## Part 1 of our Wind Load Series

“Wind load” is a calculated value representing the total force on a structure or object cause by pressure from wind moving over it. In this blog series, we will discuss different methods for wind load calculations, the factors that influence its magnitude, and the effects a high wind load can have on a structure. Wind load is most commonly addressed by civil and structural engineers when designing buildings, but mechanical engineers can encounter the effect when designing tall objects like cranes, telescoping communications masts or wind turbine towers.

## Wind Load Essentials

As a force, wind load is the product of pressure distributed over an area (psf times ft^{2} or Pa times m^{2}). In this case, the pressure is the “velocity pressure”, governed primarily by wind speed. As one might imagine, higher wind speed means higher velocity pressure. The area in the equation does not represent the surface area of the object, but instead the projected area of the object on a plane normal to the wind direction (see Figure 1). Imagine a light source at the location where the wind originates, and the shadow cast behind the object is the projected area. Further modifying these factors is the “drag coefficient”, which represents the shape of the object. This differentiates shapes that might have the same profile. For instance, a tall flat plate, a cylindrical pole, and a streamlined airfoil-like body might have the same projected area from a certain wind direction, but their drag coefficients are 2, 0.6 and 0.04, respectively. The plate is very non-aerodynamic and the force against it is high, while the streamlined body feels a significantly smaller force.

Together, these three values make up the simplest equation for wind load, shown in Equation 1.

F = P × A × C_{d} |
(1) |

Where:

F = wind load (in N or lbf)

P = wind pressure (in Pa or psf)

A = projected area (in m^{2} or ft^{2})

C_{d} = drag coefficient (unitless)

## Factors Affecting Wind Load

So, how accurate is Equation 1? Since it uses only the most basic values in calculating the wind load, it can provide an estimate on the magnitude of the wind force. However, for more accurate representations of the wind load, one can multiply the force by a number of other coefficients that more accurately account for the conditions a structure will experience. The first step up in accuracy comes from including an “exposure coefficient” and “gust response factor”, shown in Equation 2.

F = P × A × C_{d }_{× }K_{z }× G |
(2) |

Where:

K_{z} = exposure coefficient

G = gust response factor

The (K_{z}) represents the increase in air velocity as height above ground level increases. A low object with most of its area within the boundary layer will experience a low force (K_{z} ≈ 0). A 100’ tall object would have a K_{z} of around 1, while One World Trade Center at 1,776’ would have a K_{z} of over 2.5.

Gust response factor (G) reflects the consistency of air velocity over the height of an object. Higher off the ground, wind velocity tends to stay more consistent, and G ≈ 1. Closer to the ground, with boundary effects and turbulence from surrounding trees and buildings, and wind speed can be more irregular. G increases to 2 as the height of the object drops closer to 0.

The International Building Code (previously the Uniform Building Code), uses the above factors, as well as replacing the simple drag coefficient with a tabulated “net pressure coefficient”. This coefficient more accurately accounts for the slopes, eaves, and other additions that affect airflow around a building. However, this IBC equation is only designed for use on buildings that are less than 75’ tall. The Telecommunications Industry Association offers its own version in TIA-222-G, modifying the equation with topographic and exposure factors, based on the tower’s installation environment. Again, this version has its limits, as it is designed specifically to work for towers and antennae. The progenitor for all of these versions of the wind load equation is given in the American Society of Civil Engineer’s ASCE-7. This version has the most complex and detailed set of coefficients for modifying the wind pressure, projected area and drag coefficients. Nonetheless, regardless of how complicated the chosen wind load equation might be, it still only outputs a single force value.

## Limitations to Manual Wind Load Calculations

The calculations mentioned above can offer a very accurate simulation of the ultimate wind load on a structure, but they do not offer a complete picture. They cannot indicate where wind load might be concentrated on a complex structure, nor simulate the resulting stresses and deflection of the structure. For a more complete understanding of how a structure will react to high wind loads, an engineer can use computational fluid dynamics (CFD) and finite element analysis (FEA) programs to simulate the interaction of the wind and structure as a whole. The results are only as accurate as the computer model is precise, however, so there is a tradeoff between the accuracy necessary for analysis and the time available for modeling the structure and running the simulations.

## Using Wind Load Calculations and CFD Together

As is usually the case, the safest and most thorough method of analyzing a structure’s response to wind is to use both manual calculations and CFD. The results of these different methods should ultimately agree. If there are significant differences in the two outcomes, then one of the methods needs amendment or improvement. Over the next few blogs, we will compare the manual calculations and CFD results for simple structures, in order to find out how well the two correspond.

## Resources

- International Code Council. (2014).
*2015 International Building Code*. Country Club Hills, IL: ICC. - Telecommunications Industry Association. (2011).
*2012 TIA-222-G Structural Standard for Antenna Supporting Structures and Antennas*. Arlington, VA. - American Society of Civil Engineers. (2010).
*ASCE 7 Minimum Design Loads for Buildings and Other Structures*. Reston, Va.

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