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re: calculating windload of pv modules
14 dec 2002
jerry krinock   wrote:

>when calculating the windload on a pv array, is it accepted engineering
>practice to assume that wind blows horizontally, and to project the area of
>the tilted module onto a vertical surface, then multiply by the design wind
>pressure (such as 30 or 40 lb per square foot).

sounds good to me. section 1611 of the 1993 boca code has a us map with
design windspeeds and a formula for the basic wind velocity pressure,
pv = 12.5 psf (0.00256v^2) for 70 mph in phila.

they also have various exposure categories, eg 

  exposure b: urban and suburban areas... with numerous closely-spaced
  obstructions having the size of single family dwellings or larger...
  in the upwind direction for a distance of at least 1,500' or 10x the
  height of the building or structure, whichever is greater, and 

  exposure c: open terrain with scattered obstructions having heights
  generally less than 30'. this category includes flat, open country
  and grasslands. 

to get a windward design pressure, they multiply this by an importance
factor i which depends on what's inside or under the structure, 1.15 for
hospitals, etc, 1.0 for "ordinary buildings," and 0.9 for "those with
a low hazard to human life in the event of failure," eg a pv array.

then they multiply by [kzghcp-khgcpi], where

kz is a "velocity pressure exposure coefficient" evaluated at somewhat
ill-defined "height of interest" or "height above ground" z, which might
be the mean roof height h. table 1611.7(4) says kz = 0.8 for a z = 12'
in exposure c (vs 0.37 in exposure b.)

gh is a gust response factor, 1.32 for z = 12' in exposure c.

cp is an external pressure coefficient, 0.8 for windward walls (vs -0.48
(negative pressure) for a 25 degree sloped roof with a mean height h = 12'
and a wind direction normal to the ridge and a horizontal dimension l = 18'
parallel to the wind direction.)

kh is another "velocity pressure exposure coefficient," 0.8 for z = 12'.

gcpi is the product of an internal pressure coefficient and a gust response
factor. table 1611.7(6) says gcpi = +/-0.75. note c says "to ascertain the
critical load requirements for the appropriate condition, two cases shall be
considered: a positive value of gcpi applied simultaneously to all surfaces,
and a negative value of gcpi applied simultaneously to all surfaces."

so it looks like the max windward wall pressure in this case is 
p = 12.5(1)[0.8(1.32)0.8-0.8(-0.25)] = 13.06 psf. multiplying by
the wind tributary area a = 8'x33' = 264 ft^2 for a 3-car solar
garage makes the windward wall force f = pa = 3448 pounds.  

>now, here's a harder question:  what is the direction of the resulting live
>load force on the mounts?  is it vertical, horizontal, or in-between?

probably something between. the boca code says "the design pressure shall be
applied simultaneously on windward and leeward walls, and on roof surfaces...
the external and internal pressures shall be combined to determine the most
critical load."

nick




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