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Why a C Purlin Should Not Be Laid Flat (and Why Sag Rods Still Matter)

By 8 min readUpdated

On small steel roofs I sometimes see C purlins laid flat (nakahiga): the web on top, along the roof, and both flanges pointing down onto the truss top chord. Perhaps the flat web looks like a wide seat for the roof sheet.

But a C purlin is strong in one direction only. Laid flat, it carries the roof with its weak side. Here are the numbers for a sample roof checked to NSCP 2015.

A C section has a strong axis and a weak axis

Think of a plank: on its edge it hardly bends, laid flat it sags. A C purlin is the same.

For the C150×50×14×2.0 in this example:

  • Bending strength about the strong axis: φMnx = 4.173 kN·m
  • About the weak axis: φMny = 0.917 kN·m with the web side in compression (0.922 kN·m with the flange tips in compression), less than a quarter of the strong-axis strength
  • Stiffness: Ix / Iy = 1,733,263 / 161,176 = 10.75, so it bends almost 11 times more on the weak axis

On a sloping roof, the load on each purlin splits in two:

  • wn, normal to the roof: the big part, including all of the wind.
  • ws, along the slope: the small part.
C purlin laid flat and upright on a 1 : 3 top chord (sections, to scale) Two sections of the same C150x50x14x2.0 purlin on a truss top chord sloping 1 to 3, drawn to the same scale. Left, laid flat: the 150 mm web lies on top along the roof and both 50 mm flanges point down onto the chord. Marked wrong. Right, upright: the web is square to the chord, bolted to an angle cleat, with the roof sheet on the top flange. Marked as detailed. Laid flat (nakahiga) web on top, flanges down WRONG web 150 mm flange 50 mm roof sheet truss top chord 3 1 slope Upright (nakahilig) web square to the roof AS DETAILED web 150 mm angle cleat, bolted flange 50 mm roof sheet truss top chord
Figure 1. The same C150×50×14×2.0 purlin drawn to scale on a 1 : 3 top chord. Left, laid flat: the 150 mm web on top along the roof, both 50 mm flanges down. Right, upright: the web square to the roof, bolted to an angle cleat.

The correct way is upright, with the web square to the roof (nakahilig), usually bolted to an angle cleat on the top chord as detailed. Then wn goes on the strong axis and only ws on the weak axis. Laid flat, it is the reverse.

The test roof

I used the shipped sample of our Roof Framing Designer (NSCP 2015):

  • One-storey shop in Metro Manila, 12 × 24 m, trusses at 4.0 m (the purlin span)
  • Roof slope 1 : 3 (18.43°), purlins at 0.79 m along the slope, 0.40 mm roof sheet
  • C150×50×14×2.0, ASTM A1011 SS Grade 33 (Fy = 230 MPa), on the main lines. The sample uses a heavier C200×75×16×2.5 on the edge lines at the eave and ridge strips (P0, P1, P8, P9).
  • Dead load: roof sheet and purlin only (no ceiling hung from the purlins)
  • Wind 260 km/h, Exposure C

The governing gravity combination is 1.2D + 1.6Lr + 0.5W (NSCP Eq. 203-3), with D = 0.0799 kN/m, Lr = 0.75 kPa (Table 205-3) × 0.75 m on plan = 0.5625 kN/m, and the wind pressure W⁺ = 0.981 kN/m:

vertical part = 1.2 × 0.0799 + 1.6 × 0.5625 = 0.996 kN/m
ws = 0.996 × sin 18.43° = 0.315 kN/m
wn = 0.996 × cos 18.43° + 0.5 × 0.981 = 1.435 kN/m

Uplift (0.9D + 1.0W, Eq. 203-6) uses the suction instead: W⁻ = 2.360 kPa × 0.7906 m = 1.866 kN/m, so w_up = 1.866 − 0.9 × 0.0799 × cos 18.43° = 1.797 kN/m and Mu = 1.797 × 4.0² / 8 = 3.595 kN·m.

One honest note. The sheet has no laid-flat input, so Case A is my hand calculation with the sheet's loads and section values. Cases B and C are the sheet's own results for the design line, a C150 main line.

Case A: laid flat

With M = wL²/8 over the 4.0 m span:

Check Demand Capacity Ratio Result
Weak axis, Muy = 1.435 × 4.0² / 82.87 kN·m0.917 kN·m3.13FAIL
Strong axis, Mux = 0.315 × 4.0² / 80.63 kN·m4.173 kN·m0.15see combined
Combined bending (553.5)3.28FAIL
Wind uplift, weak axis (section only)3.595 kN·m0.922 kN·m3.90FAIL
Sag under Lr54.4 mm26.7 mm (L/150)2.04FAIL
The load on a purlin splits in two: which axis each part bends The factored load of 1.2D + 1.6Lr + 0.5W on one purlin is wn = 1.435 kN/m normal to the roof and ws = 0.315 kN/m along the slope; the two arrows are drawn to scale. Laid flat, wn bends the weak axis: 2.87 kN-m needed against 0.917 kN-m, and ws bends the strong axis: 0.63 against 4.173. Upright, wn bends the strong axis: 2.87 against 4.173, and ws bends the weak axis: 0.63 against 0.917 when there are no sag rods. Laid flat (nakahiga) wn = 1.435 kN/m normal to the roof ws = 0.315 kN/m along the slope wn bends the WEAK axis needs 2.87 kN·m, has 0.917 FAIL ws bends the strong axis needs 0.63 kN·m, has 4.173 Upright (nakahilig) wn = 1.435 kN/m normal to the roof ws = 0.315 kN/m along the slope wn bends the STRONG axis needs 2.87 kN·m, has 4.173 PASS ws bends the weak axis 0.63 kN·m with no sag rods, has 0.917
Figure 2. The load on one purlin, with the two arrows to scale: wn = 1.435 kN/m normal to the roof and ws = 0.315 kN/m along the slope. Laid flat, wn bends the weak axis, which needs 2.87 kN·m and has 0.917. Upright, the same wn bends the strong axis, which has 4.173.

The purlin is more than three times over. A cross-check on the gross section gives 3.01, also a FAIL. The 3.28 is higher because the wide flat web buckles locally.

The sag is the upright value times the stiffness ratio. Under D + Lr, for information, it is 5.77 mm upright and about 62 mm laid flat (5.77 × 10.75). Under workers and materials, the roof sheet goes visibly wavy between the trusses. The limits L/120 and L/150 are from IBC 2009 Table 1604.3, which the sheet uses; NSCP 2015 prints no purlin deflection limit.

If your existing roof already has laid-flat purlins, please do not panic, and do not walk on them. These ratios use the full design loads, including typhoon wind; a roof can stand for years and still lack the code strength. Have a licensed civil or structural engineer, ideally the engineer of record, assess it before typhoon season.

Case B: upright, but no sag rods

Upright, strong-axis bending is 2.870 / 4.173 = 0.688. But with no sag rods, the sheet still says no:

Check (Design Check Summary) Ratio Result
Strong-axis bending only0.688PASS
Combined bending, gravity1.375FAIL
Wind uplift, design line2.075FAIL
Torsion bound of the free flange3.025FAIL

Overall: REVISE THE ROOF FRAMING.

Why? The small slope load ws still bends the weak axis over the full 4.0 m: 0.630 / 0.917 = 0.687, and 0.688 + 0.687 = 1.375. In wind uplift the bottom flange is in compression. With no rods, the sheet conservatively treats it as unbraced over 4.0 m, so the lateral-torsional strength drops to 1.732 kN·m. The torsion row is the sheet's conservative bound for the twisting of that free flange.

Check only strong-axis bending and you see a pass. That is the trap.

Case C: upright, with sag rods

This is the sheet's own sample: 12 mm sag rods at the third points (every 1.33 m), a line near each flange, plus a ridge tie between the two ridge purlins.

Check Ratio Result
Combined bending, gravity0.703PASS
Wind uplift, design line (3.595 / 4.173)0.861PASS
Torsion bound of the free flange0.855PASS
Worst purlin line, interior bays0.994PASS

Overall: ROOF FRAMING ADEQUATE (with the sample's C200 edge lines).

The governing formula is the combined-bending interaction of NSCP 553.5, with no axial load:

Mux / φMnx + Muy / φMny ≤ 1.0

Crops of the sheet's own Design Check Summary for the two upright cases (purlin rows and the overall result; the rows in between are left out). Top, no sag rods: combined (biaxial) bending 1.375, uplift 2.075 and torsion bound 3.025, all FAIL, REVISE THE ROOF FRAMING. Bottom, with sag rods: 0.703, 0.861, 0.855 and 0.994, all PASS, ROOF FRAMING ADEQUATE.
Figure 3. Crops of the sheet's own Design Check Summary for the two upright cases (purlin rows and the overall result; the rows in between are left out). Top, no sag rods: combined (biaxial) bending 1.375, uplift 2.075 and torsion bound 3.025, all FAIL, REVISE THE ROOF FRAMING. Bottom, with sag rods: 0.703, 0.861, 0.855 and 0.994, all PASS, ROOF FRAMING ADEQUATE.

Hand check at mid-span. The rods turn the weak axis into three spans of l = 1.333 m, so Muy = 0.025 × 0.315 × 1.333² = 0.014 kN·m, on the tip side (0.922):

2.870 / 4.173 + 0.014 / 0.922 = 0.688 + 0.015 = 0.703, OK

In uplift, the bottom rods brace the free flange every 1.33 m. Lateral-torsional buckling rises to 4.69 kN·m, so the distortional strength, 4.173 kN·m, governs: 3.595 / 4.173 = 0.861.

The lesson: orientation first, then sag rods

Same main purlin, same roof, same loads. Laid flat: 3.28 in gravity and 3.90 in uplift (section strength only). Upright with no rods: 1.375 and 2.075. Upright with rods: 0.703 and 0.861.

Demand over capacity for the same purlin: laid flat, upright without rods, upright with rods Horizontal bar chart of demand over capacity ratios against the limit of 1.00, for the same C150x50x14x2.0 purlin on a 4.0 m span. Laid flat (hand calculation): gravity 3.28 FAIL, wind uplift 3.90 FAIL (section strength only). Upright with no sag rods: gravity 1.375 FAIL, wind uplift 2.075 FAIL. Upright with sag rods at the third points near both flanges: gravity 0.703 PASS, wind uplift 0.861 PASS. Demand ÷ capacity (1.00 or less passes) 0.0 2.0 3.0 4.0 Laid flat hand calculation gravity 3.28 FAIL wind uplift 3.90 FAIL Upright, no sag rods gravity 1.375 FAIL wind uplift 2.075 FAIL Upright, with sag rods gravity 0.703 PASS wind uplift 0.861 PASS limit 1.00 Same C150×50×14×2.0 purlin, 4.0 m span, same loads. Laid-flat uplift: section strength only.
Figure 4. Ratios against the limit of 1.00 for the same main purlin. Laid flat: 3.28 in gravity and 3.90 in uplift. Upright with no rods: 1.375 and 2.075. Upright with rods: 0.703 and 0.861.

Two more runs on the same sheet:

  • Rods near the top flange only. Gravity passed at 0.703, but uplift stayed at 2.075, FAIL. A top line does not brace the bottom flange.
  • A bigger purlin instead of rods. A C200×75×16×2.5 has about 73% more steel (903.2 against 522.8 mm²). Without rods it passed gravity and the main uplift check, but still failed the sheet's conservative free-flange torsion check (1.634).

Here the rods solved it with far less steel.

What to check on site

  1. Purlins upright as detailed, seated and bolted on the cleat. Never laid flat unless the engineer of record designed it that way.
  2. Sag rods: the number of lines and their positions exactly as the plans show. In this sample, two lines at the third points (common practice for a 4.0 m span).
  3. If the plans show rods near both flanges, check both lines. The bottom line braces the free flange in uplift.
  4. The ridge tie and the ties at the ends of the rod lines, as detailed.
  5. Rods straight and snug, nuts on both sides, every cleat fully bolted and welded. If anything differs from the plans, or there is no purlin detail, ask the engineer of record.
Sag rods in one 4.0 m bay (plan of one roof slope, to scale) Plan of one roof slope between two trusses 4.0 m apart, drawn to scale. Ten purlin lines, P0 at the eave to P9 at the ridge, 0.79 m apart along the slope; the edge lines P0, P1, P8 and P9 are C200x75x16x2.5 and the main lines P2 to P7 are C150x50x14x2.0. Two lines of 12 mm sag rods cross the purlins at the third points, 1.33 m apart; at each position there is a rod line near the top flange (solid) and one near the bottom flange (dashed). At the ridge, a straight tie continues across to the ridge purlin of the other slope. One bay of one roof slope, seen square to the roof truss truss ridge P0 P1 P2 P3 P4 P5 P6 P7 P8 P9 eave 1.33 m 1.33 m 1.33 m purlin span 4.0 m (truss to truss) 0.79 m Ridge tie straight rod across the ridge to the ridge purlin of the other slope Edge lines P0, P1, P8, P9 C200×75×16×2.5 (heavy lines) 12 mm sag rods, two positions at the third points of the span line near the top flange line near the bottom flange Main lines P2 to P7 C150×50×14×2.0 Rod lines tied at both ends as detailed on the plans
Figure 5. Plan of one 4.0 m bay of the sample roof, to scale: purlin lines at 0.79 m (the overhang line P0 is 0.63 m below P1), two positions of 12 mm sag rods at the third points (1.33 m apart), a line near the top flange and a line near the bottom flange at each, and the ridge tie.

This is not about any one trade. A laid-flat purlin looks tidy, and a purlin without rods looks finished. The fix is a clear purlin detail on the plans and a quick look before the roofing goes on.

General information only. Follow the approved structural plans and the engineer of record.