Design Checks
Armatura implements structural design checks against EN 1993-1-1:2005 (Eurocode 3: Design of Steel Structures). This page describes which checks are performed, what code clauses they reference, and what assumptions are made.
This is not a substitute for reading the standard itself. Engineers using Armatura for design should be familiar with EN 1993-1-1 and the applicable National Annex. The check implementations follow the standard's equations and flow, but the engineer remains responsible for confirming that the analysis model and design assumptions are appropriate for the structure.
Overview
Design checks produce a utilization ratio for each member:
utilization = demand / capacity
A utilization ≤ 1.0 means the member satisfies the check. A utilization > 1.0 means the member fails.
Each check result includes:
- The utilization ratio
- The governing clause reference (e.g., "EN 1993-1-1, §6.2.3")
- The governing load case or combination
- Pass/fail status
Checks performed
The following checks are run for each member, skipping any check where the relevant force component is negligible (< 1×10⁻⁶):
Cross-section checks (§6.2)
| Check | Clause | Condition | What it verifies |
|---|---|---|---|
| Axial tension | §6.2.3 | N > 0 | Yielding of the gross cross-section |
| Bending | §6.2.5 | My or Mz ≠ 0 | Moment resistance of the cross-section |
| Shear | §6.2.6 | Vy or Vz ≠ 0 | Shear resistance using Av (shear area) |
| Torsion | §6.2.7 | T ≠ 0 | St. Venant torsion capacity |
Member stability checks (§6.3)
| Check | Clause | Condition | What it verifies |
|---|---|---|---|
| Flexural buckling | §6.3.1 | N < 0 | Column buckling about both axes, using χ reduction factor and buckling curves |
| Lateral-torsional buckling | §6.3.2 | My ≠ 0 | LTB reduction factor χLT, using elastic critical moment Mcr |
| Combined bending + axial | §6.3.3 | N and M both ≠ 0 | Interaction equations 6.61 and 6.62 (Annex B method) |
Serviceability checks
| Check | Reference | What it verifies |
|---|---|---|
| Deflection | EN 1990, Annex A1.4 | Member deflection against L/250 (total) or L/300 (variable) |
Global screening
| Check | Clause | What it verifies |
|---|---|---|
| αcr sensitivity | §5.2.1, Eq. 5.1 | Whether first-order analysis is sufficient (αcr ≥ 10) |
Elastic critical moment (Mcr)
The lateral-torsional buckling check requires the elastic critical moment Mcr, which is not given directly in EN 1993-1-1. Armatura uses the 3-factor formula from NCCI SN003a:
Mcr = C1 · (π²EIz / L²) · √[ Iw/Iz + L²GIt / (π²EIz) ]
With simplifying assumptions: kz = kw = 1.0 (fork supports), zg = 0 (load at shear centre).
The C1 factor accounts for the moment distribution along the member. For end moments with ratio ψ = M_min / M_max:
C1 = min( 1.88 − 1.40ψ + 0.52ψ², 2.70 )
The C1 formula is from [SN003a] §2. For uniform moment (ψ = 1.0), C1 = 1.0. For anti-symmetric moment (ψ = −1.0), C1 = 2.70.
Hollow sections and sections not susceptible to LTB return zero utilization for this check.
Flexural buckling curves
The flexural buckling reduction factor χ depends on the relative slenderness λ̄ and the imperfection factor α, which varies by buckling curve (a0, a, b, c, d). The implementation follows §6.3.1.2, Eq. 6.49:
χ = 1 / (Φ + √(Φ² − λ̄²))
where Φ = 0.5 · [1 + α(λ̄ − 0.2) + λ̄²]
Buckling curves are selected based on section type and fabrication method per Table 6.2 of EN 1993-1-1. The section data interface (IEN1993SectionData) provides the buckling curve classification.
Interaction equations (§6.3.3)
For members subjected to combined bending and axial force, the Annex B interaction method uses two equations (6.61 and 6.62) that must both be satisfied:
NEd/(χy·NRk/γM1) + kyy·My,Ed/(χLT·My,Rk/γM1) + kyz·Mz,Ed/(Mz,Rk/γM1) ≤ 1.0
NEd/(χz·NRk/γM1) + kzy·My,Ed/(χLT·My,Rk/γM1) + kzz·Mz,Ed/(Mz,Rk/γM1) ≤ 1.0
The k-factors (kyy, kyz, kzy, kzz) are taken from Table B.1/B.2 of Annex B. The implementation uses the real χLT value from the LTB check rather than a conservative default of 1.0.
Section properties required for design
Beyond the basic stiffness properties, design checks require:
| Property | Symbol | Used by |
|---|---|---|
| Shear area | Av | §6.2.6 shear check |
| Plastic section modulus | Wpl,y / Wpl,z | §6.2.5 bending (Class 1, 2) |
| Elastic section modulus | Wel,y / Wel,z | §6.2.5 bending (Class 3) |
| Warping constant | Iw | Mcr calculation |
| Torsion constant | It (= J) | Mcr and §6.2.7 |
| Section class | 1–4 | Determines which modulus to use |
| Buckling curve | a0, a, b, c, d | §6.3.1 flexural buckling |
| Rolled / welded | boolean | Affects buckling curve and LTB |
For standard I-sections, Iw can be approximated as Iz · (h − tf)² / 4 and J (torsion constant) as Σ(b·t³/3) for the individual plate parts. These thin-walled approximations are accurate to within ~5% for standard rolled profiles and are conservative.
Partial safety factors (γM)
| Factor | Value | Usage |
|---|---|---|
| γM0 | 1.00 | Cross-section resistance |
| γM1 | 1.00 | Member stability (buckling) |
| γM2 | 1.25 | Net section in tension |
These are the recommended values from EN 1993-1-1, Table 6.1. National Annexes may specify different values.
αcr screening check
EN 1993-1-1 §5.2.1 requires checking whether first-order analysis is sufficient. The simplified check estimates αcr per member as:
αcr = Ncr / NEd
Where Ncr = π²EI / Lcr² is the Euler buckling load and NEd is the design compression force. The minimum αcr across all compressed members governs.
- αcr ≥ 10: first-order analysis is sufficient for elastic design
- 3 ≤ αcr < 10: second-order effects are significant, results may be unconservative
- αcr < 3: second-order analysis is required (§5.2.1(4)B)
This is a screening tool, not a design check — it produces a warning on the evaluation result, not a pass/fail. The true αcr from eigenvalue buckling analysis (planned) gives the exact value; the simplified per-member estimate is conservative.
Code traceability
Every check result carries a ClauseReference with the standard name, clause number, and equation number. This is a core design value of Armatura — all results should be traceable back to the governing code clause.
The PDF reporting pipeline includes these references, making the calculation traceable for third-party review.
Limitations and assumptions
- Section classification is currently simplified — all sections are assumed Class 1 or 2 (plastic resistance available). Class 3 and 4 checks are not yet implemented.
- The Mcr formula assumes fork supports (kz = kw = 1.0) and load applied at the shear centre (zg = 0). Destabilising loads applied to the top flange would require a non-zero zg correction.
- Combined biaxial bending with torsion is not explicitly checked beyond the §6.3.3 interaction equations.
- Only EN 1993-1-1 is implemented. AISC 360 and AS4100 are planned.
References
- EN 1993-1-1:2005, §6.2 (cross-section checks), §6.3 (stability checks), §5.2.1 (second-order sensitivity)
- EN 1993-1-1:2005, Annex B: interaction factors for §6.3.3
- EN 1993-1-1:2005, Table 6.1: partial factors, Table 6.2: buckling curves
- EN 1990:2002, Annex A1.4, Table A1.4: deflection limits
- NCCI SN003a-EN-EU: elastic critical moment Mcr calculation
- Kassimali (2015), Chapter 10: buckling analysis fundamentals