wind load cycle.
• Number of Cycles: The number of cycles represents the total number of wind load cycles experienced over the design life.
• Material Properties: The material properties, such as the fatigue strength, depend on the type of material used in the structure.

Also See: Application of Notional Loads on Structures | EHF

Sources & Citations

• Burgess I (2010)-Concise Eurocodes: Loadings on Structures.
• BS EN 1991-1-4:2005. Eurocode 1: Actions on structures. Part 1-4: General actions – Wind actions. London, British Standards Institution, 2005.
• UK NA to BS EN 1991-1-4:2011. National Annex to Eurocode 1: Actions on structures. Part 1-4: General actions – Wind actions. London, British Standards Institution, 20011.