Article authored by Paulo H. Naves Silva, Cesar Rother, Marília Guimarães Silva, and Emily Carriero.

Abstract

The structural analysis of slender assets, such as towers, chimneys, wind turbines, and suspension bridges, which have a significantly greater height than width, presents a technical challenge requiring the consideration of various factors, with wind action being a critical one.

Wind-induced loads significantly influence internal stresses and overall stability, making knowledge and application of the latest standards essential for a more accurate structural assessment. The Brazilian Standard NBR 6123, 2nd Edition, “Wind Forces on Buildings,” establishes guidelines for accounting for static and dynamic wind forces, considering factors such as geographical location, topography, surface roughness, and specific structural characteristics.

The standard underwent a significant update in December 2023, introducing improvements over the 1988 edition. While the isopleth map was not updated due to a lack of consensus within the responsible Study Committee, adjustments to velocity correction factors were made based on recent climatic data, enhancing calculation accuracy. Additionally, the update introduced specific regulations for addressing vortex shedding vibrations in slender and flexible structures.

This technical bulletin highlights the main updates to the NBR 6123 standard and its application in the fitness-for-service assessment of slender structures with quasi-static behavior. A case study of a tower is presented to quantify the influence of wind under different scenarios.

1. Introduction

Wind pressures and forces are calculated based on meteorological and aerodynamic parameters. The characteristic wind speed depends on meteorological parameters and can be expressed by the equation:

Where:

• V0 V_0 V0​: Basic wind speed
• S1 S_1 S1​: Topographic factor
• S2 S_2 S2​: Surface roughness and building dimension factor
• S3 S_3 S3​: Statistical factor

The basic wind speed varies by region in Brazil and can be obtained from the isopleth map of wind speeds shown in Figure 1, developed based on extreme wind speed data recorded at meteorological stations.

The correction factors (S1 S_1 S1​, S2 S_2 S2​, S3 S_3 S3​) vary depending on terrain topography, equipment dimensions, application, and the risk associated with structural damage, as defined by tables and equations in the standard. For instance, a deep valley typically experiences lower wind incidence than flat terrain. Wind speed also tends to increase with height above ground, so tall equipment is evaluated based on elevation ranges.

Additionally, structures housing toxic substances or those critical for emergency response, such as hospitals or fire stations, have higher correction factors compared to temporary structures or those not intended for human occupancy.

Once the characteristic wind speed is calculated, the dynamic pressure can be determined using the equation:

The wind force on the structure depends on aerodynamic parameters and can be calculated using the expression:

Where:

• C C C: Aerodynamic coefficient
• A A A: Reference area
• Fv F_v Fv​: Neighborhood factor

Wind exhibits fluctuations around the mean speed, which can induce significant oscillations in flexible structures, particularly in tall and slender buildings. The standard specifies that if a structure has a fundamental natural frequency f0<1 f_0 < 1 f0​<1 Hz, the dynamic effects due to atmospheric turbulence must be considered.

Another phenomenon, particularly relevant in structures with long sections of constant cross-section, is “vortex shedding.” In this case, fluctuating forces acting perpendicular to the wind direction are caused by the alternating release of vortices from either side of the structure. If the vortex shedding frequency is close to the structure’s natural frequency, these alternating forces can cause large-amplitude vibrations, leading to fatigue damage.

The standard mandates that vortex shedding effects be investigated for structures with a slenderness ratio greater than six (λ>6 \lambda > 6 λ>6). The critical wind speed is expressed as:

Where:

• L L L: Characteristic cross-sectional dimension
• St St St: Strouhal number

Dynamic effects due to vortex shedding can be neglected if:

2. Case Study

A fictional case study was developed to explore the impact of wind on a tall steel tower with a uniform cross-section. The main dimensions and properties are listed below:

• Material: Steel
• Tower diameter: 2.8 m
• Height: 45 m
• Design temperature: 200 °C
• Allowable stress: 108 MPa

A linear elastic analysis was performed using the Finite Element Analysis (FEA) method in ANSYS 2023 R1. Figure 2 illustrates the simplified tower model, including caps, shell, and skirt.

Figure 2 – Simplified tower model

According to the isopleth map, wind intensity varies significantly across Brazil. If the tower is installed in a southern city with a basic wind speed V0=45 m/s V_0 = 45 \, \text{m/s} V0​=45m/s, the dynamic pressure on the shell is 50% higher than in a northeastern region with V0=30 m/s V_0 = 30 \, \text{m/s} V0​=30m/s.

For the selected thicknesses, the tower exhibits a stress of approximately 60 MPa in the skirt region under a wind speed of 35 m/s, as shown in Figure 3. However, under a wind speed of 45 m/s, the stress increases to 120 MPa, as shown in Figure 4, exceeding the allowable stress of 108 MPa for this material.

Figure 4 – Stress in the tower under 45 m/s wind

The stress analysis revealed significant differences simply by relocating the tower geographically within Brazil, potentially impacting thickness design, reinforcements, and the remaining life of the asset subject to corrosion.

A modal analysis identified a fundamental natural frequency of 4.65 Hz in the first mode, as shown in Figure 5. Consequently, both dynamic effects due to atmospheric turbulence and vortex shedding were deemed negligible.

In real structures, various other loads act on the tower and must be evaluated, along with other damage mechanisms such as fatigue, buckling, and progressive plastic deformation.

3. Conclusion

The Brazilian Standard NBR 6123, 2nd Edition, “Wind Forces on Buildings,” establishes guidelines for considering static and dynamic wind forces, factoring in geographical location, topography, surface roughness, and specific structural characteristics.

Accounting for wind effects is crucial in both the design and construction of tall, slender towers and the fitness-for-service assessment of assets. Neglecting this aspect can jeopardize not only structural safety but also the protection of all stakeholders involved.

Advanced techniques, such as the Finite Element Method, assist in determining the forces acting on the structure and verifying protection against various failure mechanisms outlined in other specific standards.

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