Roof Loads

* Snowpack dictates building design criteria in many locations.

* The nature of snow deposition depends on both the micro and macro climatological conditions.

* In sheltered locations with significant accumulations, uniform snow distribution on roofs is typically the design criterion.

* Drifts constitute the most critical design consideration for structures subjected to snow accompanied by significant winter winds.

* Structures must be designed to accommodate a specific return interval of snow load so as to minimize the potential of failure without adding undue economic factors by gross overdesign. You need to choose an acceptable risk level and design for that load.

* A complete knowledge of the actual snow loads expected during the design life of a structure is critical for design.

* There are 2 basic issues to be resolved to determine roof snow loads: 1) the ground snow load and its relationship to the roof snow and 2) the depth, density and distribution of snow on the roof.

* The ground to roof conversion factor defines the uniform roof snow load.

* To obtain the building snow load, the designer must also consider the effects of: roof slope, roof material, building thermal losses, unbalanced loads, drifting patterns, ice damming, lateral pressures and rain on snow.

* Recurrence intervals are typically analyzed using a Log Pearson III probability analysis.

* American National Standards prescribe a 50 year recurrence interval as a standard, but local building codes may vary.

* Flat Roofs (simple analysis): exposure of the roof to wind, sun, thermal losses, roof geometry, roof material and obstructions on the roof or on the ground are some to the factors that can influence roof snow loads. The ground to roof conversion is as follows:

Pr = C*Pg

Where Pg is the ground snow load, C is a dimensionless coefficient that depends upon roof environment and geometry and Pr is the structural design load for the roof.

Structural design loads are typically expressed in pounds per square foot (PSF) and as you know, data from SNOTEL and snow courses are typically expressed in inches of snow water equivalent. Water weighs 62.4 lbs per cubic foot, so: you simply divide the SWE by 12 inches to get feet of SWE and multiply that by 62.4 to get PSF.

Example: 36" SWE/12*62.4 = 187.2 PSF as a ground snow load. 0.80*187.2 = 149.8 as a design roof load.
 
 

C, in general is about 0.80 for sheltered locations and may be reduced by 25% for windy areas such as prairie locations.

Flat Roofs (better analysis):

Pf = 0.7*Ce*Ct*I*Pg where:

Ce is a dimensionless exposure factor, Ct is a dimensionless thermal factor and I is a dimensionless importance factor which allows converting the ground snow load to a mean recurrence interval different than a 50 year value and, Pg is the ground snow load.

* Each of these values are subjective and typically range from 0.8 to 1.3 - The exposure factor allow you to adjust for forest to prairie situations. the Thermal factor allows adjustment for unheated structures (or designed thermal loss through the roof), the importance factor is basically how important the structure is which allows a greater or smaller mean recurrence interval.

Example: 36" SWE again or 187.2PSF with average exposure, average thermal loss and is filled with cats, which I hate, having gone through the rabies vaccination series - so the importance factor is very low, even lower than 0.8 at 0.5

0.7*1*1*.5*187.2PSF= 65.5 psf design load.

Example: all else being equal (thermal, importance, and exposure) the equation is simply 0.7*ground load which is 0.7*187.2= 131PSF
 
 

Sloped Roof Loads

Ps = Cs*Pf where: Ps is the sloped roof snow load and Cs is a dimensionless coefficient dependent on the slope, roofing materials and thermal characteristics.

The values of Cs are: Cs = 1.0- ((a-A)/B)

Warm roofs: (Ct <= 1.0) Dimensionless thermal factor represents designed heat loss or average heat loss.

a) for unobstructed slippery surfaces, A=0 degrees, B=70 degrees and ‘a’ is the roof slope in degrees. (valid for a= 0 to 70 degrees)

b) for all other surfaces use: A=30 degrees, B= 40 degrees and ‘a’ is the roof slope in degrees. (valid for a= 30 to 70 degrees)

Cold Roofs: (Ct > 1.0) (well insulated or not frequently occupied or supplied with heat)

a) for unobstructed slippery surfaces use: A=15 degrees, B= 55 degrees and a is roof slope, (valid for ‘a’ = 15 to 70 degrees)

b) for all other surfaces use A=45 degrees, B= 25 Degrees, (valid for ‘a’ = 45 to 70 degrees)

Example: for a metal roof of 45 degrees, average insulation, average importance and average exposure with no obstructions. Using our 36 inches of swe we have

0.7*187.2= 131PSF as our flat roof assumption.

So - Cs=1-((45-0)/70) = 0.36

Design load = 0.36 * 131 = 47PSF

See how a steep roof angle and the use of appropriate materials can dramatically lower the design load of a building? The offset is much higher building costs involved in steep pitched roofs.

Values of Cs = 1.0 for slopes below the sliding threshold (i.e. a= 15, 30 and 45 degrees for categories of 1a, 1b, 2a and 2b respectively.)

* Sliding snow will reduce the load on the roof of origin, but can impose significant static and dynamic loads on a lower receiving roof. Ansi standards prescribe using the entire snow load from the upper roof to adjust the value of the lower roof and defines no distribution of the load on the lower roof.

Nonuniform snow loads

* Snow deposition is affected by wind speed and direction, terrain around the structure, temperature, humidity and building geometry. examples include: unbalanced loads for gables, arched, curved and multi span curved or sloped roofs, drifts on lower roofs and areas adjacent to roof projections.

* Unbalanced loads: wind blowing normal to the ridge of a structure will create an area of aerodynamic shade on the leeward surface and yield greater deposition on that side. In addition, wind will transport existing snow from the upslope side to the leeward deposition side further compounding the unbalance. Typical procedure is 0 to 50% Pf on the upslope side and 100 to 150% Pf on the leeward side.

* Drifts: a major part of snow load failure cases is associated with drifts. Drift height and shape (and thus load) is a function of the length of the upper and lower roofs, the ground snow load and the difference in height of the 2 roofs or the space available for drift formation.

* The triangular geometry of the snow drift surcharge load (to be superimposed on the balanced roof load) has a maximum height of:

hd = 0.43(Lu)1/3 * (Pg+10)1/4 - 1.5

where Lu is the length of the upper roof and may not be less than 25 feet nor greater than 600 feet.

The density of the drift (lbs/ftcubed) is

D = 0.13Pg +14 for densities less than 35 lb/ft3

The extra snow load then is:

hd*D

Which is then added to the normal balanced snow load to get the total load on the roof.

Example: you have a roof 100 feet long.

0.43(100)1/3*(3+10)1/4-1.5 = 0.43(4.63)*(1.89)-1.5 = 2.26

D= 0.13* ground load+14 = 0.13*3+14=14.39

14.39*2.26 = 32.52 PSF because of drifting added to the current roof load of our previous sloped roof of 47 PSF … becomes 79PSF.
 
 

Note that the max height of our drift surcharge is 2.26 feet or 27.1 inches of water equivalent. At a density of 25% (early season snow) this is a depth of 108 inches or about 9 feet. Assuming that we have 0.7*36/0.25 inches of snow on the upper roof this gives about 100 inches of depth without drifting. Given that our subroof (accumulation of the drift) is 10 feet below our upper roof, this drift could grow. As the drift approaches the level of the snow on the upper roof, it will fill in and cease relative vertical growth - i.e. both the upper and lower levels have merged and are one at the junction of the roofs and deepen as one level. Horizontal growth can continue as we have assumed a triangular drift. So, if the difference between the upper roof and lower roof was only 3 feet, the total surcharge would be 3 feet plus the depth of snow on the upper roof. In this case, the 3 feet would easily become overrun and the total surcharge would only be the SWE of the additional 3 feet of snow. Again assuming a maximum density of 40% * 3*62.4lbs/ft cubed=74.9PSF
 
 

* Quadrilateral drifts: there are about 4 times more triangular drifting features than there are quads. There are procedures for calculating quads but - the triangular drift is more likely, larger and weighs more than the quadrilateral and thus if designed for, certainly encompasses the safety design for a quad.

Settlement pressures on roof structures:

* There are areas where winter snowfall sometimes accumulates enough to bury structures: buildings at Mt hood, Mt rainier have been completely or partially buried. Many recreational buildings and campground facilities such as cabins, boweries, restrooms and lodges are at risk.

* The settlement forces of snow at time can be much higher that the projected weight of the snowpack itself. The additional snowload is transferred through shear stress from the adjacent pack.

* Currently there are no direct/simple approaches to determining roof loads for conditions of complete burial. A theoretical approach by R. G. Albrecht follows.

total snow load = {(a)*b)*(d) + (fv)*(h)*(2a+2b)}

where:

a= width of building

b= length of building

d= average density of snow above the eaves

fv= the average shear strength of the snow from the eave line to the snow surface

h= depth of snow above the roof (average)

g= gravitational constant

All of the following roof photographs were taken on the same day, at the same elevation and
same aspect on the Weber Watershed, near 8000 feet.
 

Notice the affect of the chimney on this roof load: all to the side and below the chimney has slid off due to the metal roof but the chimney is holding a large portion of this pack in place.  Notice the accumulation on the deck - should have continued the roof line further out over the deck.

Same roof, different angle - notice how clean it is except for the chimney which is on an exterior wall, and should have a gable to support it. Also notice that the deck is covered on this side, good design.

Another Chimney, opposite aspect on a different cabin.  The entire roof is clean except for that part affected by the Chimney, again on an exterior wall without a gable support.  Notice the vent to the right, close to the top of the roof line - good place but still should have either a small gable or a wire support or it will get scrubbed off when the pack avalanches off this side.  In the same vein as chimneys, all vents, etc should either be gabled or have a cricket or wire support and be mounted as high on the roof line as possible - otherwise they will be sheared off when the snow slides.

Close view of the deck area - to prevent this, extend the roof line over the deck.


See how this area will need a huge support system in order to keep the deck from collapsing and how, over time, this area will be high maintenance.

Complex roof lines - secondary roof with a much lower pitch than the primary roof line, gable adding to the secondary. Note the primary roof line has only a foot or so of snow but the covered deck is getting 3 times the load.  This requires a much greater roof design for the deck area.  Notice also that the deck roof is actually supporting a higher roof load on the primary such that the primary is not clearing as it normally would.  Notice also that above the gable structure, the snow is double what it is on the relatively clear section of primary.

Same roof, different view.  Notice the strenght of the pack on the lower left corner, curling over the roof which puts a lot of shear stress on the corner of the roof.  Remember, in previous pictures, the very clean areas of roof  in simple, straight designs.  Notice again the accumulation on the deck on the left.

A structure of obvious high importance but unheated.

Not important, and the pack continues to rip these small sheds down.

Notice all the joint areas - where complex angles in the roof lines come together and the increased snowpack in these weakest areas.

Pretty stoopid place to put a door - shovel this out each and every snow event.

Very small example of an unbalanced roof load, left to right.  On this particular cabin, the snow on the right can easily be 4 to 5 times a deep as it is on the left side. Correct door placement and notice the upper level door for entry in case there is massive snowpack.

Small woodshed, low importance, asphalt shingles, steep roof pitch.  Stresses on this building could easily crack the glass windows and jam the door.
 

General snow load discussion:

1. snow on the roof will typically be less than snow on the ground due to the influence of wind and the non contiguous nature of the snowpack on the roof. also, the edge effect of wind eroding the snow from the roof and the fact that wind velocities on the roof are higher than those next to the snow/ground surface.

2. roof orientation with respect to the prevailing winds can have a dramatic affect on the amount of snow retained on a roof.

3. Microtopography of the roof can determine the size and location of snow drifts.

4. drift surcharge is typically responsible for the majority of failures. overall the total roof load isn’t exceeded very often, it is typically a drift in a specific area or other unusual circumstances such as Ice buildup or rain on snow with plugged drains, etc.

5. in deep snow country, avoid gutters, they will just get ripped off by snow creep, etc. they will also allow the edge of the roof to be damages, water to seep back through the eave structure to the inside as they pull off/apart.

6. always put a gable over every entrance to a building such that the snow falls to each side of the entryway. this will prevent small scale avalanches from killing/injuring people as the enter/leave a structure. the sliding snow will be diverted to each side of the entrance. this also helps with snow removal, you don’t have to shovel as much.

7. complex roofs: those with many gables, levels, dormers, and protrusions have the highest potential for drift surcharge and can have the weakest points at the joining surfaces. They are also the ones that are currently "in style" and you see more and more very complex roof lines in various applications. The areas between dormers can easily fill to the overall roof level, easily doubling the roof load in those areas, which again are the weakest part of the overall roof.

8. wind patterns in and around the roof location dramatically affect the snow catch on the site. Trees adjacent to the site can either act as a snow fence, adding to the snow load or as a venturi, eroding the snow from the roof. Most sites/owners prefer a lot of trees to get a ‘deep forest’ kind of feel and this generally adds to the roof load. those who are on a mountainside and have a view, tend to open up the downhill side to get an unobstructed view of the peasants below, this typically opens up a venturi effect which will typically erode off one side and deposit on another yielding unbalanced loads.

9. north south aspects: there is always a disparate snow load on these two sides of the roof: under no wind redeposition scenario the north will always have a higher load than the south and at time, it can be severely overbalanced with the north having 2 to 4 times as much snow as the south, particularly at this time of year. This is the can opener affect where one side of the roof tries to peel off the opposite side. typically the walls will try to buckle inward on the heavy side.

10. snow sliding onto lower roof levels. upper decks can contribute a great deal of snow and ice to lower levels both through snow sliding and creep as well as meltwater reforming in ice layers and ice dams on gentler slopes. as this snow accumulates through the year, it can easily submerge the structure adding significant shear stress to the building as the snow settles and compresses later in the season. this shear stress can pull a structure down. this shear stress is great enough to bend schedule 40 galvanized steel tubing sections 7 feet long by as much as 6 inches.

10. SNOTEL sites with 20 inches of swe or less, get a standard fence. those with 20 to 50 inches, get a reinforced fence and those with over 50 inches get a 3 leg fence. the force of snow on various structures is immense - fences of all kinds can be laid horizontal or stripped off the posts and laid on the ground.

Snow creep moving down steep slopes can shear off telephone poles, towers, ski lifts towers, radio facilities and anything else that protrudes through the snow. At heavenly valley where we have a 26 foot rain gage, we have to have a splitter device uphill of the gage so the snow doesn’t knock it over - it is a 6 inch angle iron about 20 feet high with the angle pointed uphill. we started out with a 4 inch angle but it was damaged.

11. Shear strength in a snowpack is dependent on its density, structure and the temperature within the pack. Very cold, small crystalline structure with high density has the highest shear strength. large crystals with poor cohesion and high temperatures has lower shear. Ice has the highest shear strength and can be a troublesome nuisance such as when the bear river bay froze over in 84’ with water backed up to record levels, it covered 2 major electrical lines to a depth of 1 to 2 feet, froze solid and then through expansion, sheared hundreds of power poles off at the base.

12. snow creep can occur, given the right conditions, on angles as low as 8% slope. They can transmit vertical forces of over 150% of the ground load and far greater forces in shear stress.