Balanced and Unbalanced Snow Loads on a Gable Roof

Design of roofs to resist snow loads consists of two main parts: first, determining the load (appropriate amount of snow), and, second, selecting roof components (sheathing, roof framing, etc.) strong enough to resist it (the snow, load). For a gable roof we need to consider two conditions: a uniform snow (load) over the entire roof, and, an unbalanced load, where, say, snow drifts from one side (over the ridge) and accumulates on the other. In this article we will look determining the appropriate Snow loads for design, and in following article the selection roof sheathing, joists, and a ridge beam for a particular design example in Moscow, Idaho.

The roof under consideration is a gable roof 32 ft wide with ridge down the middle and slopes of 5/12. Eaves and rake extend 12 in. beyond the exterior walls. Dimension lumber roof joists span from side walls to ridge. Walls are 2 x 6 wood frame. The roof is 24 ft long (end wall to end wall, excluding rakes).

Snow Loads

The design of a structure is governed by the Building Authority (Building Department) having jurisdiction over the location of the structure. Building Departments generally adopt one or several of the `model' building codes with amendments appropriate to locale. In Moscow, Idaho the Building Department has adopted (as of the time of this writing) the 2006International Building Code (IBC) and 2006 International Residential Code (IRC). These codes provide the information generally needed to design in this city. One thing is missing, however; ... the Snow load ... and for good reason. The Snow load is to be provided by the Building Authority. Snow load information for design in Moscow can be found on the City website under their Design Standards. From these Standards:

Ground Snow Load ... 64 psf

Roof Snow Load for pitched roofs ... 40 psf.

From the above information we may commence our `design'.

The IBC with regard to Snow loads essentially sends us to ASCE 7, Minimum Design Loads for Buildings and Other Structures. ASCE 7 provides us with the way to take Ground Snow load and determine various roof Snow loads, including the flat roof snow load, p_f, and sloped roof snow load, p_s, by taking into account roof exposure, roof slope, thermal properties of the roof itself, etc. In my practice I take the 40 psf provided by the City to apply to heated structures with mild slopes and not accounting for unbalanced loading and drifting (say from upper roof surfaces), hence p_s.

Now let's look at ASCE 7.

7.6 UNBALANCED ROOF SNOW LOADS

Balanced and unbalanced loads shall be analyzed separately. Winds from all directions shall be accounted for when establishing unbalanced loads.

7.6.1 Unbalanced Snow Loads for Hip and Gable Roofs. For hip and gable roofs with a slope exceeding 70° or with a slope less than the larger of 70/W + 0.5 with W in ft ... and 2.38° (½ on 12) unbalanced snow loads are not required to be applied. Roofs with an eave to ridge distance, W, of 20 ft ... or less, having simply supported prismatic members spanning from ridge to eave shall be designed to resist ... on the leeward side ... I p_g. For these roofs the windward side shall be unloaded. For all other gable roofs ...

Now let's look at our particular example.

First let's see if we `fall' in the range of roof slopes for which the unbalanced snow load info is excerpted from the Code (ASCE 7).

Roof slope: 5/12 which is equal to 22.6°. Well, it doesn't exceed 70°.

Is it less than the greater of 70/W + 0.5 and 2.38°? ... Well, let's see.

The 70/W + 0.5 is not dimensionally consistent, but is taken to be in degrees when W is submitted in ft. I will take W to be the slope distance (eave to ridge), and for simplicity take the plan distance to be half the building width. So,

W = 16 ft / cos 22.6° = 17.3 ft (which is 20 ft or less), and

70/W + 0.5 = 4.5(°).

So, yeah, our `roof' falls within the criteria listed. (22.6° is not less than the greater of 4.5° and 2.38°.)

So, the roof rafters (joists) must be designed to resist I p_g, where I is the Importance Factor obtained in Table 7-4 (of ASCE 7) which is 1.0 for a residential structure (Category II structure per Table 1-1). Thus,

I p_g = (1.0) 64 psf = 64 psf. This is the load that will be used for the rafter design, and is taken to be the horizontal projection of the snow load. To this will be added the Dead load (in our case 15 psf).

For the windward side of the roof, acting simultaneous with Ip_g on the leeward side, we will have Dead load only (15 psf + 0 psf).

However, we must consider wind from any direction, so the windward side must also be considered a leeward side; thus, these joists also must be designed to resist 64 + 15 (while the joists on the opposite side are enjoying no snow load).

Hence, the joists must be designed for 64 + 15 (BOTH SIDES), while the ridge beam will be designed for the `worse' of 40 + 15 on both sides simultaneously, or 0 + 15 on one side and 64 + 15 on the other. (The 40 + 15 on both sides will govern.)

The design of the roof sheathing, joists, and ridge beam will covered in a following article.

References

International Building Code, International Code Council, 4051 West Flossmoor Road, Country Club Hills, IL 60478.

International Residential Code, International Code Council, 4051 West Flossmoor Road, Country Club Hills, IL 60478.

Design Standards, City of Moscow, Climate and Geographic Design Criteria, City of Moscow, 211 E. Second Street, Moscow, Idaho, 83843.

Minimum Design Loads for Buildings and Other Structures, ASCE Standard ASCE/SEI 7, American Society of Civil Engineers, www.asce.org.