Eurocode 3-1-1 Section 6.3.1 | Fire design per EC3-1-2 | Section classification per EN 1993-1-1 Table 5.2
⚠️ Positive loads = compression
⚠️ Class 4 Section Detected: This section contains slender elements that may buckle locally. Effective properties are calculated per EN 1993-1-5 to account for reduced capacity.
ULS Classification (at fy = - MPa)
Overall Class
-
ε = √(235/fy)
-
Governing Element
-
Effective Area
-
| Element | c (mm) | t (mm) | c/t | Limit (Class 3) | Class | λp | ρ | ceff (mm) |
|---|
Class 4 Section: Effective properties calculated per EN 1993-1-5. Area reduced by -% to account for local buckling.
📐 Plate Reduction Factor (ρ) - EN 1993-1-5
Class 4 sections use EN 1993-1-5 to calculate effective widths for slender plate elements. Each plate gets a reduction factor ρ (0 to 1.0):
- ρ = 1.000: Plate is fully effective (no reduction needed)
- ρ = 0.900-0.999: Minor reduction (< 10%)
- ρ < 0.900: Significant reduction (≥ 10%)
Why can ρ = 1.0 for Class 4 elements?
EN 1993-1-1 Table 5.2 (classification) is conservative. EN 1993-1-5 uses refined plate slenderness λp with buckling coefficient kσ. If λp is below the limit, the plate is fully effective even if classified as Class 4.
Formulas (EN 1993-1-5 Section 4.4):
Internal elements:
λp = (c/t) / (28.4ε√kσ), where ε = √(235/fy)
ρ = (λp - 0.055ψ) / λp² ≤ 1.0, if λp > λp,limit
λp,limit = 0.5 + √(0.085 - 0.055ψ), where ψ = stress ratio (1.0 for compression)
Outstand elements (flanges):
ρ = (λp - 0.188) / λp² ≤ 1.0, if λp > 0.748
Fire Classification (at fy,θ = - MPa, θ = -°C)
Overall Class
-
εfire = √(235/fy,θ)
-
Governing Element
-
Effective Area
-
| Element | c (mm) | t (mm) | c/t | Limit (Class 3) | Class | λp | ρ | ceff (mm) |
|---|
Class 4 Section: Effective properties calculated per EN 1993-1-5. Area reduced by -% to account for local buckling.
📐 Plate Reduction Factor (ρ) at Elevated Temperature - EN 1993-1-5
At elevated temperature, reduced yield strength fy,θ affects plate slenderness. This may result in different ρ values compared to ULS (ε increases as fy decreases).
- ρ = 1.000: Plate is fully effective (no reduction needed)
- ρ = 0.900-0.999: Minor reduction (< 10%)
- ρ < 0.900: Significant reduction (≥ 10%)
Temperature Effect:
Higher temperature → Lower fy,θ → Higher ε = √(235/fy,θ) → Higher λp → Potentially lower ρ
ULS Effective Section Properties (EN 1993-1-5)
Effective Area
-
Gross: -
Ieff,y
-
Gross: -
Ieff,z
-
Gross: -
Removed Strips
-
Neutral Axis Shift
eN,y (shift in Y direction)
-
eN,z (shift in Z direction)
-
For pure compression with symmetric reductions, eN ≈ 0
Area Reduction
-
Iy Reduction
-
Iz Reduction
-
Fire Effective Section Properties (EN 1993-1-5)
Effective Area
-
Gross: -
Ieff,y
-
Gross: -
Ieff,z
-
Gross: -
Removed Strips
-
Neutral Axis Shift
eN,y (shift in Y direction)
-
eN,z (shift in Z direction)
-
For pure compression with symmetric reductions, eN ≈ 0
Area Reduction
-
Iy Reduction
-
Iz Reduction
-
Section Visualization
ULS Results
Slenderness (y-axis)
-
Slenderness (z-axis)
-
Governing Axis
-
χy - Reduction factor (y)
-
χz - Reduction factor (z)
-
χmin - Governing
-
Nb,Rd - Buckling Resistance
-
Utilization (NEd / Nb,Rd)
-
Fire Design Results
ky,θ - Yield reduction
-
kE,θ - Stiffness reduction
-
Nb,fi,Rd (kN)
-
Utilization at θ = -°C
-
θcr - Critical Temperature (Utilization = 100%)
-
ky,θ at θcr
-
kE,θ at θcr
-
Nb,fi,Rd at θcr (kN)
-