----- | -------------------------- | ---------------------------------------------------------- | | LC1 | 1.4D | Minimum gravity (rarely governs for roofs) | | LC2 | 1.2D + 1.6Lr + 0.5S | Low-snow regions where Lr exceeds S | | LC3 | 1.2D + 1.6S + 0.5Lr | Snow regions where S exceeds Lr (most common gravity case) | | LC4 | 1.2D + 1.6Lr + 0.5W + 0.5S | Roof live load with companion wind | | LC5 | 1.2D + 1.6W + 0.5Lr + 0.5S | Wind as primary load (lateral design) | | LC6 | 1.2D + 1.6R + 0.5Lr | Rain load primary (flat roofs with blocked drainage) | | LC7 | 0.9D + 1.0W | Net uplift (wind opposes dead load) | | LC8 | 0.9D + 1.0E | Seismic uplift (only for seismic regions) |

Critical observations:

• Snow and roof live load are never both factored at 1.6 in the same combination. One is primary (1.6) and the other is companion (0.5). This reflects their non-concurrent nature.
• Rain load R only appears with 1.6 factor in LC6. In other combinations, rain is not considered as a companion action because rain and snow/wind are not expected to occur simultaneously at design intensity.
• LC7 (0.9D + 1.0W) is the only combination that can produce net tension (uplift) in roof members. The 0.9 factor on dead load is a lower bound to account for dead load variability — the actual dead load could be less than calculated.
• For LC7, W includes the positive (inward) pressure on the windward wall and the negative (uplift) pressure on the roof. The net effect on the roof is typically uplift.

Dead load estimation by roof component

Accurate dead load estimation is critical for roof design because dead load appears in every load combination and directly affects the net uplift calculation in LC7. The following table provides typical dead load ranges for common roof components:

Typical total dead loads by roof type:

The dead load range matters significantly for the LC7 uplift check: a metal building roof at 4 psf dead load with 35 psf wind uplift produces net uplift of 0.9(4) + 1.0(-35) = -31.4 psf, while a commercial flat roof at 15 psf produces 0.9(15) + 1.0(-35) = -21.5 psf. The lighter roof has 46% more net uplift, requiring more robust connections.

Rain load detailed calculation

ASCE 7-22 Section 8.2 defines rain load R as the weight of water that accumulates on the roof when the primary drainage system is blocked and the secondary (overflow) drainage system is functioning. The calculation is straightforward but requires careful attention to the geometry of the drainage system:

R = 5.2 x (ds + dh)    (psf, where depths are in inches)

Where:

• ds = static head = depth of water from the roof surface to the inlet of the secondary drainage system (in). This is the vertical distance from the low point of the roof (at the secondary drain) to the secondary drain inlet elevation. For a scupper 2 in above the roof surface, ds = 2.0 in.
• dh = hydraulic head = additional depth of water above the secondary drain inlet required to force the design flow rate through the secondary drainage system (in). This depends on the drain type and flow rate.

Hydraulic head determination:

• For secondary scuppers: dh = (Q / (2.49 x W))^0.67, where Q = design flow rate (gpm) and W = scupper width (in).
• For secondary drains (roof drains): dh is obtained from manufacturer flow charts, typically 0.5 to 2.0 in for properly sized drains.
• For free discharge (open scupper through parapet): dh is minimal, approximately 0.5 to 1.0 in.

Design flow rate: The rainfall intensity for drain sizing is typically based on a 100-year, 1-hour rainfall event per the plumbing code (IPC or UPC). The rainfall rate i (in/hr) and the tributary roof area A (sf) determine Q = 0.0104 x i x A (gpm).

Rain load examples:

The most dangerous rain loading scenario occurs when the secondary drainage capacity is inadequate or the secondary drain inlet is set too high. In the 1998 collapse of a warehouse in Oregon, the primary drains were blocked by leaves, and the secondary scuppers were set 8 in above the roof surface (to keep water off the roof membrane). The resulting rain load of 5.2 x (8 + 2) = 52 psf exceeded the roof capacity by a factor of 2.

Ponding instability per AISC 360-22 Appendix 2

Ponding instability is a serviceability and strength limit state unique to roof structures. It occurs when rainwater accumulation on a flexible roof causes deflection that traps more water, which causes more deflection, in a positive feedback loop. AISC 360-22 Appendix 2 provides a simplified stability check and a more detailed analysis method.

Simplified stability criterion:

Cp + 0.9 x Cs <= 0.25    (AISC Appendix 2, Eq. A-2-1)

Where:

• Cp = 32 x Ls x Lp^4 / (10^7 x Ip) — primary member flexibility
• Cs = 32 x Ls^4 / (10^7 x Is) — secondary member (joist/purlin) flexibility
• Lp = primary member span (ft), Ip = primary member moment of inertia (in^4)
• Ls = secondary member span (ft), Is = secondary member moment of inertia (in^4)

If Cp + 0.9Cs exceeds 0.25, the roof is potentially ponding-unstable and requires either: (1) stiffer members, (2) increased roof slope, (3) additional secondary drainage, or (4) a detailed ponding analysis using the iterative method in AISC Appendix 2 Section 2.2.

Detailed analysis method: The iterative approach computes the water depth at each step, calculates the resulting deflection, adds the deflected water depth, and repeats until convergence (stable) or divergence (unstable). If the water depth converges, the final member forces are checked against the member capacity. If the depth diverges (grows without bound), the roof is unstable and must be stiffened.

Practical guidance for avoiding ponding problems:

Even with adequate slope, secondary (overflow) drains must be provided at every low point. Primary drains alone are insufficient because debris can block them. The secondary drainage system must be independent and sized for the full design rainfall.

Combined loading worked example — snow + wind + dead

Given: A warehouse in Minneapolis, MN (pg = 60 psf). The roof is a flat commercial roof with steel deck on open web steel joists at 5 ft on center. Joists span L = 45 ft. Dead load = 14 psf. Wind uplift (Zone 2, edge zone) = -42 psf. Rain load R = 15.6 psf.

Step 1 — Calculate individual loads:

• Dead load D = 14 psf
• Snow load pf = 0.7 x 1.0 x 1.0 x 1.0 x 1.0 x 60 = 42 psf
• Roof live load Lr = 12 psf (tributary area = 45 x 5 = 225 sf > 200 sf, R1 = 1.2 - 0.001 x 225 = 0.975, but using 12 psf minimum)
• Wind uplift W = -42 psf (Zone 2, edge)
• Rain load R = 15.6 psf

Step 2 — Evaluate governing gravity combination: LC3: 1.2(14) + 1.6(42) + 0.5(12) = 16.8 + 67.2 + 6.0 = 90.0 psf LC2: 1.2(14) + 1.6(12) + 0.5(42) = 16.8 + 19.2 + 21.0 = 57.0 psf LC6: 1.2(14) + 1.6(15.6) = 16.8 + 25.0 = 41.8 psf LC3 governs at 90.0 psf.

Step 3 — Evaluate net uplift combination: LC7: 0.9(14) + 1.0(-42) = 12.6 - 42.0 = -29.4 psf (net uplift) The joists, deck attachments, and connections must resist 29.4 psf net uplift.

Step 4 — Design joist for gravity (LC3): wu = 90.0 x 5 / 1000 = 0.450 klf. Mu = 0.450 x 45^2 / 8 = 113.9 kip-ft. Required Zx = 113.9 x 12 / (0.90 x 50) = 30.4 in^3.

Step 5 — Check deflection under service snow (LC3 service level): w_service = (14 + 42) x 5 / 1000 = 0.280 klf (dead + snow, unfactored). delta_allow = 45 x 12 / 240 = 2.25 in. I_req = 5 x 0.280/12 x (540)^4 / (384 x 29000 x 2.25) = 5 x 0.02333 x 8.503 x 10^10 / (2.506 x 10^7) = 396 in^4.

Joist selection: A 28K10 joist at 45 ft span with I approximately 400 in^4 would satisfy both strength and deflection. Verify against SJI load tables for the specific joist designation.

Step 6 — Check ponding stability: Cp (girder): assume W21x44 girder spanning 45 ft, Ip = 843 in^4. Cp = 32 x 45 x 45^4 / (10^7 x 843) = 32 x 45 x 4.1 x 10^6 / (8.43 x 10^9) = 0.070. Cs (joist): assume 28K10, Is approximately 400 in^4. Cs = 32 x 45^4 / (10^7 x 400) = 32 x 4.1 x 10^6 / (4.0 x 10^9) = 0.033. Cp + 0.9 x Cs = 0.070 + 0.030 = 0.100 less than 0.25. Ponding stable.

Step 7 — Check net uplift on connections: Net uplift per joist = 29.4 x 5 x 45 / 1000 = 6.6 kips (total uplift per joist). Each joist seat (2 seats) resists 3.3 kips. Joist seat weld capacity (typical 1/4 in fillet, 2 in long each side): phiRn = 0.75 x 2 x 0.928 x 2 x 2 = 5.6 kips per seat. OK.

Common mistakes engineers make

1. Applying snow load and roof live load simultaneously. ASCE 7 treats S and Lr as non-concurrent variable loads. They appear in different positions in the load combinations (one as the primary 1.6 factor, the other as 0.5 companion). Adding them together overestimates the demand.

2. Ignoring rain loading because "the roof has drains." Rain load R per ASCE 7 Section 8 assumes the primary drains are fully blocked. The design rain depth is measured to the secondary drainage level. Engineers who delete R from the load combinations are ignoring a load that has caused real collapses.

3. Using floor live load reduction for roof members. ASCE 7 Section 4.7 live load reduction applies to floor live loads, not roof live loads. Roof live load reduction uses the separate R1/R2 factors from Section 4.8. Applying the 15-psf-per-tributary-area floor reduction to roof framing is incorrect.

4. Designing roof framing for gravity only without checking net uplift. At building edges and corners, wind uplift can exceed twice the dead load. If the dead load is light (15–20 psf metal roof) and the wind uplift is high (40–65 psf in Zones 2 and 3), the net uplift is substantial and governs connection design.

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Related references

• Load Combinations ASCE 7
• Live Load Reference
• How to Verify Calculations
• load combinations
• wind load basics
• beam deflection limits reference
• structural wind load calculator
• snow load calculator
• Purlin Girt

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