ACI 318-25 / ASCE 7 Structural Design Guide

Quick-reference for concrete material properties, strength reduction factors, load combinations, and reinforcement design per ACI 318-25 and ASCE 7-22.

1. Material Properties

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1.1 Concrete (f'c)

Parameter	US (psi)	SI (MPa)	Reference
Minimum f'c	2,500 psi	17 MPa	ACI 318-25 §19.2.1.1
Maximum f'c (normal provisions)	10,000 psi	70 MPa	ACI 318-25 §19.2.1.3
Typical structural use	3,000–6,000 psi	21–42 MPa	—

Higher f'c values permitted with special provisions per §19.2.1.3.

Unit weight (normalweight concrete): US: 150 pcf | SI: 24 kN/m³ (ACI 318-25 §19.2.2)

1.2 Reinforcing Steel (fy)

Parameter	US (ksi)	SI (MPa)	Reference
Minimum fy	40 ksi	280 MPa	ACI 318-25 §20.2.2.4
Maximum fy (general)	80 ksi	550 MPa	ACI 318-25 §20.2.2.4
Common grades	Grade 60 (60 ksi)	Grade 420 (420 MPa)	—

Modulus of elasticity (rebar): US: 29,000 ksi | SI: 200,000 MPa (ACI 318-25 §20.2.2.2)

1.3 Modulus of Elasticity (Concrete)

US: E_c = 57,000√f'_c (f'_c in psi)

SI: E_c = 4,700√f'_c (f'_c in MPa)

ACI 318-25 §19.2.2.1

See Concrete Properties Reference for full unit weight, strength class, and elastic modulus tables.

1.4 Lightweight Concrete — Modification Factor (λ)

ACI 318-25 §19.2.4.2

Concrete Type	λ
Normalweight	1.00
Sand-lightweight (sanded)	0.85
All-lightweight (unsanded)	0.75

Linear interpolation permitted between values based on volumetric fraction of normalweight sand replacement.

Alternative (test-based) method — §19.2.4.3:

US: λ = f_ct / (6.7√f'_c), capped at λ ≤ 1.0

SI: λ = f_ct / (0.56√f'_c), capped at λ ≤ 1.0

where f_ct = average splitting tensile strength (measured)

2. Ductility Classification

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2.1 Seismic Design Category (SDC)

ASCE 7-22 §11.6 — SDC is determined from Risk Category and spectral response parameters (S_DS, S_D1).

Table 11.6-1 (based on S_DS):

S_DS Value	Risk Category I, II, III	Risk Category IV
S_DS < 0.167g	A	A
0.167g ≤ S_DS < 0.33g	B	C
0.33g ≤ S_DS < 0.50g	C	D
0.50g ≤ S_DS	D	D

Table 11.6-2 (based on S_D1): Similar tiered structure based on S_D1 values.

Final SDC = the more critical (higher) result from the two tables.

Site-specific seismic parameters (S_DS, S_D1) require a geotechnical/seismic hazard report.

2.2 Moment Frame Ductility Classes

ACI 318-25 §18.2.1.3 — permitted frame types by SDC:

SDC	Permitted Frame Type	ACI 318-25 Reference
A, B	Ordinary Moment Frame (OMF)	Ch. 1–17 (no Ch. 18 special detailing required)
C	Intermediate Moment Frame (IMF) minimum	§18.4
D, E, F	Special Moment Frame (SMF) required	§18.6–18.10

2.3 Response Modification Factor (R) — System Limitations

ASCE 7-22 Table 12.2-1 — R factor is tied to specific system limitations (height, SDC permissibility, and force-sharing rules). Selecting R without checking these triggers a code violation.

2.3.1 Moment Frame Systems (selected values)

System	R	SDC B	SDC C	SDC D	SDC E	SDC F
Ordinary RC Moment Frame	3	NL	NP	NP	NP	NP
Intermediate RC Moment Frame	5	NL	NL	NP	NP	NP
Special RC Moment Frame	8	NL	NL	NL	NL	NL

NL = Not Limited (height) · NP = Not Permitted

Note: ACI 318-25 §18.2.1.3 — Ordinary moment frame is permitted in lieu of intermediate for SDC B/C only.

2.3.2 Shear Wall Systems — Bearing Wall (no frame backup)

System	R	SDC B	SDC C	SDC D	SDC E	SDC F
Ordinary RC Shear Wall	4	NL	NL	NP	NP	NP
Special RC Shear Wall	5	NL	NL	160 ft (48.8 m)	160 ft (48.8 m)	100 ft (30.5 m)

Bearing wall = shear walls support both gravity AND lateral load, no separate moment frame for redundancy.

2.3.3 Shear Wall Systems — Building Frame (gravity frame separate)

System	R	SDC D/E	SDC F
Ordinary RC Shear Wall	5	NP	NP
Special RC Shear Wall	6	160 ft	100 ft

Building frame system = gravity frame is separate; shear walls resist 100% of lateral load (gravity frame is not designed to share lateral resistance).

2.3.4 Dual Systems — Moment Frame + Shear Wall

ASCE 7-22 §12.2.5.1 — In a dual system, the moment frame must be capable of resisting at least 25% of the design seismic forces, independent of the shear wall contribution. The total lateral resistance is distributed between the moment frame and shear walls in proportion to their relative rigidities.

System	R (SMF + Special Wall)	Frame min. share
Dual System — Special Moment Frame + Special RC Shear Wall	7–8 (varies by SDC)	≥ 25% of base shear

If the moment frame does not achieve this 25% minimum, the system cannot be classified as "dual" — it must be redesigned as a bearing wall or building frame system with the corresponding (lower) R value.

2.3.5 Shear Wall–Frame Interactive System (Ordinary, SDC A/B only)

ASCE 7-22 §12.2.5.8 — A distinct combination available only in SDC A and B:

Shear walls must resist at least 75% of the design story shear at any level
Moment frames must independently resist at least 25% of the design story shear

R = 4.5 (typical, verify against current Table 12.2-1 edition)

2.3.6 Practical Note

R selection is not a standalone choice — it locks in: (1) height limit applicability, (2) SDC permissibility, (3) minimum force-sharing ratios for combined systems, and (4) the detailing chapter required (Section 8). Always verify against the current edition of ASCE 7-22 Table 12.2-1 and §12.2.5, as values are subject to periodic revision.

2.4 Practical Implication

Once SDC is determined, the required frame type is established. This governs which subsection of Section 8 (Reinforcement Detailing) applies.

3. Section Sizing

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3.1 Minimum Dimensions (Non-Seismic)

Element	US	SI	Reference
Beam width (practical min)	10 in	250 mm	—
Column dimension (practical min)	12 in	300 mm	—
Slab thickness (min, non-deflection govern)	4 in	100 mm	§7.3.1.1

3.2 Span-to-Depth Ratios (Deflection Control)

ACI 318-25 Table 7.3.1.1 / 9.3.1.1 — minimum thickness without deflection computation:

Support Condition	Minimum h
Simply supported	L/20
One end continuous	L/24
Both ends continuous	L/28
Cantilever	L/10

Values for non-prestressed beams/one-way slabs, normalweight concrete, fy = 60,000 psi (420 MPa). See §7.3.1.1 for adjustment factors.

3.3 SDC-Dependent Minimum Dimensions (Seismic)

Element	SMF Requirement	Reference
Beam width	≥ 10 in (250 mm), b_w/h ≥ 0.3	§18.6.2.1
Column min dimension	≥ 12 in (300 mm)	§18.7.2.1
Column aspect ratio	shortest/longest ≥ 0.4	§18.7.2.1

See Section 2 for SDC → frame type mapping.

4. Load Standards (ASCE 7-22)

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4.1 Dead Loads

Actual self-weight of materials and fixed equipment. ASCE 7-22 §3.1. Typical material unit weights: see Concrete Properties Reference and Steel Properties Reference pages.

4.2 Live Loads

Occupancy-based minimum uniform/concentrated loads — ASCE 7-22 Table 4.3-1 (selected):

Occupancy	US (psf)	SI (kPa)
Office (general)	50 psf	2.4 kPa
Residential (private)	40 psf	1.9 kPa
Assembly (fixed seats)	60 psf	2.9 kPa
Parking garage (passenger vehicles)	40 psf	1.9 kPa

Full table: ASCE 7-22 Table 4.3-1. Live load reduction permitted per §4.7.

4.3 Wind Loads (Overview)

ASCE 7-22 Ch. 26-30 — Directional Procedure or Envelope Procedure for MWFRS.

Basic wind pressure: q = 0.00256·K_z·K_zt·K_d·K_e·V² (US, psf) | q = 0.613·K_z·K_zt·K_d·K_e·V² (SI, Pa, V in m/s)

K_z = velocity pressure exposure coefficient (§26.10), V = basic wind speed (Ch. 26 maps), K_zt = topographic factor, K_d = directionality, K_e = ground elevation factor.

Full procedure requires site-specific risk category, exposure category, and topographic data — see ASCE 7-22 Ch. 26-30.

4.4 Snow Loads (Overview)

ASCE 7-22 Ch. 7 — Flat roof snow load:

p_f = 0.7·C_e·C_t·I_s·p_g (US & SI, consistent units)

p_g = ground snow load (site-specific, Ch. 7 maps), C_e = exposure factor, C_t = thermal factor, I_s = importance factor.

5. Seismic Design (ASCE 7-22 Ch. 11–22)

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5.1 Site Class

ASCE 7-22 Table 20.3-1 — based on soil shear wave velocity / SPT / undrained shear strength:

Site Class	Description
A	Hard rock
B	Rock
C	Very dense soil / soft rock
D	Stiff soil (default if unknown, §11.4.3)
E	Soft soil
F	Special soils requiring site-specific analysis

5.2 Equivalent Lateral Force Procedure

ASCE 7-22 §12.8 — Base shear:

V = C_s · W

C_s = S_DS / (R / I_e) [upper bound, §12.8.1.1]

where W = effective seismic weight, R = response modification factor (Section 2.3), I_e = importance factor.

Minimum and long-period C_s limits apply — see §12.8.1.1 Eq. 12.8-3 through 12.8-6.

5.3 Vertical Distribution of Seismic Force

ASCE 7-22 §12.8.3:

F_x = C_vx · V, where C_vx = (w_x·h_x^k) / Σ(w_i·h_i^k)

k = distribution exponent: 1.0 for T ≤ 0.5 s, 2.0 for T ≥ 2.5 s, linear interpolation between.

6. Load Combinations

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6.1 ACI 318-25 Strength Design (§5.3.1)

Combination	Equation
U1	1.4D
U2	1.2D + 1.6L + 0.5(L_r or S or R)
U3	1.2D + 1.6(L_r or S or R) + 1.0L (or 0.5W)
U4	1.2D + 1.0W + 1.0L + 0.5(L_r or S or R)
U5	1.2D + 1.0E + 1.0L + 0.2S
U6	0.9D + 1.0W
U7	0.9D + 1.0E

Identical in US and SI (dimensionless load factors). Reference: ACI 318-25 §5.3.1, ASCE 7-22 §2.3.6.

7. Member Design (Strength)

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7.1 Flexural Design

R_n = M_u / (φ·b·d²)

ρ = (0.85f'_c/f_y)·[1 − √(1 − 2R_n/0.85f'_c)]

A_s = ρ·b·d

ρ_min = max(3√f'_c/f_y, 200/f_y) [US] | max(0.25√f'_c/f_y, 1.4/f_y) [SI] — §9.6.1.2

φ = 0.90 (tension-controlled) — Table 21.2.2

7.2 Shear Design

φV_c = φ·2λ√f'_c·b_w·d [US, psi] | φ·0.17λ√f'_c·b_w·d [SI, MPa] — §22.5.5.1

V_s = A_v·f_y·d/s (stirrup contribution) — §22.5.10.5.3

φ = 0.75 (shear) — Table 21.2.1

7.3 Shear-Friction

V_n = A_vf·f_y·μ — §22.9.4.2

Interface Condition	μ
Monolithic concrete	1.4λ
Roughened hardened concrete	1.0λ
Non-roughened hardened concrete	0.6λ
Concrete to steel (anchored)	0.7λ

Applies to: corbels, brackets, cold joints, composite member interfaces. V_n capped per §22.9.4.4.

7.4 Column Design (Axial + Flexure)

PMM interaction — combined axial load (P_n) and biaxial moment (M_nx, M_ny) checked against interaction diagram. See Column PMM Design Calculator for interactive diagram generation.

φ = 0.65 (compression-controlled) to 0.90 (tension-controlled), transition per Table 21.2.2.

7.5 Torsion

Threshold (torsion may be neglected below):

T_th = 0.083λ√f'_c·(A_cp²/p_cp) [SI] | λ√f'_c·(A_cp²/p_cp) [US] — §22.7.4.1

Above threshold, full torsion design per §22.7 required (closed stirrups + longitudinal bars).

8. Reinforcement Detailing

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8.1 Non-Seismic Detailing (SDC A/B, Ch. 1-17, 20-25)

Standard cover (§20.5.1), standard development length (§25.4), standard stirrup/tie spacing (§25.7). No special ductile detailing required.

8.2 Ordinary Moment Frame (OMF) — SDC A/B (§18.3)

Minimal additional requirements beyond Ch. 1-17. Beam-column joints follow standard provisions.

8.3 Intermediate Moment Frame (IMF) — SDC C (§18.4)

Hoop spacing at beam/column ends: s_o ≤ min(8d_b, 24·d_tie, 0.5h or b, 12 in / 300 mm) — §18.4.2 / 18.4.3

Stirrups required over length 2h from member face.

8.4 Special Moment Frame (SMF) — SDC D/E/F (§18.6-18.10)

Hoop spacing (boundary regions): s_o ≤ min(6d_b, 6 in / 150 mm) — §18.6.4.4

Boundary element requirements (shear walls) — §18.10.6: special transverse reinforcement where compression strain demand exceeds threshold.

Strong column-weak beam requirement: ΣM_nc ≥ (6/5)ΣM_nb — §18.7.3.2

9. Special Topics

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9.1 Diaphragm Design (Overview)

ACI 318-25 Ch. 12 / ASCE 7-22 §12.10 — in-plane shear and chord force transfer for floor/roof systems acting as horizontal diaphragms.

9.2 Drift Limits

ASCE 7-22 Table 12.12-1 — Allowable story drift (Δ_a) as fraction of story height (h_sx):

Risk Category	Δ_a Limit
I, II	0.025·h_sx (most structures)
III	0.020·h_sx
IV	0.015·h_sx

Eurocode 2 / EN 1998 Structural Design Guide

Quick-reference for concrete design per EN 1992-1-1, ductility classification per EN 1998-1, load combinations per EN 1990, and actions per EN 1991.

1. Material Properties

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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	f_ck (MPa)	f_cd (MPa)	f_cm (MPa)	f_ctm (MPa)	E_cm (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 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). E_s = 200,000 MPa.

Grade	f_yk (MPa)	f_yd (MPa)	Ductility Class	ε_uk
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, Class C for DCH — Class A not permitted for primary seismic elements.

1.3 Partial Factors

Material	Persistent/Transient (γ)	Accidental (γ)
Concrete (γ_c)	1.50	1.20
Reinforcing steel (γ_s)	1.15	1.00

1.4 Coefficient α_cc

EN 1992-1-1 §3.1.6: accounts for long-term effects and unfavourable load application. Recommended: 0.85 (NDP). Some National Annexes (UK, Germany) adopt α_cc = 1.0 — always verify.

2. Ductility Classification

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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
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

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

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

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

Irregular structures: q reduced by 20% (§4.3.3.1(8)).

2.3 Ground Types (EN 1998-1 Table 3.1)

Ground Type	Description	v_s,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 / medium-stiff clay	180–360
D	Loose-to-medium cohesionless or soft-to-firm cohesive soil	< 180
E	Surface alluvium over Type C or D	—
S₁, S₂	Special soils — site-specific study required	—

2.4 Practical Implication

Chosen ductility class determines behaviour factor q, required rebar ductility class (A/B/C), and detailing provisions in Section 8. Higher q reduces design forces but demands more stringent detailing.

3. Section Sizing

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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

Modify for flanged beams (×0.8 if b_eff/b_w > 3) and tensile steel ratios. See §7.4.2 for full formula.

3.2 Minimum Dimensions — Non-Seismic

Element	Minimum	Reference
Beam width b_w	Practical minimum 200 mm	§9.2
Column min dimension	Practical minimum 200 mm	§9.5
One-way slab thickness	≥ 70 mm	§9.3.1.1
Flat slab thickness	≥ 150 mm	§9.4.1

3.3 Seismic Minimum Dimensions (EN 1998-1)

Element	DCM	DCH	Reference
Beam width b_w	≥ 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 b_c/h_c	≥ 0.25	≥ 0.25	§5.4.3.2.1
Normalised axial force n_d	≤ 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.

4. Actions (EN 1991)

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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 and reinforced — EN 1991-1-1 Table A.1).

4.2 Imposed Loads (Q_k) — EN 1991-1-1 Table 6.2

Category	Use	q_k (kN/m²)	Q_k (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	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

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

Wind pressure: w_e = q_p(z_e)·C_pe

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

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

s = μ_i·C_e·C_t·s_k

s_k = characteristic ground snow load (National Annex maps), μ_i = 0.8 for flat roofs.

5. Seismic Design (EN 1998-1)

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5.1 Design Spectrum — EN 1998-1 §3.2.2.5

Period range	S_d(T)
0 ≤ T ≤ T_B	a_g·S·[2/3 + T/T_B·(2.5/q − 2/3)]
T_B ≤ T ≤ T_C	a_g·S·2.5/q (plateau)
T_C ≤ T ≤ T_D	a_g·S·2.5/q·(T_C/T)
T_D ≤ T	a_g·S·2.5/q·(T_C·T_D/T²)

a_g = peak ground acceleration (National Annex zone map), S = soil factor, q = behaviour factor. 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: C_t = 0.075 (RC frames), 0.085 (steel frames), 0.050 (walls/other)

λ = 0.85 if T₁ ≤ 2·T_C and > 2 storeys; otherwise λ = 1.0

m = 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 — §4.3.3.2.3

F_i = F_b·(z_i·m_i) / Σ(z_j·m_j) — linear (inverted triangle)

Valid for T₁ ≤ 2.0 s and T₁ ≤ 2·T_C. Otherwise: modal response spectrum analysis required (§4.3.3.3).

6. Load Combinations (EN 1990)

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6.1 ULS — Fundamental Combination (Eq. 6.10)

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): 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. 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, ψ₁ = frequent, ψ₂ = quasi-permanent. Values are NDP — verify National Annex.

6.4 SLS Combinations

Combination	Expression	Use
Characteristic	G_k + Q_k,1 + Σ(ψ_0,i·Q_k,i)	Irreversible limit states
Frequent	G_k + ψ_1,1·Q_k,1 + Σ(ψ_2,i·Q_k,i)	Reversible limit states
Quasi-permanent	G_k + Σ(ψ_2,i·Q_k,i)	Creep, deflection, long-term

7. Member Design (Strength)

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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: A_s = ω·f_cd·b·d / f_yd

Neutral axis limit: x_u/d ≤ 0.617 for f_ck ≤ 50 MPa, f_yk = 500 MPa.

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

A_s,max = 0.04·A_c — §9.2.1.1

7.2 Shear Design — EN 1992-1-1 §6.2

Without shear reinforcement:

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 = 0.12, k = 1+√(200/d) ≤ 2.0, v_min = 0.035·k^3/2·f_ck^1/2

With stirrups (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

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

N-M interaction checked for combined N_Ed and biaxial moments. See Column PMM Design Calculator.

Slenderness limit: λ_lim = 20·A·B·C/√n (A=0.7, B=1.1, C=0.7 simplified). If λ > λ_lim, second-order effects required (§5.8.7 or §5.8.8).

7.4 Torsion — EN 1992-1-1 §6.3

Below threshold T_Rd,c = 2·A_k·f_ctd·t_ef,i, torsion may be neglected when combined with VRd,c.

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.

8. Reinforcement Detailing

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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.

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 d_bw ≥ 6 mm; minimum 2 hoop legs in critical region.

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

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

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

Boundary elements required when compression zone exceeds threshold. DCH boundary element length: l_c ≥ max(0.15·l_w, 1.5·b_w) — §5.5.3.4.5.

9. Special Topics

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9.1 Interstorey Drift Limits — EN 1998-1 §4.4.3.2

Non-structural partition type	Limit (d_r·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.

9.2 Diaphragm Action — EN 1998-1 §4.3.1

Floor/roof diaphragms assumed rigid in plan for standard buildings (§4.3.1(4)). In-plane shear transfer designed per EN 1992-1-1 §6.2.4 and EN 1998-1 §5.9. Flexible diaphragm assumption required for large spans or significant openings.

9.3 Capacity Design Principles — EN 1998-1 §4.4.2

Capacity design ensures ductile failure mechanisms govern over brittle failure:

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

IS 456:2000 / IS 1893 Structural Design Guide

Quick-reference for concrete design per IS 456:2000, seismic design per IS 1893:2016, ductility detailing per IS 13920:2016, and loads per IS 875.

1. Material Properties

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1.1 Concrete Grades — IS 456:2000 Cl. 6.1 & Table 2

Design compressive strength: f_cd = 0.67·f_ck/γ_c = 0.447·f_ck (γ_c = 1.5). E_c = 5000√f_ck MPa (Cl. 6.2.3.1).

Grade	f_ck (MPa)	f_cd (MPa)	E_c (MPa)	Min. exposure use
M20	20	8.9	22,361	Mild exposure (RC min)
M25	25	11.2	25,000	Moderate exposure
M30	30	13.4	27,386	Severe exposure
M35	35	15.6	29,580	Very severe exposure
M40	40	17.9	31,623	Extreme exposure

0.67 factor accounts for cube-to-cylinder (×0.8) and sustained loading (×0.85). Min. RC grade: M20 (Cl. 6.1.1).

See Concrete Properties Reference for full IS 456 values.

1.2 Reinforcing Steel — IS 456:2000 Cl. 5.6

f_yd = 0.87·f_y. E_s = 200,000 MPa.

Grade	f_y (MPa)	f_yd (MPa)	Seismic use
Fe 250	250	217	Not for primary seismic
Fe 415	415	361	OMRF acceptable
Fe 415D	415	361	SMRF preferred
Fe 500D	500	435	SMRF required (IS 13920 Cl. 5.2)

2. Ductility Classification

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2.1 Seismic Zones — IS 1893:2016 Table 3

Zone	Z	Intensity
II	0.10	Low
III	0.16	Moderate
IV	0.24	Severe
V	0.36	Very Severe

2.2 Frame Type & Response Reduction Factor R — IS 1893:2016 Table 9

System	R	Detailing
Special RC Moment Frame (SMRF)	5	IS 13920:2016
Ordinary RC Moment Frame (OMRF)	3	IS 456:2000
RC Shear Walls + SMRF (dual)	5	IS 13920:2016
RC Load Bearing Shear Walls	3	IS 13920:2016

OMRF not permitted in Seismic Zones IV and V — IS 1893:2016 Cl. 7.2.1.

2.3 Importance Factor I — IS 1893:2016 Table 8

Category	I
General (residential, commercial)	1.0
Important (schools, hospitals)	1.2
Critical / post-disaster	1.5

3. Section Sizing

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3.1 Span-to-Depth Ratios — IS 456:2000 Cl. 23.2 (Table 15)

Support Condition	Beam	One-way Slab
Simply supported	20	20
Continuous	26	26
Cantilever	7	7

For Fe 500: multiply by ≈ 0.9 (Fig. 4 factor). For flanged beams: ×0.8.

3.2 SMRF Minimum Dimensions — IS 13920:2016

Element	Requirement	Reference
Beam width	≥ 200 mm; b_w/D ≥ 0.3	Cl. 6.1.2
Column min dimension	≥ 300 mm; aspect ratio ≥ 0.4	Cl. 7.1.2
Column axial ratio	P_u/(A_g·f_ck) ≤ 0.40	Cl. 7.1.1

4. Load Standards (IS 875)

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4.1 Imposed Loads — IS 875 Part 2 (selected)

Occupancy	UDL (kN/m²)
Residential (bedrooms, living)	2.0
Office (general)	2.5
Assembly hall (fixed seats)	4.0
Assembly hall (moveable)	5.0
Retail shops	4.0

4.2 Wind — IS 875 Part 3

V_z = V_b·k₁·k₂·k₃·k₄, p_z = 0.6·V_z² (N/m²)

V_b = basic wind speed from IS 875 Fig. 1 (33–55 m/s).

5. Seismic Design (IS 1893:2016)

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5.1 Design Seismic Coefficient — IS 1893:2016 Cl. 6.4.2

A_h = (Z/2) · (I/R) · (S_a/g)

5.2 Spectral Acceleration S_a/g (5% damping)

T (s)	Type I (Rock)	Type II (Medium)	Type III (Soft)
0–0.1	1+15T
0.1–0.40	2.5	—	—
0.1–0.55	—	2.5	—
0.1–0.67	—	—	2.5
0.40–4.0	1.0/T	—	—
0.55–4.0	—	1.36/T	—
0.67–4.0	—	—	1.67/T

5.3 Base Shear & Distribution — Cl. 7.7

V_B = A_h·W; Q_i = V_B·(W_i·H_i²)/Σ(W_j·H_j²)

T_a = 0.075·h^0.75 (RC frames)

6. Load Combinations

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6.1 IS 456:2000 ULS Combinations — Cl. 18.2.3.1

Combination	Equation
DL + IL	1.5(DL + IL)
DL + IL + WL/EL	1.2(DL + IL ± WL/EL)
DL + WL/EL	1.5(DL ± WL/EL)
Uplift check	0.9DL ± 1.5WL/EL

Seismic and wind are not combined simultaneously.

7. Member Design (Strength)

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7.1 Flexural Design — IS 456:2000 Cl. 38

A_s = (0.5·f_ck/f_y)·[1 − √(1 − 4.6·M_u/(f_ck·b·d²))]·b·d

M_u,lim = 0.138·f_ck·b·d² (Fe 415); x_u,max/d = 0.48 (Fe 415), 0.46 (Fe 500)

A_s,min = 0.85·b·d/f_y; A_s,max = 0.04·b·D

7.2 Shear — IS 456:2000 Cl. 40

τ_v = V_u/(b·d); check vs τ_c (Table 19) and τ_c,max (Table 20).

Stirrups when τ_v > τ_c: A_sv·0.87·f_y·d/s_v = (τ_v − τ_c)·b·d

7.3 Column — IS 456:2000 Cl. 39

P-M interaction for combined loading. See Column PMM Design Calculator.

e_min = max(L/500 + D/30, 20 mm). A_sc: 0.8%–4% of A_g.

8. Reinforcement Detailing

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8.1 SMRF Beam Detailing — IS 13920:2016 Cl. 6

Confinement region: 2d from face of column. Hoop spacing: s_o ≤ min(d/4, 8d_bL, 100 mm) — Cl. 6.3.5

Outside confinement: s ≤ d/2. Positive moment capacity at joint ≥ 50% negative moment capacity.

8.2 SMRF Column Detailing — IS 13920:2016 Cl. 7

Confinement l_o = max(L_c/6, max column dim, 450 mm). Hoop spacing: s_o ≤ min(b/4, 100 mm).

Strong column–weak beam: ΣM_u,col ≥ 1.4·ΣM_u,beam — Cl. 7.2

9. Special Topics

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9.1 Storey Drift — IS 1893:2016 Cl. 7.11.1

Δ_a ≤ 0.004·h_s (h_s = storey height) under design seismic forces.

9.2 Soft / Weak Storey — IS 1893:2016 Cl. 4.15 & Table 6

Soft storey: lateral stiffness < 70% of storey above (or < 80% avg of 3 above). Weak storey: strength < 80% of storey above. Special design required in Zones III–V.

TS 500 / TBDY 2018 Structural Design Guide

Quick-reference for concrete design per TS 500:2000, seismic design per TBDY 2018 (Turkish Building Earthquake Code), load combinations per TS 498, and ductile detailing.

1. Material Properties

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1.1 Concrete — TS 500:2000 Table 2.1

f_cd = 0.85·f_ck/γ_c = 0.567·f_ck (γ_c = 1.5). E_c = 3250·√f_ck + 14000 (MPa).

Class	f_ck (MPa)	f_cd (MPa)	f_ctk (MPa)	E_c (MPa)
C20	20	11.3	1.60	28,500
C25	25	14.2	1.80	30,250
C30	30	17.0	1.90	31,820
C35	35	19.8	2.10	33,230
C40	40	22.7	2.20	34,520
C50	50	28.3	2.50	36,970

TBDY 2018 Madde 7.2.2: min C25 for YDMÇ/YDPB; min C20 for SDMÇ/SDPB.

See Concrete Properties Reference for full class values.

1.2 Reinforcing Steel

f_yd = f_yk/1.15. E_s = 200,000 MPa.

Grade	f_yk (MPa)	f_yd (MPa)	Seismic use
S420	420	365	SDMÇ acceptable
B420C	420	365	YDMÇ / YDPB required
B500C	500	435	YDMÇ / YDPB required

TBDY 2018 Madde 7.2.3: B420C or B500C mandatory for primary seismic elements in high ductility systems.

2. Ductility Classification (TBDY 2018)

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2.1 Seismic Design Class (DTS) — TBDY 2018 Table 3.4

S_DS	BKS 1 & 2	BKS 3 & 4
≥ 0.75	DTS 1	DTS 1a
0.33–0.75	DTS 2	DTS 2a
< 0.33	DTS 3	DTS 4

BKS 1 = critical · BKS 2 = important · BKS 3 = normal · BKS 4 = low risk

2.2 R Factor — TBDY 2018 Table 4.1

System	Ductility	R	D
RC Moment Frame (YDMÇ)	High	8	3
RC Moment Frame (SDMÇ)	Limited	4	2.5
RC Shear Wall bearing (YDPB)	High	6	2.5
Dual YDMÇ + YDPB	High	7	2.5

2.3 Site Classes — TBDY 2018 Table 2.1

Class	Description	V_S30 (m/s)
ZA	Hard rock	> 1500
ZB	Rock	760–1500
ZC	Very dense / soft rock	360–760
ZD	Stiff soil	180–360
ZE	Soft soil	≤ 180

S_DS = F_SS·S_S, S_D1 = F₁·S₁ from AFAD seismic hazard maps (TDTH).

3. Section Sizing

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3.1 Minimum Beam Depths — TS 500:2000 Cl. 6.1.5

Support Condition	Beam h/L	One-way Slab h/L
Simply supported	1/10	1/30
One end continuous	1/12	1/35
Both ends continuous	1/15	1/40
Cantilever	1/5	1/12

3.2 YDMÇ Seismic Minimum Dimensions — TBDY 2018

Element	Requirement	Reference
Beam width b_w	≥ 250 mm; b_w/h ≥ 0.3	Madde 7.3.1
Column min dim	≥ 300 mm; b_k/h_k ≥ 0.4	Madde 7.4.1
Column axial ratio	N_d/(A_c·f_cd) ≤ 0.40	Madde 7.4.1

4. Load Standards (TS 498)

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4.1 Imposed Loads — TS 498 Table 3 (selected)

Occupancy	q_k (kN/m²)
Konutlar (residential)	2.0
Bürolar (office)	3.0
Toplantı, sınıf	3.0–4.0
Mağaza, market	4.0–5.0
Depo, arşiv	5.0–10.0

4.2 Seismic Mass — TBDY 2018 Madde 4.4.2

m_t = Σ(G_i + n·Q_i)/g

n = 0.3 (residential/office), 0.6 (storage), 0.0 (roof live/snow)

5. Seismic Design (TBDY 2018)

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5.1 Design Spectrum — TBDY 2018 Madde 2.3 (DD-2)

Period range	S_aR(T)
0 ≤ T ≤ T_A	(0.4 + 0.6·T/T_A)·S_DS
T_A ≤ T ≤ T_B	S_DS
T_B ≤ T ≤ T_L	S_D1/T
T > T_L	S_D1·T_L/T²

T_A = 0.2·T_B, T_B = S_D1/S_DS, T_L = 6 s

5.2 Reduced Spectrum & Base Shear — Madde 4.3.3

S_ad(T) = S_aR(T)/R_a(T); for T ≥ T_B: R_a(T) = R/I

V_t = m_t·S_ad(T₁); minimum V_t,min = 0.04·m_t·S_DS·g

T₁ ≈ C_t·H^3/4: C_t = 0.07 (RC frames), 0.05 (walls/other)

5.3 Vertical Distribution — Madde 4.3.4

F_i = V_t·(m_i·H_i^α)/Σ(m_j·H_j^α)

α = 1.0 (T ≤ 0.5 s), α = 2.0 (T ≥ 2.0 s). Additional ΔF_N = 0.07·T₁·V_t if T₁ > 0.7 s.

6. Load Combinations (TBDY 2018 Madde 4.4.3)

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Comb.	Equation
G1	1.4G
G2	1.2G + 1.6Q + 0.5(Q_a or S)
G3	1.2G + 1.6(Q_a or S) + max(0.5Q, 0.8W)
G4	1.2G + 1.6W + 0.5Q + 0.5(Q_a or S)
G5	1.2G + 1.0E_d + 1.0Q + 0.3S
G6	0.9G + 1.6W
G7	0.9G + 1.0E_d

G=dead, Q=live, Q_a=roof live, S=snow, W=wind, E_d=seismic.

7. Member Design (Strength)

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7.1 Flexural Design — TS 500:2000 Cl. 7.1

μ = M_d/(f_cd·b·d²), ω = 1 − √(1 − 2μ), A_s = ω·f_cd·b·d/f_yd

A_s,min = 0.8·f_ctd·b_w·d/f_yd

7.2 Shear — TS 500:2000 Cl. 8

V_cr = 0.65·f_ctd·b_w·d; V_r,max = 0.22·f_cd·b_w·d

Stirrups: V_r = V_cr + (A_sw/s)·f_ywd·d·cot α

7.3 Column — TS 500:2000 Cl. 7.4

P-M interaction. See Column PMM Design Calculator. A_s: 1%–4% of A_c.

8. Reinforcement Detailing (TBDY 2018)

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8.1 YDMÇ Beam Detailing — Madde 7.3

Sarılma bölgesi: 2h from face of column. s_e ≤ min(h/4, 8d_bL, 24d_bw, 200 mm)

Outside confinement: s ≤ h/2. Positive capacity at support ≥ 50% negative capacity.

8.2 YDMÇ Column Detailing — Madde 7.4

l₀ = max(H_k/6, b_k, h_k, 500 mm). s_e ≤ min(b₀/3, 6d_bL, 150 mm)

Güçlü kolon–zayıf kiriş: ΣM_ra(kol) ≥ 1.2·ΣM_ra(kiriş) — Madde 7.4.2

8.3 SDMÇ Detailing — Madde 7.8 / 7.9

Beam: s_e ≤ min(h/3, 10d_bL, 200 mm) in 2h confinement region.

Column: s_e ≤ min(b₀/2, 8d_bL, 200 mm).

9. Special Topics

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9.1 Interstorey Drift — TBDY 2018 Madde 4.9

δ_i = R·u_i/I (amplified from elastic analysis, checked under DD-3)

Condition	Limit δ_i,max/h_i
RC frames with brittle infill	0.008
RC frames with ductile / no infill	0.016

9.2 Irregularity Checks — TBDY 2018 Madde 3.6

A1 (torsion): max/mean drift ratio > 1.2. B1 (soft storey): stiffness < 70% of storey above. B2 (mass): storey mass > 1.5× adjacent. Irregular buildings require modal analysis (§4.3.2).

1. Material Properties

1.1 Concrete (f'c)

1.2 Reinforcing Steel (fy)

1.3 Modulus of Elasticity (Concrete)

1.4 Lightweight Concrete — Modification Factor (λ)

2. Ductility Classification

2.1 Seismic Design Category (SDC)

2.2 Moment Frame Ductility Classes

2.3 Response Modification Factor (R) — System Limitations

2.3.1 Moment Frame Systems (selected values)

2.3.2 Shear Wall Systems — Bearing Wall (no frame backup)

2.3.3 Shear Wall Systems — Building Frame (gravity frame separate)

2.3.4 Dual Systems — Moment Frame + Shear Wall

2.3.5 Shear Wall–Frame Interactive System (Ordinary, SDC A/B only)

2.3.6 Practical Note

2.4 Practical Implication

3. Section Sizing

3.1 Minimum Dimensions (Non-Seismic)

3.2 Span-to-Depth Ratios (Deflection Control)

3.3 SDC-Dependent Minimum Dimensions (Seismic)

4. Load Standards (ASCE 7-22)

4.1 Dead Loads

4.2 Live Loads

4.3 Wind Loads (Overview)

4.4 Snow Loads (Overview)

5. Seismic Design (ASCE 7-22 Ch. 11–22)

5.1 Site Class

5.2 Equivalent Lateral Force Procedure

5.3 Vertical Distribution of Seismic Force

6. Load Combinations

6.1 ACI 318-25 Strength Design (§5.3.1)

7. Member Design (Strength)

7.1 Flexural Design

7.2 Shear Design

7.3 Shear-Friction

7.4 Column Design (Axial + Flexure)

7.5 Torsion

8. Reinforcement Detailing

8.1 Non-Seismic Detailing (SDC A/B, Ch. 1-17, 20-25)

8.2 Ordinary Moment Frame (OMF) — SDC A/B (§18.3)

8.3 Intermediate Moment Frame (IMF) — SDC C (§18.4)

8.4 Special Moment Frame (SMF) — SDC D/E/F (§18.6-18.10)

9. Special Topics

9.1 Diaphragm Design (Overview)

9.2 Drift Limits

1. Material Properties

1.1 Concrete (fck) — EN 1992-1-1 §3.1

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

1.3 Partial Factors

1.4 Coefficient αcc

2. Ductility Classification

2.1 Ductility Classes (EN 1998-1 §5.1.2)

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

2.3 Ground Types (EN 1998-1 Table 3.1)

2.4 Practical Implication

3. Section Sizing

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

3.2 Minimum Dimensions — Non-Seismic

3.3 Seismic Minimum Dimensions (EN 1998-1)

4. Actions (EN 1991)

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

4.2 Imposed Loads (Qk) — EN 1991-1-1 Table 6.2

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

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

5. Seismic Design (EN 1998-1)

5.1 Design Spectrum — EN 1998-1 §3.2.2.5

5.2 Base Shear — EN 1998-1 §4.3.3.2

5.3 Vertical Distribution — §4.3.3.2.3

6. Load Combinations (EN 1990)

6.1 ULS — Fundamental Combination (Eq. 6.10)

6.2 ULS — Seismic Combination (Eq. 6.12b)

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

6.4 SLS Combinations

7. Member Design (Strength)

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

7.2 Shear Design — EN 1992-1-1 §6.2

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

7.4 Torsion — EN 1992-1-1 §6.3

8. Reinforcement Detailing

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

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

1.4 Coefficient α_cc

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

4.2 Imposed Loads (Q_k) — EN 1991-1-1 Table 6.2

5.2 Spectral Acceleration S_a/g (5% damping)