Figure 1: Wind load factors (pressure and area)
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 × Cd × Kz × G|
Kz = exposure coefficient
G = gust response factor
The (Kz) 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 (Kz ≈ 0). A 100’ tall object would have a Kz of around 1, while One World Trade Center at 1,776’ would have a Kz 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.
- 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.