Cold-formed thin-walled section in compression to SIA 263
Checks a thin-walled cold-formed section in compression at the ultimate limit state, to SIA 263:2013: effective widths of the walls, distortional buckling of the edge stiffeners, flexural buckling about both axes on the reduced section, and section resistance. Every step shows its formula and the clause it comes from.
Basic SIA 263:2013
Part of the Basic plan
This module is included in the Basic plan and above, with its calculation note.
About this check
clauses, worked example and questions
Checks a thin-walled cold-formed section in compression at the ultimate limit state, to SIA 263:2013: effective widths of the walls, distortional buckling of the edge stiffeners, flexural buckling about both axes on the reduced section, and section resistance. Every step shows its formula and the clause it comes from.
What it checks
- Gross section from the mid-line of the walls, with sharp corners: A, Iy, Iz, iy and iz.
- Effective width beff of every flat, compressed at σ = fy,k: the web as an internal flat (k = 4.000), the flanges and lips as parts of an edge stiffener.
- Distortional buckling of the flange-and-lip stiffener: the spring stiffness K given by the web, EN 1993-1-3 (5.10b); the elastic critical stress σcr,s = 2 · √(K · E · Is)/As, (5.15); and χd from λ̄d = √(fy,k/σcr,s), 5.5.3.1. The stiffener is then taken with the thickness χd · t.
- Effective area Aeff = Σbeff · t and the thinness factor βA = Aeff/A, never above 1.0.
- Relative slenderness λ̄K = (λK/λE) · √βA, with λK on the gross section.
- Flexural buckling about both axes, clause 4.5.1: curve b for a plain or lipped channel, and NK = χK · βA · A · fy,k. The resistance with stocky walls (βA = 1) is shown for comparison.
- Section resistance, clause 4.1.3: the effective section yielding, Aeff · fy,k/γM1, and the net section fracturing, 0.9 · Anet · fu,k/γM2.
- Shift of the effective centroid eN, the moment NEd · eN it causes, and the force on each intermediate support, FEd = 0.01 · NEd.
What you enter and what you get
You enter fy,k (the value the manufacturer guarantees) and fu,k, E (clause 2.2), the section (plain channel or lipped channel from h, b, the lip c and the core thickness t without the zinc coating, or any other thin-walled section by its properties), the member length, the end conditions and intermediate supports about each axis or the buckling lengths directly, the inclination α, the loading (a centred axial force, or an axial force with uniaxial bending), NEd, γM1 and γM2 (clause 4.1.3) and any holes deducted.
You get the effective widths, the distortional buckling steps, every resistance with its clause, the governing axis and the utilisation of each check with a pass or fail. With the Basic plan, it prints as an A4 calculation note.
Assumptions and limits
- Torsional and flexural-torsional buckling, which can govern for an open thin-walled section such as a channel, are not checked.
- A channel is symmetric about y only. When its flanges lose width, the effective centroid moves by eN, and the moment NEd · eN about z is not included in the buckling check; it must be added in an interaction check.
- Under an eccentric force only the compressed part is reduced, so the reduced section loses its symmetry.
- Intermediate supports count only when tied to a bracing.
Worked example
A lipped channel with h = 150 mm, b = 60 mm, c = 20 mm and t = 2 mm in fy,k = 350 N/mm², 3.00 m long with pinned ends held against sway and one intermediate support about the weak axis, under a centred NEd = 60 kN. These are the module's own results for its worked example, computed when this page was built.
| Input | Value | Ref. |
|---|---|---|
| Characteristic yield strength fy,k | 350 N/mm² | § t.1 |
| Modulus of elasticity E | 210000 N/mm² | § 2.2 |
| Section | Lipped channel (C with lips) | |
| Overall depth h | 150 mm | |
| Flange width b | 60 mm | |
| Lip depth c | 20 mm | |
| Wall thickness t | 2 mm | |
| Length of the member l | 3000 mm | |
| Buckling lengths | From the end conditions and intermediate supports | |
| Ends, buckling about the strong axis y | Held against sway — both ends pinned | |
| Intermediate supports against buckling about y ny | 0 | |
| Ends, buckling about the weak axis z | Held against sway — both ends pinned | |
| Intermediate supports against buckling about z nz | 1 | |
| Inclination of the member to the horizontal α | 90 ° | |
| Loading | Centred axial force — (6.68) | |
| Design compressive force NEd | 60 kN | |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| Section resistance | Considered | |
| Characteristic tensile strength fu,k | 420 N/mm² | § t.1 |
| Resistance factor of the net section γM2 | 1.25 | § 4.1.3 |
| Reduction of the section | None — the effective section |
| Step | Value | Ref. |
|---|---|---|
| Gross areaFrom the mid-line of the walls, sharp corners. | A = 604 mm² | |
| Second moments of area of the gross section | Iy · Iz = 2,129,273 · 310,622 mm⁴ | |
| Radii of gyration of the gross section | iy · iz = 59.4 · 22.7 mm | |
| Bottom lip — effective widthMid-line width 19.0 mm, part of an edge stiffener (flange and lip), λp = 0.577; its parts next to the lip keep the reduced thickness χd·t. | beff = 19.0 mm | |
| Bottom flange — effective widthMid-line width 58.0 mm, part of an edge stiffener (flange and lip), λp = 0.623; its parts next to the lip keep the reduced thickness χd·t. | beff = 58.0 mm | |
| Web — effective widthMid-line width 148.0 mm, internal, k = 4.000, λp = 1.589. 54.2 % of it works. | beff = 80.3 mm | |
| Top flange — effective widthMid-line width 58.0 mm, part of an edge stiffener (flange and lip), λp = 0.623; its parts next to the lip keep the reduced thickness χd·t. | beff = 58.0 mm | |
| Top lip — effective widthMid-line width 19.0 mm, part of an edge stiffener (flange and lip), λp = 0.577; its parts next to the lip keep the reduced thickness χd·t. | beff = 19.0 mm | |
| Edge stiffener — spring stiffness of the webBoth flanges compressed: K = E·t³/(4(1 − ν²))·1/(b1²·hw + b1³ + 0,5·b1²·hw), b1 = 49.2 mm. | K = 0.7018 N/mm² | EN 1993-1-3 (5.10b) |
| Edge stiffener — elastic critical stress2·√(K·E·Is)/As with As = 96.0 mm², Is = 3,234 mm⁴. | σcr,s = 454.9 N/mm² | EN 1993-1-3 (5.15) |
| Distortional buckling — reductionλ̄d = √(fy,k/σcr,s) = 0.877; the stiffener is taken with the thickness χd·t. | χd = 0.8358 | EN 1993-1-3 5.5.3.1 |
| Effective areaΣbeff·t, every flat compressed at σ = fy,k. | Aeff = 437 mm² | |
| Thinness factorβA = Aeff/A, never above 1,0. It is the whole of how local buckling enters the buckling check, and it does so twice: in the area of NK and under the root of λ̄K. 27.7 % of the section has buckled away here. | βA = 0.7235 | |
| Shift of the effective centroidTowards the flange tips: the channel is symmetric about y only, so losing parts of its flanges moves the centroid across the web. A centred force then acts with an eccentricity eN about z, a moment NEd·eN = 0.210 kNm, which this check does not include. | eN = 3.49 mm | |
| Elastic limit slendernessλE = π√(E/fy,k). | λE = 76.95 | |
| Plastic axial force of the gross sectionfy,k·A — what the member would carry with stocky walls; for comparison. | Npl = 211.4 kN |
| Step | Value | Ref. |
|---|---|---|
| Buckling lengthk·l with k = 1.0 — held against sway — both ends pinned. | lK,y = 3,000 mm | |
| SlendernessλK = lK/i on the GROSS section; the reduction enters through √βA below. | λK,y = 50.53 | |
| Relative slendernessλ̄K = (λK/λE)·√βA, with λE = 76.95. Not an extra rule but the ordinary definition rewritten: √(Aeff·fy/Ncr) = √βA·√(A·fy/Ncr). | λ̄K,y = 0.5585 | |
| RegimeBetween the extremes, the relative slenderness above is what couples local and flexural buckling. | – = Interaction of the two | |
| Buckling curveCurve b. Plain or lipped channel: curve b about both axes. | α = 0.34 | |
| Buckling coefficient | χK,y = 0.8574 | § 4.5.1 |
| Ultimate buckling resistanceNK = χK·Aeff·fy,k = χK·βA·A·fy,k. | NK,y = 131.1 kN | § 4.5.1 |
| Design buckling resistanceNK/γM1. | NK,Rd,y = 124.9 kN | § 4.5.1 |
| Without the local-buckling reductionThe same member with stocky walls. The gap is what the thin walls cost — 23 % here.for comparison | NK,Rd(βA = 1) = 162.6 kN |
| Step | Value | Ref. |
|---|---|---|
| Buckling lengthl/(nz + 1): the member buckles between its supports. | lK,z = 1,500 mm | |
| SlendernessλK = lK/i on the GROSS section; the reduction enters through √βA below. | λK,z = 66.14 | |
| Relative slendernessλ̄K = (λK/λE)·√βA, with λE = 76.95. Not an extra rule but the ordinary definition rewritten: √(Aeff·fy/Ncr) = √βA·√(A·fy/Ncr). | λ̄K,z = 0.7311 | |
| RegimeBetween the extremes, the relative slenderness above is what couples local and flexural buckling. | – = Interaction of the two | |
| Buckling curveCurve b. Plain or lipped channel: curve b about both axes. | α = 0.34 | |
| Buckling coefficient | χK,z = 0.7659 | § 4.5.1 |
| Ultimate buckling resistanceNK = χK·Aeff·fy,k = χK·βA·A·fy,k. | NK,z = 117.1 kN | § 4.5.1 |
| Design buckling resistanceNK/γM1. | NK,Rd,z = 111.6 kN | § 4.5.1 |
| Without the local-buckling reductionThe same member with stocky walls. The gap is what the thin walls cost — 19 % here.for comparison | NK,Rd(βA = 1) = 138.3 kN |
| Step | Value | Ref. |
|---|---|---|
| Governing axisThe smaller of the two design resistances. | – = Weak axis (z–z) | |
| BucklingNEd ≤ NK,Rd | η = 0.538 · Pass54 % of the capacity used | § 4.5.1 |
| Step | Value | Ref. |
|---|---|---|
| Effective section, yielding | Aeff·fy,k/γM1 = 145.7 kN | § 4.1.3 |
| Net areaNo reduction: the gross area. | Anet = 604 mm² | |
| Net section, fracture | 0,9·Anet·fu,k/γM2 = 182.6 kN | § 4.1.3 |
| Section resistanceNEd ≤ NRd | η = 0.412 · Pass41 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Force each intermediate support must resist1 % of the axial force, FEd = 0,01·NEd, across the member in the plane it holds, passed on to a bracing. | FEd = 0.60 kN |
How this module is verified
Verified clause by clause against SIA 263:2013 and against independent calculations used on real projects, before release.
Questions
How does local buckling enter the buckling check?
Only through βA, and twice: in the area of NK and under the root of λ̄K. This is the ordinary definition rewritten, since √(Aeff · fy,k/Ncr) = √βA · √(A · fy,k/Ncr).
Why does the module refer to EN 1993-1-3?
For the distortional buckling of the flange-and-lip stiffener: the spring stiffness, the critical stress and the reduction χd follow its expressions (5.10b) and (5.15) and clause 5.5.3.1.
Which plan includes this module?
The Basic plan, with its calculation note.
Related
- Cold-formed lipped channel in bending
- Steel member in compression from its section properties
- Steel compression: all sections
- SIA 263: modules and clauses
Norm: SIA 263:2013 · Page updated: 27 October 2026