Signboards, with their captivating visuals and strategic placements, are very popular elements for advertisement in our towns, streets, and highways. However, the structural stability of signboards hinges on their ability to withstand the dynamic forces of wind. This requires a detailed wind load analysis from the design engineer.

Billboard advertising, despite facing competition from digital alternatives, remains a significant player in the marketing landscape. To understand its economic impact, global billboard advertising spending reached $36.8 billion in 2022, with predictions of a steady rise to $44.2 billion by 2027. The United States accounts for the largest share (around 40%), followed by China and Europe.

**Wind Loads** **on Signboards**

Wind force is the most critical action on billboards. Their cantilevered design, supported by a single column, exposes them to wind-induced stresses. Failure due to wind and hurricanes has been reported, necessitating rigorous analysis and design. Other effects, such as imperfections and the p-delta phenomenon, also impact structural performance under wind load. Wind exerts pressure on objects, generating a force proportional to the wind speed squared. This force, known as wind load, varies with factors like:

**Location:**Geographic location determines wind speeds within established design wind speed maps.**Terrain:**Topography influences wind turbulence and local wind speeds.**Exposure category:**Building codes categorize zones based on surrounding obstructions, impacting wind pressures.**Signboard geometry:**Size, shape, and orientation of the signboard directly influence the wind load experienced.

**Methods and Tools** **for Wind Load Analysis**

Several methods are employed for wind load analysis of signboards:

**Simplified methods:**Building codes often provide simplified equations based on specific geometries and exposure categories. However, these methods may not always be suitable for complex designs.**Wind tunnel testing:**Physical scale models of the signboard are subjected to simulated wind conditions in a wind tunnel, providing accurate pressure data. This method is expensive but precise, especially for unique designs.**Computational Fluid Dynamics (CFD) simulations:**Numerical simulations model wind flow around the signboard using specialized software. This is a cost-effective alternative to wind tunnel testing, offering valuable insights into complex geometries.

**Dynamic Considerations**

While static wind loads are vital, signboards may experience dynamic effects like flutter and vortex shedding, resulting in vibrations and potential fatigue failure. Advanced analysis methods or wind tunnel testing may be necessary to assess these dynamic effects, especially for tall and slender signboards.

**Wind Load Analysis Example**

Let us carry out a wind load analysis on an 8m high signboard in a city centre where the basic wind speed is 35 m/s. The calculated effective wind pressure w_{eff}, total wind force F_{W}, and total wind overturning moment M_{W} correspond to the total wind action effects and they are appropriate for global verifications of the element according to the force coefficient method.

For local verifications, appropriate wind pressure on local surfaces must be estimated according to the relevant external pressure coefficients, as specified in EN1991-1-4 §5.2. The calculated wind action effects are characteristic values (unfactored). Appropriate load factors should be applied to the relevant design situation. For ULS verifications the partial load factor *γ*_{Q} = 1.50 is applicable for variable actions.

**Input Data**

- Terrain category: = II
- Basic wind velocity:
*v*= 35 m/s_{b} - Width of the signboard wind-loaded area:
*b*= 10 m - Height of the signboard wind-loaded area:
*h*= 3 m - Separation height of the signboard wind-loaded area from the ground:
*z*= 5 m_{g} - Orography factor at reference height
*z*_{e}:*c*= 1_{0}(z_{e}) - Structural factor:
*c*= 1_{s}c_{d} - Air density:
*ρ*= 1.25 kg/m^{3} - Additional rules defined in the National Annex for the calculation of peak velocity pressure
*q*_{p}(*z*_{e}): = None - The horizontal eccentricity of the centre of pressure from the centre of the signboard as a fraction of the width
*b*:*e/b*= 0.25

**Calculation of peak velocity pressure**

**Reference area and height**

The reference height for the wind action *z*_{e} is located at the centre of the signboard, as specified in EN1991-1-4 §7.4.3(3). The reference area for the wind action A_{ref }is the wind-loaded area of the signboard, as specified in *EN1991-1-4 §7.4.3(3)*. Therefore:

*z*_{e} = *z*_{g} + *h* / 2 = 5.000 m + 3.000 m / 2 = 6.500 m*A*_{ref} = *b* ⋅ *h* = 10.000 m ⋅ 3.000 m = 30.00 m^{2}

**Basic wind velocity**

The basic wind velocity *v*_{b} is defined in *EN1991-1-4 §4.2(2)P* as a function of the wind direction and time of year at 10 m above ground of terrain category II. The value of *v*_{b} includes the effects of the directional factor c_{dir} and the seasonal factor cseason and it is provided in the National Annex. In the following calculations, the basic wind velocity is considered as *v*_{b} = 35.00 m/s.

**Terrain roughness**

The roughness length *z*_{0} and the minimum height *z*_{min} are specified in *EN1991-1-4 Table 4.1* as a function of the terrain category. For terrain category II the corresponding values are *z*_{0} = 0.050 m and *z*_{min} = 2.0 m. The terrain factor *k*_{r} depending on the roughness length *z*_{0} = 0.050 m is calculated in accordance with *EN1991-1-4 equation (4.5)*:

*k*_{r} = 0.19 ⋅ (*z*_{0} / *z*_{0,II})^{0.07} = 0.19 ⋅ (0.050 m / 0.050 m)^{0.07} = 0.1900

The roughness factor *c*_{r}(*z*_{e}) at the reference height *z*_{e} accounts for the variability of the mean wind velocity at the site. It is calculated in accordance with *EN1991-1-4 equation 4.4*. For the examined case *z*_{e} ≥ *z*_{min}:

*c*_{r}(*z*_{e}) = *k*_{r} ⋅ ln(max{*z*_{e}, *z*_{min}} / *z*_{0}) = 0.1900 ⋅ ln(max{6.500 m, 2.0 m} / 0.050 m) = 0.9248

**Orography factor**

Where orography (e.g. hills, cliffs etc.) is significant its effect on the wind velocities should be taken into account using an orography factor c0(ze) different than 1.0, as specified in EN1994-1-1 §4.3.3. The recommended procedure in EN1994-1-1 §4.3.3 for the calculation of the orography factor *c*_{0}(*z*_{e}) is described in *EN1994-1-1 §A.3*.

In the following calculations, the orography factor is considered as *c*_{0}(*z*_{e}) = 1.000.

**Mean wind velocity**

The mean wind velocity *v*_{m}(*z*_{e}) at reference height *z*_{e} depends on the terrain roughness, terrain orography and the basic wind velocity *v*_{b}. It is determined using *EN1991-1-4 equation (4.3)*:

*v*_{m}(*z*_{e}) = *c*_{r}(*z*_{e}) ⋅ *c*_{0}(*z*_{e}) ⋅ *v*_{b} = 0.9248 ⋅ 1.000 ⋅ 35.00 m/s = 32.37 m/s

**Wind turbulence**

The turbulence intensity *I*_{v}(*z*_{e}) at reference height *z*_{e} is defined as the standard deviation of the turbulence divided by the mean wind velocity. It is calculated in accordance with *EN1991-1-4 equation 4.7*. For the examined case *z*_{e} ≥ *z*_{min}.

*I*_{v}(*z*_{e}) = *k*_{I} / [ *c*_{0}(*z*_{e}) ⋅ ln(max{*z*_{e}, *z*_{min}} / *z*_{0}) ] = 1.000 / [ 1.000 ⋅ ln(max{6.500 m, 2.0 m} / 0.050 m) ] = 0.2054

**Basic velocity pressure**

The basic velocity pressure *q*_{b} is the pressure corresponding to the wind momentum determined at the basic wind velocity *v*_{b}. The basic velocity pressure is calculated according to the fundamental relation specified in *EN1991-14 §4.5(1)*:

*q*_{b} = (1/2) ⋅ *ρ* ⋅ *v*_{b}^{2} = (1/2) ⋅ 1.25 kg/m^{3} ⋅ (35.00 m/s)^{2} = 766 N/m^{2} = 0.766 kN/m^{2}

where *ρ* is the density of the air in accordance with *EN1991-1-4 §4.5(1)*. In this calculation the following value is considered: *ρ* = 1.25 kg/m^{3}. Note that by definition 1 N = 1 kg⋅m/s^{2}.

**Peak velocity pressure**

The peak velocity pressure *q*_{p}(*z*_{e}) at reference height *z*_{e} includes mean and short-term velocity fluctuations. It is determined according to *EN1991-1-4 equation 4.8*:

*q*_{p}(*z*_{e}) = (1 + 7⋅*I*_{v}(*z*_{e})) ⋅ (1/2) ⋅ *ρ* ⋅ *v*_{m}(*z*_{e})^{2} = (1 + 7⋅0.2054) ⋅ (1/2) ⋅ 1.25 kg/m^{3} ⋅ (32.37 m/s)^{2} = 1597 N/m^{2}

⇒ *q*_{p}(*z*_{e}) = 1.597 kN/m^{2}

Note that by definition 1 N = 1 kg⋅m/s^{2}.

**Calculation of wind forces on the structure**

**Structural factor**

The structural factor *c*_{s}*c*_{d} is determined in accordance with *EN1991-1-4 Section 6*. A value of *c*_{s}*c*_{d} = 1.0 is generally conservative for small structures not susceptible to wind turbulence effects. In the following calculations, the structural factor is considered as *c*_{s}*c*_{d} = 1.000.

**Force coefficient**

The force coefficient *c*_{f} is given in *EN1991-1-4 Sections 7 and 8* depending on the type of structure or structural element. According to *EN1991-1-4 §7.4.3*, for signboards with *z*_{g} ≥ *h* / 4 or *b* / *h* ≤ 1, the force coefficient is *c*_{f} = 1.800.

**Total wind force**

The wind force on the structure *F*_{w} for the overall wind effect is estimated according to the force coefficient method as specified in *EN1991-1-4 §5.3*.

*F*_{w} = *c*_{s}*c*_{d} ⋅ *c*_{f} ⋅ *q*_{p}(*z*_{e}) ⋅ *A*_{ref} = 1.000 ⋅ 1.800 ⋅ 1.597 kN/m^{2} ⋅ 30.00 m^{2} = 86.216 kN

The total wind force *F*_{w} takes into account the overall wind effect. The corresponding effective wind pressure *w*_{eff} on the reference wind area *A*_{ref} is equal to:

*w*_{eff} = *F*_{w} / *A*_{ref} = 86.216 kN / 30.00 m^{2} = 2.874 kN/m^{2}

This effective pressure *w*_{eff} = 2.874 kN/m^{2} is appropriate for global verifications of the structure according to the force coefficient method. It is not appropriate for local verifications of structural elements. For the latter case appropriate wind pressure on local surfaces must be estimated according to the relevant pressure coefficients, as specified in *EN1991-1-4 §5.2*.

**Overturning moment**

According to *EN1991-1-4 §7.4.3* the resultant force normal to the signboard should be taken to act at the height of the center of the signboard. The total overturning moment *M*_{w} acting at the base of the structure is equal to:

*M*_{w} = *F*_{w} ⋅ (*z*_{g} + *h* / 2) = 86.216 kN ⋅ (5.000 m + 3.000 m / 2) = 560.40 kNm

The overturning moment corresponds to the wind action total effect, i.e. it is the total overturning moment for all the base supports.

**Horizontal eccentricity**

According to *EN1991-1-4 §7.4.3* and the National Annex, the resultant force normal to the signboard should be taken to act with a horizontal eccentricity *e*. In this calculation, the following normalized eccentricity is considered *e/b *= ±0.250, where b is the width of the signboard wind-loaded area. The total torsional moment *T*_{w} acting at the base of the structure is equal to:

*T*_{w} = ±0.250 ⋅ *b* ⋅ *F*_{w} = ±0.250 ⋅ 10.000 m ⋅ 86.216 kN = 215.54 kNm

The torsional moment corresponds to the wind action total effect, i.e. it is the total torsional moment for all the base supports.

**Conclusion**

Wind load analysis is a crucial step in ensuring the safety and durability of signboards. By understanding wind forces, employing appropriate analysis methods, and considering structural design principles, engineers can guarantee structurally sound signboards that stand the test of time.