Eurocode 2 / EN 1998 Structural Design Guide

1.1 Concrete (f_ck) — EN 1992-1-1 §3.1

Design compressive strength: f_cd = α_cc·f_ck/γ_c  (α_cc = 0.85, γ_c = 1.5 persistent/transient)

Mean compressive strength: f_cm = f_ck + 8 MPa

Mean tensile strength: f_ctm = 0.30·f_ck^2/3 (f_ck ≤ 50 MPa)

Class	fck (MPa)	fcd (MPa)	fcm (MPa)	fctm (MPa)	Ecm (GPa)
C16/20	16	9.1	24	1.90	29
C20/25	20	11.3	28	2.21	30
C25/30	25	14.2	33	2.56	31
C30/37	30	17.0	38	2.90	33
C35/45	35	19.8	43	3.21	34
C40/50	40	22.7	48	3.51	35
C45/55	45	25.5	53	3.80	36
C50/60	50	28.3	58	4.07	37

f_cd using α_cc = 0.85 (NDP — verify with applicable National Annex). E_cm = 22000·(f_cm/10)^0.3 [MPa] per Table 3.1.

See Concrete Classes Reference for full EN 1992-1-1 Table 3.1 values.

1.2 Reinforcing Steel — EN 1992-1-1 §3.2

Design yield strength: f_yd = f_yk/γ_s  (γ_s = 1.15 persistent/transient)

Modulus of elasticity: E_s = 200,000 MPa — §3.2.7(4)

Grade	fyk (MPa)	fyd (MPa)	Ductility Class	εuk
B500A	500	435	A (low)	≥ 2.5%
B500B	500	435	B (normal)	≥ 5.0%
B500C	500	435	C (high)	≥ 7.5%

EN 1998-1 requires Class B minimum for DCM and Class C for DCH — Class A is not permitted for primary seismic elements.

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1.3 Partial Factors (EN 1990 / EN 1992-1-1)

Material	Persistent/Transient (γ)	Accidental (γ)
Concrete (γc)	1.50	1.20
Reinforcing steel (γs)	1.15	1.00

Seismic combinations use γ_c = 1.5, γ_s = 1.15 unless National Annex specifies otherwise.

1.4 Coefficient α_cc

EN 1992-1-1 §3.1.6: accounts for long-term effects and unfavourable load application on compressive strength. Recommended value: 0.85 (NDP). Some National Annexes (e.g., UK, Germany) adopt α_cc = 1.0 — always verify the applicable NA before computing f_cd.

2.1 Ductility Classes (EN 1998-1 §5.1.2)

Class	Name	q range (typical)	Detailing chapter
DCL	Ductility Class Low	q ≤ 1.5	EN 1992-1-1 only (no seismic detailing)
DCM	Ductility Class Medium	1.5 < q ≤ ~4	EN 1998-1 §5.4
DCH	Ductility Class High	q up to ~5–6	EN 1998-1 §5.5

DCL may be used in low-seismicity regions (a_g·S ≤ 0.1g per §3.2.1(4)). Choice of DC is a design decision subject to National Annex and project requirements.

2.2 Behaviour Factor (q) — EN 1998-1 Table 5.1

q reduces elastic spectral forces to design forces accounting for ductility and overstrength. Actual q depends on structural regularity and α_u/α₁ overstrength ratio.

Structural System	DCM q	DCH q
Frame system (multi-storey, multi-bay)	3.0·(αu/α1) ≈ 3.9	4.5·(αu/α1) ≈ 5.85
Frame system (one-storey)	3.0·1.1 = 3.3	4.5·1.1 = 4.95
Wall system (slender, α0 ≥ 2)	3.0·kw = 3.0	4.0·(αu/α1)·kw
Wall system (squat, α0 ≤ 0.5)	3.0·0.5 = 1.5	varies
Dual / wall-equivalent dual	3.0·(αu/α1)	4.5·(αu/α1)

α_u/α₁: overstrength ratio — default 1.0 for regular structures; up to 1.3 for regular multi-bay frames. k_w = (1+α₀)/3 ≥ 0.5 (wall aspect ratio factor).

For irregular structures, q is reduced by 20% (§4.3.3.1(8)).

2.3 Ground Types (EN 1998-1 Table 3.1)

Ground Type	Description	vs,30 (m/s)
A	Rock or rock-like geological formation	> 800
B	Dense sand, gravel, or stiff clay	360–800
C	Deep deposits of medium-dense sand, gravel, or medium-stiff clay	180–360
D	Loose-to-medium cohesionless soil or predominantly soft-to-firm cohesive soil	< 180
E	Surface alluvium layer over type C or D material	—
S1, S2	Special soils requiring site-specific study	—

Soil factor S (amplification) ranges from 1.0 (Type A) to 1.4–1.8 (Types C/D) depending on seismicity zone — EN 1998-1 Table 3.2/3.3.

2.4 Practical Implication

The chosen ductility class (DCL/DCM/DCH) determines the behaviour factor q, the required rebar ductility class (A/B/C), and the applicable detailing provisions in Section 8. High q values reduce design forces but demand more stringent detailing.

3.1 Span-to-Effective-Depth Ratios (EN 1992-1-1 §7.4, Table 7.4N)

Minimum l/d to avoid explicit deflection calculation (f_ck = 30 MPa, ρ ≈ 0.5%, normalweight concrete):

Support Condition	Beam	Flat Slab	Ribbed Slab
Simply supported	20	24	16
End span (one end continuous)	26	30	21
Interior span (both ends continuous)	30	35	24
Cantilever	8	10	6

Multiply by factor K = 1.0 for simply supported, 1.3 for end spans, 1.5 for interior spans, 0.4 for cantilevers. Modify for flanged beams (×0.8 if beff/bw > 3) and for tensile steel ratios. See §7.4.2 for full formula.

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3.2 Minimum Dimensions — Non-Seismic

Element	Minimum	Reference
Beam width bw	≥ 100 mm (cover + bar + access), practical ≥ 200 mm	§9.2
Column min dimension	Practical minimum 200 mm	§9.5
Slab thickness (one-way)	≥ 70 mm (§9.3.1.1)	§9.3.1.1
Flat slab thickness	≥ 150 mm (§9.4.1)	§9.4.1

3.3 Seismic Minimum Dimensions (EN 1998-1)

Element	DCM Requirement	DCH Requirement	Reference
Beam width bw	≥ 200 mm	≥ 250 mm	§5.4.1.2.1 / §5.5.1.2.1
Column min dimension	≥ 250 mm	≥ 300 mm	§5.4.3.2.1 / §5.5.3.2.1
Column aspect ratio bc/hc	≥ 0.25	≥ 0.25	§5.4.3.2.1
Normalized axial force nd	≤ 0.65	≤ 0.55	§5.4.3.2.1 / §5.5.3.2.1

n_d = N_Ed/(A_c·f_cd) — if exceeded, section must be enlarged or load path reconsidered.

4.1 Permanent Actions (G_k) — EN 1991-1-1 §3

Self-weight of structure and fixed equipment. Concrete unit weight: 25 kN/m³ (plain), 25 kN/m³ (reinforced — EN 1991-1-1 Table A.1). Superimposed dead loads (finishes, partitions) treated as G or Q per §3.3.

4.2 Variable Actions — Imposed Loads (Q_k) — EN 1991-1-1 §6

Table 6.2 (selected values — verify with applicable National Annex):

Category	Use	qk (kN/m²)	Qk (kN)
A	Domestic / residential floors	1.5–2.0	2.0–3.0
B	Office floors	2.0–3.0	2.0–4.5
C1	Assembly — tables, chairs (school, café)	3.0	4.0
C5	Assembly — large crowd / dancing	5.0	4.5
D	Shopping / retail	4.0–5.0	4.0–7.0
E	Storage / warehousing	≥ 7.5	7.0

Live load reduction per §6.3.1 permitted for large loaded areas.

4.3 Wind Actions (Overview) — EN 1991-1-4

Peak velocity pressure: q_p(z) = c_e(z) · q_b

q_b = 0.5 · ρ · v_b²  (ρ ≈ 1.25 kg/m³, v_b = c_dir·c_season·v_b,0)

Wind pressure on surfaces: w_e = q_p(z_e) · C_pe

c_e(z) = exposure factor (terrain roughness + orography, §4.5); v_b,0 = fundamental basic wind velocity (National Annex map); C_pe = external pressure coefficient (§7).

Full MWFRS procedure requires site exposure category, building geometry, and National Annex wind map values.

4.4 Snow Actions (Overview) — EN 1991-1-3

Snow load on roof: s = μ_i · C_e · C_t · s_k

s_k = characteristic ground snow load (National Annex site maps), μ_i = shape coefficient (0.8 for flat roofs), C_e = exposure coefficient (0.8–1.2), C_t = thermal coefficient (1.0 typical).

5.1 Design Spectrum — EN 1998-1 §3.2.2.5

Horizontal design spectrum (Type 1 or 2 — National Annex choice):

Period range	Sd(T)
0 ≤ T ≤ TB	ag·S·[2/3 + T/TB·(2.5/q − 2/3)]
TB ≤ T ≤ TC	ag·S·2.5/q  (plateau)
TC ≤ T ≤ TD	ag·S·2.5/q·(TC/T)
TD ≤ T	ag·S·2.5/q·(TC·TD/T²)

a_g = peak ground acceleration (National Annex seismic zone map), S = soil factor (ground type A–E), q = behaviour factor (Section 2.2). Minimum: S_d(T) ≥ β·a_g (β = 0.2 recommended).

5.2 Base Shear — EN 1998-1 §4.3.3.2

F_b = S_d(T₁) · m · λ

T₁ ≈ C_t·H^3/4  [period approximation §4.3.3.2.2]

Structure type	Ct
RC moment frames	0.075
Steel moment frames	0.085
Other structures (shear walls, mixed)	0.050

λ = 0.85 if T₁ ≤ 2·T_C and building has more than 2 storeys; otherwise λ = 1.0.

m = total seismic mass = Σ(G_k,j + ψ_E,i·Q_k,i), ψ_E,i = φ·ψ_2,i (§3.2.4).

5.3 Vertical Distribution of Seismic Force — §4.3.3.2.3

F_i = F_b · (z_i·m_i) / Σ(z_j·m_j)

Linear distribution (inverted triangle) — valid for T₁ ≤ 2.0 s and T₁ ≤ 2·T_C. For taller/flexible buildings, modal response spectrum analysis (§4.3.3.3) is required.

6.1 ULS — Fundamental Combination (Eq. 6.10)

Σ(γ_G,j·G_k,j) + γ_Q,1·Q_k,1 + Σ(γ_Q,i·ψ_0,i·Q_k,i)

Typical: 1.35·G_k + 1.5·Q_k,1 + 1.5·Σ(ψ_0,i·Q_k,i)

Alternative Eq. 6.10a/b (some NAs): use max of (1.35·G_k + 1.5·ψ_0,1·Q_k,1) and (ξ·1.35·G_k + 1.5·Q_k,1), ξ = 0.85.

6.2 ULS — Seismic Combination (Eq. 6.12b)

Σ(G_k,j) + A_Ed + Σ(ψ_2,i·Q_k,i)

A_Ed = design seismic action (derived from S_d(T₁), Section 5). γ factors = 1.0 for seismic combination.

6.3 Combination Factors ψ (EN 1990 Annex A1, Table A1.1)

Action / Category	ψ0	ψ1	ψ2
Imposed — Category A (residential)	0.7	0.5	0.3
Imposed — Category B (office)	0.7	0.5	0.3
Imposed — Category C (assembly)	0.7	0.7	0.6
Imposed — Category D (shopping)	0.7	0.7	0.6
Imposed — Category E (storage)	1.0	0.9	0.8
Wind	0.6	0.2	0
Snow (altitude ≤ 1000 m)	0.5	0.2	0

ψ₀ = combination value, ψ₁ = frequent value, ψ₂ = quasi-permanent value. Values are NDP — verify National Annex.

6.4 ULS — Accidental Combination (Eq. 6.11b)

Σ(G_k,j) + A_d + ψ_1,1·Q_k,1 + Σ(ψ_2,i·Q_k,i)

A_d = design accidental action (impact, explosion — EN 1991-1-7).

6.5 SLS Combinations

Combination	Expression (Eq.)	Typical Use
Characteristic	Gk + Qk,1 + Σ(ψ0,i·Qk,i) — Eq. 6.14b	Irreversible limit states
Frequent	Gk + ψ1,1·Qk,1 + Σ(ψ2,i·Qk,i) — Eq. 6.15b	Reversible limit states
Quasi-permanent	Gk + Σ(ψ2,i·Qk,i) — Eq. 6.16b	Long-term effects, creep, deflection

7.1 Flexural Design — EN 1992-1-1 §6.1

Rectangular stress block (f_ck ≤ 50 MPa): depth factor λ = 0.8, strength factor η = 1.0.

Normalised moment: μ = M_Ed/(f_cd·b·d²)

Mechanical reinforcement ratio: ω = 1 − √(1 − 2μ)

Required steel area: A_s = ω·f_cd·b·d / f_yd

Neutral axis limit (balanced): x_u/d ≤ ε_cu2/(ε_cu2 + ε_yd) = 3.5/(3.5 + 2.5) ≈ 0.617 for f_ck ≤ 50 MPa, f_yk = 500 MPa.

Minimum steel — §9.2.1.1: A_s,min = max(0.26·f_ctm/f_yk·b_t·d, 0.0013·b_t·d)

Maximum steel — §9.2.1.1: A_s,max = 0.04·A_c

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7.2 Shear Design — EN 1992-1-1 §6.2

Without shear reinforcement (V_Rd,c):

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

C_Rd,c = 0.18/γ_c = 0.12, k = 1+√(200/d) ≤ 2.0, ρ_l ≤ 0.02

v_min = 0.035·k^3/2·f_ck^1/2

With shear reinforcement (variable strut inclination — §6.2.3):

V_Rd,s = (A_sw/s)·z·f_ywd·cot θ

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

1.0 ≤ cot θ ≤ 2.5 (21.8° ≤ θ ≤ 45°), ν₁ = 0.6·(1 − f_ck/250), z ≈ 0.9d

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7.3 Column Design — EN 1992-1-1 §6.1 + §5.8

N-M interaction diagram — biaxial bending checked by combined axial force (N_Ed) and moments (M_Edx, M_Edy). See Column PMM Design Calculator.

Slenderness check: λ = L₀/i ≤ λ_lim = 20·A·B·C/√n (§5.8.3.1) — A = 0.7, B = 1.1, C = 0.7 (simplified). n = N_Ed/(A_c·f_cd).

If λ > λ_lim: second-order effects must be considered (§5.8.7 Nominal Stiffness or §5.8.8 Nominal Curvature method).

7.4 Torsion — EN 1992-1-1 §6.3

Threshold (torsion may be neglected if combined with shear below threshold):

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

Above threshold, closed stirrups + longitudinal bars required. T_Rd,max = 2·ν·α_cw·A_k·t_ef,i·f_cd·sin θ·cos θ.

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8.1 Non-Seismic Detailing (DCL) — EN 1992-1-1

Standard cover (§4.4), anchorage and development lengths (§8.4), lap lengths (§8.7), stirrup/tie spacing (§9.2, §9.5). No special seismic detailing required.

Crack width control: see Crack Width Calculator for EN 1992-1-1 §7.3.4 procedure.

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8.2 DCM Detailing (EN 1998-1 §5.4)

Beams — Critical Region:

Length: l_cr = max(h_w, l_c1/6, 0.45 m) from face of support — §5.4.3.1.1

Hoop spacing: s_o ≤ min(h_w/4, 24d_bw, 225 mm, 8d_bL) — §5.4.3.1.2

Minimum 2 hoop legs within the critical region; minimum d_bw ≥ 6 mm.

Columns — Critical Region:

Length: l_o = max(l_cl/6, h_c, b_c, 0.45 m) — §5.4.3.2.2

Hoop spacing: s_o ≤ min(b_o/2, 175 mm, 8d_bL) — §5.4.3.2.2

b_o = dimension of confined core (to centreline of hoop).

8.3 DCH Detailing (EN 1998-1 §5.5)

Beams — Critical Region:

Hoop spacing: s_o ≤ min(h_w/4, 6d_bL, 24d_bw, 150 mm) — §5.5.3.1.3

Columns — Critical Region:

Length: l_o = max(l_cl/4, h_c, b_c, 0.60 m) — §5.5.3.2.2

Hoop spacing: s_o ≤ min(b_o/3, 125 mm, 6d_bL) — §5.5.3.2.2

Strong Column–Weak Beam (DCH — §5.5.3.3.4):

ΣM_Rc ≥ 1.3 · ΣM_Rb  at each joint — columns must have greater moment capacity than beams framing in.

8.4 Shear Wall Boundary Elements (EN 1998-1 §5.4.3.4 / §5.5.3.4)

Boundary elements required if normalised neutral axis depth: x_u/l_w > (ε_sy,d + 0.00175)/(ε_cu2 + ε_sy,d) [simplified].

DCH boundary element length: l_c ≥ max(0.15·l_w, 1.5·b_w) — §5.5.3.4.5.

9.1 Interstorey Drift Limits — EN 1998-1 §4.4.3.2

Damage limitation requirement — design interstorey drift d_r under frequent seismic action:

Non-structural partition type	Limit (dr·ν / h)
Brittle (rigid) partitions attached to structure	0.005
Ductile partitions	0.0075
No partitions / partitions isolated from structure	0.010

ν = importance factor (0.4–0.5 per §4.4.3.2), h = interstorey height. d_r = q_d·d_s where d_s is displacement from spectral analysis and q_d = q (displacement behaviour factor, §4.3.4).

9.2 Diaphragm Action — EN 1998-1 §4.3.1

Floor and roof diaphragms assumed rigid in plan for standard buildings (§4.3.1(4)). In-plane diaphragm forces are transferred to lateral load-resisting elements via in-plane shear — design per EN 1992-1-1 §6.2.4 (shear between concrete flanges) and EN 1998-1 §5.9 (RC diaphragms).

Flexible diaphragm assumption may be required for large spans, unusual plan geometry, or significant openings — explicit modelling needed.

9.3 Capacity Design Principles — EN 1998-1 §4.4.2

Capacity design ensures ductile failure mechanisms (beam plastic hinges) govern over brittle failure (shear, column failure). Key rules:

• Beams: shear design using capacity-derived forces (§5.4.2.2 / §5.5.2.1) — V_Ed from gravity + plastic hinge moments, not elastic analysis
• Columns: design for moments amplified to exceed beam capacity (§5.4.2.3 / §5.5.2.2) — columns remain elastic while beams yield
• Shear walls: shear design using amplified shear from capacity approach (§5.4.2.4 / §5.5.2.4)