Mass Density of Air and Wind Pressure
It is no secret to anybody who runs, hikes, bikes, or generally performs any physical activity in higher elevations that it is harder to keep up a similar level of activity that you would have been able to do at sea level. A big portion of this difference is related to the lesser concentrations of oxygen present at higher elevations. By now you are probably already thinking, ‘I thought he would be writing something related to structures‘. Don’t despair, I’ll get there, but just wanted to use this analogy to point out that the heavier gases that make up our atmosphere are more concentrated at the lower elevations (probably obvious to most people).
So how does that relate to our structures? Well, the noted density variation in gases with change in elevation as I described in the example above means that the air density at altitude is less than at sea level. This means the weight of one cubic foot of air at the same temperature decreases as you move upward away from sea level.
This is not a new or novel concept. Nor is it a new or novel concept to ASCE7. The constant used in ASCE7 has been based upon the average air density at sea level per Bernoulli’s equation:
?P=1/2 ρV2 or ?P=Constant*V2,where ρ=m/g and Constant= ρ/2=m/2g
For the resulting conversion from density to pressure, the code has always used a unique constant which is a combination of the mass density of the air and dimensional unit conversion factors to keep the resulting pressure in pounds per square foot given a velocity in miles per hour. As noted in the ASCE7 commentary for years, this dimensionally consistent constant can be easily calculated by
Constant=1/2 ρ=[0.0765 lb/ft3*((5280 ft/mi)(hr/3600 s))2]/(2*32.2 ft/s2) = 0.00256 lb hr2/(ft2 mi2)
The commentary of the code has also included average mass densities for air at other elevations above sea level. Provided that adequate data was present to substantiate utilizing a reduced mass density based on elevation and average temperature, then the code allowed the designer to utilize the reduction in pressure through modification of the constant. For example, at Mean Sea Level (MSL), an average mass density of air is 0.0765 lb/ft3. At 1000 ft above MSL, the mass density of air at the same temperature is 0.0742 lb/ft3. This results in a reduction in pressure of 3% (see Table 1). While one can see that reductions in pressure might approach 16% at 6000 feet elevation, it has always been at the discretion of the Jurisdiction Having Authority (JHA) as to the limits of the reduction. For example, the City of Denver limits the reduction to 15% (most likely in recognition that the majority of Denver proper is at or near 5000 feet in elevation).
At Felten Group, we have taken advantage of this reduction in the past in order to provide value to our clients and to properly recognize that the resulting pressures acting on the lateral systems of our structures are lower at elevations above MSL. This is important to understand because the newest version of ASCE7 (7-16) that will be released soon has a new factor for elevation in the velocity pressure equation. The factor is called the Elevation Factor (KE) and is multiplied along with the 0.00256 constant. It is achieving the same result; but instead of having to look for it in the commentary it is now part of the main standard.
Firms that weren’t utilizing the reduction before will recognize the marked decrease in design pressures at elevation. Further, firms like ours that did utilize the reduction will see slight improvements in the old conversion factors (see Table 1) – especially as you move higher up in elevation above MSL.
As engineers and designers we will need to be prepared for how the JHA’s choose to amend, limit or implement the reductions. Also, regardless of whether you have or have not been taking advantage of the reduction, you will still need to modify your design aides to account for the new factor where allowed.
||Average Ambient Air Density (pcf)
||Reduction Factor Based on ASCE7-10
||New Elevation Factor KE in ASCE7-16