Ultimate limit state
Determine the support hogging and span sagging design moments by pattern loading, then verify bending and shear resistance, with National-Annex-correct coefficients (EN recommended or DIN EN 1992-1-1/NA).
SKL-000054 · Skill
EN 1990EN 1991-1-1EN 1992-1-1Design a two-span continuous concrete beam to Eurocode 2
Describe the National Annex, spans, section, concrete class, cover, bar diameters, and loads per span. Mia derives the support and span design moments, checks bending, shear, crack width, and deflection, and reports anchorage, curtailment, and end-support detailing, explaining the governing result step by step.
Mia guides you step by stepShe guides you through the inputs and explains the results.
Worked example
300×500 mm · C30/37 · 6.00 + 6.00 m
Design verified: shear at the middle support governs- System
- Two-span continuous beam (equal spans)
- Section
- 300 × 500 mm · C30/37 · B500
- Spans
- L1 = L2 = 6.00 m
- Bar diameters
- Ø22 support · Ø20 span
- Loads
- gk = 16.25 kN/m + self-weight · qk = 15.00 kN/m per span
- Cover
- cnom = 35 mm
Design a two-span continuous concrete beam, spans 6 m and 6 m, section 300×500 mm, C30/37, B500, nominal cover 35 mm, main bars Ø22 (support) / Ø20 (span), with gk = 16.25 kN/m (plus self-weight) and qk = 15 kN/m per span, ψ2 = 0.3, wmax = 0.3 mm, to EN 1992-1-1 (EN recommended values). Check bending, shear, crack width, deflection, and detailing.
Key results
- Support hogging moment MEd,B
- 222.8 kNm
- Span sagging moment MEd,span
- 145.9 kNm
- Design shear at support VEd
- 185.6 kN
- Crack width wk (span)
- 0.14 mm ≤ 0.30 mm
- Governing utilisation
- η = 0.86 (shear)
All values are deterministic for the stated inputs. ULS combination 6.10 (γG = 1.35, γQ = 1.5) with γC = 1.5, γS = 1.15 to EN 1992-1-1 (EN recommended values); crack width under the quasi-permanent combination with ψ2 = 0.3.
- — Effective depth computed per section from the actual bar diameter. Dsupport = 454 mm (h = 500 mm, cnom = 35 mm, Ø22), dspan = 455 mm (Ø20); never a fixed assumed diameter.
- — Support reinforcement 4 Ø22 (1520 mm² ≥ 1282 mm² required, η = 0.84); span reinforcement 3 Ø20 (943 mm² ≥ 796 mm² required, η = 0.84).
- — Shear links Ø10/325 mm, two-leg, at the middle support (483 mm²/m ≥ 417 mm²/m required, η = 0.86).
- — Crack width (span, quasi-permanent Mqp = 62.0 kNm) wk = 0.14 mm ≤ wmax = 0.30 mm (η = 0.45); the §9.2.1.1 ULS minimum (206 mm²) governs over the §7.3.2 crack-control minimum (150 mm²).
- — Deflection screening: actual L/d = 13.2 against an allowable 27.0 (η = 0.49) per EN 1992-1-1 §7.4.2.
- — Anchorage lengths lbd ≈ 797 mm (Ø22 support), ≈ 725 mm (Ø20 span); curtailment shift al ≈ 511 mm; end-support minimum 236 mm² satisfied by continuing 2 of the 3 span bars (628 mm², η = 0.38).
Required inputs
- National Annex: EN recommended or DIN EN 1992-1-1/NA
- Static system: spans L1, L2, and support conditions
- Loads per span: permanent gk and variable qk
- Cross-section b × h, concrete class, nominal cover, and the actual main-bar diameter at the support and at the span
- Quasi-permanent factor ψ2 and the crack-width limit wmax
What you receive
- Governing check and utilisation
- Support hogging and span sagging design moments
- Required and provided reinforcement at each critical section, from its own effective depth
- Shear design and link spacing
- Crack width and minimum crack-control reinforcement
- Deflection screening (span/effective-depth ratio)
- Anchorage lengths, curtailment shift, and end-support minimum reinforcement
- 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 continuous beam
System sketch
L1 = 6 mL2 = 6 mgk,1 = 16.25 kN/mqk,1 = 15 kN/mgk,2 = 16.25 kN/mqk,2 = 15 kN/m
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Inputs completeReady to calculate
What this skill checks
Reinforcement design
Size the tension reinforcement at each critical section, using the actual bar diameter per section, and the shear links, checked against the EN 1992-1-1 §9.2 minimum and maximum limits.
Serviceability
Screen deflection with the §7.4.2 span/effective-depth ratio method and verify crack width under the quasi-permanent combination to §7.3, including the minimum crack-control reinforcement.
Detailing
Report anchorage lengths (§8.4) at the end and middle supports, the tension-force envelope shift a_l (§9.2.1.3), and the 25% end-support minimum anchored reinforcement (§9.2.1.4).
Normative basis
Standards & references
The checks follow these standards. Nationally determined parameters come from the National Annex selected in the form.
EN 1992-1-1
WithdrawnEurocode 2: Design of concrete structures – Part 1-1: General rules and rules for buildings
Edition used: DIN EN 1992-1-1:2011-01 (EN 1992-1-1:2004 + AC:2010) + DIN EN 1992-1-1/A1:2015-03
- §6.1
- §6.2
- §7.3
- §7.4
- §9.2
DIN MediaNewer edition: DIN EN 1992-1-1:2025-09 (EN 1992-1-1:2023)
| Country | National Annex | Factors | Source |
|---|---|---|---|
| DE | DIN EN 1992-1-1/NA:2013-04 + DIN EN 1992-1-1/NA/A1:2015-12Current | γC = 1.50γS = 1.15αcc = 0.85 | DIN Media |
| AT | ÖNORM B 1992-1-1:2018-01-01Current | γC = 1.50γS = 1.15αcc = 1.00 | Austrian Standards |
| CZ | ČSN EN 1992-1-1 ed. 2 (73 1201):2019-11 + Z1, NACurrentNewer edition: ČSN EN 1992-1-1 ed. 3 (73 1201) | γC = 1.50γS = 1.15αcc = 1.00 | shop.normy.biz |
| EN | Recommended valuesEN 1992-1-1:2004 + AC:2010 + A1:2014 | γC = 1.50γS = 1.15αcc = 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
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
EN 1991-1-1
CurrentEurocode 1: Actions on structures – Part 1-1: General actions – Densities, self-weight, imposed loads for buildings
Edition used: DIN EN 1991-1-1:2010-12 (EN 1991-1-1:2002 + AC:2009)
| Country | National Annex | Factors | Source |
|---|---|---|---|
| DE | DIN EN 1991-1-1/NA:2010-12 + DIN EN 1991-1-1/NA/A1:2015-05Current | DIN Media |
Status checked on
Frequently asked questions
Frequently asked questions
InputsWhich inputs does Mia need for the design?
At minimum, the National Annex, the two spans, loads per span, section, concrete class, cover, the bar diameter at each section, and the crack-width parameters. Mia asks targeted questions when a governing input is missing.
ScopeAre unequal spans supported?
Yes. Mia uses the three-moment (Clapeyron) equation for unequal spans and the closed-form pattern-loading results for equal spans.
VerificationIs crack width checked automatically?
Yes. Mia calculates the minimum crack-control reinforcement and the crack width under the quasi-permanent combination to EN 1992-1-1 §7.3, in addition to the deflection screening.
VerificationWhat changes if I use the German National Annex?
Mia uses the DIN EN 1992-1-1/NA values for αcc, CRd,c, vmin, and the shear crushing factor ν₁ (a constant 0.75 for concrete up to C50/60) instead of the EN-recommended formulas.
Results & reportCan I document the calculation?
CALC presents inputs, assumptions, checks, the governing utilisation, and normative references in a structured answer that can be exported as a PDF.
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