If you’re not accustomed to designing buildings in more mountainous regions of the United States, the addition of a “Site Elevation Factor” to the design wind load equations in ASCE 7-16 may have taken you somewhat by surprise. However, those native to Denver and other high-elevation US cities have actually been doing something similar for a long time.
Air density is actually a core feature of the wind load equations, though it’s been abstracted by lumping it in with the unit conversion factor to get a standard, conservative single-coefficient value of 0.000256.
Code officials chose to simplify things, as, for most of the country, the reduction from accounting for differences in air density is minimal. However, when designing in the Rocky Mountains or other high-altitude areas, reductions of 15% or more can be attained by getting just a little bit more accurate in the calculations.
History & Physical Background
Several years ago, my team was working on a project in Denver, CO, and had submitted our design criteria sheet for review of our loads and assumptions, prior to getting too far along in our design. The Engineer of Record for the building sent back a comment asking why we hadn’t adjusted for the lower air density at their high-altitude building site.
Confused, we asked for further clarification, at which point he pointed us to §C27.3.2 “Velocity Pressure” in the commentary of ASCE 7-10 “Minimum Design Loads for Buildings and Other Structures”, which outlines what all gets lumped together into that 0.00256 constant in the velocity pressure equation.
The Velocity Pressure Constant
ASCE 7-10 §C27.3.2 “Velocity Pressure”, which was relocated in ASCE 7-16 to the correct chapter and renumbered as §C26.10.2, explains the one single constant and no dependence on altitude/air density in the velocity pressure equation.
Physically, Bernoulli’s law gives us that, along a given flow line, the total head (sum of the velocity head, pressure head, and elevation head) is constant. Assuming a “puff” of wind is traveling horizontally, there’s no change in elevation head, so the maximum pressure change we can get from this wind is the conversion of all the velocity head into pressure head.
Full conversion of velocity head to pressure head gives us what’s called the Stagnation Pressure, which is mathematically defined as:
where ρ is the density of the fluid, in this case, the air density.
The velocity pressure coefficient simply combines the 1/2 term with the average density of air at sea level, which is 0.0765 lbm/ft³, and some unit conversions:
Accounting for Elevation – ASCE 7-10 and Prior
Before we had official guidance in the body of the code, only a paragraph in the commentary showed the way:
The numerical constant of 0.00256 should be used except where sufficient weather data are available to justify a different value of this constant for a specific design application. The mass density of air will vary as a function of altitude, latitude, temperature, weather, and season. Average and extreme values of air density are given in Table C27.3-2
ASCE 7-10 §C27.3.2 ¶3
Unpacking that a bit, ASCE 7-10 Table C27.3-2 shows the expected range of variation for the air density at given altitudes, and we are cautioned that other factors influence the air density as well. Barring extremely unique cases, most engineers do not have “sufficient weather data” available, nor the time and expertise to analyze it, so we typically opt to use the maximum values in the table for the given altitude.
Note the linear dependence of the velocity pressure constant on air density. There’s no need to crunch all the nasty unit conversions each time, simply select the appropriate air density off the table and scale the constant by site density over average sea-level density. The velocity pressure and final design wind pressures are also linearly-related, so a 10% reduction in air density does carry through as a 10% reduction in final design wind pressures.
For example, at a site located 6000 ft above sea level, the “Maximum Air Density” column gives 0.0672 lbm/ft³. Taking advantage of that linear relationship, we can calculate the reduction as:
Ground Elevation Factor – ASCE 7-16 and Later
Starting with ASCE 7-16, a new “Ground Elevation Factor”, K.e, reduces the Velocity Pressure (eq 26.10-1) with increasing site elevation above sea level.
The Ground Elevation Factor is defined in §26.9:
The ground elevation factor to adjust for air density, Ke, shall be determined in accordance with Table 26.9-1. It is permitted to take Ke =1 for all elevations.
ASCE 7-16 §26.9
It is conservative, and permitted per code, to take this factor as 1.0, thereby neglecting the reduction due to altitude.
In addition to the Table, a footnote provides us with an equation for calculating the Ground Elevation Factor as a function of z.g, the ground elevation above sea level (in ft):
| Ground Elevation above Sea Level [ft] | Ground Elevation Factor, K.e |
|---|---|
| 0 | 1.00 |
| 1000 | 0.96 |
| 2000 | 0.93 |
| 3000 | 0.90 |
| 4000 | 0.86 |
| 5000 | 0.83 |
| 6000 | 0.80 |
Notably, the wind load reductions with the new ASCE 7-16 method are much greater than were calculated by using the conservative assumptions listed above under the old ASCE 7-10 approach.
Looking back at the ASCE 7-10 example above, we achieved a little over a 15% reduction, using the most conservative “maximum air density” value for 6000 ft elevation. But the table and equation in ASCE 7-16 give a full 20% reduction! That’s actually closest to using the minimum air density column from the ASCE 7-10 tables, which would imply a 20.5% reduction.
This unexpected increase in the reduction we can take bears a little more investigation, and the reasoning appears to actually be quite disappointing.
The code committee, in their “infinite wisdom”, opted to use a physical equation for the air density, which is a great idea. They then fixed the air temperature at 518 Rankine (note the LACK of a degree symbol, which is appropriate for absolute temperature scales like Rankine and Kelvin, and also note that they included a degree symbol in the code, which is somewhat pathetic…), which is 58.3° Fahrenheit.
No explanation is given as to why this temperature was arbitrarily selected, and if you check out the air density as a function of temperature graphs over at Engineering Toolbox, you’ll note this is unconservative for lower air temperatures.
I personally would recommend against using this new equation, unless you have good knowledge of what temperature can be expected alongside the design wind speeds. It’s also interesting that the old cautions on other influences present in the commentary of ASCE 7-10 have all been removed.
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