Mark Meshulam is an expert witness and consultant for wind damage to buildings.
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Here in the windy city, the pressure of the wind plays a big role in the specification and design of buildings, and especially the part of the envelope we like to lick: the windows and glass.
When designing and testing windows, curtainwalls, panel systems and other vertical facade elements, we typically see three categories of wind pressure utilized:
1. Pressures used for testing air infiltration and water penetration. These can vary from .56 psf to 15 psf depending on product type, building type and application.
2. Pressures used for structural design (this is called “design load” or “design pressure”). These can vary from 20 psf to 70 psf and more.
3. Pressures used for safety factor. These run 50% greater than design load, so they can vary from 30 psf to 105 psf and more.
“Psf” means “pounds per square foot”. It refers to the number of pounds of force applied (in this case by the wind) to each square foot of the building’s exterior, including our beloved windows. Psf is a measure of pressure which is an amount of force per an amount of area.
There are other ways to express this. Wind pressure can also be expressed, for instance, as kilograms per square meter (kg/m^2) for you sick Euro-freaks out there who espouse the so-called “metric” system.
Not only can you convert wind pressure to other units of measure, you can also convert wind pressure to an equivalent wind speed, because it has been calculated that a uniform wind blowing against a building at a given speed will produce a predictable wind pressure. This phenomenon has earned its very own formula, the “Emswiler Formula”, widely used in our industry, thanks to John Edward Emswiler:
If you know the velocity, find the pressure with this formula: P = .002496 V^2
If you know the pressure, find the velocity with this formula: V = SQRT(P/.002496)
In order to convert from wind velocity V to wind pressure P, simply multiply the velocity (in mph) by itself (square it), then multiply the result times .002496. That’s it. The result is in psf.
Let’s try one. According to one study, Chicago’s average wind speed is 10.3 mph. Calc it out and you find that it converts to .26 psf. Surprisingly low – only one quarter pound per square foot.
And so, you might think: What gives? Chicago Window Expert just said structural design pressures involve a range of 20 psf to 70 psf, yet our average wind speed only produces 1/4 psf!
Well, the wind “gives”. Notice that the wind pressure formula involves squaring the wind velocity. Math whizzes out there will immediately recognize that the equivalency between wind pressure and wind speed is not linear. It will not provide a straight line on a graph, and here’s a graph to prove it. Each time the wind speed increases just a little, the wind pressure increases a lot.
Let’s try it again. In a 66 year study (1930-1996) Chicago’s peak wind gust recorded at O’Hare airport was 84 mph. I remember it being a bad hair day. Calc that on your abacus and you find that 84 mph converts to 17.61 psf.
So let’s compare these two conditions:
|Chicago’s average wind||10.3 mph||.26 psf|
|Chicago’s 66 year peak wind gust||84 mph||17.61 psf|
Comparing an average wind with a gusting wind, the wind speed increased by a factor of about 8 (10.3 mph to 84 mph), but the wind pressure increased by a factor of over almost 68 (from .26 to 17.61 psf).
We can see that the range of historical wind behavior is similar to the test pressures commonly used for air infiltration and water penetration, but structural design pressures are very much higher.
There are three main reasons higher structural design loads are used:
Reason 1: Historical official wind data is typically taken at only 33 above the ground, yet our big buildings are much higher than that where the wind roams freely across the skies. The Willis Tower is over 1400 feet tall. What? You haven’t heard of the Willis Tower? You will never believe this. To induce a new tenant, Willis Group Holdings, to lease a few floors of office space, the Sears Tower changed its name! First Frango Mints were outsourced, then Marshall Fields became Macy’s, and now this! At least they didn’t take away the bean!
Reason 2:Our urban canyons create constricted spaces where the wind becomes funneled between buildings, dramatically increasing wind speeds and pressures. This “venturi effect” was put to good use in the carburetors of pre-fuel injection cars, causing the intake air to accelerate and better mix with the gasoline.
Reason 3: As the wind passes a building, it creates a negative pressure on the leeward side that can be even more powerful than the positive pressures on the windward side. We see this effect a lot in our lives. It is the same negative pressure (meaning it really sucks) that lifts airplanes and propels sailboats.
If you are an engineer attempting to design a big building, you will need to arrive at a reasonable determination of the design pressure for that building. In order to do this, you first consult the local building code. This will tell you the minimum design pressure you can use, by law. Then, you will need to go beyond the code and look for compelling reasons to increase the design pressure. There may be special atmospheric reasons, such as adjacency to large body of water (we have a rather large lake to consider) or mountains (we have them, too. Ever heard of Mount Trashmore (elev +67′-2″ above Lake Michigan)?
Beyond these considerations, the big kahuna of design pressure determination is: how to design for the wild and wacky winds that blow through the jumble of architecture known as downtown Chicago?
We’ve got everything: tight spots where wind roars out of the West, squeezes between buildings and takes off like the Super Chief, sudden open spaces where winds expand and form eddy currents and whirlpools in nooks and corners and mini-twisters in open plazas, and tops of buildings where unfettered Northeasterlies thunder from Canada on the racetrack known as Lake Michigan only to plow into their first resistance since the Arctic Circle. Even our sentences run on. Try boiling all of that down into a formula!
One of the most taxing sets of calculations confronting any super-computer would be the modeling of gas or fluid dynamics as these substances collide with complex structures from multiple directions.
We simply don’t have the computer modeling tools that would enable us to know what will happen on every surface of every building when the wind hits downtown.
When designing big buildings, it is actually easier to build a scale model of the downtown area, load each building model with pressure sensors, and put the whole shebang on a turntable inside a wind tunnel. Turn on the fan and start collecting data.
For one or two hundred thousand dollars, you can commission your very own Boundary Layer Wind Tunnel Test and get all the data you will ever need to adequately design your building. Be sure to bring a hat.
Wind-related definitions from NOAA (National Oceanic & Atmospheric Administration)
The horizontal motion of the air past a given point. Winds begin with differences in air pressures. Pressure that’s higher at one place than another sets up a force pushing from the high toward the low pressure. The greater the difference in pressures, the stronger the force. The distance between the area of high pressure and the area of low pressure also determines how fast the moving air is accelerated.
The rate at which air is moving horizontally past a given point. It may be a 2-minute average speed (reported as wind speed) or an instantaneous speed (reported as a peak wind speed, wind gust, or squall).
Rapid fluctuations in the wind speed with a variation of 10 knots or more between peaks and lulls. The speed of the gust will be the maximum instantaneous wind speed.
The true direction from which the wind is blowing at a given location (i.e., wind blowing from the north to the south is a north wind). It is normally measured in tens of degrees from 10 degrees clockwise through 360 degrees. North is 360 degrees. A wind direction of 0 degrees is only used when wind is calm.
Determining Wind Loads on Buildings, Part 1, Craig. H. Wagner, P.E., Architectural Testing, Inc.
Determining Wind Loads on Buildings, Part 2, Craig. H. Wagner, P.E., Architectural Testing, Inc.
Pressure / Velocity Equivalency Chart
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