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 solid rectangular steel section in bending about its major or minor axis at the ultimate limit state, to SIA 263:2013, including lateral-torsional buckling. Every step shows its formula and the clause it comes from.
You enter fy,k from table 1 of your copy of SIA 263, the axis of bending, the width b and depth h, γM1 (clause 4.1.3) and MEd. For lateral-torsional buckling you choose whether it is prevented by construction measures or checked; if checked, you enter lD, the moment diagram between the lateral supports, where the load is applied, and E and G (clause 2.2).
You get the section properties, the class, the section resistance, the critical moment, the slenderness, the reduction factor and the utilisation of each check with a pass or fail, each with its clause. With the Basic plan, it prints as an A4 calculation note.
A solid bar b × h = 45 × 300 mm in fy,k = 235 N/mm², bent about its major axis by MEd = 150 kNm, simply supported under a uniformly distributed load applied on the compressed face, with lateral supports 3,000 mm apart. 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 |
| Bending about | Major axis (y–y) | |
| Width b | 45 mm | |
| Depth h | 300 mm | |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| Design bending moment MEd | 150 kNm | |
| Lateral-torsional buckling | Checked | § 4.5.2 |
| Distance between lateral supports lD | 3000 mm | |
| Moment diagram between the lateral supports | Uniformly distributed load, simply supported | |
| Load applied at | Top face — the compressed side | |
| Modulus of elasticity E | 210000 N/mm² | § 2.2 |
| Shear modulus G | 81000 N/mm² | § 2.2 |
| Step | Value | Ref. |
|---|---|---|
| Characteristic yield strength | fy,k = 235 N/mm² | § t.1 |
| Area | A = 13,500 mm² | |
| Second moment of areaI = b·h³/12, about the axis of bending. It plays no part in the section resistance — the deflection is inversely proportional to I, but that is a serviceability parameter, not a structural safety one. | I = 101.2500 10⁶ mm⁴ | |
| Elastic section modulusWel = b·h²/6 | Wel = 675,000 mm³ | |
| Plastic section modulusWpl = b·h²/4 | Wpl = 1,012,500 mm³ | |
| Shape factorExactly 3/2 for any solid rectangle, whatever its proportions — every fibre helps, so the plastic block gains the most it can. A rolled I reaches only 1,10 to 1,15, because its flanges are already at the extreme fibre and have little left to give. | Wpl/Wel = 1.5000 | |
| Section classA solid section has no slender plate element to buckle locally. The class limits concern the compressed plates of a built-up or rolled section, and a solid one has none. | – = Class 1 | § t.4 |
| Resistance modelDecided by the class, not asked for: class 1 admits the plastic resistance, MR = fy·Wpl, for the section and for lateral-torsional buckling alike. | – = Plastic | § t.4 |
| Ultimate bending resistanceMR = fy·Wpl | MR = 237.94 kNm |
| Step | Value | Ref. |
|---|---|---|
| Design bending resistance | MR/γM1 = 226.61 kNm | § 4.1.3 |
| Elastic resistanceTwo thirds of the plastic value, always, for this section. It is what an elastic calculation — sometimes chosen for a gusset or a splice plate — would give.not the governing value | fy·Wel/γM1 = 151.07 kNm | |
| Section modulus requiredW ≥ γM1·MEd/fy,k, the sizing form of the same check. | Wpl,req = 670,213 mm³ | |
| Bending resistance of the sectionMEd ≤ MR/γM1 | η = 0.662 · Pass66 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Second moment of area out of the plane of bendingIz = h·b³/12, with b the dimension ACROSS the plane of bending. It is the lateral bending stiffness that resists the sideways movement. | Iz = 2.2781 10⁶ mm⁴ | |
| Torsion constantK = β·h·t³ for a solid rectangle h × t (h ≥ t), β = 0.3018 at h/t = 6.67, from the exact series of Saint-Venant. It tends to 1/3 for a thin plate and is 0,141 for a square. | K = 8,251,029 mm⁴ | |
| Warping constantTaken as zero: a solid rectangle has no flanges whose bending could resist warping, so it resists twisting by uniform torsion alone. | Iω = 0 mm⁶ | |
| Moment-diagram factorsUniformly distributed load, simply supported, at kv = 1 — the supports do not prevent lateral bending. | C1 · C2 = 1.13 · 0.46 | |
| Load position from the centroidOn the compressed face, −h/2: the load follows the buckling movement and DESTABILISES. | za = -150.0 mm | |
| Elastic critical momentMcrD = C1·π²·E·Iz/lD² · [√((C2·za)² + G·K·lD²/(π²·E·Iz)) + C2·za] — the general critical moment with Iω = 0. For a constant moment and za = 0 it is (π/lD)·√(E·Iz·G·K). | McrD = 629.5 kNm | |
| Relative slenderness√(MR/McrD), with the plastic MR of the class 1 section. | λ̄D = 0.6148 | § 4.5.2 |
| Reduction factorαD = 0.49 — buckling curve c, which SIA 263 gives to sections other than rolled or welded I sections. | χD = 0.7766 | § 4.5.2 |
| Lateral-torsional buckling resistanceχD·MR/γM1. It replaces MR/γM1 wherever it is the smaller. | MD,Rd = 175.98 kNm | § 4.5.2 |
| Lateral-torsional bucklingMEd ≤ MD,Rd | η = 0.852 · Pass85 % of the capacity used | § 4.5.2 |
Verified clause by clause against SIA 263:2013 and against independent calculations used on real projects, before release.
For any solid rectangle, Wpl = b · h²/4 and Wel = b · h²/6, whatever the proportions. A rolled I reaches only 1.10 to 1.15, because its flanges are already at the extreme fibre.
Curve c, αD = 0.49, which SIA 263 clause 4.5.2 gives to sections other than rolled or welded I sections. In the worked example, lateral-torsional buckling costs 22% of the section resistance.
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