RC Column Capacity — Eurocode 2

1. Column Cross-Section Geometry

b_x = mm height (dir. of bending)

b_z = mm width

c = mm nominal cover to reinf. centroid

A_g = b_x · b_z = 180000 mm²

d = b_x – c = 550 mm (eff. depth, tension bars)

Fig. 1 — Column cross-section

2. Reinforcement (Symmetric, Both Faces)

Tension face (As.a) & Compression face (As.b)

φ = mm bar diameter

n = bars per face (symmetric)

A_s = n · π·φ²/4 = 603.2 mm² (each face)

ρ = 2·A_s / A_g = 0.670 % total reinf. ratio

3. Material Properties & Partial Factors

Concrete — EN 1992-1-1:2004, §3.1

Class

f_ck = 30 MPa

γ_c = Table 2.1N

α_cc = §3.1.6(1)

f_cd = α_cc·f_ck/γ_c = 20.00 MPa

ε_cu3 = 3.500 ‰ Table 3.1

λ = 0.800 stress block factor, §3.1.7

η = 1.000 effective strength factor

Reinforcement — EN 1992-1-1:2004, §3.2

f_yk = MPa yield strength

γ_s = Table 2.1N

f_yd = f_yk/γ_s = 434.78 MPa

Ductility Annex C, Table C.1

ε_uk = 5.000 %

ε_ud = 0.9·ε_uk = 4.500 % §3.2.7, Note 1

E_s = 200 GPa §3.2.7(4)

4. M–N Interaction Diagram — Capacity Envelope (5-Point Method)

Case	Description	N_cap (kN)	M_cap (kN·m)	Strain state

5. M–N Interaction Diagram

Fig. 2 — Axial force–bending moment interaction diagram with design load combinations

6. Design Load Combinations

Combo	M_cap @ N (kN·m)	Utilisation	Status
CO1	—	—	—
CO2	—	—	—
CO3	—	—	—

Maximum Compressive Capacity (Pure Compression, Case 4)

—

Maximum Moment Capacity (Balanced, Case 2)

—

Overall Status

—

Reference: EN 1992-1-1:2004 — Eurocode 2: Design of Concrete Structures — Part 1-1: General rules and rules for buildings, Sections 3.1.3, 3.1.6, 3.1.7, 3.2.7 and Annex C