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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

1.1 Concrete (f'c)

ParameterUS (psi)SI (MPa)Reference
Minimum f'c2,500 psi17 MPaACI 318-25 §19.2.1.1
Maximum f'c (normal provisions)10,000 psi70 MPaACI 318-25 §19.2.1.3
Typical structural use3,000–6,000 psi21–42 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)

ParameterUS (ksi)SI (MPa)Reference
Minimum fy40 ksi280 MPaACI 318-25 §20.2.2.4
Maximum fy (general)80 ksi550 MPaACI 318-25 §20.2.2.4
Common gradesGrade 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: Ec = 57,000√f'c  (f'c in psi)

SI: Ec = 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 Typeλ
Normalweight1.00
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 = fct / (6.7√f'c), capped at λ ≤ 1.0

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

where fct = average splitting tensile strength (measured)

2. Ductility Classification

2.1 Seismic Design Category (SDC)

ASCE 7-22 §11.6 — SDC is determined from Risk Category and spectral response parameters (SDS, SD1).

Table 11.6-1 (based on SDS):

SDS ValueRisk Category I, II, IIIRisk Category IV
SDS < 0.167gAA
0.167g ≤ SDS < 0.33gBC
0.33g ≤ SDS < 0.50gCD
0.50g ≤ SDSDD

Table 11.6-2 (based on SD1): Similar tiered structure based on SD1 values.

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

Site-specific seismic parameters (SDS, SD1) require a geotechnical/seismic hazard report.

2.2 Moment Frame Ductility Classes

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

SDCPermitted Frame TypeACI 318-25 Reference
A, BOrdinary Moment Frame (OMF)Ch. 1–17 (no Ch. 18 special detailing required)
CIntermediate Moment Frame (IMF) minimum§18.4
D, E, FSpecial 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)

SystemRSDC BSDC CSDC DSDC ESDC F
Ordinary RC Moment Frame3NLNPNPNPNP
Intermediate RC Moment Frame5NLNLNPNPNP
Special RC Moment Frame8NLNLNLNLNL

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)

SystemRSDC BSDC CSDC DSDC ESDC F
Ordinary RC Shear Wall4NLNLNPNPNP
Special RC Shear Wall5NLNL160 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)

SystemRSDC D/ESDC F
Ordinary RC Shear Wall5NPNP
Special RC Shear Wall6160 ft100 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.

SystemR (SMF + Special Wall)Frame min. share
Dual System — Special Moment Frame + Special RC Shear Wall7–8 (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

3.1 Minimum Dimensions (Non-Seismic)

ElementUSSIReference
Beam width (practical min)10 in250 mm—
Column dimension (practical min)12 in300 mm—
Slab thickness (min, non-deflection govern)4 in100 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 ConditionMinimum h
Simply supportedL/20
One end continuousL/24
Both ends continuousL/28
CantileverL/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)

ElementSMF RequirementReference
Beam width≥ 10 in (250 mm), bw/h ≥ 0.3§18.6.2.1
Column min dimension≥ 12 in (300 mm)§18.7.2.1
Column aspect ratioshortest/longest ≥ 0.4§18.7.2.1

See Section 2 for SDC → frame type mapping.

4. Load Standards (ASCE 7-22)

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):

OccupancyUS (psf)SI (kPa)
Office (general)50 psf2.4 kPa
Residential (private)40 psf1.9 kPa
Assembly (fixed seats)60 psf2.9 kPa
Parking garage (passenger vehicles)40 psf1.9 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·Kz·Kzt·Kd·Ke·V² (US, psf) | q = 0.613·Kz·Kzt·Kd·Ke·V² (SI, Pa, V in m/s)

Kz = velocity pressure exposure coefficient (§26.10), V = basic wind speed (Ch. 26 maps), Kzt = topographic factor, Kd = directionality, Ke = 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:

pf = 0.7·Ce·Ct·Is·pg (US & SI, consistent units)

pg = ground snow load (site-specific, Ch. 7 maps), Ce = exposure factor, Ct = thermal factor, Is = importance factor.

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

5.1 Site Class

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

Site ClassDescription
AHard rock
BRock
CVery dense soil / soft rock
DStiff soil (default if unknown, §11.4.3)
ESoft soil
FSpecial soils requiring site-specific analysis

5.2 Equivalent Lateral Force Procedure

ASCE 7-22 §12.8 — Base shear:

V = Cs · W

Cs = SDS / (R / Ie)   [upper bound, §12.8.1.1]

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

Minimum and long-period Cs 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:

Fx = Cvx · V,   where Cvx = (wx·hxk) / Σ(wi·hik)

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

6. Load Combinations

6.1 ACI 318-25 Strength Design (§5.3.1)

CombinationEquation
U11.4D
U21.2D + 1.6L + 0.5(Lr or S or R)
U31.2D + 1.6(Lr or S or R) + 1.0L (or 0.5W)
U41.2D + 1.0W + 1.0L + 0.5(Lr or S or R)
U51.2D + 1.0E + 1.0L + 0.2S
U60.9D + 1.0W
U70.9D + 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)

7.1 Flexural Design

Rn = Mu / (φ·b·d²)

ρ = (0.85f'c/fy)·[1 − √(1 − 2Rn/0.85f'c)]

As = ρ·b·d

ρmin = max(3√f'c/fy, 200/fy) [US] | max(0.25√f'c/fy, 1.4/fy) [SI] — §9.6.1.2

φ = 0.90 (tension-controlled) — Table 21.2.2

7.2 Shear Design

φVc = φ·2λ√f'c·bw·d [US, psi] | φ·0.17λ√f'c·bw·d [SI, MPa] — §22.5.5.1

Vs = Av·fy·d/s (stirrup contribution) — §22.5.10.5.3

φ = 0.75 (shear) — Table 21.2.1

7.3 Shear-Friction

Vn = Avf·fy·μ — §22.9.4.2

Interface Conditionμ
Monolithic concrete1.4λ
Roughened hardened concrete1.0λ
Non-roughened hardened concrete0.6λ
Concrete to steel (anchored)0.7λ

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

7.4 Column Design (Axial + Flexure)

PMM interaction — combined axial load (Pn) and biaxial moment (Mnx, Mny) 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):

Tth = 0.083λ√f'c·(Acp²/pcp) [SI] | λ√f'c·(Acp²/pcp) [US] — §22.7.4.1

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

8. Reinforcement Detailing

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: so ≤ min(8db, 24·dtie, 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): so ≤ min(6db, 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: ΣMnc ≥ (6/5)ΣMnb — §18.7.3.2

9. Special Topics

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 (Δa) as fraction of story height (hsx):

Risk CategoryΔa Limit
I, II0.025·hsx (most structures)
III0.020·hsx
IV0.015·hsx

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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

1.1 Concrete (fck) — EN 1992-1-1 §3.1

Design compressive strength: fcd = αcc·fck/γc  (αcc = 0.85, γc = 1.5 persistent/transient)

Mean compressive strength: fcm = fck + 8 MPa

Mean tensile strength: fctm = 0.30·fck2/3 (fck ≤ 50 MPa)

Classfck (MPa)fcd (MPa)fcm (MPa)fctm (MPa)Ecm (GPa)
C16/20169.1241.9029
C20/252011.3282.2130
C25/302514.2332.5631
C30/373017.0382.9033
C35/453519.8433.2134
C40/504022.7483.5135
C45/554525.5533.8036
C50/605028.3584.0737

fcd using αcc = 0.85 (NDP — verify National Annex). Ecm = 22000·(fcm/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: fyd = fyk/γs  (γs = 1.15). Es = 200,000 MPa.

Gradefyk (MPa)fyd (MPa)Ductility Classεuk
B500A500435A (low)≥ 2.5%
B500B500435B (normal)≥ 5.0%
B500C500435C (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

MaterialPersistent/Transient (γ)Accidental (γ)
Concrete (γc)1.501.20
Reinforcing steel (γs)1.151.00

1.4 Coefficient αcc

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 αcc = 1.0 — always verify.

2. Ductility Classification

2.1 Ductility Classes (EN 1998-1 §5.1.2)

ClassNameq range (typical)Detailing chapter
DCLDuctility Class Lowq ≤ 1.5EN 1992-1-1 only
DCMDuctility Class Medium1.5 < q ≤ ~4EN 1998-1 §5.4
DCHDuctility Class Highq up to ~5–6EN 1998-1 §5.5

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

Structural SystemDCM qDCH q
Frame (multi-storey, multi-bay)3.0·(αu/α1) ≈ 3.94.5·(αu/α1) ≈ 5.85
Frame (one-storey)3.0·1.1 = 3.34.5·1.1 = 4.95
Wall system (slender, α0 ≥ 2)3.0·kw = 3.04.0·(αu/α1)·kw
Dual / wall-equivalent dual3.0·(αu/α1)4.5·(αu/α1)

αu/α1: overstrength ratio — default 1.0; up to 1.3 for regular multi-bay frames. kw = (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 TypeDescriptionvs,30 (m/s)
ARock or rock-like geological formation> 800
BDense sand, gravel, or stiff clay360–800
CDeep deposits of medium-dense sand / medium-stiff clay180–360
DLoose-to-medium cohesionless or soft-to-firm cohesive soil< 180
ESurface alluvium over Type C or D—
S1, S2Special 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

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

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

Support ConditionBeamFlat SlabRibbed Slab
Simply supported202416
End span (one end continuous)263021
Interior span (both ends continuous)303524
Cantilever8106

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

3.2 Minimum Dimensions — Non-Seismic

ElementMinimumReference
Beam width bwPractical minimum 200 mm§9.2
Column min dimensionPractical 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)

ElementDCMDCHReference
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
Normalised axial force nd≤ 0.65≤ 0.55§5.4.3.2.1 / §5.5.3.2.1

nd = NEd/(Ac·fcd) — if exceeded, section must be enlarged.

4. Actions (EN 1991)

4.1 Permanent Actions (Gk) — 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 (Qk) — EN 1991-1-1 Table 6.2

CategoryUseqk (kN/m²)Qk (kN)
ADomestic / residential floors1.5–2.02.0–3.0
BOffice floors2.0–3.02.0–4.5
C1Assembly — tables, chairs3.04.0
C5Assembly — large crowd / dancing5.04.5
DShopping / retail4.0–5.04.0–7.0
EStorage / warehousing≥ 7.57.0

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

Peak velocity pressure: qp(z) = ce(z)·qb,  qb = 0.5·ρ·vb²

Wind pressure: we = qp(ze)·Cpe

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

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

s = μi·Ce·Ct·sk

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

5. Seismic Design (EN 1998-1)

5.1 Design Spectrum — EN 1998-1 §3.2.2.5

Period rangeSd(T)
0 ≤ T ≤ TBag·S·[2/3 + T/TB·(2.5/q − 2/3)]
TB ≤ T ≤ TCag·S·2.5/q  (plateau)
TC ≤ T ≤ TDag·S·2.5/q·(TC/T)
TD ≤ Tag·S·2.5/q·(TC·TD/T²)

ag = peak ground acceleration (National Annex zone map), S = soil factor, q = behaviour factor. Minimum: Sd(T) ≥ β·ag (β = 0.2 recommended).

5.2 Base Shear — EN 1998-1 §4.3.3.2

Fb = Sd(T1)·m·λ

T1 ≈ Ct·H3/4: Ct = 0.075 (RC frames), 0.085 (steel frames), 0.050 (walls/other)

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

m = seismic mass = Σ(Gk,j + ψE,i·Qk,i),  ψE,i = φ·ψ2,i (§3.2.4)

5.3 Vertical Distribution — §4.3.3.2.3

Fi = Fb·(zi·mi) / Σ(zj·mj) — linear (inverted triangle)

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

6. Load Combinations (EN 1990)

6.1 ULS — Fundamental Combination (Eq. 6.10)

1.35·Gk + 1.5·Qk,1 + 1.5·Σ(ψ0,i·Qk,i)

Alternative Eq. 6.10a/b (some NAs): max of (1.35·Gk + 1.5·ψ0,1·Qk,1) and (ξ·1.35·Gk + 1.5·Qk,1), ξ = 0.85.

6.2 ULS — Seismic Combination (Eq. 6.12b)

Σ(Gk,j) + AEd + Σ(ψ2,i·Qk,i)

AEd = design seismic action. γ factors = 1.0 for seismic combination.

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

Action / Categoryψ0ψ1ψ2
Imposed — Category A (residential)0.70.50.3
Imposed — Category B (office)0.70.50.3
Imposed — Category C (assembly)0.70.70.6
Imposed — Category D (shopping)0.70.70.6
Imposed — Category E (storage)1.00.90.8
Wind0.60.20
Snow (altitude ≤ 1000 m)0.50.20

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

6.4 SLS Combinations

CombinationExpressionUse
CharacteristicGk + Qk,1 + Σ(ψ0,i·Qk,i)Irreversible limit states
FrequentGk + ψ1,1·Qk,1 + Σ(ψ2,i·Qk,i)Reversible limit states
Quasi-permanentGk + Σ(ψ2,i·Qk,i)Creep, deflection, long-term

7. Member Design (Strength)

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

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

Normalised moment: μ = MEd/(fcd·b·d²)

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

Required steel: As = ω·fcd·b·d / fyd

Neutral axis limit: xu/d ≤ 0.617 for fck ≤ 50 MPa, fyk = 500 MPa.

As,min = max(0.26·fctm/fyk·bt·d, 0.0013·bt·d) — §9.2.1.1

As,max = 0.04·Ac — §9.2.1.1

7.2 Shear Design — EN 1992-1-1 §6.2

Without shear reinforcement:

VRd,c = [CRd,c·k·(100·ρl·fck)1/3 + k1·σcp]·bw·d ≥ vmin·bw·d

CRd,c = 0.12, k = 1+√(200/d) ≤ 2.0, vmin = 0.035·k3/2·fck1/2

With stirrups (variable strut inclination — §6.2.3):

VRd,s = (Asw/s)·z·fywd·cot θ

VRd,max = αcw·bw·z·ν1·fcd/(cot θ + tan θ)

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

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

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

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

7.4 Torsion — EN 1992-1-1 §6.3

Below threshold TRd,c = 2·Ak·fctd·tef,i, torsion may be neglected when combined with VRd,c.

Above threshold: closed stirrups + longitudinal bars required. TRd,max = 2·ν·αcw·Ak·tef,i·fcd·sin θ·cos θ.

8. Reinforcement Detailing

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: lcr = max(hw, lc1/6, 0.45 m) from face of support — §5.4.3.1.1

Hoop spacing: so ≤ min(hw/4, 24dbw, 225 mm, 8dbL) — §5.4.3.1.2

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

Columns — Critical Region:

Length: lo = max(lcl/6, hc, bc, 0.45 m) — §5.4.3.2.2

Hoop spacing: so ≤ min(bo/2, 175 mm, 8dbL) — §5.4.3.2.2

8.3 DCH Detailing (EN 1998-1 §5.5)

Beams — Critical Region:

Hoop spacing: so ≤ min(hw/4, 6dbL, 24dbw, 150 mm) — §5.5.3.1.3

Columns — Critical Region:

Length: lo = max(lcl/4, hc, bc, 0.60 m) — §5.5.3.2.2

Hoop spacing: so ≤ min(bo/3, 125 mm, 6dbL) — §5.5.3.2.2

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

ΣMRc ≥ 1.3·ΣMRb 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: lc ≥ max(0.15·lw, 1.5·bw) — §5.5.3.4.5.

9. Special Topics

9.1 Interstorey Drift Limits — EN 1998-1 §4.4.3.2

Non-structural partition typeLimit (dr·ν / h)
Brittle (rigid) partitions attached to structure0.005
Ductile partitions0.0075
No partitions / partitions isolated from structure0.010

ν = importance factor (0.4–0.5 per §4.4.3.2), h = interstorey height. dr = qd·ds.

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) — VEd 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)

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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

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

Design compressive strength: fcd = 0.67·fck/γc = 0.447·fck (γc = 1.5). Ec = 5000√fck MPa (Cl. 6.2.3.1).

Gradefck (MPa)fcd (MPa)Ec (MPa)Min. exposure use
M20208.922,361Mild exposure (RC min)
M252511.225,000Moderate exposure
M303013.427,386Severe exposure
M353515.629,580Very severe exposure
M404017.931,623Extreme 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

fyd = 0.87·fy. Es = 200,000 MPa.

Gradefy (MPa)fyd (MPa)Seismic use
Fe 250250217Not for primary seismic
Fe 415415361OMRF acceptable
Fe 415D415361SMRF preferred
Fe 500D500435SMRF required (IS 13920 Cl. 5.2)

2. Ductility Classification

2.1 Seismic Zones — IS 1893:2016 Table 3

ZoneZIntensity
II0.10Low
III0.16Moderate
IV0.24Severe
V0.36Very Severe

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

SystemRDetailing
Special RC Moment Frame (SMRF)5IS 13920:2016
Ordinary RC Moment Frame (OMRF)3IS 456:2000
RC Shear Walls + SMRF (dual)5IS 13920:2016
RC Load Bearing Shear Walls3IS 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

CategoryI
General (residential, commercial)1.0
Important (schools, hospitals)1.2
Critical / post-disaster1.5

3. Section Sizing

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

Support ConditionBeamOne-way Slab
Simply supported2020
Continuous2626
Cantilever77

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

3.2 SMRF Minimum Dimensions — IS 13920:2016

ElementRequirementReference
Beam width≥ 200 mm; bw/D ≥ 0.3Cl. 6.1.2
Column min dimension≥ 300 mm; aspect ratio ≥ 0.4Cl. 7.1.2
Column axial ratioPu/(Ag·fck) ≤ 0.40Cl. 7.1.1

4. Load Standards (IS 875)

4.1 Imposed Loads — IS 875 Part 2 (selected)

OccupancyUDL (kN/m²)
Residential (bedrooms, living)2.0
Office (general)2.5
Assembly hall (fixed seats)4.0
Assembly hall (moveable)5.0
Retail shops4.0

4.2 Wind — IS 875 Part 3

Vz = Vb·k1·k2·k3·k4,  pz = 0.6·Vz² (N/m²)

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

5. Seismic Design (IS 1893:2016)

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

Ah = (Z/2) · (I/R) · (Sa/g)

5.2 Spectral Acceleration Sa/g (5% damping)

T (s)Type I (Rock)Type II (Medium)Type III (Soft)
0–0.11+15T
0.1–0.402.5——
0.1–0.55—2.5—
0.1–0.67——2.5
0.40–4.01.0/T——
0.55–4.0—1.36/T—
0.67–4.0——1.67/T

5.3 Base Shear & Distribution — Cl. 7.7

VB = Ah·W;  Qi = VB·(Wi·Hi²)/Σ(Wj·Hj²)

Ta = 0.075·h0.75 (RC frames)

6. Load Combinations

6.1 IS 456:2000 ULS Combinations — Cl. 18.2.3.1

CombinationEquation
DL + IL1.5(DL + IL)
DL + IL + WL/EL1.2(DL + IL ± WL/EL)
DL + WL/EL1.5(DL ± WL/EL)
Uplift check0.9DL ± 1.5WL/EL

Seismic and wind are not combined simultaneously.

7. Member Design (Strength)

7.1 Flexural Design — IS 456:2000 Cl. 38

As = (0.5·fck/fy)·[1 − √(1 − 4.6·Mu/(fck·b·d²))]·b·d

Mu,lim = 0.138·fck·b·d² (Fe 415); xu,max/d = 0.48 (Fe 415), 0.46 (Fe 500)

As,min = 0.85·b·d/fy;  As,max = 0.04·b·D

7.2 Shear — IS 456:2000 Cl. 40

τv = Vu/(b·d); check vs τc (Table 19) and τc,max (Table 20).

Stirrups when τv > τc: Asv·0.87·fy·d/sv = (τv − τc)·b·d

7.3 Column — IS 456:2000 Cl. 39

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

emin = max(L/500 + D/30, 20 mm). Asc: 0.8%–4% of Ag.

8. Reinforcement Detailing

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

Confinement region: 2d from face of column. Hoop spacing: so ≤ min(d/4, 8dbL, 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 lo = max(Lc/6, max column dim, 450 mm). Hoop spacing: so ≤ min(b/4, 100 mm).

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

9. Special Topics

9.1 Storey Drift — IS 1893:2016 Cl. 7.11.1

Δa ≤ 0.004·hs (hs = 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.

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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

1.1 Concrete — TS 500:2000 Table 2.1

fcd = 0.85·fck/γc = 0.567·fck (γc = 1.5). Ec = 3250·√fck + 14000 (MPa).

Classfck (MPa)fcd (MPa)fctk (MPa)Ec (MPa)
C202011.31.6028,500
C252514.21.8030,250
C303017.01.9031,820
C353519.82.1033,230
C404022.72.2034,520
C505028.32.5036,970

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

fyd = fyk/1.15. Es = 200,000 MPa.

Gradefyk (MPa)fyd (MPa)Seismic use
S420420365SDMÇ acceptable
B420C420365YDMÇ / YDPB required
B500C500435YDMÇ / YDPB required

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

2. Ductility Classification

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

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

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

2.2 R Factor — TBDY 2018 Table 4.1

SystemDuctilityRD
RC Moment Frame (YDMÇ)High83
RC Moment Frame (SDMÇ)Limited42.5
RC Shear Wall bearing (YDPB)High62.5
Dual YDMÇ + YDPBHigh72.5

2.3 Site Classes — TBDY 2018 Table 2.1

ClassDescriptionVS30 (m/s)
ZAHard rock> 1500
ZBRock760–1500
ZCVery dense / soft rock360–760
ZDStiff soil180–360
ZESoft soil≤ 180

SDS = FSS·SS, SD1 = F1·S1 from AFAD seismic hazard maps (TDTH).

3. Section Sizing

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

Support ConditionBeam h/LOne-way Slab h/L
Simply supported1/101/30
One end continuous1/121/35
Both ends continuous1/151/40
Cantilever1/51/12

3.2 YDMÇ Seismic Minimum Dimensions — TBDY 2018

ElementRequirementReference
Beam width bw≥ 250 mm; bw/h ≥ 0.3Madde 7.3.1
Column min dim≥ 300 mm; bk/hk ≥ 0.4Madde 7.4.1
Column axial ratioNd/(Ac·fcd) ≤ 0.40Madde 7.4.1

4. Load Standards (TS 498)

4.1 Imposed Loads — TS 498 Table 3 (selected)

Occupancyqk (kN/m²)
Konutlar (residential)2.0
Bürolar (office)3.0
Toplantı, sınıf3.0–4.0
Mağaza, market4.0–5.0
Depo, arşiv5.0–10.0

4.2 Seismic Mass — TBDY 2018 Madde 4.4.2

mt = Σ(Gi + n·Qi)/g

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

5. Seismic Design (TSC 2018)

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

Period rangeSaR(T)
0 ≤ T ≤ TA(0.4 + 0.6·T/TA)·SDS
TA ≤ T ≤ TBSDS
TB ≤ T ≤ TLSD1/T
T > TLSD1·TL/T²

TA = 0.2·TB, TB = SD1/SDS, TL = 6 s

5.2 Reduced Spectrum & Base Shear — Madde 4.3.3

Sad(T) = SaR(T)/Ra(T); for T ≥ TB: Ra(T) = R/I

Vt = mt·Sad(T1); minimum Vt,min = 0.04·mt·SDS·g

T1 ≈ Ct·H3/4: Ct = 0.07 (RC frames), 0.05 (walls/other)

5.3 Vertical Distribution — Madde 4.3.4

Fi = Vt·(mi·Hiα)/Σ(mj·Hjα)

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

6. Load Combinations (TSC 2018)

Comb.Equation
G11.4G
G21.2G + 1.6Q + 0.5(Qa or S)
G31.2G + 1.6(Qa or S) + max(0.5Q, 0.8W)
G41.2G + 1.6W + 0.5Q + 0.5(Qa or S)
G51.2G + 1.0Ed + 1.0Q + 0.3S
G60.9G + 1.6W
G70.9G + 1.0Ed

G=dead, Q=live, Qa=roof live, S=snow, W=wind, Ed=seismic.

7. Member Design (Strength)

7.1 Flexural Design — TS 500:2000 Cl. 7.1

μ = Md/(fcd·b·d²),  ω = 1 − √(1 − 2μ),  As = ω·fcd·b·d/fyd

As,min = 0.8·fctd·bw·d/fyd

7.2 Shear — TS 500:2000 Cl. 8

Vcr = 0.65·fctd·bw·d;  Vr,max = 0.22·fcd·bw·d

Stirrups: Vr = Vcr + (Asw/s)·fywd·d·cot α

7.3 Column — TS 500:2000 Cl. 7.4

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

8. Reinforcement Detailing (TSC 2018)

8.1 YDMÇ Beam Detailing — Madde 7.3

Sarılma bölgesi: 2h from face of column. se ≤ min(h/4, 8dbL, 24dbw, 200 mm)

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

8.2 YDMÇ Column Detailing — Madde 7.4

l0 = max(Hk/6, bk, hk, 500 mm). se ≤ min(b0/3, 6dbL, 150 mm)

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

8.3 SDMÇ Detailing — Madde 7.8 / 7.9

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

Column: se ≤ min(b0/2, 8dbL, 200 mm).

9. Special Topics

9.1 Interstorey Drift — TBDY 2018 Madde 4.9

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

ConditionLimit δi,max/hi
RC frames with brittle infill0.008
RC frames with ductile / no infill0.016

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).

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AISC 360-22 Structural Steel Design Guide

Comprehensive quick-reference for structural steel design per AISC 360-22, load combinations per ASCE 7-22, and seismic provisions per AISC 341-22. Covers LRFD and ASD design approaches.

1. Steel Material Properties

1.1 Common Structural Steel Grades

GradeFy (ksi/MPa)Fu (ksi/MPa)Primary use
ASTM A3636 / 25058–80 / 400–550Plates, angles, channels
ASTM A572 Gr. 5050 / 34565 / 450W-shapes, plates — most common grade
ASTM A99250 / 34565 / 450W-shapes only; Fy/Fu ≤ 0.85; preferred seismic
ASTM A500 Gr. B (rect. HSS)46 / 31758 / 400Rectangular / square HSS
ASTM A500 Gr. B (round HSS)42 / 29058 / 400Circular HSS (tubes)
ASTM A53 Gr. B35 / 24060 / 415Standard pipe sections
ASTM A108550 / 34565 / 450HSS — uniform wall; preferred for seismic
ASTM A913 Gr. 6565 / 45080 / 550High-strength W-shapes (Q&T)

1.2 Elastic Constants

PropertyUSSI
Modulus of elasticity (E)29,000 ksi200,000 MPa
Shear modulus (G)11,200 ksi77,200 MPa
Poisson's ratio (ν)0.30
Thermal expansion (α)6.5×10⁻⁶/°F11.7×10⁻⁶/°C
Unit weight490 pcf77.0 kN/m³

1.3 Expected (Probable) Strengths — Seismic (AISC 341-22 §A3.2)

GradeRyRt
A992, A572 Gr. 501.11.1
A361.51.2
A500 / A10851.31.3

Expected yield = Ry·Fy; expected tensile = Rt·Fu. Used for capacity design of connections and protected elements.

2. Section Classification — AISC 360-22 Table B4.1

Sections are classified as compact, noncompact, or slender based on element width-to-thickness ratios. For seismic design, highly ductile (λhd) and moderately ductile (λmd) apply per AISC 341-22 Table D1.1.

2.1 Flexure — W-shapes (Table B4.1b)

ElementRatio (λ)λp (compact)λr (noncompact)
Flange (b/t)bf/(2tf)0.38√(E/Fy)1.0√(E/Fy)
Web (h/tw)hc/tw3.76√(E/Fy)5.70√(E/Fy)

For A992 (Fy = 50 ksi): λp,flange = 9.15; λr,flange = 24.1; λp,web = 90.6; λr,web = 137.

2.2 Compression — Slender Limit (Table B4.1a)

Elementλr
W-shape flange (outstanding)0.56√(E/Fy)
W-shape web1.49√(E/Fy)
HSS rectangular wall1.40√(E/Fy)
HSS circular (D/t)0.15·E/Fy

2.3 Seismic Compactness (AISC 341-22 Table D1.1)

ElementHighly Ductile (λhd)Moderately Ductile (λmd)
W-shape flange0.30√(E/CaFy)0.38√(E/CaFy)
HSS rect. flange0.55√(E/Fy)0.64√(E/Fy)
HSS circular D/t0.053E/Fy0.076E/Fy

Ca = Pu/(φcFyAg) (LRFD). Highly ductile required for SMF beams/columns, EBF members outside link, BRBF beams/columns. Moderately ductile for IMF, SCBF braces.

3. Load Standards — ASCE 7-22

3.1 Dead Loads

Structural steel: 490 pcf / 77.0 kN/m³. Normal-weight concrete: 150 pcf / 23.6 kN/m³. Steel deck + concrete topping: ≈ 50–75 psf / 2.4–3.6 kN/m². Roofing/insulation: 5–15 psf / 0.24–0.72 kN/m².

3.2 Floor Live Loads — ASCE 7-22 Table 4.3-1

OccupancyLo (psf)Lo (kN/m²)
Residential (private rooms)401.92
Office areas502.40
Lobbies / first floors1004.79
Corridors above first floor803.83
Assembly — fixed seats602.87
Assembly — movable / standing1004.79
Retail — first floor1004.79
Storage — light1255.99
Storage — heavy25011.97
Parking (passenger vehicles)401.92

3.3 Live Load Reduction — ASCE 7-22 §4.7

L = Lo·(0.25 + 15/√(KLL·AT)) ≥ 0.50·Lo (single floor) or 0.40·Lo (columns / ≥2 floors). KLL = 4 (interior columns/two-way beams), 2 (edge beams / interior one-way beams). No reduction when Lo > 100 psf or for assembly areas.

4. Load Combinations — ASCE 7-22

4.1 LRFD Strength Combinations — ASCE 7-22 §2.3.1

#Combination
LC11.4D
LC21.2D + 1.6L + 0.5(Lr or S or R)
LC31.2D + 1.6(Lr or S or R) + (L or 0.5W)
LC41.2D + 1.0W + L + 0.5(Lr or S or R)
LC50.9D + 1.0W
LC61.2D + 1.0E + L + 0.2S
LC70.9D + 1.0E

4.2 ASD Combinations — ASCE 7-22 §2.4.1

#Combination
A1D
A2D + L
A3D + Lr (or S or R)
A4D + 0.75L + 0.75(Lr or S or R)
A5D + 0.6W (or 0.7E)
A6D + 0.75·0.6W + 0.75L + 0.75(Lr or S or R)
A70.6D + 0.6W
A80.6D + 0.7E

4.3 Resistance Factors (LRFD) / Safety Factors (ASD)

Limit Stateφ (LRFD)Ω (ASD)
Flexure (φb)0.901.67
Compression (φc)0.901.67
Tension — yielding (φt)0.901.67
Tension — rupture (φt)0.752.00
Shear (W-shapes, compact)1.001.50
Shear (general)0.901.67
Connections / welds0.752.00

For seismic E: E = ρ·QE ± 0.2·SDS·D (ASCE 7-22 §12.4.3), where ρ = redundancy factor (1.0 or 1.3 per §12.3.4).

5. Tension Members — Chapter D

5.1 Limit States — Design Tensile Strength

Tensile yielding (§D2a): Pn = Fy·Ag   (φt = 0.90)

Tensile rupture (§D2b): Pn = Fu·Ae   (φt = 0.75)

Ae = An·U — effective net area. Net area deducts hole diameter = dbolt + ⅛ in (3.2 mm) per §B4.3.

5.2 Shear Lag Factor U — Table D3.1

Connection typeU
All elements connected (plates)1.00
W-shape: flanges connected, bf ≥ ⅔d, ≥3 bolts/line0.90
W-shape: flanges connected, bf < ⅔d0.85
W-shape: web only, ≥4 bolts/line0.70
Angle: single row ≥4 bolts0.80
Angle: single row 2–3 bolts0.60
Alternative (general): U = 1 − x̄/L—

5.3 Block Shear Rupture (§J4.3)

Rn = 0.60·Fu·Anv + Ubs·Fu·Ant ≤ 0.60·Fy·Agv + Ubs·Fu·Ant

φ = 0.75. Ubs = 1.0 (uniform tension) or 0.5 (non-uniform). Governs for short connections and coped beams.

5.4 Slenderness

L/r ≤ 300 preferred for tension members (§D1). For structural integrity, L/r ≤ 240 typical for primary members.

6. Compression Members — Chapter E

6.1 Column Curve — Flexural Buckling (§E3)

Pn = Fcr·Ag   (φc = 0.90 / Ωc = 1.67)

Fe = π²·E / (KL/r)²   (Euler elastic buckling stress)

Inelastic buckling (KL/r ≤ 4.71√(E/Fy)):
Fcr = [0.658^(Fy/Fe)]·Fy

Elastic buckling (KL/r > 4.71√(E/Fy)):
Fcr = 0.877·Fe

Threshold KL/r for A992 (Fy=50 ksi): 4.71√(29000/50) = 113. Slenderness limit: KL/r ≤ 200 (AISC §E2).

6.2 Effective Length Factor K

ConditionK (ideal)K (recommended)
Pin–pin1.01.0
Fixed–fixed (no sway)0.50.65
Fixed–pin (no sway)0.70.80
Fixed–free (cantilever)2.02.10
Fixed–fixed (sway)1.01.20
Fixed–pin (sway)2.02.00

For Direct Analysis Method (DAM, Appendix 1): use K = 1.0 with reduced stiffness EI* = 0.8τbEI and notional loads.

6.3 Local Buckling Reduction (§E7)

Slender element sections: Pn reduced using Q = Qs·Qa. Qs for unstiffened elements (flanges, legs); Qa for stiffened elements (web, HSS walls). Q = 1.0 for non-slender sections.

7. Flexural Members — Chapter F

7.1 Doubly Symmetric Compact I-Shapes — §F2

Mp = Fy·Zx   (φb = 0.90 / Ωb = 1.67)

Yielding (Lb ≤ Lp): Mn = Mp

Inelastic LTB (Lp < Lb ≤ Lr):
Mn = Cb·[Mp − (Mp − 0.7FySx)·(Lb−Lp)/(Lr−Lp)] ≤ Mp

Elastic LTB (Lb > Lr):
Mn = Fcr·Sx ≤ Mp

7.2 Plastic and Elastic Unbraced Lengths

Lp = 1.76·ry·√(E/Fy)

Lr = 1.95·rts·(E / 0.7Fy)·√[Jc/(Sxho) + √((Jc/Sxho)² + 6.76·(0.7Fy/E)²)]

rts² = √(Iy·Cw)/Sx; c = 1.0 for doubly symmetric I-shapes.

7.3 Cb — Moment Gradient Factor

Cb = 12.5Mmax / (2.5Mmax + 3MA + 4MB + 3MC)

MA, MB, MC = moments at ¼, ½, ¾ points of unbraced segment. Cb = 1.0 for uniform moment (conservative). Typical values: uniform distributed load ≈ 1.14, midspan point load ≈ 1.32.

7.4 Other Sections

Section§Key limit states
HSS rectangularF7Yielding, FLB, WLB — no LTB (closed section)
HSS roundF8Yielding, local buckling (D/t)
Tees / double anglesF9LTB, FLB, stem local buckling
ChannelsF6LTB, FLB
Single anglesF10LTB, leg local buckling

→ Steel Beam Design Calculator

8. Shear Design — Chapter G

8.1 Unstiffened Webs — §G2.1

Vn = 0.6·Fy·Aw·Cv1   Aw = d·tw

For most W-shapes (A992): h/tw ≤ 2.24√(E/Fy) = 53.9 → Cv1 = 1.0 and φv = 1.00 / Ωv = 1.50. All AISC W-shapes in Gr. 50 satisfy this.

8.2 Stiffened Webs with Tension-Field Action — §G3

Vn = 0.6FyAw[Cv2 + (1−Cv2) / (1.15√(1+(a/h)²))]

a = clear distance between stiffeners. Not permitted for end panels or when Aw/(Afc+Aft) > 2.5.

8.3 HSS Shear — §G4

Vn = 0.6Fy·Aw·Cv2. For rectangular HSS: Aw = 2·h·t (two webs). φv = 0.90.

9. Combined Loading — Chapter H

9.1 Doubly / Singly Symmetric Members — §H1-1

When Pr/Pc ≥ 0.2 (high axial):

Pr/Pc + (8/9)·(Mrx/Mcx + Mry/Mcy) ≤ 1.0

When Pr/Pc < 0.2 (low axial):

Pr/(2Pc) + (Mrx/Mcx + Mry/Mcy) ≤ 1.0

Pc = φc·Pn (LRFD). Mcx, Mcy = φb·Mn for each axis.

9.2 Unsymmetric / General — §H2

fra/Fca + frbw/Fcbw + frbz/Fcbz ≤ 1.0

Stress-based check at critical point including combined biaxial bending stresses.

9.3 Combined Shear + Torsion (HSS) — §H3

√(Vr/Vc)² + (Tr/Tc)² ≤ 1.0

9.4 Second-Order Effects

Direct Analysis Method (DAM): notional loads Ni = 0.002Yi; reduced stiffness EI* = 0.8τbEI; K = 1.0 permitted. Alternative: Effective Length Method (Appendix 7) or First-Order Method (Appendix 8).

10. Connections — Chapter J

10.1 Bolt Types and Strengths — Table J3.2

BoltFnt (ksi)Fnv (ksi)*
A3074527
F3125 Gr. A3259054
F3125 Gr. A49011368

* Threads excluded from shear plane. If threads included: ×0.80.

10.2 Bearing Connections (φ = 0.75)

Bolt shear: Rn = Fnv·Ab

Bearing on material: Rn = 2.4·Fu·d·t (standard holes)
Tearout: Rn = 1.2·lc·t·Fu

10.3 Slip-Critical Connections — §J3.8

Rn = μ·Du·hsc·Tb·ns

μ = 0.35 (Class A), 0.50 (Class B), 0.70 (Class C). Tb from Table J3.1 (e.g., ¾" A325: 28 kips). φ = 1.00 (serviceability) or 0.85 (strength).

10.4 Fillet Welds (φ = 0.75)

Rn = Fw·Awe = 0.60·FEXX·0.707w·L·(1 + 0.50sin¹·⁵θ)

FEXX = 70 ksi for E70 electrodes. θ = 0° (longitudinal) to 90° (transverse — 50% stronger). Min. weld size per Table J2.4; max = t − 1/16 in for t ≥ ¼ in.

10.5 Block Shear Rupture — §J4.3

Rn = 0.60FuAnv + UbsFuAnt ≤ 0.60FyAgv + UbsFuAnt   (φ = 0.75)

Ubs = 1.0 (uniform tension), 0.5 (non-uniform, e.g., coped beams).

10.6 Bolt Spacing and Edge Distance — §J3

Min. spacing: 2⅔db (absolute); 3db preferred. Min. edge distance: varies by db and hole type (Table J3.4). Max. spacing: 12t or 6 in (whichever less) for painted/exposed members.

11. Seismic Design — AISC 341-22

11.1 System Types, R, Ωo, Cd — ASCE 7-22 Table 12.2-1

System RΩoCd SDC D/E height
Moment Frame Systems
Special Moment Frame (SMF)835.5NL
Intermediate Moment Frame (IMF)4.53435 ft
Ordinary Moment Frame (OMF)3.533NP
Braced Frame Systems
Special CBF (SCBF)625NL
Ordinary CBF (OCBF)3.2523.2535 ft
Eccentrically Braced Frame (EBF)824NL
Buckling-Restrained BF (BRBF)82.55NL
Special Plate Shear Wall (SPSW)726NL
Dual Systems
SMF + SCBF72.55.5NL
SMF + EBF82.54NL
SMF + BRBF82.55NL

NL = Not Limited; NP = Not Permitted in SDC D/E/F. Ωo = overstrength; Cd = deflection amplification.

11.2 Special Moment Frame (SMF) — AISC 341-22 §E3

  • Connections: prequalified per AISC 358-22 or qualified by test — §E3.6a
  • Protected zone: no attachments, holes, or notches in plastic hinge region — §E3.5c
  • Beam compactness: highly ductile (λhd) required — §D1.1
  • Strong column–weak beam: ΣM*pc/ΣM*pb > 1.0 (using Ry·Fy) — §E3.4a
  • Panel zone shear: checked per §E3.6e; doubler plates as needed
  • Continuity plates per §E3.6f when column flange local force transfer inadequate
  • Common prequalified connections: RBS, WUF-W, bolted extended end-plate (AISC 358)

11.3 Special CBF (SCBF) — AISC 341-22 §F2

  • Brace compactness: moderately ductile (λmd); KL/r ≤ 200 — §F2.5b
  • V/chevron braces: beam must resist unbalanced force (one brace buckles at Pcr, other reaches RyFyAg) — §F2.4b
  • Capacity design: columns/beams designed for brace forces using expected strengths — §F2.3
  • Gusset plate hinge clearance ≥ 2tgp — §F2.5c

11.4 Eccentrically Braced Frame (EBF) — AISC 341-22 §F3

  • Shear link: e ≤ 1.6Mp/Vp; rotation limit γp ≤ 0.08 rad — §F3.4b
  • Moment link: e ≥ 2.6Mp/Vp; rotation limit γp ≤ 0.02 rad
  • Members outside link: capacity designed for 1.25Ry·Vlink — §F3.3
  • Link stiffeners + full lateral bracing at both ends of link required

11.5 BRBF — AISC 341-22 §F4

BRB elements qualified by testing (§K3). Adjusted brace forces: ω·β·RyFyAsc (compression) and ω·RyFyAsc (tension), where ω ≈ 1.5, β ≈ 1.1 (test-based). Beams and columns: highly ductile (λhd).

12. Serviceability & Deflections

12.1 Deflection Limits — AISC 360-22 §L3

ConditionTypical limit
Floor beams — live load onlyL/360
Floor beams — total (L+D post-SDL)L/240
Roof beams — live/snow/windL/240
Cantilever beams — live loadL/180
Spandrel (masonry/glass)L/600–L/1000
Interstory drift — windH/400–H/600
Interstory drift — seismic (ASCE 7 §12.12)0.010H–0.025H (RC dep.)

12.2 Camber

Typically camber 75–80% of dead load deflection. Minimum practical ≈ ¾ in; no camber for spans < 25 ft.

12.3 Floor Vibration — AISC Design Guide 11

Acceleration limit for office/residential: ap/g ≤ 0.5%. Natural frequency fn ≈ π/2·√(g/Δtotal). Target fn > 4 Hz for typical steel framing; > 8 Hz preferred for sensitive environments.

12.4 Ponding — AISC 360-22 Appendix 2

Flat roofs: check Cp + 0.9·Cs ≤ 0.25 (simplified). Provide minimum ¼:12 slope or design for full ponding load.

12.5 Thermal Expansion

α = 6.5×10⁻⁶/°F (11.7×10⁻⁶/°C). Expansion joints for structures > 200 ft (60 m). ΔL = α·L·ΔT.

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