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 in PSF, 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
Or 56% density.
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*(187.2+10)1/4-1.5 = 0.43(4.63)*(3.74)1.5 = 5.95
D= 0.13* ground load+14 = 0.13*187.2+14=38.3
5.95*38.3 = 228 PSF because of drifting added to
the current roof load of our previous sloped roof
of 47 PSF … becomes 275PSF.
Note that the max height of our drift surcharge is
15.86 feet or ~95.2 inches of water equivalent at
50% density. Very deep! The difference in roof
heights must now be taken into account. If less
than 15.86 feet, then we assume that the drift
surcharge is the difference in height between the 2
roof levels. Given that our subroof (accumulation
of the drift) is greater than 15 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.
The maximum height of the drift must not exceed
(hr-hb) where r is the difference in height between
the two roofs and b is the depth of the uniform
snow deposition on the roof.
The drift surcharge diminishes to zero at
approximately 4Hd.
* 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
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.