1 · Scope of the simplified method
The notes use EN 1994-1-1 simplified design for a concrete-encased, doubly symmetric UC section with a uniform cross-section along the member length.
0.2 ≤ δ ≤ 0.9- steel contribution factor: below this treat as reinforced concrete; above this treat as steel
λ̄ ≤ 2.0- relative slenderness limit for the simplified method
0.30% ≤ ρs ≤ 6%- longitudinal reinforcement ratio used in the resistance calculation
Ncr,eff ≥ 10 NEd- criterion for ignoring second-order effects in the member length
For encased I-sections the notes also call out detailing cover: typical fire/detailing checks require enough concrete around both the steel section and the longitudinal bars.
2 · Composite section model
The workbench models a rectangular concrete encasement around a UC, with longitudinal reinforcement placed symmetrically near the perimeter.
Aa = area of the UC section table As = n · π · φbar² / 4 Ac = bc · hc - Aa - As ρs = As / Ac
bc, hc- overall concrete width and depth
Aa, Ac, As- steel section, concrete and reinforcement areas
ρs- reinforcement ratio checked against 0.30% to 6%
3 · Design strengths and creep
Steel, concrete and reinforcement strengths are reduced with partial factors. For encased columns, the concrete elastic modulus is also reduced for creep.
fyd = fy / γA fcd = fck / γC fsd = fsk / γS αfcd = α · fcd where α = 0.85 for encased sections
Ec,eff = Ecm / (1 + (NG,Ed / NEd) · φt)
NG,Ed / NEd- permanent part of the design axial load
φt- creep coefficient from EC2
Ec,eff- creep-adjusted concrete modulus used in stiffness
4 · Plastic axial resistance
The plastic resistance is the short-column squash load before member buckling reduction. The notes then use the steel contribution factor to check that the member is in the composite range.
Npl,Rd = Aa · fyd + Ac · αfcd + As · fsd Npl,Rk = Aa · fy + Ac · αfck + As · fsk Npm,Rd = Ac · αfcd
δ = (Aa · fyd) / Npl,Rd
5 · Effective stiffness and buckling
For each axis, steel, reinforcement and concrete inertias are combined into an effective flexural stiffness. A reduced stiffness is used when second-order effects are included.
(EI)eff = Ea · Ia + Es · Is + Ke · Ec,eff · Ic (EI)eff,II = K0 · (Ea · Ia + Es · Is + Ke,II · Ec,eff · Ic)
Ncr = π² · (EI)eff / Lcr² λ̄ = sqrt(Npl,Rk / Ncr) Φ = 0.5 · (1 + αbuckling · (λ̄ - 0.2) + λ̄²) χ = 1 / (Φ + sqrt(Φ² - λ̄²)) Nb,Rd = χ · Npl,Rd
6 · Second-order moments and imperfections
If the reduced critical load is not at least ten times the design axial load, the member moments are amplified. The notes also add an initial imperfection moment in the plane expected to govern.
Ncr,eff = π² · (EI)eff,II / Lcr² second-order effects may be ignored when Ncr,eff ≥ 10 · NEd
β = 0.66 + 0.44 · r where r = M2 / M1 k_end = β / (1 - NEd / Ncr,eff) k_imp = 1 / (1 - NEd / Ncr,eff) e0 = L / imperfection denominator Mimp = NEd · e0 MEd = max(M1, k_end · M1 + k_imp · Mimp)
7 · A-C-D-B interaction polygon
The notes simplify the full compression-bending interaction curve into polygon A-C-D-B. Concrete in tension is ignored and a rectangular stress block is assumed.
A- pure plastic axial resistance: N = Npl,Rd, M = 0
B- pure bending plastic resistance: N = 0, M = Mpl,Rd
C- concrete compression block at Npm,Rd with Mpl,Rd
D- peak moment point, commonly around 0.5 Npm,Rd
Mpl,N,Rd = bending resistance read from the polygon at the applied NEd μd = Mpl,N,Rd / Mpl,Rd
8 · Final member checks
The workbench reports axial buckling, uniaxial bending about each axis, and the EC4 biaxial linear interaction. If a scope check is outside the simplified method, the status is REVIEW.
Axial: NEd / Nb,Rd ≤ 1 Uniaxial y: My,Ed / Mpl,N,Rd,y ≤ αM Uniaxial z: Mz,Ed / Mpl,N,Rd,z ≤ αM
Biaxial: My,Ed / (μdy · Mpl,Rd,y) + Mz,Ed / (μdz · Mpl,Rd,z) ≤ 1
Implemented in lib/composite-column.ts and components/composite-column-workbench.tsx.