Cold-formed channel under bending and axial force to SIA 263
Checks a cold-formed channel without lips under a moment about its major axis and an axial force in compression or tension, on its effective section, to SIA 263:2013: the section, flexural buckling and their interaction. 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 a cold-formed channel without lips under a moment about its major axis and an axial force in compression or tension, on its effective section, to SIA 263:2013: the section, flexural buckling and their interaction. Every step shows its formula and the clause it comes from.
What it checks
- Class of each flat, with ε = √(235/fy): the web in bending (table 5a) and the compressed flange as an outstand (table 5b), on the mid-line widths hp = h − t and bp = b − t/2.
- Effective section in bending, at σmax = fy: effective widths from ψ, k, σcr,P and λp, zeff by iteration, and Weff, the smaller of Weff,c and Weff,t.
- Effective section in compression, EN 1993-1-3 6.1.3: every flat compressed at fy,k, giving Aeff and βA = Aeff/A.
- Shift of the effective centroid eN, EN 1993-1-3 6.1.9: the channel is symmetric about y only, so NEd adds ΔMz,Ed = NEd · eN, resisted by Mz,Rd = fy,k · Wz,eff/γM1.
- Resistances, clause 4.1.3: Nc,Rd = Aeff · fy,k/γM1 and MRd = fy,k · Weff/γM1.
- Flexural buckling about both axes, clause 4.5.1, curve b: NK,Rd = χK · Aeff · fy,k/γM1, with λ̄K = (lK/i)/λE · √βA and i on the gross section.
- Check 1, section, EN 1993-1-3 6.1.9: NEd/Nc,Rd + My,Ed/MRd + ΔMz,Ed/Mz,Rd ≤ 1.
- Check 2, stability: NEd/NK,Rd, with the smaller buckling resistance, plus the moment terms amplified by 1/(1 − NEd/Ncr,y), Ncr,y on Ieff, and 1/(1 − NEd/Ncr,z).
What you enter and what you get
You enter fy,k (table 1), E (clause 2.2), the out-to-out depth h and flange width b, the core thickness t, γM1 (clause 4.1.3), the sense of the axial force, NEd, the largest moment My,Ed and the moment diagram. For buckling, the length l with the end conditions and the intermediate supports ny and nz in each plane, or the buckling lengths directly.
You get both effective sections, the resistances and the two utilisations with a pass or fail. With the Pro plan, it prints as an A4 calculation note.
Assumptions and limits
- SIA 263 refers to SN EN 1993-1-3 for thin-walled members; the rows that follow it name the EN clause.
- ω = 0.6 + 0.4 · Mmin/Mmax, at least 0.4, for end moments only; otherwise ω = 1.0. No shape factor ξ: local buckling has taken the plastic reserve.
- Under tension the member checks fall away, since the tension would stabilise the member.
- The shear centre of a C lies outside the web. The member is assumed held against twist, by the sheeting or by pairing the channels; lateral-torsional, torsional and flexural-torsional buckling are not checked.
- Not covered: shear and web crippling at the supports, the fixings, deflection and the construction stage.
Worked example
A channel 200 × 70 × 2 mm with fy,k = 350 N/mm² and γM1 = 1.05, 4,000 mm long and pinned at both ends, with three intermediate supports about z, under a compression of 8 kN and a moment of 3.0 kNm from a transverse load. 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 |
| The axial force is | Compression | |
| Design axial force NEd | 8 kN | |
| Largest moment about y along the member My,Ed | 3.0 kN·m | |
| Moment diagram | Transverse load between the ends — ω = 1,0 | |
| Buckling lengths | From the end conditions and intermediate supports | |
| Length of the member l | 4000 mm | |
| 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 | 3 |
| 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. |
|---|---|---|
| Bottom flange — effective width in compressionOutstand, ψ = 1, k = 0.426, λp = 2.270. 39.8 % of it works. | beff,N = 27.5 mm | |
| Web — effective width in compressionInternal, ψ = 1, k = 4.000, λp = 2.126. 42.2 % of it works. | beff,N = 83.5 mm | |
| Top flange — effective width in compressionOutstand, ψ = 1, k = 0.426, λp = 2.270. 39.8 % of it works. | beff,N = 27.5 mm | |
| Effective area in compressionEvery flat compressed at σ = fy,k. 41.2 % of the gross area A = 672 mm² works. | Aeff = 277 mm² | EN 1993-1-3 6.1.3 |
| Thinness factorβA = Aeff/A. | βA = 0.4119 | |
| Shift of the effective centroidTowards the web: the channel is symmetric about y only, so losing parts of its flanges moves the centroid across the web. NEd stays at the gross centroid and acts on the effective section with this eccentricity about z. | eN = 8.72 mm | EN 1993-1-3 6.1.9 |
| Additional moment about zNEd·eN. | ΔMz,Ed = 0.0698 kN·m | EN 1993-1-3 6.1.9 |
| Effective modulus about z, section in compressionIz of the effective section, 19,433 mm⁴, over 22.0 mm from its centroid to the fibre ΔMz compresses: the end of the effective flanges, towards the tips. | Wz,eff = 883 mm³ | |
| Bending resistance about zfy,k·Wz,eff/γM1. | Mz,Rd = 0.294 kN·m | |
| Compression resistance of the effective sectionAeff·fy,k/γM1. | Nc,Rd = 92.3 kN | § 4.1.3 |
| Bending resistance of the effective sectionfy,k·Weff/γM1, Weff = 23,988 mm³ — the section in bending alone. | MRd = 7.996 kN·m | § 4.1.3 |
| Step | Value | Ref. |
|---|---|---|
| Elastic limit slendernessπ·√(E/fy,k). | λE = 76.95 | |
| Buckling length, strong axisk·l with k = 1.00. | lK,y = 4,000 mm | |
| Relative slenderness, strong axis(lK/i)/λE·√βA, i = 77.1 mm on the gross section: local buckling enters through √βA. | λ̄K,y = 0.4325 | |
| Buckling resistance, strong axisχK·Aeff·fy,k/γM1, curve b (plain or lipped channel), χK = 0.9130. | NK,Rd,y = 84.2 kN | § 4.5.1 |
| Buckling length, weak axisl/(nz + 1). | lK,z = 1,000 mm | |
| Relative slenderness, weak axis(lK/i)/λE·√βA, i = 21.2 mm on the gross section: local buckling enters through √βA. | λ̄K,z = 0.3926 | |
| Buckling resistance, weak axisχK·Aeff·fy,k/γM1, curve b (plain or lipped channel), χK = 0.9290. | NK,Rd,z = 85.7 kN | § 4.5.1 |
| Critical load of the section reduced for bendingπ²·E·Ieff/lK,y², Ieff = 2,877,127 mm⁴. | Ncr,y = 372.7 kN | |
| Critical load about zπ²·E·Iz/lK,z² on the gross section, Iz = 303,221 mm⁴; it amplifies ΔMz. | Ncr,z = 628.5 kN |
| Step | Value | Ref. |
|---|---|---|
| Section, compression with bendingNEd/Nc,Rd + My,Ed/MRd + ΔMz,Ed/Mz,Rd ≤ 1 | η = 0.699 · Pass70 % of the capacity used | EN 1993-1-3 6.1.9 |
| Step | Value | Ref. |
|---|---|---|
| Moment factor1,0 for this moment diagram. | ω = 1.0000 | |
| Amplification factor | 1/(1 − NEd/Ncr,y) = 1.0219 | |
| Axial termThe smaller of the two buckling resistances. | NEd/NK,Rd = 0.0950 | |
| Moment term, amplifiedNo shape factor ξ: local buckling has taken the plastic reserve of a thin-walled section. | (ω·MEd + ΔM)/((1 − NEd/Ncr)·MRd) = 0.3834 | |
| Term of ΔMz, amplified | ΔMz,Ed/((1 − NEd/Ncr,z)·Mz,Rd) = 0.2402 | |
| Stability, compression with bendingNEd/NK,Rd + amplified moment terms ≤ 1 | η = 0.719 · Pass72 % of the capacity used |
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 a small eccentricity weigh so much?
ΔMz,Ed acts about the weak axis, where the effective channel has little resistance. In the worked example eN = 8.72 mm gives only 0.070 kNm, yet it takes 0.237 of the section check, against Mz,Rd = 0.294 kNm.
How does local buckling enter the buckling check?
Through βA: in the area of NK,Rd, and under the root in λ̄K. In the worked example only 41.2 % of the gross area works in compression.
Which plan includes this module?
The Pro plan, with its calculation note.
Related
- Cold-formed channel in bending
- Cold-formed thin-walled section in compression
- Steel bending and axial force: all sections
- SIA 263: modules and clauses
Norm: SIA 263:2013 · Page updated: 28 October 2026