Cold-formed lipped channel in bending to SIA 263
Checks the bending resistance of a cold-formed lipped channel about its major axis, on its effective section, to SIA 263:2013, with distortional buckling of the flange and lip. Every step shows its formula and the clause it comes from.
Pro SIA 263:2013
Part of the Pro plan
This module is included in the Pro plan and above, with its calculation note.
About this check
clauses, worked example and questions
Checks the bending resistance of a cold-formed lipped channel about its major axis, on its effective section, to SIA 263:2013, with distortional buckling of the flange and lip. Every step shows its formula and the clause it comes from.
What it checks
- Reduction factor ε = √(235/fy), table 5a, with the edge stress of every flat taken as σmax = fy.
- Mid-line dimensions: hp = h − t, bp = b − t, cp = c − t/2.
- Slenderness and class of each flat, b/t: the web in bending and the compressed flange as internal flats (table 5a), the lip as an outstand (table 5b).
- Effective widths of the compressed flange (lip taken as rigid) and of the lip, with the lip coefficient kσ from EN 1993-1-3 (5.13b).
- Distortional buckling of the flange-and-lip stiffener, EN 1993-1-3 5.5.3.2: area As = t · (be2 + ceff), second moment Is, spring stiffness K given by the web (5.10b), critical stress σcr,s = 2 · √(K · E · Is) / As (5.15), slenderness λ̄d = √(fy/σcr,s) (5.5.3.1) and reduction factor χd (5.12). The stiffener is then counted with tred = χd · t.
- Effective width of the web, in two equal parts at the ends of the compressed zone.
- Effective section: zeff by iteration, Aeff, Ieff, Weff,c, Weff,t, and Weff as the smaller of the two moduli.
- Bending resistance, clause 4.1.3: MEd ≤ MRd = fy · Weff / γM1, with the gross-section value for comparison.
What you enter and what you get
You enter fy,k (table 1), E (clause 2.2), the overall depth h, the flange width b, the lip length c (all out-to-out), the core thickness t, γM1 (clause 4.1.3) and MEd as a magnitude.
You get the class of each flat, the effective widths, the distortional buckling steps, the section properties, the resistance and the utilisation with a pass or fail. With the Pro plan, it prints as an A4 calculation note.
Assumptions and limits
- Bending about the major axis, in the plane of the web, with the top flange compressed. The thickness is constant.
- Ultimate check of the section: the most compressed fibre reaches the yield strength, and the plastic reserve of the tension zone is not counted.
- The lip works best between 0.2 and 0.6 of the flange width.
- The shear centre of a C lies outside the web. The check assumes the twist is prevented, by the sheeting or by pairing the channels, and the member held laterally; lateral-torsional buckling is not checked.
- Not covered: shear and web crippling at the supports, the fixings, deflection and the construction stage.
- A channel without lips is its own module.
Worked example
A lipped channel 200 × 70 × 20 × 2 mm with fy,k = 350 N/mm², γM1 = 1.05 and a design bending moment of 10.0 kNm; every flat is class 3, and distortional buckling reduces the flange-and-lip stiffener to 77 % of its thickness. 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 |
| Overall depth h | 200 mm | |
| Flange width b | 70 mm | |
| Lip length c | 20 mm | |
| Thickness t | 2 mm | |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| Design bending moment MEd | 10.0 kNm |
| Step | Value | Ref. |
|---|---|---|
| Characteristic yield strength | fy,k = 350 N/mm² | § t.1 |
| Reduction factorε = √(235/fy) | ε = 0.8194 | § t.5a |
| Edge stress for the effective widthsfy: the ultimate check, the most compressed fibre at yield. Not asked for. | σmax = 350 N/mm² | |
| ThicknessUsual range 1.0 to 5.0 mm for a cold-formed profile, within a base material range of 0.5 to 5.0 mm. | t = 2.00 mm | |
| HeightUsual range 80 to 250 mm for a cold-formed profile. | h = 200.0 mm | |
| Web — mid-line heighth − t | hp = 198.0 mm | |
| Flange — mid-line widthb − t | bp = 68.0 mm | |
| Lip — mid-line lengthc − t/2 | cp = 19.0 mm | |
| Web — slendernessMid-line flat width 198.0 mm, internal (held along both edges), in bending. Class limits 59.0 · 68.0 · 101.6 — class 3. | b/t = 99.0 | § t.5a |
| Top flange — slendernessMid-line flat width 68.0 mm, internal (held along both edges), compressed. Class limits 27.0 · 31.1 · 34.4 — class 3. | b/t = 34.0 | § t.5a |
| Top lip — slendernessMid-line flat width 19.0 mm, outstand (one edge free), compressed. Class limits 7.4 · 8.2 · 11.5 — class 3. | b/t = 9.5 | § t.5b |
| Section classEvery compressed flat is within the class 3 limit, so the whole section works elastically — unusual for a cold-formed element. | – = Class 3 | § t.5a |
| Step | Value | Ref. |
|---|---|---|
| Compressed flange — effective width (lip taken as rigid)k = 4,0, λp = 0.730 ≤ 0,9: the whole flange works. | beff = 68.0 mm | |
| Lip — buckling coefficientkσ = 0,5 for cp/bp ≤ 0,35, else 0,5 + 0,83·∛((cp/bp − 0,35)²); here cp/bp = 0.279. | kσ = 0.500 | EN 1993-1-3 (5.13b) |
| Lip — effective widthλp = 0.577 ≤ 0,9: the whole lip works. | ceff = 19.0 mm | |
| Edge stiffener — effective areaAs = t·(be2 + ceff): the flange strip next to the lip and the effective lip. | As = 106.0 mm² | EN 1993-1-3 5.5.3.2 |
| Edge stiffener — second moment of areaAbout its own centroidal axis parallel to the flange. | Is = 3,366 mm⁴ | EN 1993-1-3 5.5.3.2 |
| Spring stiffness given by the webK = E·t³/(4(1 − ν²))·1/(b1²·hw + b1³), with b1 = 57.1 mm from the web to the stiffener centroid and the other flange in tension. It is how strongly the web holds the flange-and-lip against rotating. | K = 0.5550 N/mm² | EN 1993-1-3 (5.10b) |
| Distortional critical stressσcr,s = 2·√(K·E·Is)/As — the stiffener buckling as a strut on the elastic foundation the web provides. | σcr,s = 373.7 N/mm² | EN 1993-1-3 (5.15) |
| Distortional slenderness√(fy/σcr,s) | λ̄d = 0.968 | EN 1993-1-3 5.5.3.1 |
| Distortional reduction factor1,0 up to λ̄d = 0,65; 1,47 − 0,723·λ̄d up to 1,38; 0,66/λ̄d beyond. The stiffener is then counted with the thickness tred = χd·t = 1.541 mm. | χd = 0.770 | EN 1993-1-3 (5.12) |
| Web — effective widthψ = -0.887, k = 21.080, σcr,P = 408.2 N/mm², λp = 0.926. Winter, on the compressed width 104.9 mm: 82.3 % of it works, in two equal parts at the ends of the compressed zone. | beff = 86.4 mm | |
| Neutral axis of the gross section, from the bottom mid-line | zG = 99.00 mm | |
| Neutral axis of the effective sectionMoved by 5.94 mm away from the compressed side. Found by iteration — the effective widths depend on the stress distribution, which depends on the axis: 7 rounds here. | zeff = 93.06 mm | |
| Gross area | A = 744 mm² | |
| Effective area91.7 % of the gross area works. | Aeff = 683 mm² | |
| Second moment of area, gross | I = 4,570,760 mm⁴ | |
| Second moment of area, effective | Ieff = 4,242,124 mm⁴ | |
| Elastic section modulus, grossThe smaller of the two extreme fibres. | Wel = 45,708 mm³ | |
| Effective modulus, compressed sideIeff over the distance from the effective axis to the outer face of the compressed side. | Weff,c = 40,044 mm³ | |
| Effective modulus, tensioned side | Weff,t = 45,098 mm³ | |
| Effective section modulusThe smaller of the two: 87.6 % of the gross elastic modulus. The plastic reserve of the tension zone is not counted. | Weff = 40,044 mm³ |
| Step | Value | Ref. |
|---|---|---|
| Design bending resistanceMRd = fy·Weff/γM1 = 350 × 40,044 mm³ / 1.05. | MRd = 13.348 kNm | § 4.1.3 |
| On the gross sectionWhat the section would carry if no flat buckled — local buckling costs 12 % of it here.for comparison | fy·Wel/γM1 = 15.236 kNm | |
| Bending on the effective sectionMEd ≤ MRd | η = 0.749 · Pass75 % of the capacity used | § 4.1.3 |
How this module is verified
Verified clause by clause against SIA 263:2013 and against independent calculations used on real projects, before release.
Questions
Why does the module use EN 1993-1-3?
SIA 263 gives no rule for distortional buckling of the flange-and-lip and refers to SN EN 1993-1-3. Its clause 5.5.3.2 is applied for that part only; the effective widths are SIA 263's.
Can χ_d be refined?
Yes, by iterating with the reduced stress in the stiffener. The module takes a single step, which is the conservative one.
Which plan includes this module?
The Pro plan, with its calculation note.
Related
- Cold-formed channel in bending
- Trapezoidal sheeting in bending
- Steel bending: all sections
- SIA 263: modules and clauses
Norm: SIA 263:2013 · Page updated: 26 October 2026