| 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]
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
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
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)
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
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]
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
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).
