PSF roof loading of ballasted flat-roof arrays

[Carultch]

With few exceptions, the system weight of a ballasted PV array is not uniformly distributed down to the individual square inch. It will be concentrated where the system has a footprint, and there will be locations with nothing touching the roof. Rear footprints where ballast material is installed, will have more load concentration than front footprints. There will also be variations throughout the system, as edge modules tend to require more ballast than modules in the middle of an array.

When a structural engineer provides a number for the surplus "average" dead load in psf (lbs/ft^2), how specifically is one supposed to interpret this limit in the application of a ballasted system? How granular is the area associated with each calculation to determine this average?

As an example, consider a 10x10 array. Suppose 15 psf applies to all the modules around the perimeter (36 modules), but only 5 psf is associated with the modules in the middle of the array (64 modules). On grand total, the average psf is 8.6 psf. Only 20% of the total array footprint is in contact with the roof membrane, so locally this is really 75 psf and 25 psf immediately below the ballast footings. Given that the roof has a surplus capacity of 10 psf, would this array pass?

 

[ggunn]

With few exceptions, the system weight of a ballasted PV array is not uniformly distributed down to the individual square inch. It will be concentrated where the system has a footprint, and there will be locations with nothing touching the roof. Rear footprints where ballast material is installed, will have more load concentration than front footprints. There will also be variations throughout the system, as edge modules tend to require more ballast than modules in the middle of an array.

When a structural engineer provides a number for the surplus "average" dead load in psf (lbs/ft^2), how specifically is one supposed to interpret this limit in the application of a ballasted system? How granular is the area associated with each calculation to determine this average?

As an example, consider a 10x10 array. Suppose 15 psf applies to all the modules around the perimeter (36 modules), but only 5 psf is associated with the modules in the middle of the array (64 modules). On grand total, the average psf is 8.6 psf. Only 20% of the total array footprint is in contact with the roof membrane, so locally this is really 75 psf and 25 psf immediately below the ballast footings. Given that the roof has a surplus capacity of 10 psf, would this array pass?

I'm pretty sure it would. I went to a structural engineering training session a year or so ago where this came up. Most roof failures due to excess weight are of the whole thing or a large portion of it rather than from a hole punched through it. Point loading strength is much higher than the average PSF strength over the structure.

 

[wwhitney]

From a structural engineering point of view, absent any qualifiers, the 10 psf available capacity for additional dead load would be a uniform load applied over the entire roof. You can use the average dead load presented by the ballasted array as long as the averaging is conservative, structural engineering wise. Generally that would mean that the higher than average loads are near the ends of joist/beam spans, and the lower than average loads would be near the center of joist/beam spans.

So for your 10x10 array, if the joists for the roof under the array span from one end of the array to the other, then your averaging is conservative. If, however, the roof is larger, and one edge of the array is actually located at midspan, then it is not immediately clear if averaging is conservative, versus the reality of that 15 psf load at midspan. In that scenario it would be prudent to have the structural engineer check the loading pattern.

As for the issue of the array loading not being uniform on the small scale (over a few square feet), that is a question of whether the roof sheathing and/or purlins are adequate for transferring the load to neighboring joists. A starting assumption would be that if the roof is designed for walking on, those members should be adequate for transferring a few hundred pounds located in one square foot to the rest of the structural system. So unless your ballasted array is going to be generating point loads comparable to that, it shouldn't be an issue.

Cheers, Wayne

 

[wwhitney]

I should amend my answer above for the 10x10 example, as two of the edges of the array likely run parallel to the joists. In which case those joists are being loaded at 15 psf in the area of the array. So if the array extends over the entire span of those joists, the array loading on those joists exceeds the 10 psf surplus dead load capacity of the joists.

Cheers, Wayne

 

[310 BLAZE IT]

Important to note that a few inverters mounted in the same area or a very large duct bank should be considered in point load calculations after the array distributed load is done. Many miss these design scope items and it's hard to finalize this analysis.

 

[Carultch]

I should amend my answer above for the 10x10 example, as two of the edges of the array likely run parallel to the joists. In which case those joists are being loaded at 15 psf in the area of the array. So if the array extends over the entire span of those joists, the array loading on those joists exceeds the 10 psf surplus dead load capacity of the joists.

Cheers, Wayne

Ok, thanks Wayne. That makes sense. Joists (and beams in general) would have disproportionately higher capacity for loads near their ends, than in their center. So high load at end of joist and moderate load in middle of joist, that average to less than the maximum uniform load, would be conservative. But if it all is in the middle of a joist, it is a different case.

I suppose the applicable area to take your average, might be the tributary area associated with any one joist in the region. So given joists at 5' O.C, it would make sense to take an average over each 5'x5' square, and verify that each 5'x5' square is 10 psf or less.

 

[wwhitney]

I suppose the applicable area to take your average, might be the tributary area associated with any one joist in the region. So given joists at 5' O.C, it would make sense to take an average over each 5'x5' square, and verify that each 5'x5' square is 10 psf or less.

If joists are every 5' O.C., and the available roof dead load capacity is 10 psf, then the available dead load capacity of each joist is 50 plf (pounds per linear foot). For the typical joist, the joist tributary area is a 5' wide strip centered on the joist, so you'd take the array loading over that area and project all the points onto the joist to come up with a plf loading from the array. (Same as I did for the capacity). When that joist loading isn't uniform, then you get into the question of whether averaging is conservative or not. If the load is higher on the ends than in the middle of the joist, averaging would be conservative, and so you could compare the average array loading on the joist to the 50 plf available capacity.

Cheers, Wayne

 

[wwhitney]

BTW, the above is just the simplest case, if the joist check passes then the non-uniform load should be OK (well, it might be necessary to consider the purlins as well). But in practice the available roof dead load capacity could be controlled by the purlins, the joists, the girders, the posts, or even the lateral force restraining system for wind/seismic. So even if the simple joist check I mentioned failed, a structural engineer may find that the array loading is OK.

Cheers, Wayne

 

[BillK-AZ]

Slightly off the main topic of this post: The City of Scottsdale, AZ requires a structural PE analysis of all residential roof mounted solar (PV & SHW), but apparently does not read them. In one case the PE determined that a major area of a tile roof was DANGEROUS and already overloaded due to a previous owner removing an interior wall that was load bearing. The result was excessive span for the rafters. We were told to not even walk on the area. This was highlighted in the report and we expected that the City would require repair before we could install a PV system, but the City simply approved the PV permit.

 

[ggunn]

Slightly off the main topic of this post: The City of Scottsdale, AZ requires a structural PE analysis of all residential roof mounted solar (PV & SHW), but apparently does not read them. In one case the PE determined that a major area of a tile roof was DANGEROUS and already overloaded due to a previous owner removing an interior wall that was load bearing. The result was excessive span for the rafters. We were told to not even walk on the area. This was highlighted in the report and we expected that the City would require repair before we could install a PV system, but the City simply approved the PV permit.

Did you build the system as approved? If you did the PE probably was obligated to report you, or the City, or both.