bridge-fatigue

name	bridge-fatigue
description	Bridge fatigue design and assessment — AASHTO fatigue detail categories (A through F'), constant amplitude fatigue limit (CAFL), stress range Δσ and load-induced vs. distortion-induced fatigue, fatigue life calculation (AASHTO S-N model Δσⁿ×N = A), infinite life design, rainflow counting of stress spectra, fracture mechanics approach (Paris law), inspection-based remaining life assessment, weld fatigue classifications, NCHRP Report 721, FHWA Bridge Inspector's Manual, ASCE 7 fatigue loads, AASHTO LRFD Bridge Design Specification.
metadata	{"priority":7,"promptSignals":{"phrases":["bridge fatigue","AASHTO fatigue","detail category","CAFL","stress range"],"minScore":3}}

Bridge Fatigue Design and Assessment — Complete Skill

Fatigue Loading

AASHTO Fatigue Truck (HL-93 Fatigue Load)

Design fatigue truck: Single HS20 truck (3 axle; 72 kip = 320 kN total) with 30 ft (9 m) rear axle spacing (not 14 ft variable) Fatigue load factor: γ_f = 0.75 (LRFD) Dynamic load allowance: IM = 15% for fatigue (not 33%) Fatigue stress range: Δσ = (stress_due_to_fatigue_truck) × γ_f × (1 + IM)

Average Daily Truck Traffic (ADTT): ADTT_SL = ADTT × p [ADTT_SL = trucks per lane; p = fraction in single lane; from AASHTO Table C3.6.1.4.2-1] Typical: p = 1.0 for 1-lane; 0.85 for 2-lanes; 0.80 for 3+ lanes

Equivalent stress cycles per truck passage: n = cycles per truck passage from AASHTO Table 6.6.1.2.5-2 (depends on span length and influence line shape) n = 1.0 for simple spans (most details); 1.5–2.0 for continuous negative moment regions

Total cycles in design life: N = n × ADTT_SL × 365 × Y [Y = design life [years]; typically Y = 75 years for new bridges]

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AASHTO Fatigue Detail Categories

S-N Model

AASHTO S-N equation: Δσ^n × N = A [Δσ = stress range [ksi or MPa]; N = cycles; A = constant; n = slope] For AASHTO: n = 3 (standard); log(Δσ) = (log(A) − log(N)) / 3

AASHTO detail categories (AASHTO LRFD Table 6.6.1.2.3-1):

Category	A [ksi³ × 10⁸]	CAFL [ksi]	CAFL [MPa]	Application
A	250	24	165	Base metal, no holes; rolled I-beams
B	120	16	110	Base metal at welds, butt welds (ground flush)
B'	61	12	82	Base metal at gussets, stiffeners not welded to tension flange
C	44	10	69	Fillet welds to flange; transverse stiffeners
C'	44	12	82	Base metal at short attachments (< 2 in)
D	22	7	48	Base metal at attachments 2–4 in (50–100 mm)
E	11	4.5	31	Attachments > 4 in (100 mm) on tension flange
E'	3.9	2.6	18	Shear connectors; end of cover plates

Critical insight: Category E and E' → very low CAFL; these details should be eliminated in design if possible

Constant Amplitude Fatigue Limit (CAFL)

Infinite life design: If Δσ_max < CAFL for that detail category → infinite fatigue life (N → ∞) AASHTO: design for infinite life when (ADTT)_SL > 20,000 trucks/day (heavy traffic)

Finite life design (when Δσ > CAFL): N_life = A / Δσ^3 [design life cycles from S-N] If N_life > N_demand = n × ADTT_SL × 365 × 75 → acceptable

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Rainflow Cycle Counting

Variable Amplitude Stress Spectra

Rainflow counting algorithm (ASTM E1049): Real bridges experience variable amplitude loading (different trucks, weights, speeds) Rainflow counting: reduces complex time history to set of (Δσᵢ, nᵢ) pairs (stress range, cycle count)

Miner's rule for cumulative damage: D = Σ(nᵢ / Nᵢ) [nᵢ = applied cycles at Δσᵢ; Nᵢ = fatigue life at Δσᵢ from S-N = A/Δσᵢ³] D ≥ 1.0: failure (Miner's critical); design so D < 1.0 over design life

Equivalent constant amplitude stress range Δσ_eq: Δσ_eq = [Σ(γᵢ × Δσᵢ³)]^(1/3) [γᵢ = nᵢ/N_total; weighted cube root; accounts for non-linear S-N slope] Use Δσ_eq to check against CAFL or compute N_life

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Fracture Mechanics Approach

Crack Growth in Bridge Details

Paris Law: da/dN = C × (ΔK)^m [crack growth per cycle; ΔK = ΔK_max − ΔK_min = Δσ × Y × √(πa)] For structural steel: C ≈ 6.9 × 10⁻¹² [m/cycle, ΔK in MPa√m]; m ≈ 3

Stress intensity factor range: ΔK = F × Δσ × √(πa) [F = geometry correction factor; a = crack half-length or depth] For edge crack in plate: F ≈ 1.12; for embedded elliptical crack: F = f(a/c, a/t)

Life integration: N = ∫(a₀ to a_c) da / [C × (Δσ × F × √(πa))^m] a₀ = initial crack size (detectable limit; typically 1–2 mm for UT); a_c = critical crack (K_max = K_IC or net section yield) For m = 3: N = 2(a_c^(−1/2) − a₀^(−1/2)) / [C × (Δσ × F × √π)³]

Inspection interval from fracture mechanics: N_inspect = N_total / 2 (rule of thumb; re-inspect when crack halfway from a₀ to a_c) Or: use damage-tolerant approach with specific NDE detection probability POD(a)

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Distortion-Induced Fatigue

Secondary Stress Mechanism

Distortion-induced fatigue: caused by out-of-plane bending of web (cross-frame, diaphragm connections) Not captured by primary design forces; most common fatigue failure mode in older steel bridges

Web gap region: Short unstiffened web gap between cross-frame and web (100–300 mm); forced deformation from differential deflections → high local stress Retrofit: extend stiffener to flange to eliminate web gap (stiffen out-of-plane); or use high-strength bolts to slip-critical connection

Identification: Visible cracking at web-to-flange fillet welds; typically horizontal cracks at web gap Δσ in web gap >> primary design stress range

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Load-Induced Fatigue Design Check

AASHTO LRFD Article 6.6.1.2

Design check: γ_f × (Δσ)_n ≤ (ΔF)_n [(ΔF)_n = nominal fatigue resistance]

Finite life: (ΔF)_n = (A/N)^(1/3) [where N = 365 × Y × n × (ADTT)_SL]

Infinite life: (ΔF)_n = CAFL (if N_design > N_CAFL_threshold) N_CAFL_threshold: from S-N curve intersection at CAFL = (A/CAFL³) cycles

Special fatigue limit: For Category C transverse stiffeners: (ΔF)_n = 0.15 ΔF_TH [special provision to prevent web fatigue cracking]

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Field Inspection and Remaining Life Assessment

Inspection Protocol

FHWA Inspection: biennial bridge inspection per 23 CFR 650 (National Bridge Inspection Standards) Fracture critical members (FCM): inspected every 24 months; hands-on if accessible; enhanced NDT if suspect

NDE methods for bridge fatigue cracks: Magnetic particle (MT): surface weld cracks; quick; requires cleanup Eddy current: surface cracks at welds; no contact; fast for flanges Ultrasonic (UT): subsurface cracks in welds or base metal; phased array preferred for complex geometry

Remaining life calculation: If crack a_found detected: remaining life N_remain = Paris integration from a_found to a_c Compare N_remain to inspection interval → determine if repair required or monitor

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Standards

Standard	Scope
AASHTO LRFD Bridge Design Spec (9th ed.)	Fatigue design provisions (Article 6.6)
AASHTO Manual for Bridge Evaluation	Remaining fatigue life rating
NCHRP Report 721	Fatigue evaluation of steel bridges
ASTM E1049	Rainflow cycle counting
AWS D1.5	Bridge welding code
FHWA SI&A (23 CFR 650)	Bridge inspection standards
BS 7910	Fracture mechanics assessment (compatible approach)
ISO 5261 / IIW recommendations	Fatigue of welded joints

Output

Provide: bridge detail (member: girder/cross-frame/connection; category per AASHTO Table 6.6.1.2.3-1; category A/B/C/D/E/E'; detail description), AASHTO loading (ADTT; ADTT_SL = ADTT×p; n = cycles/passage; Y = 75 years; N = n×ADTT_SL×365×Y [cycles]), stress range (Δσ from fatigue truck analysis: unfactored [ksi]; ×γ_f=0.75 ×(1+0.15) = effective Δσ [ksi]), fatigue resistance (infinite or finite life?; if finite: (ΔF)_n = (A/N)^(1/3) [ksi]; if infinite: (ΔF)_n = CAFL [ksi]; detail A value [ksi³×10⁸]), design check (γ_f×Δσ ≤ (ΔF)_n? [ksi vs ksi]; pass or fail), variable amplitude (if spectrum: Δσ_eq = [Σ(γᵢΔσᵢ³)]^(1/3); Miner's D = Σ(nᵢ/Nᵢ) ≤ 1.0?), fracture mechanics (if crack found: a₀ [mm]; a_c [mm] from K_IC; N_remain from Paris integration; inspection interval [months]), distortion-induced (web gap identified? length [mm]; retrofit recommendation: extend stiffener / connection plate), and applicable standard (AASHTO LRFD Article 6.6.1.2; AWS D1.5 for weld quality; FHWA for inspection intervals).