Fatigue Evaluation of Steel Bridges (2012)

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F-1 APPENDIX F FATIGUE EXAMPLES F-1

Example 1: Note: The example presented below is a modification of the existing example currently in the Section 7 of the Manual for Bridge Evaluation (2011). It is assumed that the bridge structure carries two lanes of traffic in one direction only with a total ADTT of 1000 trucks. Detail: Welded cover plates on tension flanges (Detail Category E) Fatigue Load Stress Range fLL+IM = f = 4.56 ksi at cover plate weld Nominal fatigue resistance for infinite life ( F)TH = 2.6 ksi for Detail Category E LRFD Table 6.6.1.2.5-3 Infinite-Life Fatigue Check MBE 7.2.4 Span Length L = 65 ft ADTT (One Direction, all lanes) = 1000 Number of lanes nL = 2 [ADTT]PRESENT = 1000 Rp = 0.988 + 6.87x10-5 (L) + 4.01x10-6 [ADTT]PRESENT + 0.0107 / (nL) = 0.988 + (6.87x10-5) (65) + (4.01 x 10-6) (1000) + 0.0107/2 = 1.0018 MBE 7.2.2.1 Rsa = 1.0 MBE Table 7.2.2.1-1 Rst = 1.0 Rs = Rsa x Rst = 1.0 F-2 NCHRP 12-81 Fatigue Examples Using Section 7 – Fatigue Evaluation of Steel Bridges ( f)eff = (Rp)(Rs)( fFATIGUE II)=(1.0018)(1.0)(0.75)(4.56) = 3.43 ksi MBE 7.2.2

F-3 ( f)max = (Rp)( fFATIGUE I) = (1.0018)(1.50)(4.56) = 6.85 ksi > 2.6 ksi MBE 7.2.4 Thus, ( f)max > ( F)TH. The detail does not possess infinite fatigue life. Evaluate fatigue life using procedures given in Section 7 of AASHTO’s The Manual for Bridge Evaluation. CALCULATION OF FATIGUE LIFE Fatigue life determination will be based upon the finite fatigue life. 1 3log (1 ) 1365 ( ) [( ) ] log(1 ) aR SL effPRESENT R A g g n ADTT f Y g MBE 7.2.5.1 [ADTT]PRESENT (One Direction) = 1000 [(ADTT)SL]PRESENT = 0.85(1000) = 850 LRFD Table 3.6.1.4.2-1 Traffic Growth Rate g: 2% Bridge Age a: 43 years Assume Evaluation 1 Life to be used for bridge assessment. Hence, RR = 1.3 MBE Table 7.2.5.1-1 ( f)eff = 3.43 ksi A = 3.9x108 ksi3 LRFD Table 6.6.1.2.5-1 n = 1.0 simple span girders with L > 40 ft. LRFD Table 6.6.1.2.5-2 8 43 1 3 1.3(3.9 10 )log (0.02)(1 0.02) 1 365(1)(850)(3.43) 53 years log(1 0.02) x Y

F-4 CALCULATION OF FATIGUE SERVICEABILITY INDEX Fatigue Serviceability Index Y aQ GRI N MBE 7.2.6.1 No. of load paths (in this case, girders) = 4 G = 1.0 MBE Table 7.2.6.1-1 No. of Spans = 1 (Simple Span) R = 0.90 MBE Table 7.2.6.1-2 N = (larger of 100 or Y) = 100 Assuming that the bridge is on an Interstate Highway, I = 0.9 MBE Table 7.2.6.1-3 Q = 53 43 (1.0)(0.9)(0.9) 0.08 100 The serviceability rating and assessment outcome are provided in MBE Table 7.2.6.2-1 for various ranges of the Fatigue Serviceability Index. In this example, a Q value of 0.08 means that the bridge will be rated as ‘Poor’ from a fatigue standpoint and the assessment outcome would be ‘Assess Frequently’. The bridge owner will need to define how often to increase the inspection frequency based upon the importance of the structure.

F-5 Example 2: (Retrofit fatigue evaluation) In order to improve the fatigue life of the detail given in Example 1, a retrofit option would be to modify the welded cover plate detail by adding a slip-critical bolted end plate connection. In this case, based upon data available in published research, the engineer can re-classify the retrofitted detail as category B. Detail: Bolted splice for end cover plates on tension flanges (Detail Category B) Fatigue Load Stress Range fLL+IM = f = 4.56 ksi at cover plate weld Nominal fatigue resistance for infinite life ( F)TH = 16 ksi for Detail Category B LRFD Table 6.6.1.2.5-3 Infinite-Life Fatigue Check MBE 7.2.4 Span Length L = 65 ft [ADTT]PRESENT (One Direction, all lanes) = 1000 Number of lanes nL = 2 [ADTT]PRESENT = 1000 Rp = 0.988 + 6.87x10-5(L) + 4.01x10-6 [ADTT]PRESENT + 0.0107 / (nL) = 0.988 + (6.87x10-5) (65) + (4.01x10-6) (1000) + 0.0107/2 = 1.0018 MBE 7.2.2.1 Rsa = 1.0 MBE Table 7.2.2.1-1 Rst = 1.0 Rs = Rsa x Rst = 1.0 ( f)eff = (Rp)(Rs)( fFATIGUE II)=(1.0018)(1.0)(0.75)(4.56) = 3.43 ksi MBE 7.2.2 ( f)max = (Rp)( fFATIGUE I) =(1.0018)(1.50)(4.56) = 6.85 ksi < 16 ksi MBE 7.2.4 Thus, ( f)max < ( F)TH. Hence, the detail possesses infinite fatigue life.

F-6 Example 3: (Floorbeam Fatigue) A two-girder bridge with floorbeams and stringers has welded cover plates attached to the floorbeam flanges. The cover plate detail is investigated for fatigue susceptibility. It can be assumed that the width between girders is 40 ft, the floorbeams spaced at 25 ft centers, and the stringers placed at 8 ft center to center. The bridge, which was built in 1962, has 3 lanes with traffic in one direction and a span length of 100 ft. Figure 1: Bridge cross-section and lane widths.

F-7 The AASHTO LRFD design truck as specified in LRFD Article 3.6.1.4 and shown in the figure below shall be used to determine the critical stress range. Assume that the floorbeam spacing is 25. Also assume that the truck axle loads are transferred to the floor beams as simple beams. Hence, maximum Truck Load to the floorbeams can be calculated by considering various positions of the truck axles: k k 25' 14 '32 8 35.52 Controls (One 32 axle over floorbeam) 25' 25' 5' 25' (14 ' 5') or 32 8 27.52 (One 32 axle 5ft on one side of floorbeam, 25' 25' k k k k k k k k and 8 axle on opposite side) 32 or (25' (30 ' )) (25' ) 25.6 (Floorbeam between two 32 axles) 25' k kx x Fatigue Truck Wheel Load = 0.5 (35.52) = 17.76k The fatigue truck has been positioned such that the wheel load of the axle lies just above the location where the cover plate detail begins. This is done in order to maximize the stress range for the worst position of the fatigue truck load. Figure 2: Distribution of wheel loads to stringers. For distribution of 8k axle and 32k axle to stringers,

F-8 1 11 1Stringer S1 Reaction = 4 (12 10) 16 (12 10) 4.44 8 25 8 1 11 1Stringer S2 Reaction 4 ((10 4) (20 16)) 16 ((10 4) (20 16)) 22.2 8 25 8 1Stringer S3 Reaction 4 16 8 k k k k k k k 11 112 16 16 12 8.88 25 8 1Floorbeam Reaction@Girder 36(4.44 ) 28(22.2 ) 20(8.88 ) 40 23.98 Floorbeam Live-Load Moment at x=10' =23.98 (10 ') 4.44 k k k k k k k '(6 ') 213.12k k Assume that the elastic section modulus of the floorbeam just beyond the cover plate is 1470 in3. Stress Range = Mr/Sx = 12 “/’ x 213.12k’ / 1470 in3 = 1.74 ksi Impact factor IM = 15% LRFD Table 3.6.2.1-1 Critical Fatigue Section: Check fatigue at termination of bottom flange welded cover plate Fatigue Case E Use: A = 3.9x108 LRFD Table 6.6.1.2.5-1 n = 1.0 LRFD Table 6.6.1.2.5-2 Threshold = 2.6 ksi LRFD Table 6.6.1.2.5-3 Hence, ( F)TH = 2.6 ksi Stress Ranges – f = fLL+IM = LL + I = (1.00 + 0.15) x 1.74 LRFD Table 3.6.2.1-1 = 2.0 ksi Nominal fatigue resistance for infinite life ( F)TH = 2.6 ksi for Detail Category E LRFD Table 6.6.1.2.5-3

F-9 Infinite-Life Fatigue Check MBE 7.2.4 Rp = 1.0 for transverse members MBE 7.2.2.1 Rsa = 1.0 MBE Table 7.2.2.1-1 Rst = 1.0 Rs = Rsa x Rst = 1.0 ( f)eff = (Rp)(Rs)( fFATIGUE II)=(1.0)(1.0) (0.75)(2.0) = 1.5 ksi MBE 7.2.2 ( f)max = (Rp)( fFATIGUE I) = (1.0)(1.50)(2.0) = 3.0 ksi > 2.6 ksi MBE 7.2.4 Thus, ( f)max > ( F)TH. The detail does not possess infinite fatigue life. Evaluate fatigue life using procedures given in Section 7 of AASHTO’s The Manual for Bridge Evaluation. CALCULATION OF FATIGUE LIFE Fatigue life determination will be based upon the finite fatigue life. 1 3log (1 ) 1365 ( ) [( ) ] log(1 ) aR SL effPRESENT R A g g n ADTT f Y g MBE 7.2.5.1 Assume [ADTT]PRESENT (One Direction, all lanes) = 1500 Use p = 0.80 LRFD Table 3.6.1.4.2 -1 Hence, [(ADTT)SL]PRESENT = 0.80 x 1500 = 1200 Traffic Growth Rate g: 2% Bridge Age a = 2011-1962 = 49 years Assume that the owner decides to use Minimum Life for the bridge assessment.

F-10 Hence, RR = 1.0 MBE Table 7.2.5.1-1 ( f)eff = 1.5 ksi A = 3.8 x 108 ksi3 LRFD Table 6.6.1.2.5-1 n = 1.0 simple span girders with L > 40 ft. LRFD Table 6.6.1.2.5-2 8 49 1 3 (1.0)(3.9 10 )log (0.02)(1 0.02) 1 365(1)(1200)(1.5) 136 years log(1 0.02) x Y CALCULATION OF FATIGUE SERVICEABILITY INDEX Fatigue Serviceability Index Y aQ GRI N MBE 7.2.6.1 No. of Loadpaths (In this case, the minimum number of floorbeams loaded) = 3 G = 0.9 MBE Table 7.2.6.1-1 No. of Spans = 1 (Simple Span between floor beam ends) R = 0.90 MBE Table 7.2.6.1-2 N = (larger of 100 or Y) = 136 Assuming that the bridge is on an Interstate Highway, I = 0.9 MBE Table 7.2.6.1-3 Q = 136 49 (0.9)(0.9)(0.9) 0.47 136 The serviceability rating and assessment outcome are provided in MBE Table 7.2.6.2-1 for various ranges of the Fatigue Serviceability Index. In this example, a Q value of 0.47 means that the bridge will be rated as ‘Good’ from a fatigue standpoint and the assessment outcome would be ‘Continue Regular Inspection’.

F-11 Example 4: (Strategy to Increase Fatigue Serviceability Index – Accept Greater Risk) If the bridge owner is willing to accept a greater likelihood of fatigue cracking for statistically more risk, the detail given in Example 3 can be evaluated for Evaluation 2 Life with a higher resistance factor RR of 1.6. The example continues with a recalculation of the fatigue life and the Fatigue Serviceability Index. CALCULATION OF FATIGUE LIFE Fatigue life determination will be based upon the finite fatigue life. 1 3log (1 ) 1365 ( ) [( ) ] log(1 ) aR SL effPRESENT R A g g n ADTT f Y g MBE 7.2.5.1 (ADTT)PRESENT (One Direction) = 1500 [(ADTT)SL]PRESENT = 0.80(1500) = 1200 LRFD Table 3.6.1.4.2-1 Traffic Growth Rate g: 2% Bridge Age a = 2011-1962 = 49 years ( f)eff = 1.5 ksi Assume Evaluation 2 Life to be used for bridge assessment. Hence, RR = 1.6 MBE Table 7.2.5.1-1 A = 3.9 x 108 ksi3 LRFD Table 6.6.1.2.5-1 n = 1.0 simple span girders with L > 40 ft. LRFD Table 6.6.1.2.5-2 8 49 1 3 1.6(3.9 10 )log (0.02)(1 0.02) 1 365(1)(1200)(1.5) 158 years log(1 0.02) x Y CALCULATION OF FATIGUE SERVICEABILITY INDEX Fatigue Serviceability Index Y aQ GRI N MBE 7.2.6.1 No. of load paths (in this case, the minimum number of floorbeams loaded) = 3

F-12 G = 0.9 MBE Table 7.2.6.1-1 No. of Spans = 1 (Simple Span between floor beam ends) R = 0.9 MBE Table 7.2.6.1-2 N = (larger of 100 or Y) = 158 Assuming that the bridge is on an Interstate Highway, I = 0.9 MBE Table 7.2.6.1-3 Q = 158 49 (0.9)(0.9)(0.9) 0.50 158 The serviceability rating and assessment outcome are provided in MBE Table 7.2.6.2-1 for various ranges of the Fatigue Serviceability Index. In this example, a Q value of 0.50 means that the bridge will be rated as ‘Excellent’ from a fatigue standpoint and the assessment outcome would be ‘Continue Regular Inspection’.

F-13 Example 5: (Strategy to Increase Fatigue Serviceability Index – More Accurate Data) Field measurement is one of the methods that can be used to improve the accuracy of data. A more reliable value of the stress at the detail obtained through strain measurement at the critical detail will improve the life estimate. Suppose, for the detail given in Example 3, field measurements are performed which indicate a measured effective stress range of 0.9 ksi and a maximum measured stress range of 1.6 ksi. Nominal fatigue resistance for infinite life ( F)TH = 2.6 ksi for Detail Category E LRFD Table 6.6.1.2.5-3 Infinite-Life Fatigue Check MBE 7.2.4 ( f)eff = 0.9 ksi ( f)max = Larger of maximum ( fi) and (2.0)[( f)eff] MBE 7.2.4 = Larger of (1.6) and (2.0)(0.9) = Larger of 1.6 and 1.8 = 1.8 ksi < 2.6 ksi Thus, ( f)max < ( F)TH. Hence, the detail possesses infinite fatigue life.

F-14 Example 6: (Strategy to Increase Fatigue Serviceability Index – Use Inspection Information) Consider a welded plate girder bridge with a welded partial length cover plate detail. The bridge, which was built in 1966, spans 70 ft and carries two lanes of traffic. The owner is using ‘Evaluation 1 Life’ to assess the bridge condition. Assume a cover plate weld detail of Category E. Bridge age = a = 45 years [(ADTT)SL]PRESENT = 2,350 ( f)eff = 3.75 ksi n = 1 for 70 ft simple span g = 2% RR = 1.2 A = 11.0 x 108 ksi3 for Category E 1 3log (1 ) 1365 ( ) [( ) ] log(1 ) aR SL effPRESENT R A g g n ADTT f Y g MBE 7.2.5.1 8 45 1 3 1.2(11.0 10 )log 0.02(1 0.02) 1 365(1)(2350)(3.75) log(1 0.02) x Y Y = 44 years CALCULATION OF FATIGUE SERVICEABILITY INDEX Fatigue Serviceability Index Y aQ GRI N MBE 7.2.6.1 No. of Load paths (In this case, girders) = 4 G = 1.0 MBE Table 7.2.6.1-1 No. of Spans = 1 (Simple Span) R = 0.90 MBE Table 7.2.6.1-2 N = (larger of 100 or Y) = 100

F-15 Assuming that the bridge is on an Interstate Highway, I = 0.9 MBE Table 7.2.6.1-3 Q = 44 45 (1.0)(0.9)(0.9) 0.01 100 The serviceability rating and assessment outcome are provided in MBE Table 7.2.6.2-1 for various ranges of the Fatigue Serviceability Index. A fatigue serviceability index less than zero gives a fatigue rating of ‘Critical’ with an assessment outcome of ‘Consider Retrofit, Replacement, or Reassessment’. In this case the bridge owner decides to consider reassessment. Since the bridge had been thoroughly inspected and no fatigue cracking or distress was found, it was decided to recompute the fatigue life using the truncation approach described in Article 7.2.7.2.3 of AASHTO’s The Manual for Bridge Evaluation. The calculation requires computation of the mean fatigue life, Ymean. In making this calculation, the RR value for the mean life should be taken from Table 7.2.5.1-1, and the stress range previously determined should be used. RR = 1.6 for mean life Table 7.2.5.1-1 1 3log (1 ) 1365 ( ) [( ) ] log(1 ) aR SL effPRESENT mean R A g g n ADTT f Y g MBE 7.2.7.2.3 8 45 1 3 1.6(11.0 10 )log 0.02(1 0.02) 1 365(1)(2350)(3.75) log(1 0.02)mean x Y Ymean = 53.1 years Update the estimation for the lognormal distribution 450.27 0.272.19 2.19(53.1) 0.73 0.73 [ 0.93] 1 [0.93] 1 mean aLn Ln Y P 0.1762 MBE Table 7.2.7.2 -1(0.8238)

F-16 1 1 1 1 1 0.73 [0.074(1 ) ] 0.27 1 0.73 [0.074(1 0.1762) 0.1762] 0.27 0.73 [0.237] 0.27 0.73{ [1 0.237]} 0.27 0.73{ [0.763]} 0.27 0.73( 0.715) 0. ' 2.19 =2.19(53.1) =116.2 116.2 116.2 =116.2 P P Eval meanY Y e e e e e e 27 0.792 7.2.7.2 -1 =116.2 53 years MBE Table e Now compute the revised Fatigue Serviceability Index: Y aQ GRI N MBE 7.2.6.1 53 45 (1)(0.9)(0.9) 100 Q Q = 0.06 The serviceability rating and assessment outcome are provided in MBE Table 7.2.6.2-1 for various ranges of the Fatigue Serviceability Index. Based upon the fatigue serviceability index of 0.06 of the reassessed life estimate, the cover plate detail now has a ‘Poor’ fatigue rating with an assessment outcome of ‘Assess Frequently’. The owner must decide how often to examine the detail prior to the next regular inspection.

Abbreviations and acronyms used without definitions in TRB publications: AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACI–NA Airports Council International–North America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S.DOT United States Department of Transportation