Summary: The building code gates a structural analysis with an angle. A bay whose roof slope is less than one quarter of an inch per foot has to be investigated for ponding instability, and a bay at or above that slope does not. The analysis behind the gate never uses an angle again: it is a ratio of a weight of water to a weight of water, and it has a denominator that goes to zero. This article takes that gate and that ratio apart together, shows that the deflection allowance in the same code consumes most or all of the angle, and reduces the whole check to one identity that can be read with a tilt channel and a known change of load.

 

1. The One Angle in the Building Code That Is Both a Rule and a Failure Criterion

A low-slope roof does almost no structural work. It does not hold a wall back, it does not carry a vessel, it does not resist a thrust, and the bending stress in its members under a normal rain is a small fraction of what the steel can take. What it does is present a surface, and the surface has one job: get the water off. That makes the way it fails different from anything else in this series. There is no hinge to form, no wall to overturn and no shell to buckle under a vacuum. There is a shallow basin that either drains or does not.

The code treats that as a stability question and not a strength question, and it does so with a number that is an angle. Section 8.4 of ASCE 7 designates susceptible bays, which are investigated by structural analysis to confirm they have the stiffness to preclude progressive deflection. In the 2010 edition the definition was a roof slope less than one quarter of an inch per foot, qualified by the words toward points of free drainage. The 2016 edition split it into two cases that depend on how the roof is framed: a slope less than one quarter of an inch per foot where the secondary members run perpendicular to the free-draining edge, and a slope less than one inch per foot where they run parallel to it. One quarter of an inch per foot is 1.19 degrees. One inch per foot is 4.76 degrees. The two thresholds are a factor of four apart and they describe the same structure.

That is the hinge of this article. The number that decides whether a structural analysis is required is an angle, and the analysis it triggers does not contain an angle anywhere. It contains a ratio of flexibilities. So the profession is using a geometric figure to gate a calculation about something else entirely, and the two have been reconciled by a footnote rather than by a derivation.

The choice of an angle as the gate is not arbitrary either, even though the analysis behind it is not angular. The published commentary on the clause gives the reasoning in one sentence: the lesser the slope, the greater the spread of ponding. That can be turned into arithmetic, because the water surface is horizontal and the roof has to stand above it. For a depression of depth d on a roof of slope s, the flooded width is about twice d divided by s. A twenty millimetre depression on a roof at 1.19 degrees floods over roughly two metres. The same depression on a roof at three tenths of a degree floods over roughly eight. The water depth at the centre is the same in both cases, the weight of water is four times larger in the second, and nothing about the steel has changed.

The point is not academic, because the asset class is enormous. Almost every industrial building, distribution centre, big-box retail unit and light manufacturing shed in the world has a low-slope metal roof, most of them between one eighth and one half of an inch per foot, and most of them framed with open-web steel joists and a profiled deck. Those are exactly the members the code calls most susceptible, because they are the lightest and the most flexible roof type in common use.

2. What Those Slope Numbers Are in the Units an Instrument Reads

Before any of the arithmetic, the same quantity has to be put into one set of units, because the code, the drawing, the waterproofing specification and the instrument each use a different one. A slope of one quarter of an inch per foot is a ratio of 1 in 48, a grade of 2.083 percent, an angle of 1.193 degrees, and a fall of 20.83 millimetres per metre. They are the same roof.

As written	Ratio	Percent	Degrees	Millimetres per metre
1/8 inch per foot	1 in 96	1.042	0.597	10.42
1/4 inch per foot	1 in 48	2.083	1.193	20.83
1/2 inch per foot	1 in 24	4.167	2.386	41.67
1 inch per foot	1 in 12	8.333	4.764	83.33
2 percent	1 in 50	2.000	1.146	20.00
1 percent	1 in 100	1.000	0.573	10.00

Read the last three rows against the second. Two percent is the most common way of writing good drainage on a drawing, and it is four percent smaller than the number the code uses in the same clause. A roof specified at two percent is, by the letter of the clause, a susceptible bay. The gap is 0.047 of a degree, which is small enough that nobody would notice it in a specification review and large enough that the exemption does not apply.

The other observation from the table is about the instrument rather than the structure. The threshold is 1.193 degrees and the instrument’s accuracy is five thousandths of one, so the angle channel resolves the code threshold to about one part in two hundred and forty. Even the smallest angle in the table, 0.597 of a degree, is worth a hundred and nineteen steps. Resolution is not the constraint anywhere in this problem, and it is worth saying so early because the rest of the article is about a constraint that no instrument can remove.

3. The Slope That the Deflection Allowance Spends

The same code that writes the 1.19 degree threshold also writes a deflection limit for the member that has to hold that slope. Table 1604.3 of the International Building Code gives roof members a limit of L over 180 where they support no ceiling, L over 240 where they support a non-plaster ceiling and L over 360 where the ceiling is plaster. For the combination of dead plus live load the table gives L over 120, L over 180 and L over 240 respectively. Those are the numbers a designer designs to, and a member that just meets one of them is fully compliant.

Footnote e to that table then says something that ought to be more famous than it is. The preceding deflections do not ensure against ponding. Roofs that do not have sufficient slope or camber to ensure adequate drainage shall be investigated for ponding. In one sentence the code states a slope requirement, states a deflection allowance, and admits that satisfying the second does not preserve the first.

The size of the conflict is easy to compute and it is large. For a simply supported member under uniform load, the rotation at the support is 3.2 times the midspan deflection divided by the span. A member at L over 240 therefore rotates 0.764 of a degree at each end. On a deflected member the flattest point is the end, and on a roof the end is where the drain is. So the slope that the water actually has to leave through is the design slope minus that rotation.

Deflection permitted	Rotation at the support	Drain end slope from 1/4 inch per foot	From 1/8 inch per foot	From 1/2 inch per foot
L/360	0.509 degrees	0.684 degrees	0.088 degrees	1.877 degrees
L/240	0.764 degrees	0.430 degrees	reverse, 0.167 degrees	1.623 degrees
L/180	1.019 degrees	0.175 degrees	reverse, 0.422 degrees	1.369 degrees
L/120	1.528 degrees	reverse, 0.334 degrees	reverse, 0.931 degrees	0.859 degrees

Three things in that table are worth pausing on. The first is the L over 240 row, which is the ordinary case for a metal roof over a non-plaster ceiling: a roof drawn at 1.19 degrees and built to the code’s own allowance has 0.43 of a degree at the drain, which is thirty six percent of the number that was supposed to exempt it. The second is the L over 180 row, which the code permits for a roof member supporting no ceiling at all: the drain slope is down to 0.175 of a degree, fifteen percent of the threshold. The third is the bottom row, where the permitted deflection is larger than the entire design slope and the roof has a backfall before any settlement, any creep or any construction tolerance is applied.

The one eighth of an inch per foot column is the one that should worry an asset owner, because one eighth of an inch per foot is a very common as-built fall and a legitimate design value. At L over 240 it is already negative. The roof is not merely flat at the drain. It slopes the wrong way for the last part of its span, and the water has to climb to reach the outlet.

None of this is a theoretical objection. A paper published on low-slope roof drainage and repeated in the structural press records investigations of roofs with water staining, ponding, framing damage on the underside of the span and in some cases collapse, and notes that examination typically reveals a relatively level surface when compared with other roof locations. That is the same finding as the table, arrived at from the other direction: the failure is at the low end, and the low end is flat.

4. The Response That Has a Denominator

Now the loop itself. The commentary to ASCE 7 and the AISC specification both model the ponded shape as a half sine, which is sufficiently accurate for this purpose, and the derivation is short enough to do in four steps.

Take a bay whose secondary member spans L and carries a tributary width b. The member deflects by delta at midspan. Water now stands on the deflected surface, and at midspan its depth is the depth it would have had on a flat roof plus the deflection itself, because the basin is deeper than the flat surface by exactly that much. So the water load has the shape of the deflection and an amplitude of the specific weight of water times b times the quantity h plus delta, where h is the depth that the drainage arrangement would produce on a flat roof.

A sine load produces a sine deflection of amplitude equal to the load amplitude times L to the fourth, divided by pi to the fourth times E times I. Substituting, the deflection caused by the water that the deflection collected is C times the quantity h plus delta, where C is the specific weight of water times b times L to the fourth, divided by pi to the fourth times E times I.

Add the dead load deflection and solve for the total. The result is the dead load deflection plus C times h, all divided by one minus C. Read the denominator. At C equal to one the expression has no finite value, and above it the sign reverses and there is no equilibrium at all. This is not a capacity being exceeded. It is a solution ceasing to exist.

C is dimensionless and it has a physical reading, which is why it is worth carrying through the rest of the article: it is the number of millimetres the member sags for each millimetre of standing water. A bay with C of one half sags half of whatever depth stands on it, and the half it sagged now holds half as much water again, and that holds a quarter more, and the series sums to twice the depth that would have stood on a flat roof. That is why the amplification at a gain of one half is two, and it is where the denominator in the expression comes from: the sum of a geometric series whose ratio is C.

C	Amplification of the water load	Water above the flat roof case
0.10	1.11	11 percent
0.20	1.25	25 percent
0.30	1.43	43 percent
0.40	1.67	67 percent
0.50	2.00	100 percent
0.60	2.50	150 percent
0.70	3.33	233 percent
0.80	5.00	400 percent
0.90	10.00	900 percent
0.95	20.00	1900 percent

The published form of the two member check is the same expression with a coefficient on each member. ASCE 7 gives the amplification as one divided by the quantity one minus 1.15 times the primary coefficient minus the secondary coefficient. AISC states the criterion as nine tenths of the sum being less than one. They are the same eigenproblem with different constants, and on the worked example given in the ASCE commentary they differ: 1.441 against 1.342, about seven percent. A reader who needs one number should use the standard that governs the project, and a reader who needs to know whether a roof is close to the pole should notice that seven percent is the size of the disagreement.

What matters is what the expression does not contain. There is no yield stress in it, no safety factor, no load combination and no capacity. It is a ratio between two weights of water: the weight the basin can hold at its own deflected shape, and the weight that would produce that shape. Everything structural sits in the denominator, and nothing structural sits in the numerator.

ASCE 7 permits four methods for arriving at the ponding head: an iterative analysis, springs with negative stiffness, closed-form solutions for simple cases, and an amplified first-order analysis. The phrase in the middle is the most informative of the four, because it says what the water is doing mechanically. A layer that deepens as the roof sags pushes harder the further it is displaced, which is the definition of a spring with negative stiffness: it adds flexibility rather than resistance. A member and the water on it are then two springs in parallel with opposite signs, and C is the ratio of the negative one to the positive one. At C equal to one they cancel and the assembly has no stiffness at all. That is why member strength is the wrong place to look for a fix. Replacing a member with a stronger one of the same stiffness changes the gain by nothing whatsoever.

5. The Gain of a Member That Just Meets the Deflection Limit

The coefficients above are awkward to interpret because they combine a span, a spacing, a modulus and an inertia. There is a simpler identity hiding inside them. From the definition of C and the sine solution for the deflection under a uniform load q per unit area on the same tributary width, the quantity b times L to the fourth over pi to the fourth times E times I is exactly the deflection under the design load divided by that design load. So C equals the specific weight of water times the deflection under the design load, divided by the design load.

Put in words: divide the design load by the specific weight of water and you get the depth of water that weighs the same as the design load. C is the member’s sag under the design load, expressed as a fraction of that depth. When the sag equals the depth, the roof is at C equal to one. For a roof designed for twenty pounds per square foot that depth is ninety eight millimetres. For forty pounds per square foot it is a hundred and ninety five.

This identity can be checked against a published worked example rather than taken on trust. The ASCE 7 commentary gives a rectangular bay with W24 by 76 girders spanning forty feet and W18 by 35 beams spanning forty feet at eight foot spacing, a dead load of fifteen pounds per square foot, and published coefficients of 0.155 for the primary member and 0.128 for the secondary.

Quantity	Published	Recomputed here
Primary flexibility coefficient	0.155	0.1551
Secondary flexibility coefficient	0.128	0.1277
1.15 times primary plus secondary	not stated	0.306
Amplification	not stated	1.441
Rain load at a blocked primary drain	28.6 psf	28.6 psf
Rain load after amplification	not stated	47.8 psf

The two coefficients reproduce to three significant figures, which is enough to say that the identity is the same identity the standard is using and not an approximation of it. And the rest of the table is the point: the amplified rain load is sixty seven percent above the one the drainage design produced, and the extra head is ninety four millimetres of water that the roof was never drained for.

Now put the identity against the deflection limit. A member that satisfies delta equal to L over n exactly has C equal to the specific weight of water times L, divided by n times q. The member’s depth, its material, its inertia and its tributary width have all cancelled. The gain of a compliant member depends on its span and on its design load, and on nothing else.

Span	20 psf	30 psf	40 psf	50 psf
12 m	0.512	0.341	0.256	0.205
18 m	0.768	0.512	0.384	0.307
24 m	1.024	0.683	0.512	0.410
30 m	1.281	0.854	0.640	0.512
36 m	1.537	1.024	0.768	0.615

The table is the maximum gain the deflection clause permits, at L over 240, for one member. Setting it equal to one gives the span at which a member sized exactly to the code’s serviceability limit becomes ponding-unstable: 23.4 metres at twenty pounds per square foot, 35.1 at thirty, 46.9 at forty, 58.6 at fifty. Those are long spans but they are inside the catalogue. The long span open web joist series runs past forty metres, so a twenty four metre secondary member is a selection rather than a special order, and a distribution centre, a hangar or a gymnasium will have bays in that range without doing anything unusual.

There is an inversion in that table that is worth stating plainly, because it runs against the intuition of everyone who has ever specified a roof. Hold the span and the deflection ratio fixed, and the roof with the heavier design load has the smaller gain. A light industrial building in a mild climate is more ponding-susceptible than a snow-loaded roof of exactly the same geometry. The reason is arithmetic and nothing else: the gain compares the water to the design load, and the light roof has less design load to compare it to. Nothing about the steel enters, because the member’s depth, its inertia and its tributary width cancelled out of the expression in the previous paragraph.

One honest qualification belongs here. The table is one member at its limit. The standard sums two, and the sum reaches one sooner than either term does. So the table is a lower bound on the gain of a compliant bay, not an estimate of it, and the crossing spans above should be read as the point past which even a single member cannot save the bay.

The identity also names the lever, and the lever is not the obvious one. The gain falls in proportion to the member’s inertia, so doubling I halves it. But it falls with the fourth power of the span, so halving the primary member’s span divides that coefficient by sixteen. On a bay that fails, the cheap intervention is almost always an intermediate primary beam rather than a deeper secondary one, and the reason is arithmetic rather than preference. The deeper member also costs clearance, and clearance under a low-slope roof is a fixed budget set by the doors, the sprinkler mains and the racking, none of which move.

6. What the Angle Channel Reads, and What It Cannot

Everything so far has been in millimetres, and the instrument in this series measures degrees. The bridge between them is short. For a half sine deflection the rotation at the seat is pi times the deflection divided by the span, so an increment of deflection and an increment of rotation are related by that single factor. Substituting into the identity gives the operational form: C equals the specific weight of water times the change in seat rotation times the span, divided by pi times the change in load.

That form has a property worth noticing. The water depth has cancelled out. What the expression needs is a known change of load and the change of angle it produced, and the depth appears only through the load it generates. This is the reason a tilt channel belongs on this structure at all: a water depth gauge measures the numerator of the amplification, and the amplification is a property of the denominator. The same depth is a gain of two tenths on a stiff bay and eight tenths on a flexible one, and only the deflection distinguishes them.

Gain	25 mm of water	50 mm of water	75 mm of water	Times the 0.005 degree accuracy, at 50 mm
0.2	0.038 degrees	0.075 degrees	0.113 degrees	15
0.4	0.075 degrees	0.150 degrees	0.225 degrees	30
0.6	0.113 degrees	0.225 degrees	0.338 degrees	45
0.8	0.150 degrees	0.300 degrees	0.450 degrees	60
0.9	0.169 degrees	0.338 degrees	0.506 degrees	68

The table is computed for a twenty four metre span. It says that the gains that matter are between fifteen and seventy times the instrument’s accuracy, which is a comfortable margin and the opposite of the situation on a canal lining panel, where the detection threshold and the joint failure threshold fall in the same place and no instrument can separate them. Here they are separated by more than an order of magnitude, so the instrument is not the limiting factor in the chain.

The limiting factor is thermal. A roof member in sun carries a temperature gradient through its depth, and the rotation at the seat is the expansion coefficient times the gradient times the span divided by twice the depth. For a twenty four metre span and a twenty kelvin gradient that is a tenth of a degree on a one and a half metre deep member and nearly three tenths on a half metre one, which is between one and three and a half times the entire ponding signal at a gain of one half under twenty five millimetres of water. The daily cycle therefore cannot be filtered out by magnitude, and it cannot be separated by a phase test either, because both the thermal and the hydraulic signals follow the weather.

What separates them is the other half of the weather. During and immediately after rain the roof is wet, near ambient temperature and free of gradient, which is exactly when the ponding signal exists and the thermal signal does not. Reading the channel on that window, and comparing readings taken at the same temperature rather than the same clock time, is the whole of the method. The evaluation rule is correspondingly narrow: evaluate during the event, and evaluate the ratio of rotation to load rather than the rotation itself.

Two mounting consequences follow. The sensor goes on the structural member at the seat, on the top chord at the support, and it measures about the axis perpendicular to the span, because that is the axis in which the rotation defined above exists. It does not go on the membrane, where its temperature is the membrane’s temperature rather than the steel’s, and it does not go on the insulation, where it reads the insulation’s creep. The second consequence is range. The angles in this problem are fractions of a degree, so a plus or minus five degree device covers the application with a large margin and a plus or minus thirty degree device spends resolution on range nobody will use.

7. The Load Side, and a Rule That Has Been Getting Weaker

The gain is the structural half of the problem. The load half is a single line in the same standard. Rain load is five and two tenths times the sum of the static head and the hydraulic head, both in inches. The coefficient is not mysterious: it is sixty two and four tenths pounds per cubic foot divided by twelve inches per foot. One inch of water standing on a roof is 5.2 pounds per square foot, and one millimetre is 9.81 pascals.

The static head is the depth to the inlet of the secondary drainage system, so it is a construction dimension. The hydraulic head is the depth the secondary system needs above its inlet to pass the design flow, and it comes from a table: for a six inch standpipe on a four inch outlet it is one and a half inches at a hundred gallons per minute and two and a half inches at a hundred and seventy five. Together they produce the load case the structural check is run against.

Static head	Hydraulic head	Rain load	Equivalent depth
1.0 inch	not applicable	5.2 psf	25 mm
2.0 inches	not applicable	10.4 psf	51 mm
3.0 inches	not applicable	15.6 psf	76 mm
3.0 inches	2.5 inches	28.6 psf	140 mm
3.0 inches	4.0 inches	36.4 psf	178 mm

The bottom row of that table is the one the structural check assumes, and it depends entirely on the plumbing code being as strict as it once was. It has not been. Primary and overflow systems have had to be independent since 1964. In 1991 the overflow system was required to be designed for the hundred year fifteen minute rainfall, which is roughly twice the hundred year one hour figure used for the primary system, and the first International Plumbing Code in 1995 required tabulated drain capacities to be halved when sizing overflow. The current plumbing code requires the overflow system to be designed for the same rainfall as the primary system, which removed the effective doubling.

So the structural check has spent thirty years assuming a hydraulic head that the plumbing code has been progressively less inclined to provide. That is not a structural error and no amount of structural analysis will reveal it. It is the reason a bay that passed its ponding check on the drawings can still be at a gain it was never analysed for, because the secondary drain has to be taller to pass the same flow than the code once required.

8. What to Specify

Four requirements follow from the physics and none of them is about resolution.

The first is the measurement location. The seat of the secondary member, about the axis perpendicular to the span, on the steel and not on the envelope. The reason is in section six: the quantity the gain is built from is the member’s end rotation, and the end rotation exists nowhere else on the roof.

The second is a known change of load. The gain is a property of the structure and does not change with the weather, so it can be measured once and then used to interpret every subsequent storm. That measurement needs a pair of numbers taken at the same moment: a load and the rotation it caused. A staff gauge read during a storm, a rain gauge with the drainage arrangement, or a temporary load placed on the bay will all do. What will not do is a single reading, because a single reading has no denominator.

The third is weather gating. The evaluation window is the rain event and the hours after it, and the comparison is between readings at equal temperature. A channel that reports the same schedule in January and in July without knowing which is which cannot separate a gain of four tenths from an afternoon of sunshine.

The fourth is local evaluation of a ratio rather than a level. The event on this structure is not an angle exceeding a threshold. It is the ratio of rotation to load climbing, which means a device that reports only when an absolute angle is crossed will miss the beginning of the interesting part entirely, and one that reports a trend computed on the device will catch it. On a roof the difference matters more than on a wall, because the whole event happens inside a storm and the interval between uploads is the resolution of the alarm.

There is a corollary about thresholds that costs nothing to state and is regularly got wrong. Because the rotation is the gain times pi times the depth divided by the span, a single angle threshold applied across a roof with mixed spans ranks the bays by span rather than by margin. The same rotation on a twenty four metre bay is twice the gain it is on a twelve metre one, at the same depth of water. So the threshold has to be derived per bay from that bay’s own gain, or the alarm will be calibrated on the geometry of the roof rather than on the stability of it.

For selection, the bays that deserve instruments are the ones where the three factors coincide rather than the ones that look worst. That is the longest span, the lightest design load, and the highest secondary inlet above the roof surface, in the same bay. A roof with two hundred bays will typically have a handful that satisfy all three, and instrumenting those is a different proposition from instrumenting the roof.

9. Limits

No roof deployment is claimed here. The nearest thing in this manufacturer’s published record is warehouse racking, which is indoors, has a different failure mode and is a different article in this series. The arithmetic above is a design argument reconstructed from public standards, not a record of a site.

The instrument reads the member’s rotation and nothing else. It does not read the drain, the outlet, the membrane, the deck’s local ponding between joists, or a blockage. Every one of those can produce a ponded roof at a gain below one, and none of them is visible to a tilt channel. The gain tells you what the structure would do with a given depth. It does not tell you the depth.

The design load is the drawing’s design load, and on an older roof it probably is not. Re-roofing adds dead load, and the reroofing provisions of the codes have been loosened over time to the point where a positive drainage requirement has in places replaced a slope requirement. A gain computed from the original design load on a roof that has been recovered twice is optimistic by however much the second and third layers weigh.

There is one asymmetry in the deflection clause that changes the long term answer by material. For steel members the creep component of long term dead load deflection is permitted to be taken as zero. For timber and glued laminated members the code permits the creep component to be estimated as the immediate dead load deflection from the full dead load, or from half of it under dry conditions. So a steel roof’s gain is the gain at completion, and a timber roof’s gain is the gain at completion plus a creep term that the code itself allows to be a hundred percent of the dead load deflection. Two roofs of identical geometry, identical span and identical deflection ratio do not have the same long term gain.

The last limit is the one that keeps the article honest. Most bays on most roofs pass. A gain of two tenths is not a problem, a quarter of an inch per foot on a modest span is a slope that drains, and the failures that reach the literature are the ones where a long span, a light load, a low slope and a blocked primary drain arrived at the same bay on the same night. What the analysis buys is the ability to say which bay that is before the night arrives.

Frequently Asked Questions

1. Can a tilt sensor detect ponding directly? No, and it should not be specified as if it could. What it measures is the member’s rotation, and the rotation carries the quantity that decides whether the ponding is stable: the deflection per unit of load, which is the denominator of the amplification. Detecting the water is a job for a depth gauge or a drain flow sensor, and the two channels answer different questions. The depth tells you the load. The rotation tells you what the load is doing to the structure.
2. Is a water depth sensor not the simpler answer? It is simpler and it is not sufficient. The same fifty millimetres of water is a gain of two tenths on a stiff bay and eight tenths on a flexible one, and depth cannot distinguish them because the difference is in the structure. If a single channel has to be chosen, the tilt channel answers the stability question and the depth channel answers the drainage question, and on a roof the stability question is the one that collapses.
3. Where exactly does it go? On the secondary member at its seat, on the top chord at the support, measuring about the axis perpendicular to the span. Not on the membrane, where the temperature is the membrane’s and not the steel’s, and not on the insulation, where the reading is the insulation’s creep rather than the structure’s rotation. On a bar joist roof the seat is accessible from below and the sensor can be reached without opening the roof.
4. Why does a longer span make it worse when the code already limits deflection by span? Because the limit and the consequence are different functions of span. The deflection limit is a fraction of the span, so a longer member is allowed to sag further in absolute terms. The gain compares that sag with the depth of water that weighs the same as the design load, and that depth does not grow with the span. A twenty four metre member is allowed a hundred millimetres of sag, and a hundred millimetres is more than the ninety eight millimetres of water that weighs the same as a twenty pound per square foot design load. The two numbers are allowed to cross, and the clause does not check where.
5. Does a heavier design load make the roof safer? Against ponding, at the same span and the same deflection ratio, it does. The gain is the specific weight of water times the span divided by the deflection ratio times the design load, so a bigger design load in the denominator lowers the gain. This is the opposite of the usual intuition that a roof designed for snow is a robust roof, and it is a consequence of the gain being a ratio rather than a capacity. It also explains why the susceptible bays cluster in mild climates and light occupancies, which is where the design loads are smallest.

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