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).
EN 1990EN 1991-1-1
Design 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.
Worked exampleDesign verified: shear at the middle support governs
300×500 mm · C30/37 · 6.00 + 6.00 m
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
Transparent stepsStandards-basedDocument as PDF
Worked example
300×500 mm · C30/37 · 6.00 + 6.00 m
- 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.
Calculate the example with MiaKey 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
Prepare your calculation
Configure your continuous beam
System sketch
L = 6 mgk = 15 kN/mqk = 10 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).
Frequently asked questions
Which 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.
Are unequal spans supported?
Yes. Mia uses the three-moment (Clapeyron) equation for unequal spans and the closed-form pattern-loading results for equal spans.
Is 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.
What 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.
Can 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.
Standards & references
EN 1990EN 1991-1-1EN 1992-1-1
Ready for your first check?
Start with the example and adapt it to your structural system.
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