------------ | :---------------------------------------------------------- | :--------------------------------------- | | Design life | 75 years (CSA S6) | 25-50 years (NBCC) | | Loading cycles | 50-250 million (ADTT × 365 × 75) | 20,000-2,000,000 | | Governing code | CSA S6 Clause 10 (primary) | CSA S16 Clause 26 | | Live load model | CL-625 truck + lane load | Crane wheel loads | | Critical details | Stiffener-to-web, cover plate ends, diaphragm connections | Web-to-flange fillet, stiffener brackets | | Stress range | From fatigue truck (CL-625-F) with 0.75×CL-625 axle weights | From crane wheel positions |

Stress Range Calculation for Highway Bridges

Per CSA S6, the fatigue stress range is calculated from the fatigue truck (CL-625-F):

• CL-625-F axle weights are 0.75 × CL-625 design truck axle weights
• Lane load is NOT included in fatigue stress range
• Dynamic load allowance (IM) = 0.25 (applied to fatigue truck)
• Multiple presence factor = 1.0 (single fatigue truck per bridge, regardless of number of lanes)

Calculation Procedure

1. Position the fatigue truck (CL-625-F) to produce maximum stress at the detail
2. Position the same truck to produce minimum stress (or zero if the truck moves off the span)
3. Calculate stress range: delta_sigma = sigma_max - sigma_min
4. Include dynamic load allowance: delta_sigma_design = (1 + IM) × delta_sigma

For continuous girders, the stress range at interior pier sections is typically from negative moment under truck (compression in bottom flange) to near-zero when the truck is far from the pier. This produces a full-reversal stress range that is particularly severe for welded stiffener and diaphragm details near the pier.

Effective Stress Range

For variable-amplitude loading (multiple truck types and configurations), the effective stress range per CSA S6 is:

Delta_sigma_eff = (sum(gamma_i × delta_sigma_i³))^(1/3)

Where gamma_i is the fraction of total cycles at stress range delta_sigma_i.

Detail Categories for Bridge Girders

Per CSA S16 Table 10, extended per CSA S6 Table 10.9:

Critical Bridge Details by Location

Cumulative Damage — Palmgren-Miner Rule

Per CSA S6 Clause 10.6.3, for bridges with variable traffic loading:

sum(n_i / N_i) ≤ 1.0

Where:

• n_i = number of cycles at stress range level i
• N_i = allowable number of cycles at stress range level i = C / delta_sigma_i³

For infinite-life design (preferred for highway bridges), all details shall satisfy:

delta_sigma_max ≤ CAFL / (1 + IM)

This is the simplest and most robust approach — if the maximum stress range (including impact) is below the constant amplitude fatigue limit, the detail has infinite life and no cumulative damage calculation is required.

ADTT and Cycle Calculation

Average Daily Truck Traffic (ADTT) determines the number of fatigue cycles:

The fatigue life N_i for a given stress range: N_i = C / delta_sigma³.

For Category C (C = 1.44 × 10¹²) at delta_sigma = 50 MPa: N = 1.44e12 / 50³ = 1.44e12 / 1.25e5 = 11.5 million cycles.

For a major urban arterial (68.4M cycles over 75 years), this detail would NOT satisfy infinite life and would need to be checked with cumulative damage.

Fatigue-Resistant Detailing for Bridges

Cover Plate Terminations

Partial-length cover plates on plate girder flanges create severe fatigue details at their termination. Mitigation:

1. Taper the cover plate end (1:2.5 slope minimum) to gradually transition stress
2. Use full-penetration groove weld at the cover plate end — improves category from E to C'
3. Extend cover plate to a point of low stress range (near dead-load contraflexure points)
4. Grind weld toes at the cover plate termination to improve category by one level
5. Consider bolted cover plates (drilled flange holes are Category B if drilled to close tolerance)

Transverse Stiffener Details

At pier sections (high negative moment, tension in bottom flange):

Cross-Frame Diaphragm Connections

Diaphragm connection plates welded to the girder web and bottom flange create fatigue Category E' details when the bottom flange is in tension (negative moment regions). Design strategies:

• Extend connection plate only to web — avoid welding to tension flange
• Use bolted diaphragm connections — bolt holes are Category B if drilled
• Locate diaphragms at low-stress-range locations — near contraflexure points in continuous girders

Worked Example — 3-Span Continuous Plate Girder Bridge

Given: 3-span continuous welded plate girder highway bridge: 30 m + 40 m + 30 m spans. 4 girders at 3.0 m spacing. Composite concrete deck (225 mm). ADTT = 5,000 per lane per day (major urban). 75-year design life. 350W steel (Fy = 350 MPa). Critical detail at pier: transverse intermediate stiffener welded to web and compression flange.

Step 1 — Determine Critical Section:

The intermediate pier section (over the interior support) experiences the maximum negative moment. Under the fatigue truck, the bottom flange cycles from tension (truck at/near pier) to near-zero compression (truck far from pier — dead load compression only).

Step 2 — Section Properties at Pier:

Plate girder section (negative moment, non-composite for fatigue — ignore deck contribution conservatively):

• Web: 1,500 mm × 14 mm
• Top flange: 400 mm × 30 mm (compression under dead load)
• Bottom flange: 450 mm × 40 mm (tension under dead load + live load)

I_x ≈ 28.3 × 10⁹ mm⁴. S_bottom = I_x / y_bottom = 28.3e9 / 790 = 35.8 × 10⁶ mm³.

Step 3 — Fatigue Truck Moment:

CL-625-F fatigue truck: axle loads = 0.75 × (50, 125, 125, 90, 90) = 37.5, 93.75, 93.75, 67.5, 67.5 kN. IM = 0.25.

Maximum negative moment at pier from fatigue truck (influence line analysis — truck placed to maximize negative moment with axles on both adjacent spans):

M_LL_max_pier ≈ 1,680 kN·m (approximate from 3D influence surface, single lane loaded, distributed to 1 girder via lever rule: 0.5 × dynamic moment = 840 kN·m per girder after distribution).

M_LL_min_pier ≈ 0 (truck on far span — negligible moment at this pier).

delta_M = 1.25 × (840 - 0) = 1,050 kN·m (including IM = 0.25).

Step 4 — Stress Range:

delta_sigma = delta_M / S_bottom = 1,050 × 10⁶ / 35.8 × 10⁶ = 29.3 MPa

Step 5 — Fatigue Check for Stiffener Detail (Category C):

CAFL_C = 69 MPa. delta_sigma = 29.3 ≤ 69 MPa. Detail has infinite fatigue life. OK.

Step 6 — Check Stiffener-to-Web Detail at Mid-Depth (Category C):

At web mid-depth, the stress from negative moment is lower. Detail is Category C for stiffener-to-web fillet. OK by inspection (lower stress range, same CAFL).

Step 7 — Check if Bolted Field Splice at 5 m from Pier is OK (Category B):

The field splice is in the bottom flange at 5 m from the pier. At this location, the dead load moment is lower and the live load moment is approximately 60% of the pier moment:

delta_sigma_splice = 0.60 × 29.3 = 17.6 MPa CAFL_B = 110 MPa. delta_sigma = 17.6 ≤ 110 MPa. Infinite life. OK.

Step 8 — Cumulative Damage Check:

Since the maximum stress range at the critical detail (stiffener at pier, Category C) is below CAFL (29.3 < 69 MPa), all details satisfy the infinite life criterion. No cumulative damage analysis is required.

Result: The welded plate girder satisfies CSA S16:24 and CSA S6 fatigue requirements for 75-year design life with ADTT = 5,000. All fatigue details have infinite life. No retrofits or special fatigue-resistant details are required at the current stress range levels.

Fatigue Retrofit for Existing Bridges

For existing bridges where fatigue cracks have developed, common retrofit strategies per CSA S6 Clause 14:

Frequently Asked Questions

How is highway bridge fatigue design different from building crane fatigue per CSA S16? The fundamental S-N curve approach is identical — both use CSA S16 Clause 26 detail categories and CAFL values. The key differences: (a) bridges use the CL-625-F fatigue truck with 0.75 × design axle weights, while buildings use actual crane wheel loads; (b) bridge design life is 75 years vs 25-50 for buildings, resulting in 10-100× more cycles; (c) bridge fatigue is governed by CSA S6 Clause 10 which adds requirements beyond CSA S16, including the ADTT classification system, lane distribution factors, and mandatory infinite-life design for fracture-critical members; (d) bridge fatigue details typically govern at the interior pier (negative moment, tension flange), while crane runway fatigue governs at midspan (positive moment, tension flange).

What is the fatigue truck and how does it differ from the design truck? The CL-625-F fatigue truck has axle weights equal to 0.75 × the CL-625 design truck axle weights. The fatigue truck: (a) is a single truck per bridge, regardless of lane count; (b) does NOT include the lane load (only axle loads); (c) uses IM = 0.25 dynamic load allowance; (d) is positioned to produce the maximum stress range at each detail. The 0.75 factor accounts for the fact that the heaviest trucks (those approaching the design truck weight) represent a small fraction of total truck traffic — the effective fatigue stress range from the mixed truck population is equivalent to a single reduced-weight truck.

When is cumulative damage analysis required instead of infinite-life design? Cumulative damage analysis (Palmgren-Miner rule) is required when: (a) the maximum stress range from the fatigue truck exceeds the CAFL for the critical detail, meaning finite life governs; (b) the bridge carries a variable traffic mix (e.g., high proportion of heavy industrial vehicles with different axle configurations than the standard fatigue truck); (c) for bridge evaluation (load rating) of existing bridges that do not satisfy current fatigue requirements; (d) when the bridge is on a route with documented overweight permit vehicles. For new bridges, infinite-life design (delta_sigma_max ≤ CAFL) is the preferred approach and is mandatory for fracture-critical members per CSA S6.

How do I address diaphragm connection plate fatigue in negative moment regions? Cross-frame diaphragm connection plates welded to the tension flange in negative moment regions create Category E' details (CAFL = 18 MPa), which are extremely difficult to satisfy for highway bridges. Solutions: (a) extend the connection plate to the web only, stopping 50 mm short of the tension flange — this changes the detail to Category C; (b) bolt the diaphragm connection plate to a gusset that is welded to the web only; (c) specify a cope hole at the flange-web intersection so the connection plate weld does not bridge onto the flange; (d) locate diaphragm bays at or near the dead-load contraflexure point where the stress range is minimized.

Related Pages

• Canadian Steel Fatigue Design — Clause 26
• CSA S16 Beam Design
• CSA S16 Weld Capacity
• Canadian Weld Inspection
• Canadian Steel Charpy Values
• CSA S16 Crane Support
• All Canadian References

This page is for educational reference. Highway bridge fatigue design per CSA S16:24 Clause 26 and CSA S6 Clause 10. Stress range calculations, detail categories, and cumulative damage assessment must be verified by a licensed Professional Engineer for the specific bridge geometry, traffic data (ADTT from provincial highway authority), and site conditions. Bridge fatigue design requires specialized expertise — this guide is an overview, not a substitute for detailed bridge engineering. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent PE/SE verification.

Design Resources

Reference pages

• CA Fatigue Design

Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.