Battened built-up steel member in compression to SIA 263
Checks a built-up member of two or four chords joined by battens under axial compression, to SIA 263:2013: the bar as a whole about both axes, one chord between two battens, and the forces on the battens and their welds. Every step shows its formula and the clause it comes from.
Basic SIA 263:2013
Part of the Basic plan
This module is included in the Basic plan and above, with its calculation note.
About this check
clauses, worked example and questions
Checks a built-up member of two or four chords joined by battens under axial compression, to SIA 263:2013: the bar as a whole about both axes, one chord between two battens, and the forces on the battens and their welds. Every step shows its formula and the clause it comes from.
What it checks
- Chord and bar properties: A1, Iy1, Iz1, the chord centroid e, the distance between chord centroids a = B − 2e, A = 2 · A1, and the number of battens n = ⌊l/l1⌋ + 1.
- Inertia of the bar about z: Iz = 2 · Iz1 + 2[A_1]². The chords' own inertia counts in full while λz < 75, not at all from 150, and linearly between, solved by iteration.
- Idealised slenderness: λz,id = √(λz² + λ1²), with λ1 = l1/i1. The exact form carries π²/12 on λ1²; the module uses the simpler, safe one.
- Buckling about z, where the battens work, clause 4.5.1: NEd ≤ χKz · fy,k · A/γM1, with the curve of the chord section.
- Buckling about y, where the battens do not work, clause 4.5.1: the chords buckle independently over lK,y, with iy equal to the chord's own iy1.
- One chord between two battens, clause 4.5.1: N1,Ed = N/2 + (N/a) · (l/500)/(1 − N/Ncr,z,id), with Ncr,z,id = π² · E · A/λz,id², against χ1 · fy,k · A1/γM1 over l1.
- Chord slenderness between battens: λ1 < 50.
- Forces at the end of the bar: Vmax = NEd · π/500/(1 − NEd/Ncr); in each chord N/2, V1,Ed = Vmax/2 and M1,Ed = (Vmax/2) · (l1/2).
- Battens: V2,Ed = Vmax · l1/a on the first batten, and the weld forces Fx,Ed = V2/2 along it and Fy,Ed = Fx · x/hb across it, with x = a/2.
What you enter and what you get
You enter fy,k (table 1 of your copy of SIA 263) and E (clause 2.2); two chords battened about one axis or four battened about both; the chord section (a UPN or UPE channel or a rolled I or H section by its dimensions, or any other chord by its properties) and how the channels are placed; the overall width B, the length l, which is also the buckling length about z, the batten spacing l1, the buckling length lK,y, the lever hb between the two weld runs of a batten end, NEd and γM1 (clause 4.1.3).
You get every intermediate value with its clause, the four checks with their utilisation and a pass or fail, the chord forces and the batten forces. With the Basic plan, it prints as an A4 calculation note.
Assumptions and limits
- The idealised slenderness assumes stiff battens rigidly connected to the chords, λ1 below 50 and at least two battens. The stiffness of the battens is not checked; EN 1993-1-1 6.4.3 gives a fuller method.
- Every chord has the same section. The curve belongs to the chord section: curve c for channels and angles.
- The axial force, shear and moment in the end chord act together; their interaction is not checked here.
- The battens and their welds are not designed, only the forces on them.
Worked example
Two UPN channels 160 mm deep, back to back, with an overall width of 262 mm, a 3.00 m bar with battens every 600 mm, lK,y = 2,400 mm and hb = 120 mm, in fy,k = 235 N/mm² under NEd = 780 kN. 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 | 235 N/mm² | § t.1 |
| Modulus of elasticity E | 210000 N/mm² | § 2.2 |
| Number of chords | Two chords — battened about one axis | |
| Section of each chord | Channel (UPN or UPE) | |
| Placed | Back to back — flanges pointing outwards | |
| Depth of the channel h | 160 mm | |
| Flange width b | 65 mm | |
| Web thickness tw | 7.5 mm | |
| Flange thickness tf | 10.5 mm | |
| Root radius r | 10.5 mm | |
| Flanges | Tapered at 8 % — UPN | |
| Overall width of the bar B | 262 mm | |
| Length of the bar l | 3000 mm | |
| Spacing of the battens l1 | 600 mm | |
| Buckling length of the bar about y lK,y | 2400 mm | |
| Lever between the two weld runs of a batten end hb | 120 mm | |
| Design compressive force on the whole bar NEd | 780 kN | |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| Step | Value | Ref. |
|---|---|---|
| Area of one chordFrom the dimensions, root fillets included, flanges tapered at 8 %. | A1 = 2,455 mm² | |
| One chord — second moment of area about yAbout its own axis on the line of the chords. | Iy1 = 9,503,223 mm⁴ | |
| One chord — second moment of area about its own axis parallel to z | Iz1 = 893,472 mm⁴ | |
| Chord centroid from the outer face of the barb − ew, with the web 18.8 mm from the centroid. | e = 46.2 mm | |
| Distance between the chord centroidsa = B − 2e. | a = 169.6 mm | |
| Area of the barA = 2·A1. | A = 4,910 mm² | |
| Number of battensOne at each end and every l1 between: n = ⌊l/l1⌋ + 1. At least two are needed, and they are, since l1 < l. | n = 6 | |
| Buckling curve of the chord sectionChannels and angles: curve c. The curve belongs to the chord section, not to the built-up shape. | – = c |
| Step | Value | Ref. |
|---|---|---|
| Chords' own inertia | 2·Iz1 = 1,786,944 mm⁴ | |
| Inertia from the spreadThis is what the battens buy — and it costs no steel at all, which is the whole idea of the arrangement. Here it is 19.8 times the chords' own inertia. | 2A1(a/2)² = 35,324,667 mm⁴ | |
| Share of the own inertia countedThe chords' own inertia counts in full while λz < 75, none of it at or above 150, and linearly between. λz itself depends on Iz, so this is solved by iteration. | – = 1.0000 | |
| Inertia of the bar | Iz = 37,111,611 mm⁴ | |
| Slenderness as monolithicλz = l/iz with iz = √(Iz/A). | λz = 34.51 | |
| Slenderness of a chord between battensλ1 = l1/i1 with i1 = 19.08 mm, the chord's own about its axis parallel to z. | λ1 = 31.45 | |
| Idealised slendernessλz,id = √(λz² + λ1²). The two modes add in quadrature because the bar bends as a whole AND each chord bends between the battens. | λz,id = 46.69 | |
| Before the conservative simplificationThe derivation gives λid = √(λ² + (π²/12)·λ1²); replacing π²/12 = 0,822 by 1 raises the slenderness — by 4.3 % here — and the calculation above uses that simplified, safe form.the exact form | λz,id = 44.77 | |
| Buckling coefficient about zλ̄Kz = λz,id/λE = 0.4971, curve c. | χKz = 0.8446 | § 4.5.1 |
| Buckling resistance about zNKz = χKz·fy,k·2A1. | NKz/γM1 = 928.1 kN | § 4.5.1 |
| Step | Value | Ref. |
|---|---|---|
| Buckling about z, where the battens countNEd ≤ NKz/γM1 | η = 0.840 · Pass84 % of the capacity used | § 4.5.1 |
| Step | Value | Ref. |
|---|---|---|
| Slenderness about yIy = 2·Iy1 and iy = √(Iy/A), so iy is simply the chord's own iy1: the two chords buckle independently over the buckling length of the whole bar. | λy = 38.57 | |
| Buckling resistance about yNKy = χKy·fy,k·2A1 with χKy = 0.8916, curve c. The battens have no influence on this mode at all. | NKy/γM1 = 979.7 kN | § 4.5.1 |
| Step | Value | Ref. |
|---|---|---|
| Buckling about y, where they do notNEd ≤ NKy/γM1 | η = 0.796 · Pass80 % of the capacity used | § 4.5.1 |
| Step | Value | Ref. |
|---|---|---|
| Elastic critical load of the barNcr,z,id = π²·E·A/λz,id². | Ncr,z,id = 4,668 kN | |
| Amplification factor | 1/(1 − NEd/Ncr,z,id) = 1.2006 | |
| Second-order moment at midspanMmax = NEd·v0/(1 − NEd/Ncr,z,id) with an initial bow v0 = l/500. | Mmax = 5.62 kNm | |
| Force in the more loaded chordN1 = N/2 + (N/a)·(l/500)/(1 − N/Ncr,z,id). It is NOT simply N/2: the second-order moment becomes a couple M/a that adds to the chords on one side and subtracts from the other. Here that adds 33.1 kN, or 8 %. | N1,Ed = 423.1 kN | |
| Buckling resistance of one chordNK1 = χ1·fy,k·A1 over a buckling length of l1, with χ1 = 0.9313 (curve c). | NK1/γM1 = 511.7 kN | § 4.5.1 |
| Step | Value | Ref. |
|---|---|---|
| Buckling of a chord between battensN1,Ed ≤ NK1/γM1 | η = 0.827 · Pass83 % of the capacity used | § 4.5.1 |
| Step | Value | Ref. |
|---|---|---|
| Chord slenderness between battensλ1 < 50 | η = 0.629 · Pass63 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Maximum second-order shearV = dM/dx on a sinusoidal initial bow, so Vmax = NEd·π/500/(1 − NEd/Ncr). It peaks at the ENDS of the bar and is zero at midspan — which is why a single batten in the middle would be useless. | Vmax = 5.884 kN | |
| Axial force in a chordN/2 here, not the amplified N1 above: the section is checked at the END of the bar, where the second-order moment is zero and the shear is greatest. | N1,Ed = 390.0 kN | |
| Shear force in a chordVmax/2 — the 2 chords share it. | V1,Ed = 2.94 kN | |
| Bending moment in a chord(Vmax/2)·(l1/2), from the hinge at mid-distance between battens to the batten itself. | M1,Ed = 0.883 kNm |
| Step | Value | Ref. |
|---|---|---|
| Lever from mid-batten to the chord axisx = a/2: the batten is a beam fixed at both chords, its moment zero at mid-length, where its shear acts. | x = 84.8 mm | |
| Shear on the most loaded battenV2 = Vmax·l1/a, from moment equilibrium of a segment between two hinges: the batten couple V2·a/2 balances the chord shears Vmax·l1/2. The most loaded batten is the FIRST one, at the end of the bar. | V2,Ed = 20.81 kN | |
| Weld force along the battenV2/2: the batten plates on the two faces share the shear. | Fx,Ed = 10.41 kN | |
| Weld force across the battenFx·x/hb: the moment Fx·x at the chord, taken by the two weld runs as a couple. | Fy,Ed = 7.36 kN |
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 force in a chord more than half the axial force?
The second-order moment from the initial bow l/500 becomes a couple M/a, which adds to the chords on one side. In the worked example it adds 33.1 kN, or 8 %.
Why is the first batten the most loaded?
The second-order shear peaks at the ends of the bar and is zero at midspan, which is also why a single batten in the middle would be useless.
Which plan includes this module?
The Basic plan, with its calculation note.
Related
- Rolled steel section in compression
- Steel member in compression from its section properties
- Steel compression: all sections
- SIA 263: modules and clauses
Norm: SIA 263:2013 · Page updated: 27 October 2026