Cold-formed lipped channel under bending and axial force to SIA 263
Checks a cold-formed lipped channel under a moment about its major axis and an axial force in compression or tension, on its effective section with distortional buckling of the flange and lip, 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 a cold-formed lipped channel under a moment about its major axis and an axial force in compression or tension, on its effective section with distortional buckling of the flange and lip, to SIA 263:2013. Every step shows its formula and the clause it comes from.
What it checks
- Class of each flat, with ε = √(235/fy): the web and the compressed flange as internal flats (table 5a), the lip as an outstand (table 5b), on the mid-line dimensions hp = h − t, bp = b − t and cp = c − t/2.
- Edge stiffener, EN 1993-1-3 5.5.3.2: the flange with the lip taken as rigid (k = 4.0), the lip with kσ by (5.13b), then As and Is.
- Distortional buckling: the spring stiffness K of the web, (5.10b); σcr,s = 2 · √(K · E · Is)/As, (5.15); λ̄d = √(fy/σcr,s); and χd by (5.12), giving tred = χd · t.
- Effective section in bending, at σmax = fy: 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 at fy,k, both stiffeners compressed; Aeff and βA = Aeff/A.
- Shift of the effective centroid eN, EN 1993-1-3 6.1.9, adding ΔMz,Ed = NEd · eN.
- Resistances, clause 4.1.3: Nc,Rd and MRd from Aeff and Weff at fy,k/γM1; Mz,Rd from Wz,eff.
- Flexural buckling about both axes, clause 4.5.1, curve b, on Aeff, with √βA in the slenderness λ̄K.
- 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 plus the moment terms amplified by 1/(1 − NEd/Ncr,y) 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, flange width b and lip length c, 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 the stiffener values, 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; those rows name the EN clause.
- The lip works best between 0.2 and 0.6 of the flange width.
- ω = 0.6 + 0.4 · Mmin/Mmax, at least 0.4, for end moments only; otherwise ω = 1.0. No shape factor ξ.
- Under tension the member checks fall away, since the tension would stabilise the member.
- 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 lipped channel 200 × 70 × 20 × 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 25 kN and a moment of 5.0 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 | |
| Lip length c | 20 mm | |
| Thickness t | 2 mm | |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| The axial force is | Compression | |
| Design axial force NEd | 25 kN | |
| Largest moment about y along the member My,Ed | 5.0 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 | 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. |
|---|---|---|
| Web — effective width in compressionInternal, ψ = 1, k = 4.000, λp = 2.126. 42.2 % of it works. | beff,N = 83.5 mm | |
| Flanges and lips — edge stiffeners, both compressedFlange λp = 0.730, lip λp = 0.577. | beff · ceff = 68.0 · 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 = 57.1 mm. | K = 0.3999 N/mm² | EN 1993-1-3 (5.10b) |
| Edge stiffener — elastic critical stress2·√(K·E·Is)/As. | σcr,s = 317.2 N/mm² | EN 1993-1-3 (5.15) |
| Distortional buckling — reductionλ̄d = √(fy,k/σcr,s) = 1.050; the stiffeners are taken with χd·t. | χd = 0.7105 | EN 1993-1-3 5.5.3.1 |
| Effective area in compressionEvery flat compressed at σ = fy,k. 61.0 % of the gross area A = 744 mm² works. | Aeff = 454 mm² | EN 1993-1-3 6.1.3 |
| Thinness factorβA = Aeff/A. | βA = 0.6097 | |
| 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. NEd stays at the gross centroid and acts on the effective section with this eccentricity about z. | eN = 4.68 mm | EN 1993-1-3 6.1.9 |
| Additional moment about zNEd·eN. | ΔMz,Ed = 0.1170 kN·m | EN 1993-1-3 6.1.9 |
| Effective modulus about z, section in compressionIz of the effective section, 300,330 mm⁴, over 25.1 mm from its centroid to the fibre ΔMz compresses: the outer face of the web. | Wz,eff = 11,987 mm³ | |
| Bending resistance about zfy,k·Wz,eff/γM1. | Mz,Rd = 3.996 kN·m | |
| Compression resistance of the effective sectionAeff·fy,k/γM1. | Nc,Rd = 151.2 kN | § 4.1.3 |
| Bending resistance of the effective sectionfy,k·Weff/γM1, Weff = 40,044 mm³ — the section in bending alone. | MRd = 13.348 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 = 78.4 mm on the gross section: local buckling enters through √βA. | λ̄K,y = 0.5178 | |
| Buckling resistance, strong axisχK·Aeff·fy,k/γM1, curve b (plain or lipped channel), χK = 0.8762. | NK,Rd,y = 132.5 kN | § 4.5.1 |
| Buckling length, weak axisl/(nz + 1). | lK,z = 1,000 mm | |
| Relative slenderness, weak axis(lK/i)/λE·√βA, i = 25.7 mm on the gross section: local buckling enters through √βA. | λ̄K,z = 0.3948 | |
| Buckling resistance, weak axisχK·Aeff·fy,k/γM1, curve b (plain or lipped channel), χK = 0.9281. | NK,Rd,z = 140.3 kN | § 4.5.1 |
| Critical load of the section reduced for bendingπ²·E·Ieff/lK,y², Ieff = 4,242,124 mm⁴. | Ncr,y = 549.5 kN | |
| Critical load about zπ²·E·Iz/lK,z² on the gross section, Iz = 491,495 mm⁴; it amplifies ΔMz. | Ncr,z = 1,018.7 kN |
| Step | Value | Ref. |
|---|---|---|
| Section, compression with bendingNEd/Nc,Rd + My,Ed/MRd + ΔMz,Ed/Mz,Rd ≤ 1 | η = 0.569 · Pass57 % 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) = 1.0477 | |
| Axial termThe smaller of the two buckling resistances. | NEd/NK,Rd = 0.1887 | |
| 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) = 0.3924 | |
| Term of ΔMz, amplified | ΔMz,Ed/((1 − NEd/Ncr,z)·Mz,Rd) = 0.0300 | |
| Stability, compression with bendingNEd/NK,Rd + amplified moment terms ≤ 1 | η = 0.611 · Pass61 % 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 so much less of the section work in compression than in bending?
The whole web is compressed, and with both flanges compressed the web holds the stiffeners less firmly. In the worked example Aeff falls from 91.7 % of the gross area in bending to 61.0 % in compression, and χd from 0.770 to 0.711.
Is the lip itself checked?
Yes: as an outstand for its class, then through ceff as part of the edge stiffener.
Which plan includes this module?
The Pro plan, with its calculation note.
Related
- Cold-formed lipped channel in bending
- Cold-formed channel under bending and axial force
- Steel bending and axial force: all sections
- SIA 263: modules and clauses
Norm: SIA 263:2013 · Page updated: 28 October 2026