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Fatigue Evaluation of Steel Bridges (2012)

Chapter: Appendix E - Proposed Section 7 of MBE

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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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Suggested Citation:"Appendix E - Proposed Section 7 of MBE ." National Academies of Sciences, Engineering, and Medicine. 2012. Fatigue Evaluation of Steel Bridges. Washington, DC: The National Academies Press. doi: 10.17226/22774.
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APPENDIX E PROPOSED SECTION 7 OF MBE E.1 SECTION 7 (STRIKE-OUT FORMAT)

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 2 E-2 SECTION 7 7.1—LOAD-INDUCED VERSUS DISTORTION- INDUCED FATIGUE C7.1 Fatigue damage has been traditionally categorized as either due to load-induced or distortion-induced fatigue damage. Load-induced fatigue is that due to the in-plane stresses in the steel plates that comprise bridge member cross-sections. These in-plane stresses are those typically calculated by designers during bridge design or evaluation. The previous most comprehensive codification of fatigue evaluation of steel bridges, the Guide Specifications for Fatigue Evaluation of Existing Steel Bridges (AASHTO, 1990), explicitly considered only load-induced fatigue damage. The Guide Specifications referenced NCHRP Report 299 for considering “fatigue due to secondary bending stresses that are not normally calculated,” NCHRP (1987). Distortion-induced fatigue is that due to secondary stresses in the steel plates that comprise bridge member cross-sections. These stresses, which are typically caused by out-of-plane forces, can only be calculated with very refined methods of analysis, far beyond the scope of a typical bridge design or evaluation. These secondary stresses are minimized through proper detailing. These “plates” may be the individual plates which comprise a built-up welded, bolted, or riveted plate girder, or may be the flanges, webs, or other elements of rolled shapes. The traditional approximate methods of analysis utilizing lateral live-load distribution factors have encouraged bridge designers to discount the secondary stresses induced in bridge members due to the interaction of longitudinal and transverse members, both main and secondary members. Detailing to minimize the potential for distortion- induced fatigue, such as connecting transverse connection plates for diaphragms and floorbeams to both the compression and tension flanges of girders, is specified in LRFD Design Article 6.6.1.3. 7.2—LOAD-INDUCED FATIGUE -DAMAGE EVALUATION 7.2.1—Application C7.2.1 Article 7.2 includes tTwo levels of fatigue evaluation are specified for load-induced fatigue: the infinite-life check of Article 7.2.4 and the finite-life calculations of Article 7.2.5. Only bridge details which fail the infinite-life check are subject to the more complex finite-life fatigue evaluation. Cumulative fatigue damage of uncracked members subject to load-induced stresses shall be assessed according to the provisions of Article 7.2. Except for the case of riveted connections and tack weld details specified below, the list of detail categories to be considered for load-induced fatigue-damage evaluation, and illustrative examples of these categories are shown in LRFD Design Table 6.6.1.2.3-1 and Figure 6.6.1.2.3-1. The initial infinite-life check should be made with the simplest, least refined stress-range estimate. If the detail passes the check, no further refinement is required. The stress-range estimate for the infinite-life check should be refined before the more complex procedures of the finite-life fatigue evaluation are considered. The base metal at net sections of riveted connections shall be evaluated based upon the requirements of Category C, given in LRFD Design Table 6.6.1.2.3-1, instead of the Category D as specified for new designs. The exception is for riveted members of poor physical condition, such as with missing rivets or indications of punched holes, in which case Category D shall be used. For new design, the base metal at net sections of riveted connections is specified to be Category D. This represents the first cracking of a riveted member, which is highly redundant internally. Category C more accurately represents cracking that has propagated to a critical size. This increase in fatigue life for evaluation purposes is appropriate due to the redundancy of riveted members.

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 3 E-3 Tack welds may be evaluated based upon the requirements of Category C, given in LRFD Design Table 6.6.1.2.3-1. As uncertainty is removed reduced from the evaluation by more refined analysis or site-specific data, the increased certainty is reflected in lower partial load factors, summarized in Table 7.2.2.1-1 and described in Articles 7.2.2.1 and 7.2.2.2. If cracks have already been visually detected, a more complex fracture mechanics approach for load-induced fatigue-damage evaluation is required instead of the procedure specified herein. Further, the expense and trouble of a fracture mechanics analysis may not be warranted. Generally, upon visual detection of fatigue cracking, the majority of the fatigue life has been exhausted and retrofitting measures should be initiated. If cracks have been visually detected then the fatigue life evaluation procedure specified herein should be used with caution. Generally, upon visual detection of load- induced fatigue cracking, the majority of the fatigue life has been exhausted and retrofitting measures should be initiated. Alternatively, a fracture mechanics approach can be used to evaluate the fatigue crack damage. Tack welds were frequently left in place in riveted connections. The tack welds were used to hold the members in place initially prior to placement of the rivets. Tack welds in this context are typically less than 2-in in length. The strength of tack welds was found to conform to fatigue Category C based on laboratory testing. The partial load factors specified in Article 7.2 were adapted from the Guide Specifications for Fatigue Evaluation of Existing Steel Bridges (AASHTO, 1990). 7.2.2—Estimating Stress Ranges C7.2.2 The effective stress range shall be estimated as: ( ) sefff R f∆ = ∆ ( )eff p sf R R f∆ = ∆ (7.2.2-1) where: Rp = The multiple presence factor, calculated as described in Article 7.2.2.1 for calculated stress ranges, or 1.0 for measured stress ranges Rs = The stress-range estimate partial load factor, calculated as RsaRst, unless otherwise specified, summarized in Table 7.2.2.1-1, and ∆f = Measured effective stress range; or 75 percent of thefactored calculated stress range due to the passage of the fatigue truck as specified in LRFD Design Article 3.6.1.4 for Fatigue II Load Combination, or the calculated stress range due to a fatigue truck determined by a truck survey or weigh-in-motion study The calculated stress range, either measured or calculated, is the stress range due to a single truck in a single lane on the bridge. The 0.75 applied to the calculated stress range due to the passage of the LRFD fatigue truck represents the load factor for live load specified for the fatigue limit state in LRFD Design Table 3.4.1-1. The multiple presence factor takes into account the effect of trucks present simultaneously in multiple lanes instead of a single lane loading. When using measured stress ranges, the multiple presence factor should not be used in the equation, as the effects of multiple presence are already reflected in the measured stress ranges. The load factor is 0.75 for live load specified for the Fatigue II limit state (finite load-induced fatigue life) in LRFD Design Table 3.4.1-1. 7.2.2.1—Calculating Estimated Stress Ranges The multiple presence factor Rp shall be calculated

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 4 E-4 as: Rp = 0.988 + 6.87x10-5 (L) + 4.01x10-6 [ADTT]PRESENT + 0.0107/(nL) 1.0 (7.2.2.1-1 ) where L = span length in feet, [ADTT]PRESENT = Present average number of trucks per day for all directions of truck traffic including all lanes on the bridge, and nL = number of lanes. The limits used in developing the equation are noted as follows: 2 nL 4; [ADTT]PRESENT < 8,000 for nL=2; 11,000 for nL=3, and 13,000 for nL=4, and 30 ft < L < 220 ft. These are the ranges used in the analysis, based on the WIM data available. Use of these equations may be justified outside of these ranges, but are not based on experimental evidence. The multiple presence factor is applicable to longitudinal parallel members only. For transverse members, use RP = 1.0. Two sources of uncertainty are present in the calculation of effective stress range at a particular fatigue detail: • Uncertainty associated with analysis, represented by the analysis partial load factor, Rsa, and • Uncertainty associated with assumed effective truck weight, represented by the truck-weight partial load factor, Rst.

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 5 E-5 Table 7.2.2.1-1—Partial Load Factors: Rsa, Rst, and Rs Fatigue-Life Evaluation Methods Analysis Partial Load Factor, Rsa Truck-Weight Partial Load Factor, Rst Stress-Range Estimate Partial Load Factor, Rsa For Evaluation or Minimum Fatigue Life Stress range by simplified analysis, and truck weight per LRFD Design Article 3.6.1.4 1.0 1.0 1.0 Stress range by simplified analysis, and truck weight estimated through weigh-in- motion study 1.0 0.95 0.95 Stress range by refined analysis, and truck weight per LRFD Design Article 3.6.1.4 0.95 1.0 0.95 Stress range by refined analysis, and truck weight by weigh-in- motion study 0.95 0.95 0.90 Stress range by field-measured strains N/A N/A 0.85 For Mean Fatigue Life All methods N/A N/A 1.00 a In general, s sa stR R R= 7.2.2.1.1—For the Determination of Evaluation or Minimum Fatigue Life In the calculation of effective stress range for the determination of evaluation or minimum fatigue life, the stress-range estimate partial load factor shall be taken as the product of the analysis partial load factor and the truck-weight partial load factor: s sa stR R R= (7.2.2.1.1-1) If the effective stress range is calculated through refined methods of analysis, as defined in LRFD Design Article 4.6.3: 0.95saR = (7.2.2.1.1-2) otherwise: 1.0saR = (7.2.2.1.1-3) If the effective truck weight is estimated through a weight-in-motion study at, or near, the bridge: 0.95stR = (7.2.2.1.1-4) otherwise: 1.0stR = (7.2.2.1.1-5)

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 6 E-6 7.2.2.1.2—For the Determination of Mean Fatigue Life In the calculation of effective stress range for the determination of mean fatigue life, the stress-range estimate partial load factor shall be taken as 1.0. 7.2.2.2—Measuring Estimated Stress Ranges C7.2.2.2 The effective stress range may be estimated through field measurements of strains at the fatigue-prone detail under consideration under typical traffic conditions. The effective stress range shall be taken computed as the cube root of the weighted sum of the cubes of the measured stress ranges, as given in: ( ) ( )13 3s i iefff R fΣ∆ = γ ∆ (7.2.2.2-1) where: i = Percentage of cycles at a particular stress range and fi = The particular stress range in a measured stress range histogram of magnitude greater than one half of the constant-amplitude-fatigue-threshold of the fatigue prone detail under consideration, i.e. > FTH/2. Field measurements of strains represent the most accurate means to estimate effective stress ranges at fatigue-prone details. The AASHTO LRFD Bridge Design Specifications assume that the maximum stress range is twice the effective stress range. It is unlikely that the maximum stress range during the service life of the bridge will be captured during a limited field-testing measurement session; therefore means to extrapolate from the measured effective stress range histogram to the maximum stress range must be used. The AASHTO LRFD Bridge Design Specifications assume that the maximum stress range is twice the effective stress range. If the effective truck weight is significantly less than 54 kips, a multiplier more than two should be considered. Similarly, for a measured effective truck weight greater than 54 kips a multiplier less than two would be appropriate. The lower portion of field measured stress range histograms must be truncated in order to avoid underestimating the effective stress range. 7.2.2.2.1—For the Determination of Evaluation or Minimum Fatigue Life Where field-measured strains are used to generate an effective stress range, Rs, for the determination of evaluation or minimum fatigue life, the stress-range estimate partial load factor shall be taken as 0.85. 7.2.2.2.2—For the Determination of Mean Fatigue Life Where field-measured strains are used to generate an effective stress range, Rs, for the determination of mean fatigue life, the stress-range estimate partial load factor shall be taken as 1.0. 7.2.3—Determining Fatigue-Prone Details C7.2.3 Bridge details are only considered prone to load- induced fatigue damage if they experience a net tensile stress. Thus, fatigue damage need only be evaluated if, at the detail under evaluation: The multiplier of two in the equation represents the assumed relationship between maximum stress range and effective stress range, as specified in the AASHTO LRFD Bridge Design Specifications.

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 7 E-7 ( ) - 2 s dead load compressiontensionR f f∆ > ( ) - 2 dead load compressiontensionf f∆ > (7.2.3-1) When measured stress ranges are used to evaluate fatigue life, the multiplier of two in the equation should be reconsidered based upon the discussion of Article C7.2.2.2. If the effective truck weight is significantly less than 54 kips, a multiplier more than two should be considered. Similarly, for a measured effective truck weight greater than 54 kips a multiplier less than two would be appropriate. where: Rs = The stress-range estimate partial load factor, specified in Article 7.2.2 and summarized in Table 7.2.2.1-1 ( f)tension = Factored tTensile portion of the effective stress range due to the passage of a fatigue truck as specified in Article 7.2.2, and fdead-load compression = Unfactored compressive stress at the detail due to dead load 7.2.4—Infinite-Life Check C7.2.4 If: ( ) ( ) max THf F∆ ≤ ∆ (7.2.4-1) then: Y =∞ (7.2.4-2) where: ( f)max = The maximum stress range expected at the fatigue-prone detail, which may be taken as: • Rp times the factored calculated stress range due to the passage of the fatigue truck as specified in LRFD Design Article 3.6.1.4 for Fatigue I Load Combination • 2.0( f )eff ; for calculated stress range due to a fatigue truck determined by a truck survey or weigh-in-motion study with Rs=1.0 • Larger of maximum ( fi), 2.0( f )eff, or other suitable value; for measured stress ranges with Rs=1.0 ( F)TH = The constant-amplitude fatigue threshold given in LRFD Design Table 6.6.1.2.5-3 Theoretically, a fatigue-prone detail will experience infinite life if all of the stress ranges are less than the constant amplitude fatigue threshold; in other words, if the maximum stress range is less than the threshold. When measured stress ranges are used to evaluate fatigue life, the multiplier of two in the equation for ( f)max should be reconsidered based upon the discussion of Article C7.2.2.2. The load factor is 1.50 for live load specified for the Fatigue I limit state (infinite load-induced fatigue life) in LRFD Design Table 3.4.1-1. When measured stress ranges are used to evaluate fatigue life, the maximum stress range should be taken as the larger value of two times field measured effective stress range or the field measured maximum stress range, unless another suitable value is justified.

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 8 E-8 Otherwise, the total fatigue life shall be estimated as specified in Article 7.2.5. 7.2.5—Estimating Finite Fatigue Life 7.2.5.1—General C7.2.5.1 Three Four levels of finite fatigue life may be estimated: • The minimum expected fatigue life (which equals the conservative design fatigue life), • Evaluation 1 fatigue life (which is a somewhat less conservative fatigue life for evaluation), • The eEvaluation 2 fatigue life (which equals a more conservative fatigue life for evaluation), and • The mean fatigue life (which equals the statistically most likely fatigue life). The total finite fatigue life of a fatigue-prone detail, in years, shall be determined as: ( ) ( ) 3365 R SL eff R A Y n ADTT f = ∆ [ ] 1 3log (1 ) 1365 ( ) [( ) ] log(1 ) aR SL effPRESENT R A g g n ADTT f Y g −+ + ∆ = + (7.2.5.1-1) Much scatter, or variability, exists in experimentally derived fatigue lives. For design, a conservative fatigue resistance two standard deviations shifted below the mean fatigue resistance or life is assumed. This corresponds to the minimum expected finite fatigue life of this Article. Limiting actual usable fatigue life to this design fatigue life is very conservative and can be costly. As such, means of estimating the two evaluation fatigue life lives and the mean finite fatigue life are also included to aid the evaluator in the decision making. Figure C7.2.5.5-1 may be used to estimate the average number of trucks per day in a single lane averaged over the fatigue life, (ADTT)SL, from the present average number of trucks per day in a single lane, [(ADTT)SL]present, the present age of the bridge, a, and the estimated annual traffic-volume growth rates, g. Recent research has made it possible to obtain a closed-form solution for the total finite fatigue life using an estimated traffic growth rate and the present (ADTT)SL. For cases with zero traffic growth, a very small value of g should be selected (less than 0.01%) for use in the expression for Y.

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 9 E-9 where: RR = Resistance factor specified for evaluation, minimum, or mean fatigue life as given in Table 7.2.5.21-1 A = Detail-category constant given in LRFD Design Table 6.6.1.2.5-1 n = Number of stress-range cycles per truck passage estimated according to Article 7.2.5.2 g = Estimated annual traffic-volume growth rate in percentage a = Present age of the detail in years [(ADTT)SL]PRESENT = Present Average average number of trucks per day in a single lane averaged over the fatigue life as specified in LRFD Design Article 3.6.1.4.2 ( f)eff = The effective stress range as specified in Article 7.2.2 The resistance factors for fatigue life, specified in Table 7.2.5.21-1, represent the variability of the fatigue life of the various detail categories, A through E . The minimum life, evaluation 1 life and evaluation 2 life fatigue-life curves are shifted from the mean fatigue-life S-N curves in log-log space. Scatter of the fatigue lives at given stress range values from controlled laboratory testing provides statistical information on fatigue behavior of bridge details under cyclic loading. Accordingly, the probability of failure associated with each level of fatigue life, approaches 2 percent, 16 percent, 33 percent and 50 percent for the minimum, evaluation 1, evaluation 2 and mean fatigue lives, respectively. Typically, the minimum life or evaluation 1 life is used to evaluate the fatigue serviceability. If concerns are encountered regarding the computed fatigue serviceability, then the serviceability index can be revised according to Article 7.2.7.2.As the stress-range estimate grows closer and closer to the actual value of stress range, the probability of failure associated with each level of fatigue life approaches two percent, 16 percent, and 50 percent for the minimum, evaluation, and mean fatigue lives, respectively. The minimum and evaluation fatigue-life curves are two and one standard deviations off of the mean fatigue-life S-N curves in log- log space, respectively. Thus, the partial resistance factors for mean and evaluation fatigue life are calculated as raised to the power of twice and one times the standard deviation of the log of experimental fatigue life for each detail category, respectively.

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 10 E-10 Figure C7.2.5.1-1—Lifetime Average Truck Volume for an Existing Bridge

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 11 E-11 Table 7.2.5.1-1 Resistance Factor for Evaluation, Minimum or Mean Fatigue Life, RR Detail Category (from Table 6.6.1.2.5-1 of the LRFD Specifications) RR Minimum Life Evaluation 1 Life Evaluation 2 Life Mean Life A 1.0 1.5 2.2 2.9 B 1.0 1.3 1.7 2.0 B’ 1.0 1.3 1.6 1.9 C 1.0 1.3 1.7 2.1 C’ 1.0 1.3 1.7 2.1 D 1.0 1.3 1.7 2.0 E 1.0 1.2 1.4 1.6 E’ 1.0 1.3 1.6 1.9 7.2.5.2—Estimating the Number of Cycles per Truck Passage The number of stress-range cycles per truck passage may be estimated (in order of increasing apparent accuracy and complexity): Table 7.2.5.2-1—Resistance Factor for Evaluation, Minimum, or Mean Fatigue Life, RR Detail Categorya RR Evaluation Life Minimum Life Mean Life A 1.7 1.0 2.8 B 1.4 1.0 2.0 B 1.5 1.0 2.4 C 1.2 1.0 1.3 C 1.2 1.0 1.3 D 1.3 1.0 1.6 E 1.3 1.0 1.6 E 1.6 1.0 2.5 a From LRFD Design Table 6.6.1.2.3-1 and Figure 6.6.1.2.3-1

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 12 E-12 • Through the use of LRFD Design Table 6.6.1.2.5-2, • Through the use of influence lines, or • By field measurements. 7.2.6—Acceptable Remaining Fatigue Life The remaining fatigue life of a fatigue-prone detail is the total fatigue life, as determined through Article 7.2.5, minus the present age of the bridge. 7.2.6 Fatigue Serviceability Index 7.2.6.1 Calculating the Fatigue Serviceability Index The fatigue serviceability index shall be calculated as: (7.2.6.1-1)Y aQ GRI N − = where: N = Greater of Y or 100 years G = Load Path Factor, as given in Table 7.2.6.1-1 R = Redundancy Factor, as given in Table 7.2.6.1-2 I = Importance Factor, as given in Table 7.2.6.1-3 Table 7.2.6.1-1 Load Path Factor G Number of Load Path Members G 1 or 2 members 0.8 3 members 0.9 4 or more members 1 Table 7.2.6.1-2 Redundancy Factor R Type of Span R Simple 0.9 Continuous 1 C7.2.6 The fatigue serviceability index is a dimensionless relative measure of the performance of a structural detail, at a particular location in the structure, with respect to the overall fatigue resistance of the member. The load path, redundancy and importance factors are risk factors that modify the fatigue serviceability index. They reduce the index from its base value, i.e. based on fatigue resistance alone, to a reduced value that reflects greater consequences from the lack of ability to redistribute the load (load path factor), lack of redundancy (redundancy factor), or use of the structure (importance factor). The net effect of a reduction in the index will be to move the composite index value to a lower value that may initiate a lower fatigue rating. These risk factors are similar to the ductility, redundancy and operational classification factors in the AASHTO LRFD Bridge Design Specifications. Improved quantification with time will possibly modify these factors. The number of members that carry load when a fatigue truck is placed on the bridge is used to select the load path factor; e.g., two members for a two-girder bridge and for a typical truss structure; four or more members for a multi-beam or multi-girder bridge; etc. For diaphragms and secondary members, use G = 1.

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 13 E-13 Table 7.2.6.1-3 Importance Factor I Structure or Location Importance Factor, I Interstate Highway Main Arterial State Route Other Critical Route 0.90 Secondary Arterial Urban Areas 0.95 Rural Roads Low ADTT routes 1.00 7.2.6.2 Recommended Actions Based on Fatigue Serviceability Index The fatigue ratings and assessment outcomes as given in Table 7.2.6.2-1 are recommended as a guideline for actions that may be undertaken based on the obtained value for the fatigue serviceability index. A better fatigue rating may be assumed for Q values at the boundary of two ranges. In the recommended actions provided, it is expected that based upon increasing risk, the inspection frequency of the bridge shall be increased on a case-by-case assessment by the bridge owner. Table 7.2.6.2-1 Fatigue Rating and Assessment Outcomes Fatigue Serviceability Index, Q Fatigue Rating Assessment Outcome 1.00 to 0.50 Excellent Continue Regular Inspection 0.50 to 0.35 Good Continue Regular Inspection 0.35 to 0.20 Moderate Continue Regular Inspection 0.20 to 0.10 Fair Increase Inspection Frequency 0.10 to 0.00 Poor Assess Frequently < 0.00 Critical Consider Retrofit, Replacement or Reassessment 7.2.7—Strategies to Increase Remaining Fatigue LifeServiceability Index 7.2.7.1—General C7.2.7.1 If the remaining fatigue serviceability index life is deemed unacceptable, the strategies of Articles 7.2.7.2 and 7.2.7.3 may be applied to enhance the fatigue lifeserviceability index. Retrofit or load-restriction decisions should be made based upon the evaluation fatigue life unless the physical condition or fabrication quality of the bridge is poor. In general, it is uneconomical to limit the useful fatigue life of in-service bridges to the minimum (design) fatigue life. If the estimated remaining fatigue serviceability index life based upon the evaluation fatigue life is deemed unacceptable, a fatigue life approaching the mean fatigue life can be used for evaluation purposes if the additional risk of fatigue cracking is acceptable.

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 14 E-14 7.2.7.2—Recalculate the Fatigue Life Serviceability Index 7.2.7.2.1—Through Accepting Greater Risk In general, the evaluation 1 life of Article 7.2.5 is used in determining the remaining fatigue serviceability index life of a bridge detail according to Article 7.2.6. If the evaluator is willing to accept greater risk of fatigue cracking due to: • Long satisfactory cyclic performancefatigue life of the detail to date, • A high degree of redundancy, and/or • Increased inspection effort, e.g., decreased inspection interval, or • Some combination of the above the remaining fatigue serviceability indexlife may be determined using a fatigue life approaching the mean fatigue life of Article 7.2.5. 7.2.7.2.2—Through More Accurate Data The calculated fatigue life serviceability index may be enhanced refined by using more accurate data as input to the fatigue-life estimate. Sources of improvement of the estimate include: • Field measurement of stress ranges at the fatigue prone detail under construction • 3-D finite element analysis for stresses at the fatigue prone detail under consideration • Weigh-in-motion data of truck weights at or near the bridge site, • Site-specific data on average daily truck traffic (ADTT) at or near the bridge site • Effective stress range or effective truck weight, • The average daily truck traffic (ADTT), or • The number of cycles per truck passage. This strategy is based upon achieving a better estimate of the actual fatigue life. 7.2.7.2.3 Through Truncated Fatigue Life Distribution When a negative fatigue serviceability index is obtained according to Article 7.2.6, the detail’s fatigue serviceability index may be updated using equations below for mean, evaluation and minimum lives, provided a field inspection finds no evidence of fatigue cracking at the detail. C7.2.7.2.3 The fatigue life of a structural detail is modeled using a lognormally distributed random variable, as shown in the figure C7.2.7.2.3-1. When the estimated life using Article 7.2.5 is smaller than the present age, the remaining life becomes negative as illustrated. In this situation, if field inspection finds no

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 15 E-15 ( )10.73 [0.18(1 ) ] 0.27' 2.19 7.2.7.2.3 1P Pmean meanY Y e −Φ − + −= − ( )10.73 [0.12(1 ) ] 0.272' 2.19 7.2.7.2.3 2P Peval meanY Y e −Φ − + −= − ( )10.73 [0.074(1 ) ] 0.271' 2.19 7.2.7.2.3 3P Peval meanY Y e −Φ − + −= − ( )10.73 [0.039(1 ) ] 0.27minimum' 2.19 7.2.7.2.3 4P PmeanY Y e −Φ − + −= − where eval1 eval ' = Updated mean life in years = Mean life in years without updating based on no detection of cracking at detail in question Y' = Updated evaluation 1 life in years Y' mean mean Y Y 2 minimum -1 = Updated evaluation 2 life in years Y' = Updated minimum life in years = Inverse of the standard normal variable's cumulative probability function (Table 7.2.7.2-1) P = Probab Φ ( ) ility of fatigue life being shorter than current age before updating based on no crack found 0.27 2.19 = 7.2.7.2.3 5 0.73 where a = Present age mean aLn Y + Φ − in years = Standard normal variable's cumulative probability function (Table 7.2.7.2-1) Φ evidence of cracking, the estimated life is an overly- conservative estimate. The low tail of the total life distribution is truncated up to the present life. The eliminated probability P is computed, and the resulting probability density function is divided by (1 – P) to ensure that the total probability under the distribution curve is still 1.0 as shown in Figure C7.2.7.2.3-2. Then the updated life is determined to maintain the same reliability level for fatigue life distribution. Functions (.) and -1(.) are commonly available in commercial spreadsheet programs. Fig C7.2.7.2.3-1 Probability Density Function of Fatigue Life and Estimated Life as a Value on Horizontal Axis Fig C7.2.7.2.3-2 Truncated Probability Density Function of Fatigue Life and Updated Life as a value on the Horizontal Axis

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 16 E-16 Table 7.2.7.2-1 Cumulative Distribution Function (x) for Standard Normal Variable x x 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 7.2.7.3—Retrofit The Bridge C7.2.7.3 If the recalculated fatigue life serviceability index is not ultimately acceptable, the actual fatigue life serviceability index may be increased by retrofitting the critical details to change improve the detail category and thus increase the lifefatigue serviceability index. This strategy increases the actual life fatigue serviceability index when further enhancement of the calculated lifefatigue serviceability index, through improved input, is no longer possible or practical. In certain cases, Owners may wish to institute more intensive inspections, in lieu of more costly retrofits, to assure adequate safety. Restricting traffic to extend increase the fatigue life serviceability index is generally not considered cost effective. If the remaining fatigue lifefatigue serviceability index is deemed inadequate, the appropriate option to extend increase the life fatigue serviceability index should be determined based upon the economics of the particular situation. 7.3—DISTORTION-INDUCED FATIGUE EVALUATION C7.3 Distortion-induced fatigue is typically caused by out-of-plane deformation of the web plate that results in fatigue crack formation at details prone to such cracking under cyclic loading. The cracks tend to form in the member web at locations where there is a geometrical discontinuity, such as a vertical gap between a stiffener or connection plate and the girder flange or a horizontal gap between a gusset plate and a connection plate.a low- cycle fatigue phenomenon. In other words, relatively few stress-range cycles are required to initiate cracking at distortion-induced fatigue-prone details. Distortion- induced fatigue is a stiffness problem (more precisely the lack thereof) versus a load problem. Often, distortion-induced fatigue cracks initiate after Existing bridges should not be assumed to be insensitive to distortion-induced cracking if fatigue cracks do not appear after a short period of time. Experience has shown that in some cases cracking may not be evident for 10 years after the beginning of service.Distortion-induced cracks have even been discovered on bridges prior to being opened to traffic.

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 17 E-17 relatively few stress-range cycles at fatigue-prone details. However, depending upon the magnitude of the out-of- plane distortion and the geometry of the web gap detail, the crack growth may be slow and a significant period of time may be required before they become large enough to be detected visually.As such, existing bridges which have experienced many truck passages, if uncracked, may be deemed insensitive to distortion-induced cracking, even under heavier permit loads. 7.3.1 Methods to Assess Distortion-Induced Cracking Out-of-plane distortions caused by truck loading must be accommodated by the regions that contain unsupported web gaps. Even very small distortions can cause high local stresses that may induce fatigue cracking. Often, the fatigue cracks grow in a plane that is parallel to the primary stresses of the member and will slow down or even stop as the web gap becomes more flexible due to the presence of the crack. However, it is possible that the crack may turn and become perpendicular to the primary stress of the member, leading to more rapid crack growth. Therefore, distortion-induced fatigue cracks should be repaired. 7.3.2 Retrofit Options for Distortion-Induced Fatigue Cracking Retrofit should be considered if distortion-induced cracking has been detected. Two primary retrofit methods are available: softening or stiffening. The softening approach is used to increase the overall flexibility of the detail in question to accommodate the out-of-plane deformations without further cracking. The stiffening approach is used to minimize the local distortion by providing a positive load path for the forces that tend to cause the distortion. In either case, a hole should be drilled at the tip of each crack. C7.3.1 Typically, smaller web gaps are subject to higher distortion-induced stresses than larger web gaps provided the same demand for the out-of-plane distortion. The demand for out-of-plane distortion is determined by the global behavior of the structural system. Accurate quantification of the stress field in an unsupported web gap detail can be very difficult, even for finite element modeling or field measurement of strains and/or local deformations. This is especially the case when the dimension of the web gap is comparable to the thicknesses of the surrounding plates and the sizes of the connecting welds, resulting in high stress gradients across the web gap. C7.3.2 In the softening retrofit, the flexibility of the detail in question is increased. Drilling holes to eliminate the tip of distortion-induced fatigue cracks will typically increase the local flexibility somewhat. However, the primary method used to increase the flexibility is to increase the size of the web gap. This can be effective since the out-of-plane bending stresses are related to the inverse of the square of the web gap length. One critical issue for this approach is to avoid an excessive increase of out-of-plane deformation resulting from the web gap enlargement. Removal of portions of a stiffener or other plate to increase the size of the web gap will also require removal of the connecting weld in those regions to provide a smooth, flush surface. Non-destructive inspection should be conducted to ensure that no undesirable gouges, notches or discontinuities remain. In the stiffening retrofit, the stiffness of the detail in question is increased to minimize the out-of-plane distortion. Commonly, this will require the addition of a WT section, or a double or single angle section. Drilling retrofit holes to eliminate the tip of any distortion- induced fatigue cracks should be done prior to installation of the retrofit connection element. Typically, the installation of a retrofit element will increase the stiffness and significantly decrease the out-of-plane deformation at the detail. However, the force effect of the retrofit on the primary and secondary members

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 18 E-18 should be considered. One critical issue for this approach is to size the retrofit connection of sufficient thickness and strength for the loading forces to be generated at the new connection. 7.4—FRACTURE-CONTROL FOR OLDER BRIDGES C7.4 Bridges fabricated prior to the adoption of AASHTO’s Guide Specifications for Fracture-Critical Nonredundant Steel Bridge Members (1978) may have lower fracture toughness levels than are currently deemed acceptable. Destructive material testing of bridges fabricated prior to 1978 to ascertain actual toughness levels may be justified. Decisions on fatigue evaluations of a bridge can be made based upon the information from these tests.Without destructive material testing of bridges fabricated prior to 1978 to ascertain toughness levels, a fatigue-life estimate greater than the minimum expected fatigue life is questionable. An even lower value of fatigue life, to guard against fracture, may be appropriate. 7.5 ALTERNATE ANALYSIS METHODS Alternative analysis techniques, such as fracture mechanics and hot-spot stress analysis, may be used to predict the finite fatigue life of a detail. The estimate for finite life obtained from these methods should be used in place of Y in Article 7.2.6 to determine the fatigue serviceability index. The fatigue life of a steel bridge detail generally consists of crack initiation and stable crack propagation. The propagation stage continues until the crack reaches a critical length associated with unstable, rapid crack extension, namely fracture. An exception is constraint- induced fracture, where very little or no crack growth occurs prior to fracture. Fracture toughness reflects the tolerance of the steel for a crack prior to fracture. Fracture of steel bridges is governed by the total stress, including the dead load stress, and not just the live load stress range as is the case with fatigue. Older bridges with satisfactory performance histories likely have adequate fracture toughness for the maximum total stresses that they have experienced.probably have demonstrated that their fracture toughness is adequate for their total stresses, i.e., the dead-load stress plus the stress range due to the heaviest truck that has crossed the bridge. However, propagating fatigue cracks in bridges of questionable fracture toughness are is very serious, and may warrant immediate bridge closure. A rehabilitation of a bridge of unknown fracture toughness which may increase the dead-load stress must be avoided. C7.5 These analyses may be helpful in assessing cases where S-N test data from appropriately sized connections are not available. Hot-spot stress fatigue design has been used in certain industries to evaluate structures with complex geometries where nominal stress is not easily defined and where weld toe cracking is the most likely mode of failure. Fracture mechanics, on the other hand, has also been used in certain industries for a “fitness for purpose” type of assessment to establish a suitable design life for members with certain known flaw sizes. Efforts should be made to use a level of safety comparable with those levels prescribed in Article 7.2.6 for minimum, evaluation, or mean fatigue life.

SECTION 7: FATIGUE EVALUATION OF STEEL BRIDGES 19 E-19 7.57.6—REFERENCES AASHTO. 1978. Guide Specifications for Fracture-Critical Nonredundant Steel Bridge Members. American Association of State Highway and Transportation Officials, Washington, DC. AASHTO. 1990. Guide Specifications for Fatigue Evaluation of Existing Steel Bridges. American Association of State Highway and Transportation Officials, Washington, DC. AASHTO. 20072010. AASHTO LRFD Bridge Design Specifications, Fourth Fifth Edition, LRFDUS-4-M or LRFDSI- 4. American Association of State Highway and Transportation Officials, Washington, DC. Moses, F., C. G. Schilling, and K. S. Raju. 1987. Fatigue Evaluation Procedures for Steel Bridges, NCHRP Report 299. Transportation Research Board, National Research Council, Washington, DC

E-20 E.2 Section 7 (Incorporating Recommended Changes)

E-21 SECTION 7 FATIGUE EVALUATION OF STEEL BRIDGES 7.1 LOAD-INDUCED VERSUS DISTORTION- INDUCED FATIGUE Fatigue damage has been traditionally categorized as either load-induced or distortion- induced. Load-induced fatigue is that due to the in- plane stresses in the steel plates that comprise bridge member cross-sections. These in-plane stresses are those typically calculated by designers during bridge design or evaluation. Distortion-induced fatigue is that due to secondary stresses in the steel plates that comprise bridge member cross sections. These stresses, which are typically caused by out-of-plane forces, can only be calculated with very refined methods of analysis, far beyond the scope of a typical bridge design or evaluation. These secondary stresses are minimized through proper detailing. 7.2 LOAD-INDUCED FATIGUE DAMAGE EVALUATION 7.2.1 Application Two levels of fatigue evaluation are specified for load-induced fatigue: the infinite-life check of Article 7.2.4 and the finite-life calculations of Article 7.2.5. Only bridge details which fail the infinite-life check are subject to the more complex finite-life fatigue evaluation. Except for the case of riveted connections and tack weld details specified below, the list of detail categories to be considered for load-induced fatigue-damage evaluation, and illustrative examples of these categories are shown in LRFD Design Table 6.6.1.2.3-1. C7.1 The previous most comprehensive codification of fatigue evaluation of steel bridges, the Guide Specifications for Fatigue Evaluation of Existing Steel Bridges, AASHTO (1990), explicitly considered only load-induced fatigue damage. The Guide Specifications referenced NCHRP Report 299 for considering “fatigue due to secondary bending stresses that are not normally calculated,” NCHRP (1987). These “plates” may be the individual plates which comprise a built-up welded, bolted or riveted plate girder, or may be the flanges, webs, or other elements of rolled shapes. The traditional approximate methods of analysis utilizing lateral live-load distribution factors have encouraged bridge designers to discount the secondary stresses induced in bridge members due to the interaction of longitudinal and transverse members, both main and secondary members. Detailing to minimize the potential for distortion-induced fatigue, such as connecting transverse connection plates for diaphragms and floor beams to both the compression and tension flanges of girders, is specified in LRFD Design Article 6.6.1.3. C7.2.1 The initial infinite-life check should be made with the simplest, least refined stress-range estimate. If the detail passes the check, no further refinement is required. The stress-range estimate for the infinite-life check should be refined before the more complex procedures of the finite-life fatigue evaluation are considered.

E-22 The base metal at net sections of riveted connections shall be evaluated based upon the requirements of Category C, given in LRFD Design Table 6.6.1.2.3-1, instead of Category D as specified for new designs. The exception is for riveted members of poor physical condition, such as with missing rivets or indications of punched holes, in which case Category D shall be used. Tack welds may be evaluated based upon the requirements of Category C, given in LRFD Design Table 6.6.1.2.3-1. As uncertainty is reduced from the evaluation by more refined analysis or site-specific data, the increased certainty is reflected in lower partial load factors, summarized in Table 7.2.2.1-1 and described in Articles 7.2.2.1 and 7.2.2.2. If cracks have been visually detected then the fatigue life evaluation procedure specified herein should be used with caution. Generally, upon visual detection of load-induced fatigue cracking, the majority of the fatigue life has been exhausted and retrofitting measures should be initiated. Alternatively, a fracture mechanics approach can be used to evaluate the fatigue crack damage. 7.2.2 Estimating Stress Ranges The effective stress range shall be estimated as: ( ) (7.2.2-1)eff p sf R R f∆ = ∆ where: Rp = The multiple presence factor, calculated as described in Article 7.2.2.1 for calculated stress ranges, or 1.0 for measured stress ranges Rs = The stress-range estimate partial load factor, calculated as RsaRst, unless otherwise specified, summarized in Table 7.2.2.1-1, and f∆ = Measured effective stress range; or factored calculated stress range due to the passage of the fatigue truck as specified in LRFD Design Article 3.6.1.4 for Fatigue II Load Combination, or the calculated stress range due to a fatigue truck determined by a truck survey or weigh-in-motion study. For new design, the base metal at net sections of riveted connections is specified to be Category D. This represents the first cracking of a riveted member, which is highly redundant internally. Category C more accurately represents cracking that has propagated to a critical size. This increase in fatigue life for evaluation purposes is appropriate due to the redundancy of riveted members. Tack welds were frequently left in place in riveted connections. The tack welds were used to hold the members in place initially prior to placement of the rivets. Tack welds in this context are typically less than 2-in in length. The strength of tack welds was found to conform to fatigue Category C based on laboratory testing. The partial load factors specified in Article 7.2 were adapted from the Guide Specifications for Fatigue Evaluation of Existing Steel Bridges, AASHTO (1990). C7.2.2 The calculated stress range is due to a single truck in a single lane on the bridge. The multiple presence factor takes into account the effect of trucks present simultaneously in multiple lanes instead of a single lane loading. When using measured stress ranges, the multiple presence factor should not be used in the equation, as the effects of multiple presence are already reflected in the measured stress ranges. The load factor is 0.75 for live load specified for the Fatigue II limit state (finite load- induced fatigue life) in LRFD Design Table 3.4.1-1.

E-23 7.2.2.1 Calculating Estimated Stress Ranges The multiple presence factor Rp shall be calculated as: Rp = 0.988 + 6.87x10-5 (L) + 4.01x10-6 [ADTT]PRESENT + 0.0107 / (nL) 1.0 (7.2.2.1-1) where L = span length in feet, [ADTT]PRESENT = Present average number of trucks per day for all directions of truck traffic including all lanes on the bridge, and nL = number of lanes. Two sources of uncertainty are present in the calculation of effective stress range at a particular fatigue detail: Uncertainty associated with analysis, represented by the analysis partial load factor, Rsa, and Uncertainty associated with assumed effective truck weight, represented by the truck-weight partial load factor, Rst. The limits used in developing the equation are noted as follows: 2 nL 4; [ADTT]PRESENT < 8,000 for nL=2; 11,000 for nL=3, and 13,000 for nL=4, and 30 ft < L < 220 ft. These are the ranges used in the analysis, based on the WIM data available. Use of these equations may be justified outside of these ranges, but are not based on experimental evidence. The multiple presence factor is applicable to longitudinal parallel members only. For transverse members, use RP = 1.0. Table 7.2.2.1-1 Partial Load Factors: Rsa, Rst, and Rs. Fatigue-Life Evaluation Methods Analysis Partial Load Factor, Rsa Truck-Weight Partial Load Factor, Rst Stress-Range Estimate Partial Load Factor, Rsa For Evaluation or Minimum Fatigue Life Stress range by simplified analysis, and truck weight per Article 3.6.1.4 of the LRFD Specifications 1.0 1.0 1.0 Stress range by simplified analysis, and truck weight estimated through weigh- in-motion study 1.0 0.95 0.95 Stress range by refined analysis, and truck weight per Article 3.6.1.4 of the LRFD Specifications 0.95 1.0 0.95 Stress range by refined analysis, and truck weight by weigh-in-motion study 0.95 0.95 0.90 Stress range by field- measured strains NA NA 0.85 For Mean Fatigue Life All methods NA NA 1.00 a In general, Rs = RsaRst

E-24 7.2.2.1.1 For Determination of Evaluation or Minimum Fatigue Life In the calculation of effective stress range for the determination of evaluation or minimum fatigue life, the stress-range estimate partial load factor shall be taken as the product of the analysis partial load factor and the truck-weight partial load factor: Rs = RsaRst (7.2.2.1.1-1) If the effective stress range is calculated through refined methods of analysis, as defined in LRFD Design Article 4.6.3, Rsa = 0.95 (7.2.2.1.1-2) otherwise, Rsa = 1.0 (7.2.2.1.1-3) If the effective truck weight is estimated through a weigh-in-motion study at, or near, the bridge, Rst = 0.95 (7.2.2.1.1-4) otherwise, Rst = 1.0 (7.2.2.1.1-5) 7.2.2.1.2 For Determination of Mean Fatigue Life In the calculation of effective stress range for the determination of mean fatigue life, the stress- range estimate partial load factor shall be taken as 1.0. 7.2.2.2 Measuring Estimated Stress Ranges The effective stress range may be estimated through field measurements of strains at the fatigue- prone detail under consideration under typical traffic conditions. The effective stress range shall be computed as the cube root of the weighted sum of the cubes of the measured stress ranges, as given in: 1/33( ) 7.2.2.2 1eff s i if R f where: i = Percentage of cycles at a particular stress range, and if = The particular stress range in a measured stress range histogram of magnitude greater than one half of the constant-amplitude-fatigue- threshold of the fatigue prone detail under consideration, i.e. > FTH/2. C7.2.2.2 Field measurements of strains represent the most accurate means to estimate effective stress ranges at fatigue-prone details. The AASHTO LRFD Bridge Design Specifications assume that the maximum stress range is twice the effective stress range. It is unlikely that the maximum stress range during the service life of the bridge will be captured during a limited field measurement session; therefore means to extrapolate from the measured stress range histogram to the maximum stress range must be used. The lower portion of field measured stress range histograms must be truncated in order to avoid underestimating the effective stress range.

E-25 7.2.2.2.1 For Determination of Evaluation or Minimum Fatigue Life Where field-measured strains are used to generate an effective stress range, Rs, for the determination of evaluation or minimum fatigue life, the stress-range estimate partial load factor, shall be taken as 0.85 7.2.2.2.2 For Determination of Mean Fatigue Life Where field-measured strains are used to generate an effective stress range, Rs, for the determination of mean fatigue life, the stress-range estimate partial load factor, shall be taken as 1.0. 7.2.3 Determining Fatigue-Prone Details Bridge details are only considered prone to load-induced fatigue damage if they experience a net tensile stress. Thus, fatigue damage need only be evaluated if, at the detail under evaluation, 2( f)tension > fdead-load compression (7.2.3-1) where: ( f)tension = Tensile portion of the effective stress range as specified in Article 7.2.2, and fdead-load compression = Unfactored compressive stress at the detail due to dead load. 7.2.4 Infinite-Life Check If: ( f)max ( F)TH, (7.2.4-1) then: Y = , (7.2.4-2) where: ( f)max = The maximum stress range expected at the fatigue-prone detail, which may be taken as: • Rp times the factored calculated stress range due to the passage of the fatigue truck as specified in LRFD Design Article 3.6.1.4 for Fatigue I Load Combination C7.2.3 The multiplier of two in the equation repre- sents the assumed relationship between maximum stress range and effective stress range, as specified in the AASHTO LRFD Bridge Design Specifications. When measured stress ranges are used to evaluate fatigue life, the multiplier of two in the equation should be reconsidered based upon the discussion of Article C7.2.2.2. If the effective truck weight is significantly less than 54 kips, a multiplier more than two should be considered. Similarly, for a measured effective truck weight greater than 54 kips a multiplier less than two would be appropriate. C7.2.4 Theoretically, a fatigue-prone detail will experience infinite life if all of the stress ranges are less than the constant amplitude fatigue threshold; in other words, if the maximum stress range is less than the threshold. The load factor is 1.50 for live load specified for the Fatigue I limit state (infinite load-induced fatigue life) in LRFD Design Table 3.4.1-1.

E-26 2.0( f)eff ; for calculated stress range due to a fatigue truck determined by a truck survey or weigh-in-motion study with Rs=1.0 Larger of maximum ( if ), 2( f)eff , or other suitable value; for measured stress ranges with Rs=1.0 ( F)TH = The constant-amplitude fatigue threshold given in LRFD Design Table 6.6.1.2.5-3 otherwise, the total fatigue life shall be estimated as specified in Article 7.2.5. 7.2.5 Estimating Finite Fatigue Life 7.2.5.1 General Four levels of finite fatigue life may be estimated: The minimum expected fatigue life (which equals the conservative design fatigue life), Evaluation 1 fatigue life (which is a somewhat less conservative fatigue life for evaluation), Evaluation 2 fatigue life (which equals a more conservative fatigue life for evaluation), and The mean fatigue life (which equals the statistically most likely fatigue life). The total finite fatigue life of a fatigue-prone detail, in years, shall be determined as: 1 3log (1 ) 1365 ( ) [( ) ] (7.2.5.1-1) log(1 ) aR SL effPRESENT R A g g n ADTT f Y g where: RR = Resistance factor specified for evaluation, minimum, or mean fatigue life as given in Table 7.2.5.1-1 A = Detail-category constant given in LRFD Design Table 6.6.1.2.5-1 n = Number of stress-range cycles per truck passage estimated according to Article 7.2.5.2 g = Estimated annual traffic-volume growth rate in percentage a = Present age of the detail in years [(ADTT)SL]PRESENT = Present average number of trucks per day in a single lane When measured stress ranges are used to evaluate fatigue life, the maximum stress range should be taken as the larger value of two times field measured effective stress range or the field measured maximum stress range, unless another suitable value is justified. C7.2.5.1 Much scatter, or variability, exists in experimentally derived fatigue lives. For design, a conservative fatigue resistance two standard deviations shifted below the mean fatigue resistance or life is assumed. This corresponds to the minimum expected finite fatigue life of this Article. Limiting actual usable fatigue life to this design fatigue life is very conservative and can be costly. As such, means of estimating the two evaluation fatigue lives and the mean finite fatigue life are also included to aid the evaluator in the decision making. Recent research has made it possible to obtain a closed-form solution for the total finite fatigue life using an estimated traffic growth rate and the present (ADTT)SL. For cases with zero traffic growth, a very small value of g should be selected for use in the expression for Y. The resistance factors for fatigue life, specified in Table 7.2.5.1-1, represent the variability of the fatigue life of the various detail categories, A through E’. The minimum life, evaluation 1 life and evaluation 2 life fatigue-life curves are shifted from the mean fatigue-life S-N curves in log-log space. Scatter of the fatigue lives at given stress range values from controlled laboratory testing provides statistical information on fatigue behavior of bridge details under cyclic loading. Accordingly, the probability of failure associated with each level of fatigue life, approaches 2 percent, 16 percent, 33 percent and 50 percent for the minimum, evaluation 1, evaluation 2 and mean fatigue lives, respectively. Typically, the minimum life or evaluation 1 life is used to evaluate the fatigue serviceability. If concerns are encountered regarding the computed fatigue serviceability, then the serviceability index can be revised according to Article 7.2.7.2.

E-27 ( )efff = The effective stress range as specified in Article 7.2.2 Table 7.2.5.1-1 Resistance Factor for Evaluation, Minimum or Mean Fatigue Life, RR Detail Category (from Table 6.6.1.2.5-1 of the LRFD Specifications) RR Minimum Life Evaluation 1 Life Evaluation 2 Life Mean Life A 1.0 1.5 2.2 2.9 B 1.0 1.3 1.7 2.0 B’ 1.0 1.3 1.6 1.9 C 1.0 1.3 1.7 2.1 C’ 1.0 1.3 1.7 2.1 D 1.0 1.3 1.7 2.0 E 1.0 1.2 1.4 1.6 E’ 1.0 1.3 1.6 1.9 7.2.5.2 Estimating the Number of Cycles per Truck Passage The number of stress-range cycles per truck passage may be estimated (in order of increasing apparent accuracy and complexity): Through the use of LRFD Design Table 6.6.1.2.5-2, Through the use of influence lines, or By field measurements. 7.2.6 Fatigue Serviceability Index 7.2.6.1 Calculating the Fatigue Serviceability Index The fatigue serviceability index shall be calculated as: (7.2.6.1-1)Y aQ GRI N where: N = Greater of Y or 100 years G = Load Path Factor, as given in Table 7.2.6.1-1 R = Redundancy Factor, as given in Table 7.2.6.1-2 I = Importance Factor, as given in Table 7.2.6.1-3 C7.2.6 The fatigue serviceability index is a dimensionless relative measure of the performance of a structural detail, at a particular location in the structure, with respect to the overall fatigue resistance of the member. The load path, redundancy and importance factors are risk factors that modify the fatigue serviceability index. They reduce the index from its base value, i.e. based on fatigue resistance alone, to a reduced value that reflects greater consequences from the lack of ability to redistribute the load (load path factor), lack of redundancy (redundancy factor), or use of the structure (importance factor). The net effect of a reduction in the index will be to move the composite index value to a lower value that may initiate a lower fatigue rating. These risk factors are similar to the ductility, redundancy and operational classification factors in the AASHTO LRFD Bridge Design Specifications. Improved quantification with time will possibly modify these factors.

E-28 Table 7.2.6.1-1 Load Path Factor G Number of Load Path Members G 1 or 2 members 0.8 3 members 0.9 4 or more members 1 Table 7.2.6.1-2 Redundancy Factor R Type of Span R Simple 0.9 Continuous 1 Table 7.2.6.1-3 Importance Factor I Structure or Location Importance Factor, I Interstate Highway Main Arterial State Route Other Critical Route 0.90 Secondary Arterial Urban Areas 0.95 Rural Roads Low ADTT routes 1.00 The number of members that carry load when a fatigue truck is placed on the bridge is used to select the load path factor; e.g., two members for a two-girder bridge and for a typical truss structure; four or more members for a multi-beam or multi- girder bridge; etc. For diaphragms and secondary members, use G = 1. 7.2.6.2 Recommended Actions Based on Fatigue Serviceability Index The fatigue ratings and assessment outcomes as given in Table 7.2.6.2-1 are recommended as a guideline for actions that may be undertaken based on the obtained value for the fatigue serviceability index. A better fatigue rating may be assumed for Q values at the boundary of two ranges. In the recommended actions provided, it is expected that based upon increasing risk, the inspection frequency of the bridge shall be increased on a case-by-case assessment by the bridge owner. Table 7.2.6.2-1 Fatigue Rating and Assessment Outcomes Fatigue Serviceability Index, Q Fatigue Rating Assessment Outcome 1.00 to 0.50 Excellent Continue Regular Inspection 0.50 to 0.35 Good Continue Regular Inspection 0.35 to 0.20 Moderate Continue Regular Inspection 0.20 to 0.10 Fair Increase Inspection Frequency 0.10 to 0.00 Poor Assess Frequently < 0.00 Critical Consider Retrofit, Replacement or Reassessment

E-29 7.2.7 Strategies to Increase Fatigue Serviceability Index 7.2.7.1 General If the fatigue serviceability index is deemed unacceptable, the strategies of Articles 7.2.7.2 and 7.2.7.3 may be applied to enhance the fatigue serviceability index. 7.2.7.2 Recalculate Fatigue Serviceability Index 7.2.7.2.1 Through Accepting Greater Risk In general, evaluation 1 life of Article 7.2.5 is used in determining the fatigue serviceability index of a bridge detail according to Article 7.2.6. If the evaluator is willing to accept greater risk of fatigue cracking due to: Long satisfactory cyclic performance of the detail to date, A high degree of redundancy, and/or Increased inspection effort, e.g., decreased inspection interval, Some combination of the above the fatigue serviceability index may be determined using a fatigue life approaching the mean fatigue life of Article 7.2.5. 7.2.7.2.2 Through More Accurate Data The calculated fatigue serviceability index may be refined by using more accurate data as input to the fatigue-life estimate. Sources of improvement of the estimate include: Field measurement of stress ranges at the fatigue prone detail under construction 3-D finite element analysis for stresses at the fatigue prone detail under consideration Weigh-in-motion data of truck weights at or near the bridge site, Site-specific data on average daily truck traffic (ADTT) at or near the bridge site C7.2.7.1 Retrofit or load-restriction decisions should be made based upon the evaluation fatigue life unless the physical condition or fabrication quality of the bridge is poor. In general, it is uneconomical to limit the useful fatigue life of in-service bridges to the minimum (design) fatigue life. If the estimated fatigue serviceability index based upon the evaluation fatigue life is deemed unacceptable, a fatigue life approaching the mean fatigue life can be used for evaluation purposes if additional risk of fatigue cracking is acceptable.

E-30 This strategy is based upon achieving a better estimate of the fatigue life. 7.2.7.2.3 Through Truncated Fatigue Life Distribution When a negative fatigue serviceability index is obtained according to Article 7.2.6, the detail’s fatigue serviceability index may be updated using equations below for mean, evaluation and minimum lives, provided a field inspection finds no evidence of fatigue cracking at the detail. 10.73 [0.18(1 ) ] 0.27 ' 2.19 7.2.7.2.3 1P Pmean meanY Y e 10.73 [0.12(1 ) ] 0.27 2' 2.19 7.2.7.2.3 2 P P eval meanY Y e 10.73 [0.074(1 ) ] 0.27 1' 2.19 7.2.7.2.3 3 P P eval meanY Y e 10.73 [0.039(1 ) ] 0.27 minimum' 2.19 7.2.7.2.3 4 P P meanY Y e where eval1 eval ' = Updated mean life in years = Mean life in years without updating based on no detection of cracking at detail in question Y' = Updated evaluation 1 life in years Y' mean mean Y Y 2 minimum -1 = Updated evaluation 2 life in years Y' = Updated minimum life in years = Inverse of the standard normal variable's cumulative probability function (Table 7.2.7.2-1) P = Probability of fatigue life being shorter than current age before updating based on no crack found 0.27 2.19 = 7.2.7.2.3 5 0.73 where a = Present age mean aLn Y in years = Standard normal variable's cumulative probability function (Table 7.2.7.2-1) C7.2.7.2.3 The fatigue life of a structural detail is modeled using a lognormally distributed random variable, as shown in the figure C7.2.7.2.3-1. When the estimated life using Article 7.2.5 is smaller than the present age, the remaining life becomes negative as illustrated. In this situation, if field inspection finds no evidence of cracking, the estimated life is an overly- conservative estimate. The low tail of the total life distribution is truncated up to the present life. The eliminated probability P is computed, and the resulting probability density function is divided by (1 – P) to ensure that the total probability under the distribution curve is still 1.0 as shown in Figure C7.2.7.2.3-2. Then the updated life is determined to maintain the same reliability level for fatigue life distribution. Functions (.) and -1(.) are commonly available in commercial spreadsheet programs. Fig C7.2.7.2.3-1 Probability Density Function of Fatigue Life and Estimated Life as a Value on Horizontal Axis Fig C7.2.7.2.3-2 Truncated Probability Density Function of Fatigue Life and Updated Life as a value on the Horizontal Axis

E-31 Table 7.2.7.2-1 Cumulative Distribution Function (x) for Standard Normal Variable x x 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 7.2.7.3 Retrofit If the recalculated fatigue serviceability index is not ultimately acceptable, the actual fatigue serviceability index may be increased by retrofitting the critical details to improve the detail category and thus increase the fatigue serviceability index. This strategy increases the actual fatigue serviceability index when further enhancement of the calculated fatigue serviceability index, through improved input, is no longer possible or practical. 7.3 DISTORTION-INDUCED FATIGUE EVALUATION Distortion-induced fatigue is typically caused by out-of-plane deformation of the web plate that results in fatigue crack formation at details prone to such cracking under cyclic loading. The cracks tend to form in the member web at locations where there is a geometrical discontinuity, such as a vertical gap between a stiffener or connection plate and the girder flange or a horizontal gap between a gusset plate and a connection plate. Distortion-induced fatigue is a stiffness problem (more precisely the lack thereof) versus a load problem. Often, distortion-induced fatigue cracks initiate after relatively few stress-range cycles at C7.2.7.3 In certain cases, Owners may wish to institute more intensive inspections, in lieu of more costly retrofits, to assure adequate safety. Restricting traffic to increase the fatigue serviceability index is generally not considered cost effective. If the fatigue serviceability index is deemed inadequate, the appropriate option to increase the fatigue serviceability index should be determined based upon the economics of the particular situation. C7.3 Existing bridges should not be assumed to be insensitive to distortion-induced cracking if fatigue cracks do not appear after a short period of time. Experience has shown that in some cases cracking may not be evident for 10 years after the beginning of service.

E-32 fatigue-prone details. However, depending upon the magnitude of the out-of-plane distortion and the geometry of the web gap detail, the crack growth may be slow and a significant period of time may be required before they become large enough to be detected visually. 7.3.1 Methods to Assess Distortion-Induced Cracking Out-of-plane distortions caused by truck loading must be accommodated by the regions that contain unsupported web gaps. Even very small distortions can cause high local stresses that may induce fatigue cracking. Often, the fatigue cracks grow in a plane that is parallel to the primary stresses of the member and will slow down or even stop as the web gap becomes more flexible due to the presence of the crack. However, it is possible that the crack may turn and become perpendicular to the primary stress of the member, leading to more rapid crack growth. Therefore, distortion-induced fatigue cracks should be repaired. 7.3.2 Retrofit Options for Distortion-Induced Fatigue Cracking Retrofit should be considered if distortion- induced cracking has been detected. Two primary retrofit methods are available: softening or stiffening. The softening approach is used to increase the overall flexibility of the detail in question to accommodate the out-of-plane deformations without further cracking. The stiffening approach is used to minimize the local distortion by providing a positive load path for the forces that tend to cause the distortion. In either case, a hole should be drilled at the tip of each crack. C7.3.1 Typically, smaller web gaps are subject to higher distortion-induced stresses than larger web gaps provided the same demand for the out-of-plane distortion. The demand for out-of-plane distortion is determined by the global behavior of the structural system. Accurate quantification of the stress field in an unsupported web gap detail can be very difficult, even for finite element modeling or field measurement of strains and/or local deformations. This is especially the case when the dimension of the web gap is comparable to the thicknesses of the surrounding plates and the sizes of the connecting welds, resulting in high stress gradients across the web gap. C7.3.2 In the softening retrofit, the flexibility of the detail in question is increased. Drilling holes to eliminate the tip of distortion-induced fatigue cracks will typically increase the local flexibility somewhat. However, the primary method used to increase the flexibility is to increase the size of the web gap. This can be effective since the out-of-plane bending stresses are related to the inverse of the square of the web gap length. One critical issue for this approach is to avoid an excessive increase of out-of-plane deformation resulting from the web gap enlargement. Removal of portions of a stiffener or other plate to increase the size of the web gap will also require removal of the connecting weld in those regions to provide a smooth, flush surface. Non-destructive inspection should be conducted to ensure that no undesirable gouges, notches or discontinuities remain. In the stiffening retrofit, the stiffness of the detail in question is increased to minimize the out-of-plane distortion. Commonly, this will require the addition of a WT section, or a double or single angle section. Drilling retrofit holes to eliminate the tip of any distortion-induced fatigue cracks should be done

E-33 7.4 FRACTURE-CONTROL FOR OLDER BRIDGES Bridges fabricated prior to the adoption of AASHTO’s Guide Specifications for Fracture- Critical Non-Redundant Steel Bridge Members (1978) may have lower fracture toughness levels than are currently deemed acceptable. Destructive material testing of bridges fabricated prior to 1978 to ascertain actual toughness levels may be justified. Decisions on fatigue evaluations of a bridge can be made based upon the information from these tests. 7.5 ALTERNATE ANALYSIS METHODS Alternative analysis techniques, such as fracture mechanics and hot-spot stress analysis, may be used to predict the finite fatigue life of a detail. The estimate for finite life obtained from these methods should be used in place of Y in Article 7.2.6 to determine the fatigue serviceability index. prior to installation of the retrofit connection element. Typically, the installation of a retrofit element will increase the stiffness and significantly decrease the out-of-plane deformation at the detail. However, the force effect of the retrofit on the primary and secondary members should be considered. One critical issue for this approach is to size the retrofit connection of sufficient thickness and strength for the loading forces to be generated at the new connection. C7.4 The fatigue life of a steel bridge detail generally consists of crack initiation and stable crack propagation. The propagation stage continues until the crack reaches a critical length associated with unstable, rapid crack extension, namely fracture. An exception is constraint-induced fracture, where very little or no crack growth occurs prior to fracture. Fracture toughness reflects the tolerance of the steel for a crack prior to fracture. Fracture of steel bridges is governed by the total stress, including the dead load stress, and not just the live load stress range as is the case with fatigue. Older bridges with satisfactory performance histories likely have adequate fracture toughness for the maximum total stresses that they have experienced. However, propagating fatigue cracks in bridges of questionable fracture toughness is very serious, and may warrant immediate bridge closure. C7.5 These analyses may be helpful in assessing cases where S-N test data from appropriately sized connections are not available. Hot-spot stress fatigue design has been used in certain industries to evaluate structures with complex geometries where nominal stress is not easily defined and where weld toe cracking is the most likely mode of failure. Fracture mechanics, on the other hand, has also been used in certain industries for a “fitness for purpose” type of assessment to establish a suitable design life for members with certain known flaw sizes. Efforts should be made to use a level of safety comparable with those levels prescribed in Article 7.2.6 for minimum, evaluation, or mean fatigue life.

E-34 7.6—REFERENCES AASHTO. 1978. Guide Specifications for Fracture-Critical Nonredundant Steel Bridge Members. American Association of State Highway and Transportation Officials, Washington, DC. AASHTO. 1990. Guide Specifications for Fatigue Evaluation of Existing Steel Bridges. American Association of State Highway and Transportation Officials, Washington, DC. AASHTO. 2010. AASHTO LRFD Bridge Design Specifications, Fifth Edition. American Association of State Highway and Transportation Officials, Washington, DC. Moses, F., C. G. Schilling, and K. S. Raju. 1987. Fatigue Evaluation Procedures for Steel Bridges, NCHRP Report 299. Transportation Research Board, National Research Council, Washington, DC.

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TRB’s National Cooperative Highway Research Program (NCHRP) Report 721: Fatigue Evaluation of Steel Bridges provides proposed revisions to Section 7—Fatigue Evaluation of Steel Bridges of the American Association of State Highway and Transportation Officials Manual for Bridge Evaluation with detailed examples of the application of the proposed revisions.

Appendixes A-D to NCHRP Report 721 are only available electronically. The appendices, which are in one electronic document, are as follows:

• Appendix A - Survey Interview Forms

• Appendix B - AASHTO Fatigue Truck Validation Analysis Results

• Appendix C - Tack Weld Tests

• Appendix D - Distortion Induced Fatigue Tests

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