What Purlin for a 6 m Span? The Section, and the Wind-Uplift Check That Decides It

Ask an engineer "what purlin for a 6 m span" and the honest first answer is a question back: under what, and held how? For the gravity case it really is close to a table lookup, a thin folded section carrying a roof over 6 m is a well-trodden problem. The trap is that the purlin is almost never sized by the case you look up. It is sized by the case you have to remember, and on an exposed roof that case is wind uplift.

This article works one concrete purlin all the way through. A single-span cold-formed lipped channel, 6.0 m between rafters, carrying a light metal roof. We solve it on the CalcSteel finite element engine for gravity and for uplift, cross-check every moment against hand statics, then run the section capacity check for both cases. The result is the whole point of the piece: the section sits at utilisation 0.41 under the gravity combination, comfortable, and at 1.13 under uplift, overstressed. The case that carries the smaller moment is the one that fails, because it loads the flange the sheeting never braced.

Here is the member we carry through the article. A simply supported single span of L = 6.0 m, pinned at one rafter and on a roller at the other, spaced at 1.5 m on centre across the roof so each purlin collects a 1.5 m wide strip of load. The section is a cold-formed lipped channel, a C 200x75x20x2.66 in steel grade fy = 350 MPa, one of the standard NBR 6355 purlin sizes and a natural first pick for a 6 m bay.

Two facts about that section decide everything downstream. First, it is thin, 2.66 mm of folded strip, which is what makes it light and cheap, and also what makes it prone to buckling long before the steel yields. Second, it is open and singly symmetric, so it has very little torsional and warping stiffness. When the compression flange is not held, the section would rather twist sideways than keep bending, and that is lateral-torsional buckling. The roof sheeting fixed to the top flange braces it against exactly that, but only the top flange, and only while the top flange is the one in compression. Hold on to that condition.

Three load cases reach this purlin, and because they do not act at full value together we keep them separate and combine them afterward. Taken over the 1.5 m spacing, each area pressure becomes a line load along the purlin:

• Dead load D, the sheeting, fixings and the purlin itself, about 0.20 kN/m2. Over 1.5 m that is 0.30 kN/m down.
• Snow or roof imposed load S, about 0.60 kN/m2, giving 0.90 kN/m down.
• Wind load W, which on a low-slope roof is dominated by suction, the net pressure pulls up. Taken as about 0.90 kN/m2 of net uplift for an exposed bay, it is 1.35 kN/m up, the only load that lifts.

Two strength (LRFD) combinations bracket the design. The gravity maximum is 1.2D + 1.6S = 1.80 kN/m pressing down. The uplift combination pairs minimum dead load with full wind so nothing helps resist the lift: 0.9D + 1.0W, which nets to 1.08 kN/m acting up. Notice the uplift line load is smaller in magnitude than the gravity one, 1.08 against 1.80. If moment were the whole story, gravity would win and we would be done. It is not, and that is the article.

Drop the purlin into the CalcSteel engine, apply the gravity line load of 1.80 kN/m, and read the diagram. For a simply supported span under a uniform load the answer is the most familiar in structural engineering, and the engine returns it exactly:

• Peak bending moment at midspan, M = 8.10 kN·m, matching wL squared over 8 = 1.80 x 6.0 squared / 8 = 8.10 to four decimals.
• Peak shear at the supports, V = 5.40 kN, matching wL over 2 = 1.80 x 6.0 / 2 = 5.40.
• Each reaction 5.40 kN down into the rafter.

Under this gravity moment the top flange is in compression and the bottom flange in tension. The sheeting is screwed to that top flange, so the compression flange is continuously braced, it cannot buckle sideways, and the section can develop its full bending capacity. This is the easy, well-behaved case, and it is exactly the one a span table is built for. It is also, as we are about to see, not the one that sizes the purlin.

Before the uplift twist, get a feel for the gravity demand yourself. The calculator below is the CalcSteel beam calculator. Enter a span of 6 m, a uniform load of 1.80 kN/m and simple supports, and it returns the reactions, the shear and bending-moment diagrams and the mid-span deflection, the same numbers the engine gave above. Then try the uplift value of 1.08 kN/m and watch the moment fall to 4.86 kN·m. The next sections show why that smaller number is the dangerous one.

Now size the C 200x75x20x2.66 for gravity. Its section properties, the same values the CalcSteel catalog carries, are the input to every check:

Bending, gravity. With the compression flange braced by the sheeting, lateral-torsional buckling is switched off and the section reaches its yield moment, My = Fy x Sx = 350 x 63.15 x 10 cubed = 22.10 kN·m. With the resistance factor phi = 0.90 that is a design capacity of 19.9 kN·m. Against the 8.10 kN·m demand the utilisation is 8.10 / 19.9 = 0.41. Comfortable. (The full cold-formed check trims this a little for local buckling of the thin plate elements, but not enough to change the story.)

Deflection. Under the service gravity load D + S = 1.2 kN/m the engine reports a mid-span sag of 16.0 mm, matching the hand formula 5wL to the fourth over 384EI to four decimals. The common purlin limit of L/180 allows 6000 / 180 = 33.3 mm, so deflection sits at 0.48. Shear, at 5.40 kN against a web capacity many times larger, is nowhere near. Read the gravity column and the purlin looks finished: bending 0.41, deflection 0.48, shear trivial. A span table would stop here and hand you the C200.

Now run the uplift combination, 1.08 kN/m acting up. The engine returns a peak moment of 4.86 kN·m (wL squared over 8 = 1.08 x 36 / 8, matched exactly) and a shear of 3.24 kN. Both are smaller than the gravity values. The reactions also reverse: instead of 5.40 kN pressing into the rafter, the support now pulls 3.24 kN up, which is why the purlin cleats and their fasteners have to be detailed for uplift, a whole separate failure the gravity case never hints at.

But the number that matters is not the moment, it is which flange carries it. Under gravity the top flange was in compression and the sheeting braced it. Under uplift the moment reverses, so the bottom flange goes into compression, and nothing braces the bottom flange. It hangs free below the sheeting over the entire 6 m span. The section is now a long, thin, unrestrained compression element that would rather twist sideways than keep bending. That is lateral-torsional buckling, and it changes the capacity by an order of magnitude, even though the demand went down.

Put a number on it. The bottom flange is unbraced over the full Lb = 6.0 m, so we compute the elastic lateral-torsional buckling moment of the section from its own stiffness, Mcr, and map it to a capacity with the AISI Direct Strength Method global-buckling curve. With Iy = 78.28 cm4, J = 0.240 cm4 and Cw = 4267 cm6, and a moment-gradient factor Cb = 1.13 for a uniformly loaded simple span:

Read the top row. Over 6 m the elastic buckling moment is only 4.79 kN·m, so far below the yield moment of 22.10 that the section buckles long before it yields, and the design capacity is 4.31 kN·m. Against the 4.86 kN·m uplift demand the utilisation is 1.13. The purlin is overstressed. The exact same section that sat at 0.41 in gravity bending is unsafe under a load case that carries 40 percent less moment. Nothing about the demand grew, the capacity collapsed, because the compression flange lost its brace.

The instinct after a failed check is to go up a section. Here that is the expensive lever and almost the wrong one, because the uplift check is a buckling check and buckling capacity is governed by the unbraced length, not mainly by the section size. Add a single line of anti-sag rods (bridging) at midspan and the unbraced length of the bottom flange drops from 6.0 m to 3.0 m. That alone lifts the capacity from 4.31 to 13.4 kN·m and the uplift utilisation from 1.13 to 0.36. The failing purlin passes, on the same C200, for the price of a few rods and a coupler.

Line the whole design up and the shape of the problem is clear:

Gravity and deflection are both under 0.5, so the section has plenty of margin where a table would look. The only failing check is the one a table cannot show you, and it is fixed not with steel but with a brace. Bridging at midspan, or a proven diaphragm connection to the sheeting that actually restrains the bottom flange, is the standard detail. Go up a section only if the geometry rules out the brace.

The workflow, gravity demand then uplift demand then a capacity that depends on bracing, is the same everywhere. The packaging differs.

• United States (AISI S100). The Direct Strength Method computes the member from its elastic buckling moments, and the global (lateral-torsional) curve is the one that collapses under uplift. AISI also credits sheeting restraint through the R-factor procedure of AISI S908, calibrated by physical base tests.
• Europe (EN 1993-1-3). Eurocode models the sheeting as an explicit rotational spring restraining the purlin, so the free-flange check under uplift is done on a flange elastically held by the roof, an approach traced to Peköz and Soroushian. The load combination with permanent action favourable and wind leading is the uplift case.
• Brazil (NBR 14762 with NBR 6355 sections). The Brazilian cold-formed standard follows the same effective-section and global-buckling philosophy, on the NBR 6355 profile catalog this C section comes from, with serviceability for purlins commonly at L/180.

Different symbols, one idea. Every one of these codes gives you the uplift combination alongside the gravity one, and every one drops the capacity when the compression flange is unbraced. The CalcSteel engine checks the member against AISC 360, Eurocode 3 and NBR 8800 from the same forces, so the governing case is computed rather than remembered. For the load side, our note on load combinations and on wind loads covers where the 1.08 kN/m came from.

"Just check the gravity bending, it is the biggest moment." The biggest moment is not the governing check. On this purlin gravity bending is 0.41 and uplift bending is 1.13, on the same section, because uplift loads the unbraced flange. Magnitude of moment does not tell you which case wins.

"The sheeting braces the purlin, so buckling is not an issue." The sheeting braces the top flange. Under uplift the compression moves to the bottom flange, which the sheeting does not hold. That is the entire reason uplift governs. A purlin can be fully braced for gravity and completely unbraced for uplift at the same time.

"Wind uplift is smaller than gravity, so gravity governs." Smaller in load and in moment, yes. But it acts through a much smaller capacity, because the free bottom flange over 6 m buckles at a fraction of the yield moment. A case is governed by demand relative to its own capacity, and the two capacities here differ by more than four to one.

"Go up a section to fix the uplift failure." Usually the wrong lever. Buckling capacity depends on unbraced length, so a line of anti-sag rods buys more capacity, more cheaply, than a heavier gauge. Fix the length before you add the steel.

"C or Z, does it matter here?" For a single simple span the two behave similarly, and both fail this uplift check bare. Z sections shine on continuous multi-span roofs because they lap over the supports and share the moment. For one 6 m simple span, the bracing decision matters far more than the C-versus-Z decision.

So, what purlin for a 6 m span? Not a name off a table. On this roof a C 200x75x20x2.66 is the right family and gauge, but only once you have run the case the table cannot: wind uplift, which loads the unbraced bottom flange and drops the bending capacity from 19.9 kN·m to 4.31, failing a section that gravity passed at 0.41. The section is an output of the governing check, and for an exposed purlin that check is uplift.

The demand side is not guesswork, it is equilibrium: on this span the engine reproduced wL squared over 8, wL over 2 and 5wL to the fourth over 384EI to four decimals. The capacity side is where judgement lives, and it turns on one detail, whether the bottom flange is braced. CalcSteel runs the load cases, forms the combinations and reports the governing bending, shear and deflection check for the section at once, so the uplift case is computed, not forgotten. Model your own 6 m purlin in the editor, add the uplift combination, and watch the utilisation cross 1.0. For the underlying mechanism, our guides to lateral-torsional buckling and purlin sizing cover the buckling mode and the broader design loop this worked example lives inside.