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 rolled I or H section in bending at the ultimate limit state, to SIA 263:2013: section class, bending and shear resistance, lateral-torsional buckling between lateral supports, 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, E and G (clause 2.2), the profile dimensions, γM1, MEd, VEd and whether the internal forces come from an elastic or a plastic analysis. For lateral-torsional buckling: lD, the end moments of the segment, the moment diagram, the load position and the warping of the end sections. For the deflection: the static system (simply supported, or continuous over 2 to 5 equal spans), the span, the service load and the limit. Vibration is an option.
You get the section properties, the class, every resistance and each utilisation with a pass or fail and its clause, and a drawing of the profile to scale. With the Basic plan, it prints as an A4 calculation note.
A rolled section with h = 114 mm, b = 120 mm, tw = 5 mm, tf = 8 mm and r = 12 mm in fy,k = 235 N/mm², under MEd = 20.8 kNm and VEd = 24.9 kN, with lateral supports every 1,250 mm and end moments of 15.6 and 14.3 kNm of the same sign, and a deflection check over three continuous 5.00 m spans under 3.0 kN/m against l/350. 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 |
| Modulus of elasticity E | 210000 N/mm² | § 2.2 |
| Overall depth h | 114 mm | |
| Flange width b | 120 mm | |
| Web thickness tw | 5 mm | |
| Flange thickness tf | 8 mm | |
| Root radius r | 12 mm | § t.5b |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| Design bending moment MEd | 20.8 kNm | |
| Design shear force VEd | 24.9 kN | |
| Internal forces found by | Elastic analysis | |
| Lateral-torsional buckling | Considered | § 4.5.2 |
| Distance between lateral supports of the compressed flange lD | 1250 mm | |
| Larger end moment of the segment |Mmax| | 15.6 kNm | |
| Smaller end moment of the segment |Mmin| | 14.3 kNm | |
| The two moments have | The same sign at both ends of the segment | |
| Moment diagram between the lateral supports | Uniformly distributed load, simply supported | |
| Load applied at | Shear centre | |
| Warping of the end sections | Not prevented — kφ = 1,0 | |
| Shear modulus G | 81000 N/mm² | § 2.2 |
| Deflection | Considered | |
| Static system | Continuous over equal spans — uniformly distributed load | |
| Number of equal spans n | 3 | |
| Span l | 5000 mm | |
| Service load, uniformly distributed q | 3.0 kN/m | |
| Deflection limit, span divided by | 350 | |
| Vibration | Not considered |
| Step | Value | Ref. |
|---|---|---|
| Characteristic yield strength | fy,k = 235 N/mm² | § t.1 |
| Characteristic shear yield strengthFrom SIA 263 table 1, not derived as fy/√3. | τy,k = 135 N/mm² | § t.1 |
| Reduction factorε = √(235/fy). The class limits are scaled by it. | ε = 1.0000 | § t.5a |
| Resistance factor | γM1 = 1.05 | § 4.1.3 |
| Gross areaA = 2b·tf + (h − 2tf)·tw + (4 − π)·r², the plates and the four fillets. | A = 2,534 mm² | |
| Second moment of areaFlanges, web and fillets about the major axis. No resistance check uses it — the deflection is inversely proportional to it. | Iy = 6,060,890 mm⁴ | |
| Elastic section modulusWel = 2Iy/h | Wy,el = 106,331 mm³ | |
| Plastic section modulusTwice the first moment of the half section about the major axis, fillets included. | Wy,pl = 119,491 mm³ | |
| Second moment of area, minor axis | Iz = 2,308,338 mm⁴ | |
| Radius of gyration, minor axisiz = √(Iz/A). It sets the critical length between lateral supports: for the same section resistance an IPE resists lateral-torsional buckling markedly less well than an HEA, HEB or HEM. | iz = 30.18 mm | |
| Uniform torsion constant2/3·(b − 0,63tf)·tf³ + 1/3·(h − 2tf)·tw³ plus the fillet junction term — the expression the section tables use. | K = 59,942 mm⁴ | |
| Warping constantIω = tf·b³/24·(h − tf)², the flanges' lateral inertia on the lever between them. | Iω = 6,471,936,000 mm⁶ | |
| Compressed flange — flat widthc = (b − tw)/2 − r, measured to the toe of the fillet. | c = 45.50 mm | § t.5b |
| Compressed flange — slendernessLimits 9.0 · 10.0 · 14.0 for class 1, 2 and 3. | c/tf = 5.69 | § t.5b |
| Web in bending — flat widthh − 2tf − 2r | bw = 74.0 mm | § t.5a |
| Web in bending — slendernessLimits 72.0 · 83.0 · 124.0 for class 1, 2 and 3. | bw/tw = 14.80 | § t.5a |
| Section classThe least favourable of the two compressed parts. Every IPE, HEA, HEB and HEM profile is class 1 in bending except the HEA 180 to 320 in S 355. | – = Class 1 | § t.5a |
| Calculation methodDecided by the class: class 1 admits the plastic resistance, so EP — elastic analysis, plastic resistance — the general case. | – = EP | § t.5a |
| Step | Value | Ref. |
|---|---|---|
| Governing section modulusPP and EP both take the plastic modulus. | Wy,pl = 119,491 mm³ | |
| Ultimate bending resistanceMR = fy·Wy,pl | MR = 28.08 kNm | |
| Design bending resistance | MR/γM1 = 26.74 kNm | § 4.1.3 |
| Section modulus requiredW ≥ γM1·MEd/fy — the sizing form used to pick a profile out of the tables in the first place. | Wreq = 92,936 mm³ | |
| Bending resistanceMEd ≤ MR/γM1 | η = 0.778 · Pass78 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Effective shear areaAv = A − 2b·tf + (tw + 2r)·tf. The last term hands back the web-to-flange junction and both fillets. | Av = 846 mm² | § (42a) |
| Ultimate shear resistanceVR = τy·Av. | VR = 114.2 kN | |
| Design shear resistance | VR/γM1 = 108.7 kN | § 4.1.3 |
| Shear resistanceVEd ≤ VR/γM1 | η = 0.229 · Pass23 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Moment ratio over the segmentψ = Mmin/Mmax with signs, Mmin the smaller in absolute value. | ψ = 0.9167 | |
| Critical length ratiolcr = 2,7·iz·(1 − 0,5ψ)·√(E/fy), for EP. | lcr/iz = 43.72 | |
| Critical lateral-torsional length | lcr = 1,320 mm | |
| If the moment were pushed up to the resistanceA profile taken from the tables usually has a little more resistance than the moment needs, and a first approximation for the extra spacing that buys is lcr·√(MR/(γM1·MEd)), on the assumption of a second-degree relation between the two. NOT IN SIA 263. The alternative is the full lateral-torsional buckling check.not in SIA 263 | lD,max = 1,496 mm | |
| Lateral-torsional bucklinglD = 1,250 mm ≤ lcr = 1,320 mm: lateral-torsional buckling is not decisive and the bending resistance of the section stands alone. This is information, not a check. | lD / lcr = Not decisive — 0.95 |
| Step | Value | Ref. |
|---|---|---|
| Static system | – = Continuous over equal spans — uniformly distributed load | |
| Support momentFrom the three-moment equations for 3 equal spans. For three spans this comes out at exactly −0,100. | M/(q·l²) = -0.10000 | |
| Deflection coefficientw = k·q·l⁴/(E·I), that is 1/145.26. Obtained by integrating the bending moment twice over the span and scanning for the largest deflection, so it is derived rather than read off. | k = 0.0068842 | |
| Deflection | w = 10.14 mm | |
| Limitl/350. SIA 260 annex A gives indicative values; others may be agreed. | wlim = 14.29 mm | |
| Deflectionw ≤ wlim | η = 0.710 · Pass71 % of the capacity used |
Verified clause by clause against SIA 263:2013 and against independent calculations used on real projects, before release.
SIA 263 tabulates τy, and the tabulated values are not fy/√3. For S 235 the table gives 135 N/mm² where the division gives 135.7.
When lD exceeds lcr. Below it, the section resistance stands alone. In the worked example, lD = 1,250 mm ≤ lcr = 1,320 mm.
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