Ultimate limit state
Check bending, shear, their interaction, and the governing utilisation to EN 1993-1-1.
SKL-000006 · Skill
EN 1990EN 1993-1-1Design a single-span steel beam to Eurocode 3
Describe the span, section, steel grade, distributed loads, up to two optional point loads, and lateral restraints. Mia checks ultimate and serviceability limit states and explains the governing result step by step.
Mia guides you step by stepShe guides you through the inputs and explains the results.
Worked example
IPE 360 · 6.00 m · qk 10 kN/m + Pk 20 kN
Design verified: lateral-torsional buckling governs- System
- Simply supported beam
- Section
- IPE 360 · S235
- Span
- 6.00 m
- Loads
- qk = 10 kN/m · Pk = 20 kN at a = 2.00 m
- Lateral restraint
- Only at the supports (fork bearings)
Design a simply supported IPE 360 steel beam in S235, span 6 m, with qk = 10 kN/m and a point load Pk = 20 kN at a = 2 m from the left support, without self-weight, the compression flange laterally restrained only at the supports (fork bearings), to EN 1993-1-1 (DIN NA). Check ULS, lateral-torsional buckling and deflection (limit L/250).
Key results
- Design moment MEd
- 100.8 kNm
- Design shear VEd
- 65.0 kN
- Elastic deflection
- ≈ 7.2 mm ≤ 24.0 mm (L/250)
- Governing utilisation
- η = 0.96 (lateral-torsional buckling)
All values are deterministic for the stated inputs. ULS combination 6.10 (γG = 1.35, γQ = 1.5) with γM0 = 1.0 to DIN EN 1993-1-1/NA. Lateral-torsional buckling to §6.3.2.3 with γM1 = 1.1, Lcr = 6.00 m between fork bearings, load at the top flange and numerical Mcr for the combined moment shape (60 elements; relative mesh change below 0.001%).
- — Self-weight and permanent line load are excluded; the design loads are qd = 15.0 kN/m and Pd = 30.0 kN.
- — Cross-section class 1; Mc,Rd = 239.5 kNm and Vpl,Rd = 476.8 kN; VEd < 0.5·Vpl,Rd, so no moment–shear interaction.
- — LTB: Mcr = 145.85 kNm, λ̄_LT = 1.28, buckling curve c (h/b = 2.12 > 2), χLT = 0.484, Mb,Rd = 105.3 kNm.
- — The deflection uses qk = 10 kN/m and Pk = 20 kN at a = 2.00 m, with E = 210 GPa and Iᵧ = 16,270 cm⁴.
Required inputs
- Static system and span
- Loads and load positions
- Section and steel grade
- Lateral restraint of the compression flange
- National Annex and deflection limit
What you receive
- Governing check and utilisation
- Bending and shear resistance
- Lateral-torsional buckling resistance
- Deflection and applicable limit
- Assumptions and normative references
Reviewed calculation example
Start from an input template
These templates prefill the form with typical inputs. They are not calculated results; the calculation runs in CALC.
Prepare your calculation
Configure your beam
System sketch
L = 6 mgk = 5 kN/mqk = 10 kN/m
Show calculation flow
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Inputs completeReady to calculate
What this skill checks
Serviceability
Calculate deflection and compare it with the agreed project or National Annex limit.
Lateral-torsional buckling
Assess member stability using the unrestrained length, moment shape, and support conditions.
Vibration screening
Estimate the first natural frequency as a serviceability hint, not a code verification.
Normative basis
Standards & references
The checks follow these standards. Nationally determined parameters come from the National Annex selected in the form.
EN 1993-1-1
WithdrawnEurocode 3: Design of steel structures – Part 1-1: General rules and rules for buildings
Edition used: DIN EN 1993-1-1:2010-12 (EN 1993-1-1:2005 + AC:2009) + DIN EN 1993-1-1/A1:2014-07
- §5.5
- §6.1
- §6.2.5
- §6.2.6
- §6.2.8
- §6.3.2
DIN MediaNewer edition: DIN EN 1993-1-1:2025-04 (EN 1993-1-1:2022)
| Country | National Annex | Factors | Source |
|---|---|---|---|
| DE | DIN EN 1993-1-1/NA:2022-10WithdrawnNewer edition: DIN EN 1993-1-1/NA:2026-04 | γM0 = 1.00γM1 = 1.10 | DIN Media |
| AT | ÖNORM B 1993-1-1:2017-11-01Current | γM0 = 1.00γM1 = 1.00 | Austrian Standards |
| CZ | ČSN EN 1993-1-1 ed. 2 (73 1401):2011-07 + A1 + Z1, NACurrentNewer edition: ČSN EN 1993-1-1 ed. 3 (73 1401) | γM0 = 1.00γM1 = 1.00 | shop.normy.biz |
| EN | Recommended valuesEN 1993-1-1:2005 + AC:2009 + A1:2014 | γM0 = 1.00γM1 = 1.00 | – |
Status checked on
EN 1990
CurrentEurocode: Basis of structural design
Edition used: DIN EN 1990:2021-10 (EN 1990:2002 + A1:2005 + A1:2005/AC:2010)
- §6.4.3.2
- §A1.4.3
DIN MediaNewer edition: EN 1990:2023 (CEN; coexistence with the first generation until 2028-03-30)
| Country | National Annex | Factors | Source |
|---|---|---|---|
| DE | DIN EN 1990/NA:2010-12 + DIN EN 1990/NA/A1:2024-05Current | γG = 1.35γQ = 1.50 | DIN Media |
| EN | Recommended valuesEN 1990:2002 + A1:2005 + A1:2005/AC:2010 | γG = 1.35γQ = 1.50 | – |
Status checked on
Frequently asked questions
Frequently asked questions
InputsWhich inputs does Mia need for the design?
The static system (simply supported beam or cantilever) and span, the section and steel grade (S235, S275 or S355), the characteristic loads, the lateral restraint of the compression flange, the National Annex and the deflection limit. Loads can be permanent and variable line loads, up to two variable point loads with their positions and one variable partial line load. If a governing input is missing, Mia asks for it before calculating.
InputsDo I enter characteristic loads or design loads?
Enter characteristic values. Mia forms the ultimate limit state design loads with combination 6.10 of EN 1990 (γG = 1.35, γQ = 1.50) and uses the characteristic combination for deflection. In the form, point loads and the partial line load are entered as variable characteristic actions. A pre-factored design load is accepted only when you state it explicitly; Mia never guesses whether a load is already factored.
InputsIs the self-weight of the beam included?
Yes, when you include it; the form preselects Yes. Mia then adds the self-weight from the catalogue mass of the selected section as a permanent line load. If a chat request does not address the self-weight, Mia asks for it.
VerificationWhich ultimate limit state checks are performed?
Cross-section classification to EN 1993-1-1 §5.5, bending resistance §6.2.5 (plastic for class 1 and 2, elastic for class 3), shear resistance §6.2.6 with the bending–shear interaction of §6.2.8 when VEd exceeds 0.5 · Vpl,Rd, and lateral-torsional buckling §6.3.2. The result names the governing check and its utilisation.
VerificationIs lateral-torsional buckling considered automatically?
Yes, for simply supported beams whose compression flange is not continuously restrained. Mia derives the buckling length from the selected restraint, determines Mcr numerically for fork bearings and the selected load application point, and verifies Mb,Rd with γM1. If the supports are not fork bearings, intermediate restraints have unclear stiffness or the member is tapered, this hand check is not sufficient and Mia refers to RFEM. For cantilevers the lateral-torsional buckling check is not calculated; the result says so and refers to RFEM.
VerificationWhich deflection limit is used, and with which loads?
The limit you select (L/200, L/250 or L/300) under the characteristic combination. EN 1990 A1.4.3 leaves deflection limits to the project; L/250 for the total deflection is customary. The deflection is the elastic bending deflection without shear deformation, which Mia states as an assumption.
VerificationWhich partial factors apply for my National Annex?
γM0 = 1.00 for all offered annexes. γM1 = 1.10 with the German National Annex and 1.00 with the Austrian, Czech and EN-recommended values. The load factors are γG = 1.35 and γQ = 1.50. The Standards tab lists the National Annex editions.
Results & reportWhat does the result contain, and can I export it?
Inputs, assumptions, section class, internal forces, resistances, the utilisation of every check, the governing check, the deflection and the normative references. A natural-frequency estimate is added as a serviceability hint, not as a code verification. CALC can export the structured answer as a PDF.
Results & reportHow reliable are the results?
Mia computes every reported number in the run from section properties looked up in the profile library, not from memory, and checks each utilisation in the text against the calculation output. The featured example is covered by a reproducible calculation test. The result supports the engineer; checking inputs, assumptions and the applicability to the project remains the responsibility of the qualified structural engineer.
ScopeWhat is not covered, and what do I use instead?
Axial force, biaxial bending, class 4 sections, angle sections, multi-span beams, lateral-torsional buckling of cantilevers, fire, fatigue and composite beams. For these cases Mia refers to an RFEM model with structural analysis and steel design. Inclined roof beams and purlins are handled by the steel purlin skill (000010).
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