Snow Load Worked Example — Gable Roof per ASCE 7-22

Problem: Determine the design snow loads for a 6-on-12 pitched gable roof (26.6°) on a warehouse located in Syracuse, New York. The building is 60 ft wide (eave to eave) and 120 ft long, with an unobstructed, slippery roof surface (metal standing seam). The roof is unheated and has no obstructions to sliding snow. Terrain is rural (Exposure C).

Step 1: Site Data and Ground Snow Load (Chapter 7)

From ASCE 7-22 Figure 7.2-1 (ground snow load map):

Syracuse, NY is in Zone with pg = 50 psf

Ground snow load (pg) = 50 psf

Step 2: Exposure Factor (Ce) — Table 7.3-1

For rural terrain (Exposure C) and a fully exposed roof (no trees or taller buildings nearby):

Ce = 0.90 (Table 7.3-1, Exposure C, Fully Exposed)

The roof is on a low-rise warehouse in open country — qualifies as "Fully Exposed."

Step 3: Thermal Factor (Ct) — Table 7.3-2

Unheated warehouse with the roof surface above a cold space:

Ct = 1.10 (Table 7.3-2, "Unheated structures" or "Cold roofs")

Step 4: Importance Factor (Is) — Table 1.5-2

Risk Category II (warehouse) → Is = 1.00 (Table 7.3-3)

Step 5: Flat Roof Snow Load (pf) — Equation 7.3-1

pf = 0.7 × Ce × Ct × Is × pg

pf = 0.7 × 0.90 × 1.10 × 1.00 × 50

pf = 0.7 × 49.5

pf = 34.7 psf

Check minimum (Section 7.3.4):

When pg ≤ 20 psf: pf_min = pg × Is (but pg = 50 psf > 20 psf, so this does not apply)

For low-slope roofs (slope ≤ S/50 = 60/50 = 1.2°): pf_min = 20 psf for pg > 20 psf. Our roof slope is 26.6° > 1.2°, so the low-slope minimum does not apply.

pf = 34.7 psf (governs over minimums)

Step 6: Sloped Roof Snow Load (ps) — Equation 7.4-1

ps = Cs × pf

Slope Factor (Cs) — Figure 7.4-1

For an unobstructed, slippery roof with Ct = 1.10 > 1.0:

Warm roof (Ct > 1.0) curve on Figure 7.4-1(b):

For the warm roof curve, Cs = 1.0 for slope ≤ 30° (S/12 ≤ 6.9), then reduces.

Our slope = 26.6° (6-on-12). Since 26.6° ≤ 30°:

Cs = 1.0

ps = 1.0 × 34.7 = 34.7 psf (uniform snow load on sloped roof)

Step 7: Unbalanced Snow Load (Section 7.6.1)

For gable roofs with slope > S/12 (70° for S = 60 ft, meaning > 5.8°) and ≤ S/2 (30° for S = 60 ft):

Our slope = 26.6°, which satisfies 5.8° < 26.6° < 30°. Unbalanced loads must be considered.

Unbalanced load on windward side:

For slopes between 5.8° and 30°:

pd = 0.3 × pg × Cs = 0.3 × 50 × 1.0 = 15 psf (uniform on windward side)

Unbalanced load on leeward side:

The drift load at the ridge for a gable roof is:

hd = 0.43 × (Su)^(1/3) × (pg + 10)^(1/4) - 1.5 (Equation 7.6-1 approximate)

Where Su = ridge-to-eave distance = 60/2 = 30 ft (for symmetric gable)

hd = 0.43 × (30)^(1/3) × (50 + 10)^(1/4) - 1.5

30^(1/3) = 3.11 60^(1/4) = 2.78

hd = 0.43 × 3.11 × 2.78 - 1.5 hd = 3.72 - 1.5 hd = 2.22 ft

γ (snow density) = 0.13 × pg + 14 = 0.13 × 50 + 14 = 20.5 pcf (Equation 7.7-1)

Maximum leeward drift load: pd_max = hd × γ = 2.22 × 20.5 = 45.5 psf at the ridge

The leeward load varies linearly from 0 at the eave to 45.5 psf at the ridge.

Width of drift zone: w = 4 × hd = 4 × 2.22 = 8.9 ft (from ridge downward)

Step 8: Rain-on-Snow Surcharge (Section 7.10)

For sites with pg > 20 psf, a rain-on-snow surcharge applies to roofs with slopes ≤ S/50:

S/50 = 60/50 = 1.2°

Our slope = 26.6° > 1.2°, so rain-on-snow surcharge is NOT required.

Step 9: Partial Loading (Section 7.5)

For continuous beam systems, partial loading must be considered. The drift load case (unbalanced) typically governs over uniform partial loads for gable roofs with slopes > 10°.

Step 10: Design Snow Load Cases (Section 7.3)

Per ASCE 7-22, the following load cases must be considered:

Case 1: Uniform snow load applied to the full roof = 34.7 psf

Case 2: Unbalanced load on both spans (worst case for leeward drift):

• Windward: 15 psf (uniform)
• Leeward: Varies from 0 at eave to 45.5 psf at ridge (over the first 8.9 ft from ridge)

Case 3: Uniform load on one span only (for continuous purlin design)

Step 11: Snow Load Summary

For LRFD load combinations (ASCE 7-22 Chapter 2):

Combination 1: 1.2D + 1.6S + 0.5L (balanced snow)

Combination 2: 1.2D + 1.6S_unbalanced + 0.5L + 0.5W (unbalanced snow with reduced wind)

Where L = roof live load (typically 20 psf for roof).

Step 12: Snow Drift at Parapets and Roof Obstructions

If the warehouse has a parapet (even a small one), snow drift against the parapet may produce higher local loads. Drift height:

hd_drift = hd × (Pd/γ) (approximate)

For a 3 ft parapet, if the drift exceeds the parapet height, the drift load is limited by the parapet height.

For this example (no parapet), sliding from the 26.6° slope prevents significant accumulation at the eave.

Try the Calculator

Use the Snow Load Calculator to compute design snow loads per ASCE 7-22 for your own roof geometry, location, and exposure conditions.

Frequently Asked Questions

What is the difference between balanced and unbalanced snow loads? Balanced snow load represents the uniform snow accumulation on a roof under calm conditions. Unbalanced loads account for wind redistribution — snow is scoured from the windward side and deposited on the leeward side (or on lower roofs). For gable roofs, the unbalanced case typically governs the ridge and purlin design near the ridge.

When does the rain-on-snow surcharge apply? Rain-on-snow surcharge applies to roofs with slopes ≤ S/50 (about 1.15° for a 60 ft span) in regions with pg > 20 psf. It accounts for the weight of rain that cannot drain from a snow-covered roof. Since our 26.6° gable roof easily sheds water, the surcharge does not apply.

How do I convert ground snow load (pg) to roof snow load? The conversion accounts for exposure (Ce), thermal effects (Ct), importance (Is), and roof slope (Cs). The formula is pf = 0.7 × Ce × Ct × Is × pg for the flat roof snow load, then ps = Cs × pf for the sloped roof. The 0.7 factor is based on statistical correlation between ground and roof snow accumulation and is one of the most studied parameters in snow load engineering.

See Also

• Beam Capacity Calculator
• Beam Deflection Calculator
• Steel Beam Sizes Reference
• Beam Design Guide
• Beam Span Reference