AISC 360-22 Fatigue Design — Crane Runway Girder Category B Full Worked Example (Appendix 3)

Complete step-by-step fatigue design following AISC 360-22 Appendix 3 provisions (LRFD). This worked example covers a crane runway girder subject to cyclic loading from overhead crane operation: stress range determination, detail category classification per Table A-3.1, fatigue strength calculation (Equation A-3-1), cumulative damage assessment, and comparison with the constant amplitude fatigue threshold (CAFT). Every calculation step is documented with actual numerical values and code clause references.

Problem Statement

PRELIMINARY — NOT FOR CONSTRUCTION. All results presented here are for educational and reference use only. Values must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any design or construction.

A simply supported crane runway girder (W24x76, ASTM A992) spans 30 ft and serves a 20-ton overhead bridge crane. The crane operates 8 hours per day, 5 days per week, 50 weeks per year, making approximately 50 lift cycles per day. The maximum wheel load per side is 28.5 kips, and the minimum wheel load (empty hook) is 4.5 kips. The crane has two end trucks per bridge, with two wheels per end truck spaced at 8 ft centers. The structural detail of interest is the continuous fillet weld connecting the crane rail to the top flange — classified as Category B per AISC Table A-3.1.

Design parameters:

• Girder: W24x76, ASTM A992 (Fy = 50 ksi, Fu = 65 ksi)
• Span: 30 ft, simply supported
• Design life: 25 years
• Cycles per day: 50 (working days = 250/year)
• Maximum wheel load: P_max = 28.5 kips
• Minimum wheel load: P_min = 4.5 kips (return empty)
• Wheel spacing: 8 ft center-to-center
• Detail category: B (continuous fillet weld parallel to stress direction, base metal adjacent to weld toe)
• Redundancy: Non-redundant member (single girder supporting the entire crane load per side)

Section Properties (W24x76)

Step 1: Number of Loading Cycles

Design life: 25 years × 250 working days/year × 50 cycles/day = 312,500 cycles.

AISC Appendix 3 requires fatigue evaluation when the number of cycles exceeds 20,000 (Section 3.2). At 312,500 cycles, fatigue evaluation is required.

Since 312,500 cycles < 2,000,000 (the upper bound for high-cycle fatigue), we use the finite-life S-N curve approach.

Step 2: Stress Range Calculation

Step 2a: Maximum and Minimum Moments

The crane runway girder is loaded by two moving wheel loads (from the two wheels on one side of the crane bridge). The maximum moment occurs when the loads are positioned for maximum bending effect. For two equal loads spaced at 8 ft on a 30 ft simply supported span:

Maximum moment under the load closest to midspan when the loads are positioned such that the center of gravity of the loads and the nearest load are equidistant from the beam centerline. For two equal point loads P at spacing a = 8 ft on a simply supported beam of span L = 30 ft:

Position of resultant from left load: at load centroid (midpoint between loads) = 4 ft from each load.

For maximum moment: place the loads so the beam centerline bisects the distance between the resultant and the nearest load.

• Total load per side: 2 × P_max = 2 × 28.5 = 57.0 kips
• Left reaction: R_L = (57.0 × (30 - 4 - 30/2 + distance correction))

Using influence line method or moment position for two moving loads:

Distance from left support to left wheel: x = (L - a/2)/2 = (30 - 4)/2 = 13 ft
Left reaction: R_L = [28.5 × (30 - 13) + 28.5 × (30 - 21)] / 30
R_L = [28.5 × 17 + 28.5 × 9] / 30 = [484.5 + 256.5] / 30 = 741 / 30 = 24.7 kips

Moment under left wheel (at 13 ft):
M_max,P = R_L × 13 - 0 = 24.7 × 13 = 321.1 kip-ft

Step 2b: Impact Factor

Per ASCE 7-22 Section 4.9.4 for overhead crane loads, apply a vertical impact factor:

I = 25% for cab-operated or remotely operated bridge cranes.

M_max_with_impact = 321.1 × 1.25 = 401.4 kip-ft

Step 2c: Minimum Moment (Empty Hook Return)

P_min = 4.5 kips
R_L_min = [4.5 × 17 + 4.5 × 9] / 30 = [76.5 + 40.5] / 30 = 117 / 30 = 3.9 kips
M_min = 3.9 × 13 = 50.7 kip-ft

No impact factor applied for minimum load (empty hook moves slowly).

Step 2d: Stress Range

The stress at the top flange (where the crane rail weld attachment is located):

S_top = M / Sx

f_max = M_max / Sx = 401.4 × 12 / 176 = 4,816.8 / 176 = 27.37 ksi
f_min = M_min / Sx = 50.7 × 12 / 176 = 608.4 / 176 = 3.46 ksi

Stress range:

Delta_f_SR = f_max - f_min = 27.37 - 3.46 = 23.91 ksi

Step 3: Fatigue Category and Allowable Stress Range (AISC Appendix 3)

Step 3a: Detail Category Classification

From AISC 360-22 Table A-3.1 (Selected Details):

The crane rail is attached with a continuous fillet weld parallel to the direction of bending stress. Per Table A-3.1, Detail 3.2: "Base metal at toe of transverse stiffener-to-flange welds and at toe of transverse stiffener-to-web welds" is Category C. For the specific weld detail of a continuous rail-to-flange fillet weld, reference to Table A-3.1, detail for "base metal adjacent to continuously welded longitudinal attachment" — Category B or C depending on whether the attachment has a smooth transition radius.

For this example, the rail attachment is a continuously welded bar with a square end (no transition radius at the end of the weld). Per Section 5.3 of AISC 360-22 Appendix 3, fillet-welded attachments longer than 4 in. in the direction of stress that terminate without a smooth transition radius are classified as:

Category B: When the weld toe at the end of the attachment is ground to a smooth transition with a radius of at least 2 in.

Category C: When the attachment terminates without ground transition.

Assuming Category B treatment (ground transition): Detail Category = B.

Step 3b: Constant Amplitude Fatigue Threshold (CAFT)

For Category B, the CAFT per Table A-3.1:

F_TH = 16 ksi

The CAFT represents the stress range below which infinite life can be assumed (stress range below this value does not cause fatigue crack propagation). If Delta_f_SR ≤ F_TH, the detail has infinite fatigue life.

Check: Delta_f_SR = 23.91 ksi > F_TH = 16 ksi. Fatigue evaluation required for finite life.

Step 4: Fatigue Strength (AISC Equation A-3-1)

For loading conditions that do not meet the CAFT exemption, the design fatigue strength for the number of stress range cycles is computed per AISC Equation A-3-1:

(Delta_F)_n = (C_f / n_SR)^(1/m)

where:

• C_f = fatigue constant for the detail category (from AISC Table A-3.1)
• n_SR = number of stress range fluctuations (312,500 cycles)
• m = slope of the S-N curve = 3.0 for all categories (AISC Appendix 3 Section 3.4)

Category B Fatigue Constant:

From AISC Table A-3.1, the fatigue constant Cf for Category B:

C_f = 120 × 10^8 (units of ksi^3)

Alternatively, using the S-N curve relationship at 2,000,000 cycles (the constant amplitude fatigue limit or CAFL):

For Category B: F_TH at 2 × 10^6 cycles = 16 ksi (CAFT for infinite life is lower, but the CAFL at 2M cycles establishes Cf).

If more precise: Table A-3.1 lists thresholds. The fatigue constant Cf for m = 3 is:

C_f = F_TH^3 × 2 × 10^6 = 16^3 × 2 × 10^6 = 4,096 × 2 × 10^6 = 8.192 × 10^9

Wait — AISC uses different reference values. Per Table A-3.1 directly: For Category B, the fatigue design parameters per Equation A-3-1 with m = 3:

C_f × 10^8 for Category B = 120 × 10^8 = 1.20 × 10^10

Using the AISC Table A-3.1 value:

(Delta_F)_n = (C_f / n_SR)^(1/m) = (120 × 10^8 / 312,500)^(1/3)
            = (12,000,000,000 / 312,500)^(1/3)
            = (38,400)^(1/3)

(38,400)^(1/3): Cube root of 38,400:
30^3 = 27,000
33^3 = 35,937
34^3 = 39,304

(Delta_F)_n ≈ 33.7 ksi

Step 4a: Design Fatigue Strength

Per AISC Appendix 3, Section 3, the design fatigue strength uses a resistance factor:

phi × (Delta_F)_n   where the resistance factor for fatigue is not explicitly defined

AISC 360-22 uses an allowable stress approach for fatigue per Section A-3. The required fatigue strength is:

Delta_f_SR ≤ (Delta_F)_n

with no phi factor applied directly to the fatigue equation (the safety margin is built into the S-N curve through the fatigue constant Cf, which represents a lower-bound curve at two standard deviations below the mean).

Check:

Delta_f_SR = 23.91 ksi ≤ (Delta_F)_n = 33.7 ksi → OK

Step 5: Cumulative Damage Assessment (Miner's Rule)

Per AISC Appendix 3 Section 3.7, when stress ranges vary (such as crane operations with different load magnitudes), the cumulative damage ratio D ≤ 1.0 must be satisfied. For a simplified case with two loading bins:

Load Case 1 (full capacity lift, 30% of cycles):

• f_max,1 = 27.37 ksi, f_min,1 = 0 (worst case with zero when crane is not over the section)
• Delta_f_SR,1 = 27.37 ksi
• n_1 = 0.30 × 312,500 = 93,750 cycles

Load Case 2 (partial load, 70% of cycles):

• Nominal wheel load at 50% capacity: P = 0.50 × 28.5 = 14.25 kips
• M_max,2 = 321.1 × (14.25/28.5) × 1.25 = 200.7 kip-ft
• f_max,2 = 200.7 × 12 / 176 = 13.68 ksi
• f_min,2 = 3.46 ksi (empty hook)
• Delta_f_SR,2 = 13.68 - 3.46 = 10.22 ksi
• n_2 = 0.70 × 312,500 = 218,750 cycles

Allowable cycles at each stress range per Equation A-3-1 inverted:

N_i = C_f / (Delta_f_SR)^3

For Case 1: N_1 = 120 × 10^8 / (27.37)^3 = 12,000,000,000 / 20,492 = 585,600 cycles
For Case 2: N_2 = 120 × 10^8 / (10.22)^3 = 12,000,000,000 / 1,067 = 11,246,000 cycles

Note: For Case 2, Delta_f_SR,2 = 10.22 ksi < F_TH = 16 ksi. Since the stress range is below the CAFT, the CAFT exemption applies for this load level — unlimited cycles are permitted for stress ranges below the threshold. The contribution to fatigue damage from Case 2 is zero.

Miner's cumulative damage ratio:

D = n_1 / N_1 + n_2 / N_2 = 93,750 / 585,600 + 0 = 0.16 ≤ 1.0

Check: D = 0.16 < 1.0. Cumulative fatigue damage OK.

The infinite fatigue life treatment for cycles below CAFT significantly reduces the cumulative damage.

Step 6: Additional Considerations for Crane Runway Girders

• Lateral Loads: Crane runways also experience lateral loads from crane bridge acceleration and skewing (CMAA 70, ASCE 7). Lateral bending in the top flange increases the stress range and must be included in fatigue checks. For a 20-ton crane, lateral load = 20% of lifted load + trolley weight = approximately 5 kips per side, producing additional weak-axis bending stress.
• Local Flange Bending: Wheel loads produce local bending in the top flange between the web and the flange tip. This local bending stress range must be combined with the global bending stress range per AISC Design Guide 3. Local bending is checked per AISC J10 when the wheel load is treated as a concentrated force.
• Buckling Restraint: The top flange of a crane runway girder must be restrained against lateral-torsional buckling over the full unbraced length. A channel cap or continuous lateral restraint from the crane rail attachment may be required.
• Deflection Limits: Crane runway girders are subject to stringent vertical and lateral deflection limits per CMAA 70: vertical L/600 for electric overhead traveling cranes, and lateral L/400.
• Cyclic Softening: At the Category B detail adjacent to continuous fillet welds, residual tensile stresses from the welding process can approach the yield stress. These residual stresses are accounted for in the S-N curve data that forms the basis of the AISC fatigue provisions. The stress range (not the mean stress) drives fatigue behavior because residual welding stresses effectively center the stress cycle near yield regardless of applied mean stress.

Summary of Design Checks

The W24x76 crane runway girder with continuous fillet weld detail (Category B, ground transition) achieves adequate fatigue life for the 312,500-cycle, 25-year design life at a damage ratio of 0.16.

Frequently Asked Questions

What is the difference between fatigue Category A, B, C, D, E, and E' details?

AISC 360-22 Appendix 3 Table A-3.1 classifies structural details into stress categories A through E' based on fatigue resistance. Category A (CAFT = 24 ksi) includes plain rolled surfaces with no attachments. Category B (CAFT = 16 ksi) includes full-penetration groove welds ground flush and bolted connections. Category C (CAFT = 10 ksi) includes transverse stiffeners welded to the flange. Category D (CAFT = 7 ksi) includes end welds on cover plates. Category E (CAFT = 4.5 ksi) includes fillet welds parallel to stress. Category E' (CAFT = 2.6 ksi) are the most fatigue-sensitive.

How is the stress range calculated for fatigue design under AISC 360?

Per AISC 360-22 Appendix 3 Section 3.4, the required fatigue strength is based on the stress range from structural analysis using the loads specified in the applicable code. For LRFD, the required stress range Delta_f_SR is calculated using factored fatigue loads per ASCE 7 or the governing standard. For crane runways, this is computed from the maximum and minimum wheel loads, including impact factors per CMAA 70.

When can fatigue design be omitted for steel structures?

Per AISC Appendix 3 Section 3.2, fatigue need not be considered when: the number of cycles is less than 20,000, the structure is not subjected to repeated loading, or the stress range is below the CAFT (constant amplitude fatigue threshold) for the applicable detail category. For most building structures without cranes, fatigue is not a governing limit state.

How does the constant amplitude fatigue threshold (CAFT) work?

The CAFT is the stress range value below which a detail has essentially infinite fatigue life. It is a stress range threshold, not a cycle threshold. If the applied stress range Delta_f_SR is less than or equal to F_TH for the applicable detail category, no fatigue evaluation is required regardless of the number of cycles. This is the basis for the infinite-life design approach and the reason many building details (with low stress ranges) are exempt from fatigue evaluation.

What is the effect of the number of loading cycles on fatigue strength?

Per the S-N curve relationship (Delta_F)_n = (C_f / n)^(1/3), doubling the number of cycles reduces the allowable stress range by the cube root of 2, or approximately 0.79. This inverse cubic relationship means increasing the design life from 25 to 50 years (doubling cycles) would reduce the allowable stress range from 33.7 ksi to 26.8 ksi, still above the 23.91 ksi demand. For extremely high-cycle applications (storage rack systems, mechanical equipment supports), the cumulative damage must be carefully evaluated.

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