Welcome back to our blog series on the phenomenon called wind load and how it affects civil and mechanical engineers. Wind load is the force that blowing wind exerts on any device or structure that extends above ground level. After an initial introduction to the factors that affect wind load on an object, I compared three different sets of wind load calculation methods using three simple objects, hypothetically placed on a 100-foot-tall building. I started with a generic drag equation for the first equation, then added two modification coefficients called “gust factor” and “exposure coefficient” for the second equation. For the third equation, I used the model for rooftop objects explained in ASCE 7: Minimum Design Loads for Buildings and Other Structures. In general, the three different equations predicted the same relationship between the wind load on the objects. The cylinder should experience the lowest load, due to the smoother airflow path if offered for the wind around it. The square objects, with their sharper corners and larger areas for turbulence behind them, both should experience higher wind loads. The diagonal square should see the highest force, as it has the largest projected cross section (i.e. the two-dimensional shape of the object perpendicular to the direction of the wind).
The calculation results in the last blog entry showed some large discrepancies between the wind load results from the three different equations. This was especially prevalent for the square tower: the additional gust factor and exposure coefficient predicted a wind load 70% higher than the drag coefficient, and the ASCE 7 predicted a value 150% higher.
CFD Modeling Setup
Autodesk offers an advanced wind load simulation suite in their Robot™ Structural Analysis Professional program, but their standard CFD software is capable of the analysis as well. Autodesk anticipated this use, and created a guide dedicated to wind loading with Autodesk CFD. They recommend creating a large envelope around the object being simulated (see Figure 2a), to ensure enough space for the air pressure and velocity to equalize with the unaffected air outside the volume. Additionally, besides the expected wind velocity inlet and zero gauge pressure outlet boundary conditions, Autodesk recommends using the slip/symmetry on the upper and side surfaces of the envelope (see Figure 2b). The slip/symmetry condition forces the conditions of the fluid as it approaches that surface to match what would be happening on the other side of the surface. This again ensures that the airflow near the edges of the envelope is equivalent to the unimpeded airflow outside the envelope.
Wind Load Modeling Results
The wind loads simulated by our CFD program are shown in orange in Figure 3. For all three objects, the CFD results are closest to the generic drag calculation. This does not mean that the two modified equations are inaccurate, however. Rather, they serve a different purpose than the drag calculation. The drag calculation is descriptive, as it simply provides the wind force an any object whether it be a building or a baseball or a biplane. The modified wind load equations are prescriptive design calculations, in that they don’t calculate the wind load a structure or device will experience on a day-to-day basis, but the wind load they should be designed to withstand without damage. The extensive sets of modifying coefficients that account for environmental conditions, the effects of different materials and finishes, local climate factors, and fluid effects specific to high-speed winds all serve as built-in safety factors. These safety factors ensure that any structure designed to those specifications will be safe under any conceivable wind load.
Figure 4 shows the static pressure on each of the three objects as they experience the 110 mph wind, which is coming from the bottom left side of each image. It’s easy to see the significantly increased force on the wind-facing sides of the objects. One should also note the air pressure of the atmosphere in front of the object (visible on the surface underneath the object) as it is compressed between the object in front and the wind piling up behind it. The square tower oriented 45° to the wind shows a larger region of high pressure than the other two objects. This is due to that tower’s larger surface area and is reflected in that object’s ultimate wind load as shown in figure 3. It’s also interesting to note the low pressure regions directly behind the forward surfaces of the objects. These show the turbulent regions where the airflow has detached from the surface of the object after its initial deflection. These objects also create a turbulent region of air behind them, which on can see in this post’s opening animated image.
Engineering for Safety
Many different civil and mechanical design factors have similar sets of design calculations and guidelines. Most of them also guide the engineer towards a result that might be considered over-engineered for day-to-day conditions. But like a building, cell phone tower or crane that finds itself under a high wind load in the midst of a hurricane or tornado, every device or structure or vehicle must be able to withstand the unusually high loads that could otherwise cause a catastrophic failure. It’s important for any engineer to understand both how to apply these guidelines and why these codes are written to such high standards.