Eurocode Design Guide · Part 6 of 9

RC Member Design — EN 1992-1-1 (Eurocode 2)

Complete EC2 design reference for beams (flexure and shear), columns (slenderness and biaxial bending), slabs (one-way, two-way, flat slab, punching), shear walls, and seismic detailing per EC8 ductility classes.

Pre-Sizing Rules of Thumb
Beam Design — Flexure, Shear & Torsion
Column Design — Axial + Biaxial
Slab Design — One-Way, Two-Way, Flat Slab
Shear Wall Design (EC2 / EC8)
Detailing Requirements (DCL / DCM / DCH)

1. Pre-Sizing Rules of Thumb

These preliminary sizes initiate structural analysis and are refined by design checks. They do not replace formal verification.

Beam (Simple)

h ≈ L / 10 – L / 14

SI: h(mm) ≈ L(m) × 75 | US: h(in) ≈ L(ft) × 1.0

Beam (Continuous)

h ≈ L / 12 – L / 18

SI: h(mm) ≈ L(m) × 65 | US: h(in) ≈ L(ft) × 0.9

Slab (One-Way, Cont.)

h ≈ L / 25 – L / 30

L = clear span; min 100 mm

Slab (Two-Way)

h ≈ L_short / 30 – L_short / 35

Governed by shorter span

Column (Axial)

A_c ≈ N_Ed / (0.40·f_ck)

Preliminary; include eccentricity allowance ≈10–20%

Shear Wall

t_w ≥ max(150 mm, h_story/25)

EC2 §9.6.1 minimum 200 mm for double-face reinforcement

Seismic Minimum Dimensions (EC8 §5.4.3 / §5.5.3)

When designing for DCM or DCH, primary seismic members must meet the following minimum geometric requirements in addition to EC2 limits:

Parameter	DCL (EC2 only)	DCM	DCH	Reference
Beam width b_w	≥ 100 mm (practical ≥ 200 mm)	≥ 200 mm	≥ 250 mm	§5.4.1.2.1 / §5.5.1.2.1
Column min dimension	Practical ≥ 200 mm	≥ 250 mm	≥ 300 mm	§5.4.3.2.1 / §5.5.3.2.1
Column aspect ratio b_c/h_c	—	≥ 0.25	≥ 0.25	§5.4.3.2.1
Normalised axial force n_d = N_Ed/(A_c·f_cd)	—	≤ 0.65	≤ 0.55	§5.4.3.2.1 / §5.5.3.2.1
Shear wall thickness t_w	≥ max(150 mm, h_s/25)	≥ 200 mm	≥ 200 mm (boundary ≥ 250 mm)	§9.6.1 / §5.4.3.4

n_d limit: If N_Ed/(A_c·f_cd) exceeds the limit, the column section must be enlarged. Over-stressed columns cannot be compensated by adding reinforcement alone.

2. Beam Design — Flexure, Shear & Torsion

2.1 Rectangular Stress Block (EC2 §3.1.7)

EC2 uses a simplified rectangular stress distribution with depth λx and intensity η·f_cd:

EC2 — Concrete stress block parameters

f_cd = α_cc·f_ck/γ_C = 1.0·f_ck/1.5 = 0.667·f_ck MPa

λ = 0.8 (f_ck ≤ 50 MPa) | 0.8 − (f_ck−50)/400 (f_ck > 50)

η = 1.0 (f_ck ≤ 50 MPa) | 1.0 − (f_ck−50)/200 (f_ck > 50)

2.2 Flexural Design

EC2 — Moment resistance and tension steel

MRd = η·f_cd·b·λx·(d − λx/2) kN·m

Limit x_u/d ≤ 0.45 (DCH) | ≤ 0.45 (EC2 default for redistribution δ=1.0)

As1 = M_Ed / (f_yd·z) , z = d − 0.4·λx mm²

f_yd = f_yk/γ_S = 500/1.15 = 435 MPa (B500B)

Steel limits (EC2 §9.2.1):

A_s,min = max(0.26·f_ctm/f_yk·b_t·d, 0.0013·b_t·d)
A_s,max = 0.04·A_c (outside laps)

EC2 vs ACI 318 — Stress block: EC2 uses λ=0.8 (depth factor) and η=1.0 for fck ≤50 MPa. ACI 318 uses β₁ = 0.85 for f'c ≤28 MPa (decreasing to 0.65). EC2's f_cd = 0.667·f_ck vs ACI's 0.85·f'c × β₁ depth. Despite different notation, the computed stress resultants are comparable for normal-strength concrete.

2.3 Shear Without Reinforcement (EC2 §6.2.2)

EC2 — V_Rd,c (no shear reinforcement)

VRd,c = [C_Rd,c·k·(100·ρ_l·f_ck)^1/3 + k₁·σ_cp]·b_w·d kN

Min V_Rd,c,min = (ν_min + k₁·σ_cp)·b_w·d

Parameters:

C_Rd,c = 0.18/γ_C = 0.18/1.5 = 0.12
k = min(1 + √(200/d), 2.0) (d in mm)
ρ_l = A_sl/(b_w·d) ≤ 0.02
k₁ = 0.15; σ_cp = N_Ed/A_c ≤ 0.2·f_cd
ν_min = 0.035·k^3/2·f_ck^1/2

2.4 Shear With Reinforcement — Strut-and-Tie (EC2 §6.2.3)

EC2 — V_Rd,s and V_Rd,max

VRd,s = (A_sw/s)·z·f_ywd·cot θ kN

VRd,max = α_cw·b_w·z·ν₁·f_cd / (cot θ + tan θ) kN

ν₁ = 0.6·(1 − f_ck/250); z ≈ 0.9d; α_cw = 1.0 (non-prestressed)
θ = 21.8°–45° (cot θ = 1.0–2.5); Recommended start: θ = 21.8° (cot θ = 2.5) for economy

2.5 Torsion Design (EC2 §6.3)

Torsion must be checked when it contributes to structural equilibrium (equilibrium torsion). Torsion that can be redistributed (compatibility torsion) may be neglected in analysis, provided the member has sufficient ductility and detailing.

EC2 §6.3 — Torsion resistance

T_Rd,c = 2 · A_k · f_ctd · t_ef,i kN·m (threshold — §6.3.2(5))

T_Rd,max = 2 · ν · α_cw · A_k · t_ef,i · f_cd · sin θ · cos θ kN·m

A_k = area enclosed by the centreline of the thin-walled section (m²)
t_ef,i = effective wall thickness = A/u (≥ twice the cover to longitudinal bars)
ν = 0.6·(1 − f_ck/250) (strength reduction factor); α_cw = 1.0 (non-prestressed)
f_ctd = α_ct·f_ctk,0.05/γ_C (design tensile strength)

Above the threshold T_Rd,c, full torsion design is required: closed stirrups (area A_sw/s) and longitudinal torsion bars (area A_sl) are needed simultaneously. The combined shear + torsion interaction check is:

EC2 §6.3.2(4) — Combined shear + torsion

Interaction T_Ed/T_Rd,max + V_Ed/V_Rd,max ≤ 1.0

Try it yourself → RC Beam Calculator

3. Column Design — Axial + Biaxial (EC2 §5.8)

3.1 Slenderness

EC2 §5.8.3 — Slenderness ratio and limit

λ = L₀ / i ; i = radius of gyration = √(I/A)

L₀ = effective length = K·L (K from EC2 Fig. 5.7)

λ_lim = 20·A·B·C / √n

A = 1/(1+0.2φ_ef) ≈ 0.7 (conservative, unknown creep)
B = √(1+2ω) ≈ 1.1 (ω = A_s·f_yd/(A_c·f_cd))
C = 1.7 − r_m ≈ 0.7 (conservative, double curvature)
n = N_Ed/(A_c·f_cd) — relative normal force
If λ ≤ λ_lim: short column; second-order effects neglected

3.2 Short Column Resistance

EC2 — Axial and moment resistance (interaction)

NRd = f_cd·A_c + f_yd·A_s kN (pure axial)

Full interaction diagram (N-M curve) from equilibrium at each neutral axis depth.
Minimum eccentricity: e₀ = max(h/30, 20 mm) must always be checked.

3.3 Biaxial Bending (EC2 §5.8.9)

EC2 Eq. 5.39 — Biaxial interaction check

Check (M_Edz/M_Rdz)^a + (M_Edy/M_Rdy)^a ≤ 1.0

a = 2.0 (circular or elliptical cross-section)
a interpolated from Table 5.1 for rectangular: 1.0 at N_Ed/N_Rd = 0.1; 2.0 at N_Ed/N_Rd = 0.7
M_Rdz and M_Rdy = design moment resistances for each axis at the actual N_Ed

Try it yourself → Column Design Calculator

4. Slab Design

4.1 One-Way Slabs

Treat as a 1 m wide beam strip. Span-to-depth (l/d) limit from EC2 Table 7.4N governs serviceability. Shear typically not critical for slabs with adequate depth and ρ.

4.2 Two-Way Slabs — Yield Line / Coefficient Method

EC2 Annex I — Bending moment coefficients

Short span m_sx = β_sx·n·l_x² kN·m/m

Long span m_sy = β_sy·n·l_x² kN·m/m

β coefficients depend on l_y/l_x ratio and support conditions (EC2 Annex I tables).
n = design ULS load (kN/m²); l_x = short span.

4.3 Flat Slab (EC2 §5.3.4)

Minimum thickness: h ≥ max(150 mm, L/30 interior, L/25 edge panel)
With drop panels (depth ≥ 1.25h): h ≥ 120 mm
Column strip = min(0.25·l_x, 0.25·l_y) each side of column centreline
Moment distribution: 60% to column strip / 40% to middle strip (negative moments)

4.4 Punching Shear (EC2 §6.4)

EC2 — Punching shear verification

u₁ = 4c + 2π·(2d) (square column c×c, at 2d from face) mm

v_Ed = β·V_Ed,red / (u₁·d) ≤ v_Rd,c MPa

v_Rd,c = C_Rd,c·k·(100·ρ_l·f_ck)^1/3 ≥ v_min

β (eccentricity) = 1.15 (interior) | 1.40 (edge) | 1.50 (corner)

V_Ed,red = V_Ed − ΔV_Ed (subtract slab load within control perimeter)
With reinforcement: v_Rd,cs = 0.75·v_Rd,c + 1.5·(d/s_r)·A_sw·f_ywk·sinα/(u₁·d)

Try it yourself → Slab Calculator Punching Shear →

5. Shear Wall Design (EC2 §9.6 + EC8 §5.4/5.5)

5.1 In-Plane Shear (EC2)

Shear walls are designed as vertical plates. In-plane shear uses the same V_Rd,c and V_Rd,s formulations as beams. Minimum reinforcement per EC2 §9.6:

Horizontal: ρ_h ≥ 0.001 (each face if t_w ≥ 200 mm)
Vertical: ρ_v ≥ 0.002, and ≥ ρ_h/2
Bar spacing ≤ min(3t_w, 400 mm) in each direction

5.2 DCM Ductile Walls (EC8 §5.4.3.4)

Critical region height: h_cr = max(l_w, h_w/6) ≤ 2l_w (l_w = wall length)
Ductility condition: μ_φ ≥ 2q₀−1 (if T₁ ≥ T_C); 1 + (2q₀−1)T_C/T₁ otherwise
Neutral axis depth x_u ≤ (ε_cu2/(ε_cu2+ε_su))·l_w
Boundary confinement: α·ω_wd ≥ 0.035 in critical regions

5.3 DCH Ductile Walls (EC8 §5.5.3.4)

Stricter boundary confinement: ω_wd ≥ 0.12 (mechanical volumetric ratio)
Web: ρ_h ≥ 0.002, ρ_v ≥ 0.002
Capacity design shear: V_Ed,design = γ_Rd·(M_Ed,top+M_Ed,bot)/h_w
Shear amplification: ε = q/2 (DCM); higher for DCH
Moment envelope shifted up by tension shift a_l

Boundary elements — trigger: Required when x_u/l_w > (ε_cu2 − ε_sy,d·ν_u)/(ε_cu2 + ε_su) per EC8 §5.5.3.4.2. In most walls with normal axial load this condition governs in the critical region for DCH.

DCH boundary element dimensions (EC8 §5.5.3.4.5):

Length: l_c ≥ max(0.15 · l_w, 1.5 · b_w)
Thickness: ≥ 200 mm (primary seismic walls)
Confinement: ω_wd ≥ 0.12 with closed hoops at spacing ≤ min(b_o/3, 6d_bL, 125 mm)

6. Detailing Requirements (DCL / DCM / DCH)

Beams — Critical Region Confinement (EC8 §5.4.3.1 / §5.5.3.1)

DCL

Standard EC2 detailing
No special hoop requirement
ρ_min = 0.0013 (EC2)

DCM

Critical region: l_cr = 1.5·h_w
s ≤ min(h_w/4, 24d_bw, 225 mm, 8d_bl)
ρ_min,top&bot = 0.5·f_ctm/f_yk

DCH

Critical region: l_cr = 2·h_w
s ≤ min(h_w/4, 6d_bl, 24d_bw, 175 mm)
Compression steel: ≥ 50% of tension steel

Columns — Critical Region (EC8 §5.4.3.2 / §5.5.3.2)

DCL

EC2 §9.5 standard links
s ≤ min(20d_bl, b, 400 mm)
ρ = 0.002 – 0.04

DCM

Critical region: l_cr = max(h_c, L_cl/6, 0.45m)
s ≤ min(b₀/2, 8d_bl, 175 mm)
α·ω_wd ≥ 0.035

DCH

Critical region: l_cr = max(1.5h_c, L_cl/5, 0.6m)
s ≤ min(b₀/3, 6d_bl, 125 mm)
α·ω_wd ≥ 0.08

Parameter	DCL	DCM	DCH
Rebar ductility class	A or B	B (min)	C (min in critical regions)
Concrete class	C16/20 min	C20/25 min	C25/30 min
Column ρ_max	0.04	0.04	0.04
Strong column / weak beam	Not required	ΣM_Rc/ΣM_Rb ≥ 1.3	ΣM_Rc/ΣM_Rb ≥ 1.3
Capacity design (shear)	No	Yes (beams, columns)	Yes + walls

RC Beam Calculator → Column Calculator →

← Previous 5. Load Combinations Next → 7. Steel Design (EC3)

Educational use only. Design expressions in this article use EN 1992-1-1:2004 recommended values and EN 1998-1:2004 provisions. National Annexes may modify partial factors, ductility requirements, and detailing rules. Always verify against the current EN text and applicable NA for your jurisdiction.

RC Member Design — EN 1992-1-1 (Eurocode 2)

Contents

1. Pre-Sizing Rules of Thumb

Seismic Minimum Dimensions (EC8 §5.4.3 / §5.5.3)

2. Beam Design — Flexure, Shear & Torsion

2.1 Rectangular Stress Block (EC2 §3.1.7)

2.2 Flexural Design

2.3 Shear Without Reinforcement (EC2 §6.2.2)

2.4 Shear With Reinforcement — Strut-and-Tie (EC2 §6.2.3)

2.5 Torsion Design (EC2 §6.3)

3. Column Design — Axial + Biaxial (EC2 §5.8)

3.1 Slenderness

3.2 Short Column Resistance

3.3 Biaxial Bending (EC2 §5.8.9)

4. Slab Design

4.1 One-Way Slabs

4.2 Two-Way Slabs — Yield Line / Coefficient Method

4.3 Flat Slab (EC2 §5.3.4)

4.4 Punching Shear (EC2 §6.4)

5. Shear Wall Design (EC2 §9.6 + EC8 §5.4/5.5)

5.1 In-Plane Shear (EC2)

5.2 DCM Ductile Walls (EC8 §5.4.3.4)

5.3 DCH Ductile Walls (EC8 §5.5.3.4)

6. Detailing Requirements (DCL / DCM / DCH)

Beams — Critical Region Confinement (EC8 §5.4.3.1 / §5.5.3.1)

Columns — Critical Region (EC8 §5.4.3.2 / §5.5.3.2)

Related Tools & Guides