Cold-formed channel in bending to SIA 263
Checks the bending resistance of a cold-formed channel without lips about its major axis, on its effective section, to SIA 263:2013. 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 channel without lips about its major axis, on its effective section, to SIA 263:2013. 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 of the flats: hp = h − t for the web and bp = b − t/2 for the flange.
- Slenderness and class of each flat, b/t: the web as an internal flat in bending (table 5a), the compressed flange as an outstand (table 5b). The section class follows from table 5a.
- Effective widths of the web and the compressed flange, from the stress ratio ψ, the buckling coefficient k, the critical plate stress σcr,P and the plate slenderness λp. In the web the effective width sits in two equal parts at the ends of the compressed zone; in the flange it sits next to the supported edge.
- Effective section: the neutral axis zeff, found by iteration, then Aeff, Ieff, Weff,c and Weff,t. Weff is the smaller of the two.
- Bending resistance, clause 4.1.3: MEd ≤ MRd = fy · Weff / γM1, with the gross-section value fy · Wel / γM1 for comparison.
What you enter and what you get
You enter the characteristic yield strength fy,k (table 1), the modulus of elasticity E (clause 2.2), the overall depth h, the flange width b (both out-to-out), the core thickness t, the resistance factor γM1 (clause 4.1.3) and the design bending moment MEd as a magnitude.
You get the class of each flat, the effective widths, 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. 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 shear centre of a C lies outside the web, so a load in the plane of the web also twists it. The check assumes the twist is prevented, by the sheeting or by pairing the channels, and the member held laterally by the sheeting; lateral-torsional buckling is not checked.
- Not covered: shear and web crippling at the supports, the fixings, deflection and the construction stage.
- The compressed flange is an outstand held by the web alone (k = 0.426, against 4.0 for a flange held on both edges). A lip makes it an internal flat: see the lipped channel.
Worked example
A channel 200 × 70 × 2 mm with fy,k = 350 N/mm², γM1 = 1.05 and a design bending moment of 6.0 kNm; the compressed flange is class 4. 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 | |
| Thickness t | 2 mm | |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| Design bending moment MEd | 6.0 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/2 | bp = 69.0 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 69.0 mm, outstand (one edge free), compressed. Class limits 7.4 · 8.2 · 11.5 — class 4, past the class 3 limit by a factor of 3.01. | b/t = 34.5 | § t.5b |
| Section classClass 4, which is the normal condition of a thin-walled section: the flats buckle locally before the yield strength is reached, and only an EFFECTIVE section works — computed below. | – = Class 4 | § t.5a |
| Step | Value | Ref. |
|---|---|---|
| Web — effective widthψ = -0.665, k = 16.312, σcr,P = 315.9 N/mm², λp = 1.053. Winter, on the compressed width 118.9 mm: 75.1 % of it works, in two equal parts at the ends of the compressed zone. | beff = 89.4 mm | |
| Top flange — effective widthψ = 1.000, k = 0.426, σcr,P = 67.9 N/mm², λp = 2.270. Winter, on the compressed width 69.0 mm: 39.8 % of it works, next to the supported edge. | beff = 27.5 mm | |
| Neutral axis of the gross section, from the bottom mid-line | zG = 99.00 mm | |
| Neutral axis of the effective sectionMoved by 19.94 mm away from the compressed side. Found by iteration — the effective widths depend on the stress distribution, which depends on the axis: 8 rounds here. | zeff = 79.06 mm | |
| Gross area | A = 672 mm² | |
| Effective area78.8 % of the gross area works. | Aeff = 530 mm² | |
| Second moment of area, gross | I = 3,998,900 mm⁴ | |
| Second moment of area, effective | Ieff = 2,877,127 mm⁴ | |
| Elastic section modulus, grossThe smaller of the two extreme fibres. | Wel = 39,989 mm³ | |
| Effective modulus, compressed sideIeff over the distance from the effective axis to the outer face of the compressed side. | Weff,c = 23,988 mm³ | |
| Effective modulus, tensioned side | Weff,t = 35,937 mm³ | |
| Effective section modulusThe smaller of the two: 60.0 % of the gross elastic modulus. The plastic reserve of the tension zone is not counted. | Weff = 23,988 mm³ |
| Step | Value | Ref. |
|---|---|---|
| Design bending resistanceMRd = fy·Weff/γM1 = 350 × 23,988 mm³ / 1.05. | MRd = 7.996 kNm | § 4.1.3 |
| On the gross sectionWhat the section would carry if no flat buckled — local buckling costs 40 % of it here.for comparison | fy·Wel/γM1 = 13.330 kNm | |
| Bending on the effective sectionMEd ≤ MRd | η = 0.750 · 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 is the resistance so far below the gross elastic value?
The flats buckle locally before the yield strength is reached, and only the effective section works. In the worked example local buckling costs 40 % of the gross resistance.
Why does a higher yield strength not help as much as expected?
It raises the resistance, but ε falls with it, so every slenderness limit tightens at the same time.
Which plan includes this module?
The Pro plan, with its calculation note.
Related
- Cold-formed lipped 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