How to Calculate Ponding Head for ASCE 7-22 Rain Loads: Design Guide 40 and Iterative Analysis

Q: What is ponding head in ASCE 7-22?

Ponding head, dp, is the extra water that collects because the roof deflects under unfactored dead load plus unfactored rain load. ASCE 7-22 Equation 8.2-1 makes it the third term of the rain load, R = 5.2(ds + dh + dp). The secondary drainage fixes the water level; the roof sags below that level, and each inch of sag at a point adds 5.2 psf there.

Q: How do you calculate ponding head with the Design Guide 40 Bp method?

With spans and spacing in ft and moments of inertia in in.4, compute Cp = 32LsLp4/(107Ip) for the girders and Cs = 32SLs4/(107Is) for the joists (Design Guide 40 Equations 3-4 and 3-5). Use 0.8I for rolled steel and I/1.15 for joists. Then Bp = 1/(1 − 1.15Cp − Cs), the rain load is R = Bp(D + R0) − D with R0 = 5.2(ds + dh), and dp = R/5.2 − (ds + dh).

Ponding head $d_{p}$ is the extra water that collects because the roof sags under it. This article calculates it two ways on one steel joist bay: the Design Guide 40 amplification factor $B_{p}$ , a few lines by hand, and an iterative analysis that refills the deflected roof until the water stops changing.

The two can disagree by a factor of two. On the example bay, $B_{p}$ gives 79 psf and the iterative analysis gives 41 psf, because $B_{p}$ assumes a flat bay and this one slopes.

Not every jurisdiction has adopted ASCE 7-22, and the edition decides whether $d_{p}$ is part of the rain load at all. Putting the load on the members is covered in the companion article, designing steel joists and girders for ponding rain loads.

Ponding Head Calculation at a Glance

Step	What to do	On the example bay
First-order rain load	$R_{0} = 5.2 (d_{s} + d_{h})$ on the undeflected roof	23.4 psf
Method 1: $B_{p}$	Amplify $D + R_{0}$ , with $0.8 I$ on rolled steel and $I /1.15$ on joists	$B_{p} = 2.43$ , $R = 78.5$ psf
Method 2: iterative	Fill, analyze, sag, and refill until the water converges	$R = 41.2$ psf at the low point, $d_{p} = 3.4$ in.
Choose a method	$B_{p}$ loses accuracy on sloped bays and around $B_{p} \geq 2$	Outside both limits, so the iterative result is the accurate one
Apply the load	Point loads, or a shape that stays on top of the water	See the companion article

Ponding Head ( $d_{p}$ ) Is the Water the Sag Holds

ASCE 7-22 Equation 8.2-1 gives the rain load as:^[1]

R = 5.2 (d_{s} + d_{h} + d_{p})

8.2-1

Static head $d_{s}$ : depth up to the inlet of the secondary drainage system for structural loading (SDSL)
Hydraulic head $d_{h}$ : depth above the inlet needed to push the design flow through it
Ponding head $d_{p}$ : the extra depth where the roof sags below that water level

Each inch of water is 5.2 psf. $d_{s}$ and $d_{h}$ are measured on the undeflected roof and set the water level (ASCE 7-22 Section 8.1.2). The level never moves; only the roof does (Design Guide 40 Section 2.3).^[2]

Water on the undeflected roof, d_s + d_h Water the sag adds, d_p

Section along the middle joist of the example bay, low edge on the right, at the converged pass of the iterative analysis. The water level never moves; the roof sags below it. Vertical scale exaggerated.

ASCE 7-22 Commentary C8.2 accepts four ways to find where the sag stops, all covered in Design Guide 40 Chapter 3.^[1,2] This article works the two that need only a hand calculation or a spreadsheet.

Edition note: $d_{p}$ appears only in ASCE 7-22. ASCE 7-16 Equation 8.3-1 stops at $R = 5.2 (d_{s} + d_{h})$ and checks susceptible bays separately under Section 8.4.^[3] For steel, that check was AISC 360-16 Appendix 2, which AISC 360-22 removed; AISC/SJI Design Guide 40 (2024) replaced it. Design Guide 40 Section 1.2.1 notes that an ASCE 7-22 rain load including $d_{p}$ satisfies 2021 IBC Sections 1611.1 and 1611.2, so both methods also work on an ASCE 7-16 project.^[2]

The Example Bay: First-Order Rain Load of 23.4 psf

A single-story retail building in Bentonville, Arkansas, Risk Category II. The members were sized for $1.2 D + 1.6 L_{r}$ at L/240 and pass. Rain has not been checked.

Bay: 30 × 30 ft interior bay, W16×26 girders, 16K3 joists at 5 ft on center
Slope: 1/4 in. per ft along the joists, low edge along a girder
Dead load: $D = 15$ psf
SDSL: 6-in. overflow standpipe on a 4-in. outlet, inlet 2 in. above the low point, on its own drain line, no controlled flow
Roof area per overflow drain: $A = 2, 700 ft^{2}$
Rainfall intensity: $i = 6.54$ in./hr, 15-minute, 100-year (NOAA Atlas 14)^[4]

The flow through the overflow is $Q = 0.0104 A i = 0.0104 (2, 700) (6.54) = 184$ gal/min (ASCE 7-22 Commentary Equation C8.2-1). The 6-in. standpipe column of Commentary Table C8.2-1 reads 2.5 in. at both 150 and 200 gal/min, so $d_{h} = 2.5$ in.^[1]

R_{0} = 5.2 (d_{s} + d_{h}) = 5.2 (2 + 2.5) = 23.4 psf

Under ASCE 7-16 that is the whole rain load. Under ASCE 7-22 it is the starting point for $d_{p}$ . The rain load calculation guide covers the SDSL rules, $d_{s}$ , and $d_{h}$ in detail.

Method 1: Amplify the First-Order Load With $B_{p}$

Denavit's (2019) amplified first-order method multiplies the first-order load by an amplifier built from one flexibility coefficient for the girders and one for the joists (ASCE 7-22 Commentary Equations C8.2-4 to C8.2-6; Design Guide 40 Equations 3-1 to 3-5).^[5,1,2]

B_{p} = \frac{1}{1 - 1.15 C _{p} - C _{s}}

C8.2-4

C_{p} = \frac{32 L _{s} L _{p}^{4}}{1 0 ^{7} I _{p}} C_{s} = \frac{32 S L _{s}^{4}}{1 0 ^{7} I _{s}}

DG40 3-4, 3-5

Spans and spacing are in ft and $I$ in in.⁴. The 32/10⁷ is the Commentary's $γ / (π^{4} E)$ with $γ = 62.4$ pcf and $E = 29, 000$ ksi, rounded up from 31.8/10⁷.

Three rules go with it:^[2,1]

Rolled steel at $0.8 I$ , for partial yielding (Design Guide 40 Section 2.3)
Joists at $I /1.15$ , for shear deformation (Design Guide 40 Section 2.3). A joist's $I$ comes from the SJI equation $I = 26.767 W_{360} (L - 0.33)^{3} /1 0^{6}$ , with $W_{360}$ the live load for L/360 deflection from the load tables (Design Guide 40 Equation 2-1, which rounds the constant to 26.8). That equation gives the gross $I$ , without shear deformation, so the reduction always applies (Design Guide 40 Section 2.8).
Amplify dead plus rain, then take the dead load back out, because the dead load sags the roof before the rain arrives and that sag fills too (ASCE 7-22 Commentary C8.2)

R = B_{p} (D + R_{0}) - D d_{p} = \frac{R}{5.2} - (d_{s} + d_{h})

Skip both stiffness reductions on the example bay and $R$ comes out 59.8 psf instead of 78.5 psf: 24% low, and still large enough to look plausible.

$B_{p}$ Worked on the Example Bay

Effective moments of inertia: W16×26, $I_{p} = 0.8 (301) = 240.8$ in.⁴; 16K3, $I_{s} = 67.3/1.15 = 58.6$ in.⁴.

C_{p} = \frac{32 L _{s} L _{p}^{4}}{1 0 ^{7} I _{p}} = \frac{32 ( 30 ) ( 30 ) ^{4}}{1 0 ^{7} ( 240.8 )} = 0.323

DG40 3-4

C_{s} = \frac{32 S L _{s}^{4}}{1 0 ^{7} I _{s}} = \frac{32 ( 5 ) ( 30 ) ^{4}}{1 0 ^{7} ( 58.6 )} = 0.221

DG40 3-5

B_{p} = \frac{1}{1 - 1.15 C _{p} - C _{s}} = \frac{1}{1 - 1.15 ( 0.323 ) - 0.221} = \frac{1}{0.408} = 2.45

C8.2-4

R = B_{p} (D + R_{0}) - D = 2.45 (15 + 23.4) - 15 = 79.1 psf

d_{p} = R /5.2 - (d_{s} + d_{h}) = 79.1/5.2 - 4.5 = 10.7 in.

With the exact constant, 31.8/10⁷, the free calculator gets $B_{p} = 2.43$ and $R = 78.5$ psf, the values in the figure. Either way the rain load is more than three times the 23.4 psf ASCE 7-16 value.

Rain loadR = 78.5 psf Ponding headd_p = 10.6 in. Amplifying R₀ alone57 psf, too low

The B_p method on the example bay, psf. The dead load sags the roof before the rain arrives, and that sag fills too, so B_p multiplies dead plus rain. The dead load comes back out at the end.

Under ASCE 7-16, 23.4 psf looks finished, but the bay fails the Section 8.4 investigation. Its AISC 360-16 Appendix 2 index, $C_{p} + 0.9 C_{s}$ , is 0.46 against a 0.25 limit; Appendix 2 uses the full girder moment of inertia, so its $C_{p}$ is 0.26, not 0.32. Design Guide 40 Section 1.3 notes that roofs that pass the limit can still see ponding amplification of up to 40%.^[2]

What $B_{p}$ Is Doing

A load on a member makes it sag, and the sag holds $C$ times that load in more water. That water sags it again. The rounds add to $1 + C + C^{2} + \dots = 1/ (1 - C)$ , with $C = 1.15 C_{p} + C_{s}$ . If $C$ reaches 1, the rounds stop shrinking and the bay is ponding-unstable.

Sum so far2.43

On the example bay, C = 1.15C_p + C_s = 0.589. Each round of water is 0.59 times the round before, and the rounds add up to B_p = 1/(1 − C) = 2.43. If C reached 1, the rounds would stop shrinking and the bay would be ponding-unstable.

This reading is mine, and it is exact only for one member under a sine-shaped load. For a girder-and-joist bay, $B_{p}$ comes from Marino's closed-form solution, and the 1.15 is a calibration factor (Design Guide 40 Section 3.2).^[2] Both coefficients scale with span to the fourth power, which is why long bays are where ponding governs.

Method 2: Refill the Deflected Roof Until the Water Converges

Start with $d_{p} = 0$ , analyze the roof, refill the deflected shape, and repeat until the water converges. If it diverges instead, the bay is ponding-unstable (ASCE 7-22 Commentary C8.2).^[1] Design Guide 40 Section 3.4 calls it the most general method, because it handles slope, partial ponding, camber, and snow.^[2] Each pass has four steps:

Fill to the level. On the undeflected roof, 4.50 in. deep at the low edge.
Turn the water into point loads. A node every 1.5 ft along each joist takes the water on its tile (Design Guide 40 Figure 3-1).^[2]
Analyze the joists, then the girders. The girders carry the joist end reactions, doubled for the adjacent bay (Design Guide 40 Section 4.2).^[2]
Sag and refill. New depth is old depth plus girder sag plus joist sag: 4.50 + 2.01 = 6.51 in. at the low edge.

Step through one pass on the middle joist of the example bay, then run all of them:

The bay: two W16×26 girders and seven 16K3 joists at 5 ft, sloping 1/4 in. per ft to the low edge.
Each joist is cut into pieces: a node every 1.5 ft, 21 on each joist.
Water fills to the level, 4.50 in. above the low edge, held there by the overflow.
The water sags the roof, the sag holds more water, and so on. After 17 passes it settles into a dish.
Cut a section along the middle joist, go back to the first pass, and follow it through.

On the roof as built the water is 4.50 in. deep at the low edge and runs out 18 ft up the joist.

Each node takes the water on its 1.5 × 5 ft tile, halfway to the next node each way.
5.2 psf per inch of depth × 7.5 sq ft = one point load, 161 lb at the first node off the girder.

The joist takes the point loads, plus 75 plf of dead load.
It's a simple span: find the end reactions.
Find how far it sags: 1.11 in.
Each low-end reaction, doubled for the next bay, pushes down on the girder.
Find how far the girder sags: 2.01 in. at midspan.

Pass 1's water, on the roof as built.
The girders sag, carrying the joist ends down.
The joist sags between its ends. Add the two.
Refill to the same level: deeper at the low edge, and farther up the joist.
New depths, new point loads. That's pass 2.

Each pass adds a little under half of what the one before added, so the water settles: 7.92 in. at the low edge, 41.2 psf.

Step 1 of 19

The iterative analysis on the example bay (30 × 30 ft, 16K3 joists at 5 ft, W16×26 girders, 1/4 in. per ft): the whole bay, then one pass on the middle joist, then all 17 passes. Every shape is drawn from the free calculator's own analysis. Blue is water over the undeflected roof; orange is water the sag adds. Vertical scale exaggerated.

The water on the bay goes 6.3, 12.8, 15.7, then 17.0 kips over the first four passes. Each pass adds a little under half of what the one before added, so the analysis converges, here in 17 passes. If each pass added more than the last, the roof would be ponding-unstable and must be made stiffer (Design Guide 40 Section 3.4).^[2]

At convergence the water is 7.92 in. deep at the low point of the middle joist:

R = 5.2 (7.92) = 41.2 psf

d_{p} = 7.92 - (2 + 2.5) = 3.4 in.

Applying the load: 41.2 psf is the load at the low point of the middle joist, not a uniform load for the bay. The companion article, designing steel joists and girders for ponding rain loads, covers the load shapes on the joists, the load across the joists and on the girders, the load combinations, and the minimum joist shear.

Why $B_{p}$ Gives Nearly Twice the Iterative Load

$B_{p}$ treats the bay as flat. On the example bay:

$B_{p}$ method: 78.5 psf, uniform over the bay
Iterative, slope taken out: 77.2 psf at the deepest point, 55.1 psf averaged over the bay
Iterative, 1/4 in. per ft as built: 41.2 psf at the low edge, 20.3 psf averaged over the bay

d_s + d_h = 4.5 in. over the undeflected roof Ponding, d_p

Rain load on the middle joist of the example bay, low edge on the right, all on one scale. The B_p method applies one uniform load (15.1 in. of water) over a flat bay. The iterative analysis on the same bay with the slope taken out gives nearly the same peak. On the roof as built, the water runs to the low edge. Vertical scale exaggerated.

The small gap at the deepest point is $B_{p}$ 's calibration. The large gap in the averages is $B_{p}$ overstating the total water (Design Guide 40 Section 3.2).^[2] The slope is what takes 79 psf down to 41.

Choosing a Ponding Analysis Method

ASCE 7-22 Commentary C8.2 lists four acceptable methods and does not rank them. Design Guide 40 Chapter 3 covers all four:^[1,2]

Method	Suited to	Watch for
Amplified first-order ( $B_{p}$ )	Hand calculation, flat bays	Runs high on sloped or very flexible bays
Iterative analysis	Sloped roofs, partial ponding, camber	No convergence means ponding instability
Negative-stiffness springs	Water over the whole bay, in a frame program	Awkward with partial ponding
Closed-form solutions	Checking a tool on a simple case	Idealized bays only

$B_{p}$ rests on Marino's (1966) idealized bay, and Design Guide 40 Section 1.3 notes its conditions seldom exist in real structures:^[2]

Perfectly flat: no slope, camber, or tapered insulation
Water over the whole bay
Identical adjacent bays, equal girders, and equally spaced, equal joists
Simple supports and no axial load

Its calibration targets the maximum joist moment, so $B_{p}$ slightly underestimates the load at the center of the bay and overestimates the girder forces and the total water (Design Guide 40 Section 3.2). Design Guide 40 Example 1 also finds it inaccurate on very flexible roofs, giving $B_{p} \geq 2$ as the example.^[2] The example bay is outside both limits: $B_{p} = 2.43$ , on a roof sloped 1/4 in. per ft.

How I use the two methods. I run $B_{p}$ on every bay first, because it takes a few lines and shows quickly whether ponding matters on that bay. Where it comes out around 2 or more, or the roof slopes, I run the iterative analysis and design from that. This order is my practice, not a requirement of ASCE 7-22 or Design Guide 40.

Tools That Run the Iterative Analysis

Three tools run the iterative loop for you:^[6,2]

Tool	What it does	Limits
SJI Roof Bay Analysis Tool	Free Steel Joist Institute Excel workbook (Design Guide 40 Chapter 4); sizes the members, then iterates the water	Needs Excel with macros; includes camber by default
Free rain load and ponding calculator	One bay in the browser: $B_{p}$ , the AISC 360-16 Appendix 2 index, the iteration, and a calc report with ASCE 7-22 and 7-16 loads	No camber. Every iterative number in this article came from it
PyPonding	Python package named in Design Guide 40 Section 3.4	Scripted or 3D work

The Bottom Line

Start from $R_{0}$ and find $d_{p}$ with $B_{p}$ or an iterative analysis. On a sloped bay, or where $B_{p}$ reaches about 2, Design Guide 40's own limits point to the iterative analysis; the SJI tool and the free rain load and ponding calculator both run it. Prose then carries the ponding head you calculate into the rain load for every region and drainage zone on the project, with hydraulic head from the Commentary tables and each step cited in the report.

Frequently Asked Questions

What is ponding head in ASCE 7-22?

Ponding head, d_p, is the extra water that collects because the roof deflects under unfactored dead load plus unfactored rain load. ASCE 7-22 Equation 8.2-1 makes it the third term of the rain load, R = 5.2(d_s + d_h + d_p). The secondary drainage fixes the water level; the roof sags below that level, and each inch of sag at a point adds 5.2 psf there.

How do you calculate ponding head with the Design Guide 40 Bp method?

With spans and spacing in ft and moments of inertia in in.⁴, compute C_p = 32L_sL_p⁴/(10⁷I_p) for the girders and C_s = 32SL_s⁴/(10⁷I_s) for the joists (Design Guide 40 Equations 3-4 and 3-5). Use 0.8I for rolled steel and I/1.15 for joists. Then B_p = 1/(1 − 1.15C_p − C_s), the rain load is R = B_p(D + R₀) − D with R₀ = 5.2(d_s + d_h), and d_p = R/5.2 − (d_s + d_h).

Should I use Bp or an iterative ponding analysis?

ASCE 7-22 Commentary C8.2 accepts both, along with negative-stiffness springs and closed-form solutions, and does not rank them. B_p assumes a perfectly flat bay with water over all of it, and Design Guide 40 Example 1 shows it losing accuracy on very flexible roofs, around B_p ≥ 2. On a 30 by 30 ft steel joist bay sloped 1/4 in. per ft, B_p gives about 79 psf and an iterative analysis gives 41 psf at the low point.

Is there free software for a roof ponding analysis?

Yes. The Steel Joist Institute publishes the SJI Roof Bay Analysis Tool, a free Excel workbook that runs the iterative analysis described in AISC/SJI Design Guide 40. The Prose free rain load and ponding calculator runs an iterative analysis of one bay in the browser and reports the ASCE 7-22 rain load beside the ASCE 7-16 value. Design Guide 40 also names PyPonding, a Python package.

Is a ponding analysis required on an ASCE 7-16 project?

For susceptible bays, yes. ASCE 7-16 Section 8.4 requires an investigation of ponding instability and strength, but ponding is not part of the rain load R. AISC 360-16 Appendix 2 provided the steel check; AISC 360-22 removed it, and AISC/SJI Design Guide 40 replaced it. Design Guide 40 notes that an ASCE 7-22 rain load including ponding head satisfies 2021 IBC Sections 1611.1 and 1611.2.

Designing steel joists and girders for ponding rain loads: the companion to this article. Load shapes on the joists, point loads on the girders, load combinations, the minimum joist shear, and what reduces the load, on the same bay
Rain load calculation per ASCE 7: the SDSL rules, static and hydraulic head, the design storm by Risk Category, and what changed across editions
Free rain load and ponding calculator: one bay, iterative ponding analysis, ASCE 7-22 and 7-16 rain loads side by side, with a calc report
ASCE 7-22 snow load changes: the snow side of ponding, including the Section 7.11 deflection check

If you read this provision differently or have run into it applied another way on a real project, reach out at support@prose-eng.com. I'm a practicing engineer, not an infallible one.

Sample report

See a real loads package, fully cited

Wind, snow, seismic, rain — generated across ASCE 7-10/16/22 with every step traced to code.

Review a sample report

References

American Society of Civil Engineers. Minimum Design Loads and Associated Criteria for Buildings and Other Structures(ASCE/SEI 7-22), Selected provisions and commentary. Reston, VA:ASCE, 2022.
American Institute of Steel Construction and Steel Joist Institute. AISC/SJI Design Guide 40: Rain Loads and Ponding. Chicago:AISC/SJI, 2024. Replaces AISC 360-16 Appendix 2, which was removed from AISC 360-2022.
American Society of Civil Engineers. Minimum Design Loads and Associated Criteria for Buildings and Other Structures(ASCE/SEI 7-16), Selected provisions and commentary. Reston, VA:ASCE, 2016.
NOAA National Weather Service, Hydrometeorological Design Studies Center. NOAA Atlas 14 Precipitation Frequency Data Server. https://hdsc.nws.noaa.gov/pfds/ Rainfall intensity by duration and return period at a site.
Denavit, M.D.(2019). “Approximate Ponding Analysis by Amplified First-Order Analysis.” Engineering Structures, 197, 109428. https://doi.org/10.1016/j.engstruct.2019.109428 Basis for the Bp amplification factor method referenced in ASCE 7-22 Commentary C8.2.
Steel Joist Institute. Roof Bay Analysis Tool with Ponding Analysis. https://steeljoist.org/resources/roof-bay-analysis-tool-with-ponding-analysis Free Excel workbook that runs the iterative ponding analysis described in AISC/SJI Design Guide 40 Chapter 4.

Calculators

Topics

Latest