Steel box girder resistance to SIA 263
Checks a single-cell steel box girder at the sections of maximum positive and negative moment, to SIA 263:2013 with EN 1993-1-5: bending with axial force on the effective section, shear and torsion in the webs, and lateral-torsional buckling. 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 single-cell steel box girder at the sections of maximum positive and negative moment, to SIA 263:2013 with EN 1993-1-5: bending with axial force on the effective section, shear and torsion in the webs, and lateral-torsional buckling. Every step shows its formula and the clause it comes from.
What it checks
- Gross section, mid-line model: A, zG, Iy, Iz, the enclosed area Am, the torsion constant K = 4 · Am²/Σ(s/t) around the closed cell, and the web inclination φ.
- Compressed flange plate: the widest panel bp, σcr,p with kσ = 4 (EN 1993-1-5 §4.4), λp = √(fy,k/σcr,p) and ρ = 1.05 · (1/λp − 0.26/λp²) ≤ 1 above λp = 0.55, the reduction for a uniformly compressed plate. The web formulation is shown for comparison. Flange cantilevers are reduced as outstands, ρc.
- Stiffeners as struts: each stiffener with ρ · b/(ns + 1) of plate, buckling between transverse stiffeners, λ̄c = (a/isl)/λE, αe = 0.34 for a closed trough or 0.49 for an open stiffener, plus 0.09/(isl/e) (EN 1993-1-5 §4.5.3), and χc from the buckling curve (clause 4.5.1).
- Shear lag: Le (EN 1993-1-5 §3.2.1) and β^κ for each flange (§3.3). The effective width for the global analysis, min(b0, Le/8), is shown.
- Bending and axial force: web reduction ρw (§4.4), Aeff, Ieff, Weff,o, Weff,u and the fibre stresses, |σ| ≤ fy,k/γM1 (clause 4.1.3).
- Shear of the webs: τcr = 0.9 · kτ · E · (tw/hw)², VR = min(τcr, τy,k) · hw · tw; per web VEd/(2 · cos φ) plus TEd · hw/(2 · Am) in the more loaded web, against VR/γM1 (clause 4.1.3). Interaction with bending follows EN 1993-1-5 §7.1: none while η̄3 ≤ 0.5 or MEd ≤ Mf,Rd.
- Lateral-torsional buckling, clause 4.5.2: Mcr = (π/LD) · √(E · Iz · G · K), λ̄D, χD on the welded-section curve (α = 0.49), MEd ≤ χD · Weff · fy,k/γM1.
What you enter and what you get
You enter fy,k (table 1), E (clause 2.2), γM1 (clause 4.1.3); the depth h, tw, each flange's width between the web axes, thickness and cantilever, and its longitudinal stiffeners (none, flat or trough, with their number and dimensions); the transverse stiffener spacing a, or none between the bearing diaphragms; the span type, L and L2; the lateral restraints; NEd, TEd, and MEd with VEd at each section.
You get the section properties, the effective section and stresses at each section, the web shear and each utilisation with a pass or fail. With the Basic plan, it prints as an A4 calculation note.
Assumptions and limits
- Beam theory on the effective section, the cross-section kept in shape by the cross-frames. Distortion between cross-beams is not analysed.
- The isolated-strut model of a stiffened flange is conservative: the plate behaviour between the webs is not credited.
- The post-critical tension band in the webs is not counted, by choice.
- β^κ is used at the ultimate limit state. Shear lag weighs most on service and fatigue checks, which are not covered.
- Not designed here: the web-flange intersection as a compressed bar, the edge forces from torsion, and the transverse stiffeners, which must also carry 1 % of the normal force in each longitudinal stiffener they support.
Worked example
A box 2,560 mm deep in fy,k = 355 N/mm² with 18 mm webs, a top flange 4,000 × 25 mm with six trough stiffeners, a bottom flange 3,000 × 25 mm with three flat stiffeners, transverse stiffeners every 3,000 mm, in a 56 m end span next to a 70 m span, under TEd = 2,000 kNm, 65,000 kNm with 1,500 kN at the positive moment and 60,000 kNm with 5,000 kN at the negative. 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 | 355 N/mm² | § t.1 |
| Modulus of elasticity E | 210000 N/mm² | § 2.2 |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| Overall depth of the box h | 2560 mm | |
| Web thickness tw | 18 mm | |
| Width of the top flange between the web axes bo | 4000 mm | |
| Thickness of the top flange tf,o | 25 mm | |
| Cantilever of the top flange, beyond each web axis co | 1000 mm | |
| Longitudinal stiffeners on the top flange | Trough stiffeners | |
| Number of stiffeners ns | 6 | |
| Trough width at the flange a1 | 300 mm | |
| Trough width at its bottom a2 | 150 mm | |
| Trough depth hs | 280 mm | |
| Trough thickness ts | 8 mm | |
| Width of the bottom flange between the web axes bu | 3000 mm | |
| Thickness of the bottom flange tf,u | 25 mm | |
| Cantilever of the bottom flange, beyond each web axis cu | 0 mm | |
| Longitudinal stiffeners on the bottom flange | Flat stiffeners | |
| Number of stiffeners ns | 3 | |
| Stiffener height hs | 300 mm | |
| Stiffener thickness ts | 25 mm | |
| Intermediate transverse stiffeners and cross-frames | At a regular spacing | |
| Distance between them a | 3000 mm | |
| Span of the girder | End span of a continuous girder | |
| Length of this span L | 56000 mm | |
| Length of the adjacent span, over the support checked L2 | 70000 mm | |
| Lateral restraints of the girder | Only at the bearings: LD = L | |
| Shear lag in the flanges | Checked | |
| Design axial force NEd | 0 kN | |
| Design torque TEd | 2000 kN·m | |
| Positive moment (top flange compressed) | Checked | |
| Design moment MEd | 65000 kN·m | |
| Design shear force acting with it VEd | 1500 kN | |
| Negative moment (bottom flange compressed) | Checked | |
| Design moment, as a magnitude MEd | 60000 kN·m | |
| Design shear force acting with it VEd | 5000 kN |
| Step | Value | Ref. |
|---|---|---|
| Where the resistance comes fromThe bending resistance of a box depends ESSENTIALLY on the compressed flange — the webs contribute only a small proportion. That is the reverse of an I girder, and it is why longitudinal stiffeners on a box FLANGE are worth their cost where on a web they usually are not. | – = Essentially the compressed flange | |
| AreaMid-line model: flanges, cantilevers, webs and stiffeners. | A = 374,628 mm² | |
| Centroid above the bottom face | zG = 1,568.9 mm | |
| Second moment of area, horizontal axis | Iy = 447,826,947,888 mm⁴ | |
| Second moment of area, vertical axis | Iz = 832,369,573,281 mm⁴ | |
| Area enclosed by the mid-lines(bo + bu)/2 × 2,535 mm between the flange mid-planes. | Am = 8,872,500 mm² | |
| Torsion constant4·Am²/Σ(s/t) around the closed cell (Bredt). | K = 555,261,464,004 mm⁴ | |
| Inclination of the webs from the vertical | φ = 11.16 ° |
| Step | Value | Ref. |
|---|---|---|
| Widest plate panelThe larger of the trough opening a1 and the plate between two troughs. | bp = 421 mm | |
| Critical plate buckling stresskσ·π²·E/(12(1 − ν²))·(tf/bp)², kσ = 4. | σcr,p = 2,671.7 N/mm² | EN 1993-1-5 §4.4 |
| Plate slenderness√(fy,k/σcr,p). | λp = 0.365 | |
| Reduction factor, FAULKNER1,05·(1/λp − 0,26/λp²) ≤ 1, above λp = 0,55. Winter is NOT used here: initial deformations and the residual stresses of welding the stiffeners weigh MORE on a UNIFORMLY compressed plate — a box flange — than on one carrying a stress GRADIENT, such as a web. | ρ = 1.0000 | |
| What Winter would have givenThe formulation used for webs. Faulkner is 0.0 % more generous here. The two cross near λp ≈ 1,1: Faulkner is the stricter through the practical moderate range and marginally the looser at very high slenderness.the web formulation | ρ = 1.0000 | |
| Strut: stiffener with ρ·b/(ns + 1) of plate | Asl = 20,124 mm² | |
| Radius of gyration of the strut | isl = 96.1 mm | |
| Relative slenderness of the strut(a/isl)/λE, buckling between transverse stiffeners. | λ̄c = 0.408 | |
| Imperfection factor of the strut0,34 (closed trough) + 0,09/(isl/e), e = 128.7 mm — the larger distance from the strut centroid to the plate or to the stiffener. | αe = 0.460 | EN 1993-1-5 §4.5.3 |
| Strut buckling coefficientFrom the buckling curve with αe. The flange counts as ρ·χc of its plate and χc of its stiffeners: the isolated-strut model, CONSERVATIVE, since the plate-like behaviour between the webs is not credited. | χc = 0.8985 | § 4.5.1 |
| Cantilever, reduction as an outstandλp = (c/tf)/(28,4·ε·√0,43) = 2.640; the effective part next to the web. | ρc = 0.3518 | EN 1993-1-5 §4.4 |
| Step | Value | Ref. |
|---|---|---|
| Widest plate panelb/(ns + 1), between stiffener axes. | bp = 750 mm | |
| Critical plate buckling stresskσ·π²·E/(12(1 − ν²))·(tf/bp)², kσ = 4. | σcr,p = 843.6 N/mm² | EN 1993-1-5 §4.4 |
| Plate slenderness√(fy,k/σcr,p). | λp = 0.649 | |
| Reduction factor, FAULKNER1,05·(1/λp − 0,26/λp²) ≤ 1, above λp = 0,55. Winter is NOT used here: initial deformations and the residual stresses of welding the stiffeners weigh MORE on a UNIFORMLY compressed plate — a box flange — than on one carrying a stress GRADIENT, such as a web. | ρ = 0.9699 | |
| What Winter would have givenThe formulation used for webs. Faulkner is 3.0 % MORE SEVERE here. The two cross near λp ≈ 1,1: Faulkner is the stricter through the practical moderate range and marginally the looser at very high slenderness.the web formulation | ρ = 1.0000 | |
| Strut: stiffener with ρ·b/(ns + 1) of plate | Asl = 25,685 mm² | |
| Radius of gyration of the strut | isl = 87.7 mm | |
| Relative slenderness of the strut(a/isl)/λE, buckling between transverse stiffeners. | λ̄c = 0.448 | |
| Imperfection factor of the strut0,49 (open stiffener) + 0,09/(isl/e), e = 115.1 mm — the larger distance from the strut centroid to the plate or to the stiffener. | αe = 0.608 | EN 1993-1-5 §4.5.3 |
| Strut buckling coefficientFrom the buckling curve with αe. The flange counts as ρ·χc of its plate and χc of its stiffeners: the isolated-strut model, CONSERVATIVE, since the plate-like behaviour between the webs is not credited. | χc = 0.8464 | § 4.5.1 |
| Step | Value | Ref. |
|---|---|---|
| Web depth along its slope, clear | hw = 2,558 mm | |
| Critical shear stressτcr = 0,9·kτ·E·(tw/hw)², kτ = 8.25 at α = a/hw = 1.17. | τcr = 77.2 N/mm² | |
| Shear resistance of one webVR = min(τcr, τy,k)·hw·tw. The post-critical (Basler) term is NOT included: on an I girder the COMPACT flanges are a stiff enough support for the web to anchor the diagonal tension band, but on a box with SLENDER, multiply stiffened flanges that is less favourable — so it is preferable not to count on the band at all. | VR = 3,554.0 kN | |
| What Basler would have givenThe conservatism costs 48 % of the shear resistance here. It is a deliberate choice, not an omission. For the CARDIFF model the equivalent is to set the plastic anchorage lengths sc and st to zero.what the conservatism costs | VR = 6,860.7 kN | |
| Design shear resistance of one web | VR/γM1 = 3,384.8 kN | § 4.1.3 |
| Step | Value | Ref. |
|---|---|---|
| Length between points of zero moment0,85·L in an end span. | Le = 47,600 mm | EN 1993-1-5 §3.2.1 |
| Shear lag, top flange between the websκ = α0·b0/Le = 0.0488, β = 0.9850 (sagging), raised to κ at the ultimate limit state. b0 = b/2. | β^κ = 0.9993 | EN 1993-1-5 §3.3 |
| Shear lag, bottom flange between the websκ = α0·b0/Le = 0.0359, β = 0.9918 (sagging), raised to κ at the ultimate limit state. b0 = b/2. | β^κ = 0.9997 | EN 1993-1-5 §3.3 |
| Effective width for the GLOBAL analysisFor the elastic calculation of the internal forces of a CONTINUOUS box the flange effective width is the smaller of b0 and Le/8. Here b0 governs, so no reduction: the span is long enough relative to the width.for the structural analysis | min(b0, Le/8) = 2,000.0 mm | |
| Compressed flangeFrom the stresses on the gross section. | – = Top | |
| Web, reduction factorψ = -1.278, kσ = 31.04, λp = 1.104; a strip of 193 mm of each web is not counted. | ρw = 0.8281 | EN 1993-1-5 §4.4 |
| Effective area | Aeff = 321,452 mm² | |
| Effective second moment of area | Ieff = 395,658,458,487 mm⁴ | |
| Effective centroid above the bottom face | zG,eff = 1,419.5 mm | |
| Effective section modulus, top fibre | Weff,o = 346,920,441 mm³ | |
| Effective section modulus, bottom fibre | Weff,u = 278,728,426 mm³ | |
| Stress, top fibre−NEd/Aeff ∓ (MEd + NEd·eN)/Weff; tension positive. | σo = -187.4 N/mm² | |
| Stress, bottom fibre | σu = 233.2 N/mm² | |
| Bending resistance of this effective sectionWeff,min·fy,k/γM1, without axial force.for comparison | MRd = 94,237 kN·m | |
| Bending and axial force, positive moment|σ| ≤ fy,k/γM1 | η = 0.690 · Pass69 % of the capacity used | § 4.1.3 |
| Step | Value | Ref. |
|---|---|---|
| Shear force in one web from VEd | VEd/(2·cos φ) = 764.4 kN | |
| Added by the torque in the more loaded webShear flow q = TEd/(2·Am) = 112.7 N/mm along the web. | TEd·hw/(2·Am) = 291.2 kN | |
| Shear resistance of the web, positive momentVEd,w ≤ VR/γM1 | η = 0.312 · Pass31 % of the capacity used | § 4.1.3 |
| Bending and shear togetherη̄3 = 0.312; Mf,Rd = 80,951 kN·m. Above η̄3 = 0,5 the shear reduces the moment the webs can carry, unless the flanges alone carry MEd. | – = No interaction: η̄3 ≤ 0,5 | EN 1993-1-5 §7.1 |
| Step | Value | Ref. |
|---|---|---|
| Length between points of zero moment0,25·(L + L2) over the support. | Le = 31,500 mm | EN 1993-1-5 §3.2.1 |
| Shear lag, top flange between the websκ = α0·b0/Le = 0.0738, β = 0.7048 (hogging), raised to κ at the ultimate limit state. b0 = b/2. | β^κ = 0.9745 | EN 1993-1-5 §3.3 |
| Shear lag, bottom flange between the websκ = α0·b0/Le = 0.0543, β = 0.7774 (hogging), raised to κ at the ultimate limit state. b0 = b/2. | β^κ = 0.9864 | EN 1993-1-5 §3.3 |
| Effective width for the GLOBAL analysisFor the elastic calculation of the internal forces of a CONTINUOUS box the flange effective width is the smaller of b0 and Le/8. Here b0 governs, so no reduction: the span is long enough relative to the width.for the structural analysis | min(b0, Le/8) = 2,000.0 mm | |
| Compressed flangeFrom the stresses on the gross section. | – = Bottom | |
| Web, reduction factorψ = -0.557, kσ = 14.35, λp = 1.624; a strip of 715 mm of each web is not counted. | ρw = 0.5649 | EN 1993-1-5 §4.4 |
| Effective area | Aeff = 327,289 mm² | |
| Effective second moment of area | Ieff = 377,795,647,995 mm⁴ | |
| Effective centroid above the bottom face | zG,eff = 1,707.5 mm | |
| Effective section modulus, top fibre | Weff,o = 443,170,935 mm³ | |
| Effective section modulus, bottom fibre | Weff,u = 221,254,387 mm³ | |
| Stress, top fibre−NEd/Aeff ∓ (MEd + NEd·eN)/Weff; tension positive. | σo = 135.4 N/mm² | |
| Stress, bottom fibre | σu = -271.2 N/mm² | |
| Bending resistance of this effective sectionWeff,min·fy,k/γM1, without axial force.for comparison | MRd = 74,805 kN·m | |
| Bending and axial force, negative moment|σ| ≤ fy,k/γM1 | η = 0.802 · Pass80 % of the capacity used | § 4.1.3 |
| Step | Value | Ref. |
|---|---|---|
| Shear force in one web from VEd | VEd/(2·cos φ) = 2,548.2 kN | |
| Added by the torque in the more loaded webShear flow q = TEd/(2·Am) = 112.7 N/mm along the web. | TEd·hw/(2·Am) = 291.2 kN | |
| Shear resistance of the web, negative momentVEd,w ≤ VR/γM1 | η = 0.839 · Pass84 % of the capacity used | § 4.1.3 |
| Bending and shear togetherη̄3 = 0.839; Mf,Rd = 66,199 kN·m. Above η̄3 = 0,5 the shear reduces the moment the webs can carry, unless the flanges alone carry MEd. | – = No interaction: MEd ≤ Mf,Rd | EN 1993-1-5 §7.1 |
| Step | Value | Ref. |
|---|---|---|
| Elastic critical moment(π/LD)·√(E·Iz·G·K), LD = 56,000 mm: St Venant torsion only — a closed cell carries torsion by shear flow, and warping is negligible. | Mcr = 4,974,173 kN·m | |
| Relative slenderness√(Weff·fy,k/Mcr), with the smaller Weff of the negative moment. | λ̄D = 0.1257 | |
| Reduction factorBuckling curve for welded sections, α = 0,49. | χD = 1.0000 | § 4.5.2 |
| Lateral-torsional bucklingMEd ≤ χD·Weff·fy,k/γM1 | η = 0.802 · Pass80 % of the capacity used | § 4.5.2 |
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 tension field not counted in the webs?
A slender, multiply stiffened box flange anchors the diagonal band less well than the compact flange of an I girder. The resistance with the band is shown for comparison; in the worked example the choice costs 48 %.
Why does lateral-torsional buckling rarely govern?
A closed cell is torsionally very stiff. It can matter for a narrow, deep box over a long unrestrained length, or during erection.
Which plan includes this module?
The Basic plan, with its calculation note.
Related
- Welded plate girder
- Closed-cell section in torsion
- Steel bending: all sections
- SIA 263: modules and clauses
Norm: SIA 263:2013 · Page updated: 27 October 2026