Material properties, shared by every verification. The cross-section is not shared: SIA 263 classifies it from the internal forces, so it belongs to each verification and appears with it.
Checks a steel beam with web openings, castellated or cellular, by the Vierendeel model to SIA 263:2013: the chords, the montant between two openings, lateral-torsional buckling and the deflection. Every step shows its formula and the clause it comes from.
You enter fy,k and τy,k from table 1 of your copy of SIA 263, the type of openings, the parent profile (b, tf, tw, r), the opened beam (h, a, h0, e1, e0) and γM1 (clause 4.1.3). The internal forces come from the span l and the design load qEd of a simply supported beam, or are entered directly, with the distance xD to the first chord section. For lateral-torsional buckling you enter E (clause 2.2), G, the distance lD between lateral supports of the compressed flange, the loading, the load position za and the warping of the end sections. For the deflection you enter the service load and the limit.
You get the derived geometry, the class, the forces in the chords and the montant, and the utilisation of each check with a pass or fail. With the Basic plan, it prints as an A4 calculation note.
A castellated beam cut from a parent profile 200 mm deep (b = 100 mm, tf = 8.5 mm, tw = 5.6 mm), opened to h = 480 mm with a = 60 mm, h0 = 200 mm, e1 = 120 mm and e0 = 240 mm, in fy,k = 235 N/mm², simply supported over 6.24 m under qEd = 16 kN/m with lateral supports every 3.00 m, and a service load of 7 kN/m against l/350; the chord, montant and deflection checks pass, but lateral-torsional buckling does not (η = 1.43). 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 |
| Characteristic shear yield strength τy,k | 135 N/mm² | § t.1 |
| Openings | Polygonal openings — castellated | |
| Flange width b | 100 mm | |
| Flange thickness tf | 8.5 mm | |
| Web thickness tw | 5.6 mm | |
| Root radius r | 12 mm | |
| Overall depth of the opened beam h | 480 mm | |
| Depth of a chord at the opening a | 60 mm | |
| Height of the intermediate flat h0 | 200 mm | |
| Width of a montant e1 | 120 mm | |
| Clear width of an opening e0 | 240 mm | |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| Internal forces | Simply supported under a uniformly distributed load | |
| Span l | 6240 mm | |
| Design load qEd | 16 kN/m | |
| Distance from the support to the first chord section xD | 240 mm | |
| Lateral-torsional buckling | Checked, on the section at the opening | |
| Modulus of elasticity E | 210000 N/mm² | § 2.2 |
| Distance between lateral supports of the compressed flange lD | 3000 mm | |
| Shear modulus G | 81000 N/mm² | |
| Loading | Uniformly distributed load, simply supported | |
| Load applied at za from the shear centre za | 0 mm | |
| Warping of the end sections | Not prevented — kφ = 1,0 | |
| Deflection | Considered | |
| Service load, uniformly distributed q | 7 kN/m | |
| Deflection limit, span divided by | 350 |
| Step | Value | Ref. |
|---|---|---|
| Characteristic yield strength | fy,k = 235 N/mm² | § t.1 |
| Characteristic shear yield strength | τy,k = 135 N/mm² | § t.1 |
| Resistance factor | γM1 = 1.05 | § 4.1.3 |
| Height of an openingBetween the two chords. With flats it is two sloping sides of 80 mm and a vertical side of h0 = 200 mm. | h − 2a = 360 mm | |
| Rise of one sloping side | (h − 2a − h0)/2 = 80.0 mm | |
| Run of one sloping side | (e0 − e1)/2 = 60.0 mm | |
| Angle of the cutMeasured from the horizontal. It is the angle of the zig-zag the parent web was cut along. | α = 53.1 ° | |
| Depth of the parent profileNot entered: it follows from the others, since the cut runs between two levels a from each flange. Compare it with the profile you started from — if it does not match, one of h, a or h0 is not what you think it is. | d = (h − h0)/2 + a = 200.0 mm | |
| Gain in depthCastellation alone typically gives about 1,5; flats take it further. | h/d = 2.40 | |
| Area of one chordA1 = b·tf + tw·(a − tf), the fillets neglected. | A1 = 1,138.4 mm² | |
| Static moment at the openingS = b·tf·(h − tf) + tw·(a − tf)·(h − tf − a) | S = 519,452 mm³ | |
| Lever arm of the chord forcesaN = S/A1 — the distance between the centroids of the two chords. The whole external moment is turned into a couple on this arm. | aN = 456.30 mm | |
| Web area of one chordA1w = (a − tf/2)·tw | A1w = 312.2 mm² | |
| Plastic modulus of one chordAbout the axis that cuts the tee into two equal areas — 5.69 mm from the outside of the flange. | W1,pl = 10,250 mm³ | |
| Horizontal section of a montantA2 = e1·tw | A2 = 672 mm² | |
| Plastic modulus of a montantW2,pl = tw·e1²/4, the montant being a plain rectangle. | W2,pl = 20,160 mm³ | |
| Pitch of the openings | e0 + e1 = 360 mm | |
| Web slenderness at the openingLimits 9.00 · 10.00 · 14.00. The EP figure of 10 for S 235 and 8 for S 355 is the class 2 outstand limit 10ε — the web stub above an opening is an outstand, free along the cut edge. | (a − tf − r)/tw = 7.05 | § t.5b |
| Class of the chord webA castellated beam is generally designed by EP, which needs class 2 or better. | – = Class 1 | § t.5b |
| Support reaction | REd = 49.92 kN | |
| Largest moment, at midspanq·l²/8 | MEd = 77.88 kNm | |
| Chord force at midspanN1 = M/aN. The moment is carried almost entirely by a couple of axial forces in the two chords; what is left over is carried by their local bending, M1. | N1,Ed = 170.7 kN | |
| Moment at the first chord section | MD,Ed = 11.52 kNm | |
| Chord force there | N1D,Ed = 25.25 kN | |
| Chord shear thereV1 = V/2 — the vertical shear is shared equally between the two chords. | V1D,Ed = 23.04 kN | |
| Moment at the next chord section | ME,Ed = 27.07 kNm | |
| Chord force at the next section | N1E,Ed = 59.33 kN | |
| Chord shear at the next section | V1E,Ed = 20.16 kN |
| Step | Value | Ref. |
|---|---|---|
| Plastic axial resistance of a chordN1,pl = fy,k·A1: a uniform stress over the whole chord, because at midspan the shear is nil and there is no local bending. | N1,pl = 267.5 kN | |
| Chord under axial force aloneN1,Ed ≤ N1,pl/γM1 | η = 0.670 · Pass67 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Plastic shear resistance of a chordV1,pl = τy,k·A1w | V1,pl = 42.1 kN | |
| Chord under shear aloneV1,Ed ≤ V1,pl/γM1 | η = 0.574 · Pass57 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Shear stress in the chord webτ = V1,Ed/A1w | τEd = 73.8 N/mm² | |
| Reduced yield strengthfyr = √(fy,k² − 3τ²). The reduction is applied over the WHOLE chord for simplicity, even though the flanges could in fact reach the full fy,k. | fyr = 197.2 N/mm² | |
| Local bending moment in the chordM1 = V1·e1/2, the lever being half the montant width — section B-B lies there, measured from the mid-opening hinge at A. This moment is the part of the general bending that the couple of chord forces does not take. | M1,Ed = 1.382 kNm | |
| Normal stress at the governing sectionσ = N1,Ed/A1 + M1,Ed/W1,pl | σEd = 157.0 N/mm² | |
| Chord under axial force, shear and local bendingσEd ≤ fyr/γM1 | η = 0.836 · Pass84 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Horizontal shear in the montantV2 = ΔN1: the change in chord force from one opening to the next has to be handed across by the montant. | V2,Ed = 34.08 kN | |
| Plastic shear resistance of the montantV2,pl = τy,k·A2 | V2,pl = 90.7 kN | |
| Montant under horizontal shearV2,Ed ≤ V2,pl/γM1 | η = 0.394 · Pass39 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Axial force in the montantThe difference between the chord shears on either side. | N2,Ed = 2.88 kN | |
| Bending moment in the montantM2 = (V1D + V1E)·(e/2) − (N1E − N1D)·(aN − h0)/2. The horizontal shear bends the montant, so it carries tension on one side and compression on the other. | M2,Ed = 3.408 kNm | |
| Shear stress in the montant | τ2,Ed = 50.7 N/mm² | |
| Reduced yield strength | fyr = 218.0 N/mm² | |
| Normal stress in the montantσ = N2,Ed/A2 + M2,Ed/W2,pl — the same form as for the chord, applied to the montant. | σEd = 173.3 N/mm² | |
| Montant under axial force, shear and bendingσEd ≤ fyr/γM1 | η = 0.835 · Pass84 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Second moment of area at the openingComputed from the geometry, not entered: the two tees and nothing between them, Iy = 2·[b·tf³/12 + b·tf·((h − tf)/2)² + tw·(a − tf)³/12 + tw·(a − tf)·((h − a − tf)/2)²]. The flanges give 79.4 % of it. Fillets neglected, as for A1 and S; the flats sit in the montants, not in this section. | Iy = 119,038,137 mm⁴ | |
| Bending deflection of the equivalent beam5·q·l⁴/(384·E·Iy), on a beam of constant inertia equal to that at the opening. | wM = 5.53 mm | |
| Total deflectionThe bending deflection raised by about 20 % to allow for the shear deformation, which in a beam full of holes is no longer negligible. That factor is an estimate from the literature, not a norm value. | w = 6.63 mm | |
| Limitl/350 | wlim = 17.8 mm | |
| Deflectionw ≤ wlim | η = 0.372 · Pass37 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Torsion constant at the opening(2·b·tf³ + 2(a − tf)·tw³)/3. Only the two chord webs are there. | K = 46,971 mm⁴ | |
| Torsion constant between the openingsThe full web. The openings cut K by 31 % — and they cut Iz by only 0.4 % and Iω not at all. It is K that the openings take away, which is exactly why the check is made on the section at the opening. | K = 68,045 mm⁴ | |
| Elastic critical moment at the openingWith Iz, K and Iω of the OPENED section, β = 0, kφ = 1.0. The solid section would give 99.5 kNm — 4 % more, and using it would be unconservative. | McrD = 95.6 kNm | |
| Bending resistance of the opened beamfy,k·A1·aN — both chords at yield on the lever aN, which is the same couple model the chord forces use. | MR = 122.1 kNm | |
| Relative slenderness | λ̄D = 1.1297 | |
| Reduction factorαD = 0.49, taking the beam as a WELDED I — which it is, being cut and rewelded. It is treated as a welded plate girder throughout. | χD = 0.4687 | |
| Lateral-torsional bucklingMEd ≤ MD,Rd | η = 1.429 · Fail143 % of the capacity used |
Verified clause by clause against SIA 263:2013 and against independent calculations used on real projects, before release.
The openings cut the torsion constant K. In the worked example they reduce K by 31 %, leave Iz within 0.4 % and Iω untouched. The solid section would overstate McrD by 4 %, which is unconservative.
It has to be found by iteration. On a simple beam it lies at roughly a quarter of the span. The module checks only the sections it is given, so move xD along the beam and watch the utilisation.
The full calculation is shown on screen, free and without an account. A print-ready A4 calculation note is part of the Basic plan.
Norm: SIA 263:2013 · Page updated: 26 October 2026