Trapezoidal steel sheeting under bending and axial force to SIA 263
Checks a trapezoidal steel sheet under a moment and an axial force along its ribs, per metre of width, on its effective section, to SIA 263:2013: the section, flexural buckling across the span 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 trapezoidal steel sheet under a moment and an axial force along its ribs, per metre of width, on its effective section, to SIA 263:2013: the section, flexural buckling across the span and their interaction. Every step shows its formula and the clause it comes from.
What it checks
- Geometry of one rib: the web projection sw = (p − bt − bb)/2, the web length sw,L = √(sw² + (h − t)²) and the inclination φ.
- Class of each flat, table 5a, with ε = √(235/fy): both webs in bending, the compressed flange in compression, all internal flats.
- Effective section in bending, at σmax = fy: effective widths from ψ, k, σcr,P and λp, zeff by iteration, and Weff per metre width, 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 (ψ = 1, k = 4.0), giving Aeff and βA = Aeff/A.
- Shift of the effective centroid eN, EN 1993-1-3 6.1.9: the wider flange loses more than the narrower, and the axial force acts with this eccentricity.
- Resistances, clause 4.1.3: Nc,Rd and MRd from Aeff and Weff at fy,k/γM1.
- Flexural buckling across the span, clause 4.5.1, curve c: NK,Rd,y = χK · Aeff · fy,k/γM1, with √βA in λ̄K,y.
- Check 1, section, EN 1993-1-3 6.1.9: nEd/nc,Rd + (mEd + ΔmEd)/mRd ≤ 1.
- Check 2, stability: NEd/NK,Rd plus the moment term amplified by 1/(1 − NEd/Ncr,y), with Ncr,y = π² · E · Ieff/lK,y².
What you enter and what you get
You enter fy,k (table 1) and E (clause 2.2); one rib: the overall height h, the core thickness t without coating, the flange widths bt and bb at mid-thickness, and the pitch p; whether the section is sagging or hogging; γM1 (clause 4.1.3); the sense of the axial force, nEd and the largest moment mEd, both per metre width; the moment diagram; and the span l with its end conditions, or the buckling length 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 sheet buckles as a wide plate strip across its span, about the axis of its ribs. Across the ribs it is continuous and does not buckle as a whole.
- Where the shift eN relieves the compressed flanges, as in the worked example, the relief is not credited.
- A flange with a stiffening groove is not covered.
- Check both sagging and hogging: the narrower flange usually decides which case is worse.
- 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.
- Not covered: shear and web crippling at the supports, the fixings, deflection and the construction stage.
Worked example
A sheet 106 mm high and 0.75 mm thick, with flanges of 40 and 112 mm at a pitch of 250 mm, fy,k = 320 N/mm² and γM1 = 1.05, sagging over a 3,000 mm span pinned at both ends, under 8 kN/m of compression and 3.0 kNm/m 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 | 320 N/mm² | § t.1 |
| Modulus of elasticity E | 210000 N/mm² | § 2.2 |
| Overall height h | 106 mm | |
| Sheet thickness t | 0.75 mm | |
| Top flange width bt | 40 mm | |
| Bottom flange width bb | 112 mm | |
| Rib pitch p | 250 mm | |
| The section is | Sagging — in the span, top flanges compressed | |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| The axial force is | Compression | |
| Design axial force per metre width nEd | 8 kN/m | |
| Largest moment per metre width along the member mEd | 3.0 kN·m/m | |
| Moment diagram | Transverse load between the ends — ω = 1,0 | |
| Buckling length along the ribs | From the end conditions | |
| Span between the supports l | 3000 mm | |
| Ends | Held against sway — both ends pinned |
| Step | Value | Ref. |
|---|---|---|
| Characteristic yield strength | fy,k = 320 N/mm² | § t.1 |
| Reduction factorε = √(235/fy) | ε = 0.8570 | § t.5a |
| Edge stress for the effective widthsfy: the ultimate check, the most compressed fibre at yield. Not asked for. | σmax = 320 N/mm² | |
| ThicknessUsual range 0.6 to 1.5 mm for profiled sheeting, within a base material range of 0.5 to 5.0 mm. | t = 0.75 mm | |
| HeightUsual range 30 to 180 mm for profiled sheeting. | h = 106.0 mm | |
| Web — horizontal projection(p − bt − bb)/2 | sw = 49.0 mm | |
| Web — length between the bends√(sw² + (h − t)²) | sw,L = 116.1 mm | |
| Web inclination | φ = 65.0 ° | |
| Web, left — slendernessMid-line flat width 116.1 mm, internal (held along both edges), in bending. Class limits 61.7 · 71.1 · 106.3 — class 4, past the class 3 limit by a factor of 1.46. | b/t = 154.8 | § t.5a |
| Top flange — slendernessMid-line flat width 40.0 mm, internal (held along both edges), compressed. Class limits 28.3 · 32.6 · 36.0 — class 4, past the class 3 limit by a factor of 1.48. | b/t = 53.3 | § t.5a |
| Web, right — slendernessMid-line flat width 116.1 mm, internal (held along both edges), in bending. Class limits 61.7 · 71.1 · 106.3 — class 4, past the class 3 limit by a factor of 1.46. | b/t = 154.8 | § t.5a |
| 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, left — effective widthψ = -0.460, k = 12.775, σcr,P = 101.2 N/mm², λp = 1.778. Winter, on the compressed width 79.5 mm: 49.3 % of it works, in two equal parts at the ends of the compressed zone. | beff = 39.2 mm | |
| Top flange — effective widthψ = 1.000, k = 4.000, σcr,P = 266.9 N/mm², λp = 1.095. Winter, on the compressed width 40.0 mm: 73.0 % of it works, in two equal parts at the ends of the compressed zone. | beff = 29.2 mm | |
| Web, right — effective widthψ = -0.460, k = 12.775, σcr,P = 101.2 N/mm², λp = 1.778. Winter, on the compressed width 79.5 mm: 49.3 % of it works, in two equal parts at the ends of the compressed zone. | beff = 39.2 mm | |
| Neutral axis of the gross section, from the bottom mid-line | zG = 42.76 mm | |
| Neutral axis of the effective sectionMoved by 9.59 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 = 33.17 mm | |
| Gross area | A = 1,153 mm²/m | |
| Effective area76.2 % of the gross area works. | Aeff = 878 mm²/m | |
| Second moment of area, gross | I = 1,793,803 mm⁴/m | |
| Second moment of area, effective | Ieff = 1,390,143 mm⁴/m | |
| Elastic section modulus, grossThe smaller of the two extreme fibres. | Wel = 28,535 mm³/m | |
| Effective modulus, compressed sideIeff over the distance from the effective axis to the outer face of the compressed side. | Weff,c = 19,186 mm³/m | |
| Effective modulus, tensioned side | Weff,t = 41,443 mm³/m | |
| Effective section modulusThe smaller of the two: 67.2 % of the gross elastic modulus. The plastic reserve of the tension zone is not counted. | Weff = 19,186 mm³/m |
| Step | Value | Ref. |
|---|---|---|
| Bottom flange — effective width in compressionInternal, ψ = 1, k = 4.000, λp = 3.066. 30.3 % of it works. | beff,N = 33.9 mm | |
| Web, left — effective width in compressionInternal, ψ = 1, k = 4.000, λp = 3.178. 29.3 % of it works. | beff,N = 34.0 mm | |
| Top flange — effective width in compressionInternal, ψ = 1, k = 4.000, λp = 1.095. 73.0 % of it works. | beff,N = 29.2 mm | |
| Web, right — effective width in compressionInternal, ψ = 1, k = 4.000, λp = 3.178. 29.3 % of it works. | beff,N = 34.0 mm | |
| Effective area in compressionEvery flat compressed at σ = fy,k. 34.1 % of the gross area A = 1,153 mm²/m works. | Aeff = 393 mm²/m | EN 1993-1-3 6.1.3 |
| Thinness factorβA = Aeff/A. | βA = 0.3412 | |
| Shift of the effective centroidUpwards, the wider flange losing more than the narrower. NEd stays at the gross centroid, so on the effective section it acts with the eccentricity eN. Here it relieves the compressed flanges; that is not credited. | eN = 7.97 mm | EN 1993-1-3 6.1.9 |
| Compression resistance of the effective sectionAeff·fy,k/γM1. | Nc,Rd = 119.9 kN/m | § 4.1.3 |
| Bending resistance of the effective sectionfy,k·Weff/γM1, Weff = 19,186 mm³/m — the section in bending alone. | MRd = 5.847 kN·m/m | § 4.1.3 |
| Step | Value | Ref. |
|---|---|---|
| Elastic limit slendernessπ·√(E/fy,k). | λE = 80.48 | |
| Buckling lengthk·l with k = 1.00 — held against sway — both ends pinned. | lK,y = 3,000 mm | |
| Relative slenderness(lK/i)/λE·√βA, i = 39.5 mm on the gross section: local buckling enters through √βA. | λ̄K,y = 0.5520 | |
| Buckling resistanceχK·Aeff·fy,k/γM1, curve c (other cross-sections), χK = 0.8135. | NK,Rd,y = 97.5 kN/m | § 4.5.1 |
| Critical load of the section reduced for bendingπ²·E·Ieff/lK,y², Ieff = 1,390,143 mm⁴/m. | Ncr,y = 320.1 kN/m |
| Step | Value | Ref. |
|---|---|---|
| Section, compression with bendingnEd/nc,Rd + (mEd + ΔmEd)/mRd ≤ 1 | η = 0.580 · Pass58 % 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) = 1.0256 | |
| Axial termThe strip buckling across its span. | NEd/NK,Rd = 0.0820 | |
| 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) = 0.5262 | |
| Stability, compression with bendingNEd/NK,Rd + amplified moment terms ≤ 1 | η = 0.608 · 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
Where does an axial force in a sheet come from?
From the in-plane forces of a wall, or of a roof acting as a diaphragm chord, along the ribs. Like the moment, it is entered per metre width.
Why does so little of the sheet work in compression?
Under uniform compression the wide bottom flange and the webs lose most of their width. In the worked example only 34.1 % of the gross area works.
Which plan includes this module?
The Pro plan, with its calculation note.
Related
- Trapezoidal steel sheeting 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