Fatigue Evaluation of Steel Bridges (2012)

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24 As described in the previous chapter, individual items in Section 7 that were identified for revision were examined. This chapter presents the results of the examination of the items. Also included are the details of finite element analysis carried out for the experimental tests as well as the results of experimental testing for tack weld and distortion-induced fatigue tests. S-N Curve Data regarding long cyclic life behavior are provided in NCHRP Report 354 (Fisher et al., 1993) for three differ- ent types of welded details: partial-length cover plates, web attachments, and transverse web stiffeners. The results were found to support the conservative design assumption that a straight-line extension of the fatigue resistance curves can be used to predict fatigue lives with variable life loading. This was believed, however, to be overly conservative for higher strength details such as transverse stiffeners. The test results from NCHRP Report 336 (Fisher et al., 1990) for distortion-induced fatigue strength of transverse connection plates were used to compare the AASHTO and Eurocode S-N curves specified for this detail. For normal stress ranges, the Eurocode stipulates 14 detail categories for fatigue instead of the 8 stipulated by AASHTO. Each Euro- code detail category is designated by a number which repre- sents, in N/mm2, the reference value for the fatigue strength at 2 million cycles. When test data were used to determine the appropriate detail category for a particular constructional detail, the value of the stress range corresponding to 2 million cycles was calculated for a 75% confidence level of 95% prob- ability of survival for log N, taking into account the standard deviation and the sample size and residual stress effects. The Eurocode S-N curves use a slope of 3 for up to 5 million cycles where the corresponding stress range is the CAFL for that curve. From 5 million cycles to 100 million cycles, a slope of 5 is used, and the stress range corresponding to 5 million cycles is the cutoff limit for the curves. Eurocode classifies vertical stiffeners welded to a beam or plate girder as detail category 80 while AASHTO classifies the details as Category C. Figure 17 shows the comparison of the test data with the Eurocode detail category 80 S-N Curve and AASHTO detail category C (CAFL: 10 ksi). The AASHTO S-N curve has been extended below the CAFL up to the variable amplitude fatigue limit (VAFL), which is half the CAFL. As can be seen from the figure, the AASHTO S-N curve is also a reasonable curve for the distortion-induced fatigue cracking at ends of transverse connection plates, even in the long-life region. On comparison with the Eurocode S-N curve, the AASHTO S-N curve seems to equally fit the test data in the long-life region, where the Eurocode S-N curve changes its slope from 3 to 5. Changing the nature of the current AASHTO fatigue curves from linear to a more bi- linear slope would considerably increase the effort required in calculation of fatigue life. Neither does it seem that adopt- ing a bi-linear slope can considerably increase the accuracy in prediction of fatigue life in the long-life region. The test data examined here also do not seem to justify the need to change the nature of S-N curves. Hence, it was decided to not change the linearly varying nature of the current S-N curves and keep them as they are. Validation of AASHTO Fatigue Truck An analysis was performed using WIM data collected from randomly selected states, sites, truck traffic volumes, and recording months. This investigation using the analysis results was aimed at better understanding whether the AASHTO fatigue truck reasonably models the real load and, if not, how to improve this model. The analysis results are gathered in Appendix B. As seen in Appendix B, WIM data from the states of California, Florida, Idaho, New York, Michigan, Texas, and Vermont were used in this analysis. The road configuration C h a p t e r 3 Findings and Applications

25 Given this observation, there have not been obvious rea- sons and motivation to recommend a new model to better describe the fatigue load effect than the current AASHTO fatigue truck, although the latter’s lack of realistic modeling is obvious. At this point, it is recommended or further empha- sized, as done in Section 7 of the AASHTO MBE, that WIM data gathered at or near a particular site with well maintained and calibrated equipment is clearly the most reliable data to be used for fatigue load effect estimation. Multiple Presence Factor The present study uses WIM data to derive the multiple presence factor (MPF). A large amount of WIM truck weight data is used to simulate and model the behavior of trucks and their load effects in bridge components. This data set provides a reliable basis for the MPF recommended in this report for steel bridge fatigue evaluation. In general, longer spans allow more trucks to be simultaneously present on the span, higher truck traffic volumes increase the probability of such simultaneous presence, and more lanes available reduce such likelihood. The proposed MPF is thus given as a function of these three major causal factors: span length, ADTT, and number of lanes. To fully understand the behavior of truck load effects in bridge components, this study also has used a new truck-by- truck analysis approach to develop raw data of MPF. These data events are then used to perform regression analyses for developing the proposed MPFs as functions of the identified causal factors. varied from 2 to 4 lanes of truck traffic in the same direc- tion. Some states provided more cases with a varied num- ber of lanes than others. The ADTT per lane of these sites varied from tens of trucks (61) to thousands (4,703). Please note that these ADTT values are averaged over the number of lanes recorded, used here merely as an indicator, while the real ADTT on each lane can vary more notably. Among dif- ferent lanes at the same site, the truck traffic distribution can be quite uneven. One lane may have as much as 86% of the total truck traffic, compared to another lane with as little as 4%. Therefore the actual ADTT of each lane (not the aver- aged ADTT per lane) can vary much more significantly than from 61 to 4,703. The figures gathered in Appendix B use one common quantity on the vertical axis. It is the quotient of the WIM truck load effects summed according to Miner’s law and the corresponding AASHTO fatigue truck’s load effect. If the ratio is larger than 1, it means that the AASHTO model underestimates the real fatigue load effect. Otherwise if the ratio is below 1, then the model over-estimates the real fatigue load effect. As seen in the results shown in Appendix B, it was very difficult to conclude whether the AASHTO fatigue truck model over-estimates or underestimates the true loading effect or condition. In other words, the AASHTO model sometimes goes one way and at another time the other way. Higher ADTT values do not necessarily lead to a higher fatigue load effect, apparently relevant to what truck con- figurations (axle loads, axle distances, etc.) are more com- mon at a particular site. 1 10 100 1.00E+05 1.00E+06 1.00E+07 1.00E+08 St re ss R an ge (k si) Cycles to crack Test Results Eurocode Category 80 AASHTO Category C Figure 17. Comparison of test data with AASHTO and Eurocode S-N curves.

26 Concept of Multiple Presence Factor For strength limit states, MPF is intended to facilitate esti- mation of the load effect in a structural component due to all truck loads on the span, with reference to the load effect in the same component due to only one lane of truck load. Therefore, MPF for evaluation is formulated similarly as follows: MPF N-Lane Load Effect in Component One-Lane = Load Effect in Component LE LE total onelane = ( )3 where LE stands for load effect. The subscript “total” indi- cates the total load effect due to trucks in all the lanes on the bridge, and “onelane” indicates the total load effect due to only one lane of truck load. The fatigue load effect is modeled herein using the Miner’s law assuming linear accumulation of fatigue damage: LE LE f LE f LE total onelane i i_total 3 j j_one = ∑ ∑ 3 lane 3 i j =1,2,3, 3 1 2 3 4= , , , ; ( )… … The LEtotal in the numerator is the fatigue load effect of all trucks on the span in all lanes available. LEi_total here is the total fatigue load effect of the ith load event (i.e., the ith pla- toon of trucks) in the WIM data, and fi is the frequency or probability of load event i. Similarly, LEonelane in the denomi- nator is the fatigue load effect of trucks in the driving lane. LEj_onelane is the load effect of trucks in load event j (i.e., the jth platoon of trucks) in the driving lane, and fj is its frequency. This definition of MPF in Equations 3 and 4 will allow conve- nient estimation of load effects from all lanes by multiplying MPF with one lane’s load effect. The latter can be practically obtained and commonly performed using the WIM tech- nique available with state transportation agencies through- out the United States. In each load effect event (or truck platoon) i or j, there can be one or more trucks on the span contributing to the load effect in the bridge component. The superposi- tion of two or more load effects of these trucks needs to cover two perpendicular directions. One is the traffic or longitudinal direction and the other the perpendicular or transverse direction. The former can be done using influ- ence lines and the latter needs to consider lateral distribu- tion of load effect to the interested bridge component. The superposition along the longitudinal direction is performed here based on the headway distance between the trucks on the span, with reference to the corresponding load effect’s influence line. Both LEi_total and LEj_onelane need to include this superposition as deemed appropriate. On the other hand, only LEi_total needs to consider lateral superposition to include trucks in different lanes. This effect is modeled accordingly as follows: LE DF LE DF LE DF LE DF LEi_total 1 i1 2 i2 3 i3 4 i4= + + + (5) and also, LE DF LE LE LEj_onelane 1 j1 j1 i1= =( ) ( )6 where LEi1 to LEi4 are respectively load effects of trucks in Lanes 1 to N, up to all the available lanes. In this study, the maximum N is 4 because only up to 4 lanes of simultane- ously recorded WIM data are available, although the con- cept can be extended further to more lanes. Note that LEi1 to LEi4 include longitudinally superimposed load effects in the respective same lanes. DF1 to DF4 in Equations 5 and 6 are lateral distribution factors to distribute loads in Lanes 1 through 4 to the focused bridge component. For computation convenience, Equation 5 is rewritten as LE DF LE DF DF LE DF DF LE DF DF LEi 1 i1 2 1 i2 3 1 i3 4 1 i= + + + 4   ( )7 In Equation 4, both the numerator and denominator have DF1 as a factor. It will then be cancelled. Thus, only the ratios DF DF 2 1 , DF DF 3 1 , and DF DF 4 1 in Equation 7 are needed for the analy- sis defined in Equations 3 and 4. These ratios indicate the relative weights of load in Lane k to Lane 1 (for k=2, 3, or 4) in load distribution. The following values of these ratios are used in this study, based on a review of available research results for a variety of highway bridge types and span lengths (AASHTO 2010, BridgeTech et al. 2007, Zokaie et al. 1991). Their possible variation is discussed in the following section on Sensitivity Analysis and given as: For 2-lane spans, DF DF 2 1 = 0 45 8. ( ) For 3-lane spans, DF DF DF DF 2 1 3 1 = =0 40 0 15 9. ; . ( ) For 4-lane spans, DF DF DF DF DF2 1 3 1 = =0 40 0 15. ; . ; 4 1DF = 0 0 10. ( ) Note that in the AASHTO MBE (2011) only one lane of loading is specified to be considered for the fatigue limit state evaluation. For longer spans and higher ADTTs, this approach apparently underestimates fatigue damage accu- mulation since more trucks are likely to be present on the span other than just Lane 1 or driving lane. Using MPF defined in Equation 3 will simplify analysis in bridge design and evaluation for these cases, by simply multiplying one lane load effect with N and MPF to obtain the total fatigue load effect. It will help estimate more reliably fatigue load effect, especially in fatigue evaluation of steel bridges for more reli- able remaining life prediction. This will be particularly true

27 for two-girder-, two-truss-, and two-arch-systems, where each primary member needs to carry all the lanes (as opposed to multiple beams carrying several lanes so that some beams do not participate in carrying certain lanes at all). Note that current AASHTO specifications unconservatively ignore loads from lanes other than the shoulder lane. Analysis Overview and WIM Data Used The MPF proposed herein is developed using WIM data from California, Oregon, Michigan, and New York, related to span length, ADTT, and number of lanes. These states are the only ones found to have truck weight data with a time stamp of 0.01 second, the highest resolution avail- able for WIM data. This high time stamp resolution allows identification of two trucks’ headway distances as short as 1 ft at a speed of 70 miles per hour. This resolution therefore permits an accurate and reliable estimation of the additional load effect of another truck on the same span but in a different lane when two trucks are close to each other longitudinally. The 2-lane, 3-lane, and 4-lane situations are analyzed sepa- rately using WIM data from these states. A total of 18.1 mil- lion trucks over 161 months from 17 sites is used for the case of 2-lane spans, 22.2 million trucks over 137 months from 13 stations for 3-lane spans, and 27.4 million trucks over 138 months from 13 sites for 4-lane spans. Simple spans have been included in this effort of developing MPF. The ADTT ranged from 777 to 8,421 for 2-lane, 740 to 10,734 for 3-lane, and 671 to 12,816 for 4-lane roadways. The WIM data were selected to cover a realistic range of ADTT, especially the high end where MPF is significant and more critical. The data were scrubbed first before the analysis, and typically less than 4% of the recorded data were eliminated when an apparent inconsistency was seen. For the case of fatigue limit state, each month of WIM data is used to produce one point of MPF value as defined in Equa- tion 3. A total of 8 span lengths (30, 50, 70, 100, 130, 160, 190, and 220-ft) has been analyzed to produce data points for the subsequent regression analysis. The resulting regression rela- tion of MPF to the causal factors is proposed in Equation 11 for estimating the total fatigue load based on one lane of load effect. It is derived using MPF values for the WIM data from four states discussed previously, with an R2 of 0.73. MPF span length ADT = + × + ×− −0 988 6 87 10 4 01 105 6. . . T N 1+ × >−1 07 10 112. ( ) For both midspan moment and support shear, Figures 18 through 23 display comparisons of the regression relation in Equation 11 and the computed MPF values according to Equation 3 for three cases of number of lanes (N=2, 3, and 4) and three cases of simple span lengths (30, 100, and 220 ft) over a range of observed ADTT. Most MPF values are clus- tered near 1.0, and it would be difficult to see their behavior for the different number of lanes N. The figures were there- fore plotted with the MPF value divided by the number of lanes of traffic N, so that the influence of traffic lanes could be displayed. As seen, the regression line or the recommended MPF fits very well with the observed values for the practically representative ranges of the parameters. Sensitivity Analysis As discussed in the previous section on the distribution factor ratios defined in Equations 8 through 10, these ratios may vary depending on a number of factors, such as type of deck (concrete deck, timber deck, whether composite or non- composite with the supporting members, etc.); type of deck supporting system (concrete beams, steel beams, pre-stressed concrete beams, etc.); aspect ratio of deck (width to length ratio), and so on. To understand the effect of possible varia- tion in the distribution factor ratios, each of the ratio values in Equations 8 through 10 is individually varied by an amount of -0.05, 0, and +0.05. This range of variation is considered to be realistic for highway bridges in the United States. As a result, a total of 36 cases of analysis for the WIM data are repeated, and the resulting MPF values are compared with the regres- sion result, as shown in Figures 18 through 23. They exhibit no significant deviations from the recommended regression lines. Thus, Equation 11 is accepted as robust for general application. Negative Remaining Life As discussed in Chapter 2, one of the serious practical issues with current Section 7 of the AASHTO MBE (2011) is that there are no provisions for the situation of negative remaining life resulting from calculation, even though field inspection has observed no fatigue cracking for the particular steel connection detail in the bridge. This situation is illus- trated in Figure 24, duplicated here from Chapter 2. 0 0.25 0.5 0.75 1 0 5 000 10000 15000 M PF /N ADTT Moment: Span = 30ft 2-lane data 3-lane data 4-lane data 2-lane regression 3-lane regression 4-lane regression Figure 18. Comparison of proposed MPF and computed MPF using WIM data divided by number of lanes (midspan moment in 30ft span).

28 0 0.25 0.5 0.75 1 0 5 000 10000 15000 M PF /N ADTT Shear: Span = 220ft 2-lane dat a 3-lane dat a 4-lane dat a 2-lane regression 3-lane regression 4-lane regression Figure 23. Comparison of proposed MPF and computed MPF using WIM data divided by number of lanes (shear in 220ft span). 0 0.25 0.5 0.75 1 0 5 000 10000 15000 M PF /N ADTT Shear: Span = 100ft 2-lane dat a 3-lane dat a 4-lane dat a 2-lane regression 3-lane regression 4-lane regression Figure 22. Comparison of proposed MPF and computed MPF using WIM data divided by number of lanes (shear in 100ft span). 0 0.25 0.5 0.75 1 0 5 000 10000 15000 M PF /N ADTT Shear: Span = 30ft 2-lane dat a 3-lane dat a 4-lane dat a 2-lane regression 3-lane regression 4-lane regression Figure 21. Comparison of proposed MPF and computed MPF using WIM data divided by number of lanes (shear in 30ft span). 0 0.25 0.5 0.75 1 0 5 000 10000 15000 M PF /N ADTT Moment: Span = 220f t 2-lane dat a 3-lane dat a 4-lane dat a 2-lane regression 3-lane regression 4-lane regression Figure 20. Comparison of proposed MPF and computed MPF using WIM data divided by number of lanes (midspan moment in 220ft span). 0 0.25 0.5 0.75 1 0 5 000 10000 15000 M PF /N ADTT Moment: Span = 100ft 2-lane dat a 3-lane dat a 4-lane dat a 2-lane regression 3-lane regression 4-lane regression Figure 19. Comparison of proposed MPF and computed MPF using WIM data divided by number of lanes (midspan moment in 100ft span). Figure 24. Negative remaining life resulting from uncertainty in fatigue life estimation (shaded area is equal to targeted failure probability).

29 As illustrated, the real fatigue life of the detail is a random variable, expressed using the curve of probability distribution with little triangle symbols. The total life estimated according to the AASHTO MBE (2011) is a deterministic value, as the right boundary of the shaded area as the target failure prob- ability. In other words, the probability of the real life being smaller than this value is controlled to be under the targeted (acceptable) risk level expressed using the target reliability index. Due to conservative approach, the estimated remain- ing life ends at the left side of the origin, being negative. When it is known that no fatigue cracking has been identified at the detail, this information can be taken into account in the evaluation process to help reduce the uncertainty so that the evaluation result will better reflect the reality. This concept is illustrated in Figure 24. Figure 25 continues from the situation in Figure 24, with the same original fatigue life distribution using the same symbol of little triangles on the curve. Given the fact that the detail has not failed (cracked), the possibility of the total life being shorter than the present age is excluded. As expressed in Figure 25, this elimination is modeled using truncation of the original probability distribution at the value of present age. The total area under the truncated curve will be less than 1.0 due to the truncation. Thus, the remaining curve beyond the present age is increased proportionally by dividing it by 1 - ptruncated, where ptruncated is the truncated area or truncated probability. The resulting curve is shown in Figure 25, named fatigue life distribution (updated). In addition, the estimated total life of the detail can be updated using the same concept of controlling the failure probability or calibration, according to the updated fatigue life distribution. Namely, the total life computed as a deter- ministic value resulting from the evaluation process will be so determined such that the real life which is less than that value is controlled to be within the acceptable risk. Figure 26 indicates this updated total life as a point on the abscissa to the right of the truncation location or present age. The dif- ference between the two values is then the updated remaining life aimed as the evaluation result, also indicated in Figure 26. The shaded area in Figure 26 is to be made equal to the tar- geted failure probability corresponding to the target reliability index, also equal to the shaded area in Figure 24, since the same target reliability index is used in both calibration pro- cesses. This determination process is a high level of calibration taking into account the in-site information of no failure, or even detail cracking, observed for the detail. Note also that this truncated distribution model has been used in a research effort to calibrate bridge proof load factors for load rating (Fu and Tang 1995), where the bridge capac- ity’s distribution is truncated at the proof load level since the possibility for it to be below that level has been eliminated. As seen in Figure 26, since the truncation is done at present age which is always positive, the updated estimated remain- ing life will be accordingly always positive. This will eliminate negative remaining life results when no cracking is observed in the field. Obviously, if no such field inspection result is avail- able, a negative estimated remaining life may still result as illus- trated in Figure 24. Such a result should indicate the need for further information, including but not limited to: field detail condition (whether cracked or not and possibly workman- ship); WIM data for the site (for information on the load); stress range measured for the detail (more information on the load effect); and so on. The information specific for the par- ticular detail will help reduce the random variation, or make the distribution curve in Figure 24 “narrower” so that the total life estimation will become less uncertain and more credible. NCHRP Report 299 (Moses et al. 1987) provides the cali- bration basis for the current AASHTO MBE (2011). Conse- quently, the following information is used in determining the distribution in Figures 24 through 26: Lognormal distribution with Mean = 2.19 Ymean Coefficient of Variation = 0.84 Figure 26. Updating remaining life estimation using updated fatigue life distribution (shaded area is equal to targeted failure probability). Figure 25. “No fatigue cracking observed” modeled by truncated fatigue life distribution.

30 Therefore, the truncated probability P at Y = a = current age is P = probability of fatigue life being shorter than current age before updating based on no crack found =   +     Φ Ln a 2.19Ymean 0 27 0 73 12 . . ( ) As discussed, the updated fatigue life Y′ is the one that leads to the same target reliability index b: Φ Φ −( ) = ′  +      β Ln Y 2.19Ymean 0 27 0 73 . . − − P P1 13( ) Y′ is then solved from the above equation as Y Ymean P′ = − −( ) −( )+[ ]−2 19 140 73 1 1 0 27. ( ). .e PΦ Φ β to be the updated fatigue life that will not lead to negative remaining fatigue life. In the revised Section 7 of the AASHTO specifications, four different levels of nominal fatigue life are used corresponding to four different levels of fatigue evalu- ation reliability, i.e., b values. The equations derived corre- sponding to these levels of fatigue evaluation reliability are as follows: ′ = − −( )+[ ]−Y Ymean mean P2 19 0 73 1 0 18 1 0 27. (. . .e PΦ 15) ′ = − −( )+Y Yevaluation 2 mean P2 19 0 73 1 0 12 1. . .e PΦ [ ]−0 27 16. ( ) ′ = − −( )+Y Yevaluation 1 mean P2 19 0 73 1 0 074 1. . .e Φ P[ ]−0 27 17. ( ) ′ = − −( )+[ ]−Y Yminimum mean P2 19 0 73 1 0 039 1 0. . .e PΦ . ( )27 18 RR Factor Section 7 of the MBE currently provides for three levels of finite fatigue life for estimation: • Minimum expected fatigue life (which equals the conser- vative design fatigue life); • Evaluation fatigue life (which equals a conservative fatigue life for evaluation); and • Mean fatigue life (which equals the most likely fatigue life). The desired fatigue life estimate is obtained by mul- tiplying the resistance factor RR times the detail category constant. A Table for the values of RR corresponding to dif- ferent levels of finite fatigue life is provided in the MBE as given in Table 3. The accompanying commentary C7.2.5.1 explains that since much variability exists in the experimentally derived fatigue lives, a conservative fatigue resistance two standard deviations below the mean fatigue resistance or life is assumed for design. This corresponds to the minimum expected finite fatigue life given in the MBE. However, using the design- based finite fatigue resistance may be too conservative for fatigue evaluation purposes and, consequently, result in low fatigue lives. Hence, evaluation and minimum fatigue resis- tance curves have been provided, which are two and one standard deviations off the mean fatigue life S-N curves in log- log space, respectively. The probability of failure associated with each level of fatigue life approaches 2%, 16%, and 50% for the minimum, evaluation, and mean fatigue lives, respec- tively. The references for Section 7 include NCHRP Report 299 (Moses et al. 1987) and other AASHTO specifications. NCHRP Report 286: Evaluation of Fatigue Tests and Design Criteria on Welded Details by P. B. Keating and J. W. Fisher (1986) mentions that the initial AASHTO Fatigue Design Curves were derived from the linear regression analysis of the test data obtained in NCHRP Project 12-07 (NCHRP Reports 102 and 147) using the 95% confidence limits defining the lower bounds of the fatigue resistance for 95% survival. Keating and Fisher proposed to change the slope of all the design curves that existed then to a constant value of -3.0. Before this, all curves had slightly different slope values around -3.0. The proposed curves were developed using stress range intercept values at 2 million cycles. Hence, the earlier curves and the new curves have identical intercepts at 2 million cycles. In order to assess the adequacy of the new curves, the test data were com- pared with the new design curves. Since the new curves rep- resent the 95% lower confidence limit, most of the test data should plot above the curve, as was shown in the report. Since the current Section 7 of the MBE references NCHRP Report 299, it is assumed that the values for the resistance factor, RR, were calculated using data presented in NCHRP Report 299. NCHRP Report 299 specifies that it is typically assumed that scatter in fatigue data follows a lognormal sta- Detail Category 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 Table 3. Resistance factor for evaluation, minimum or mean fatigue life, RR.

31 tistical distribution for a given N. For design purposes, allow- able nominal stress ranges are usually defined two standard deviations below the mean stress ranges. This design curve is defined as NS A95b = in which S95 is the stress range two standard deviations below the mean, and A is the intercept for this allowable design curve. NCHRP Report 299 provides a Table of data for various fatigue detail categories as given in Table 4. A normal distribution can have two-sided limits or one- sided limits. Since fatigue resistance curves are one-sided (i.e., survival on one side and failure on the opposite side), one-sided limits should be used. This was done as specified in NCHRP Report 286 where 95% lower confidence limit was used with 95% survival to calculate the design curves. A 95% lower confidence limit ensures a probability of failure of 5%. On the other hand, a two standard deviation shift from the mean provides a probability of failure of 2.275% as shown in Figure 27. Thus, a two standard deviation shift from the mean does not provide the same level of safety as a 95% lower confidence limit. However, NCHRP Report 299 men- tions that the current fatigue design curves are based on a two standard deviation shift from the mean values at 2 million cycles. A calculation of the stress ranges at 2 million cycles was performed using a two standard deviation shift and a 95% lower one-sided confidence limit. The mean and stan- dard deviation for the normal distribution corresponding to the lognormal distribution were calculated. The results are shown in Table 5. The following are sample calculations of stress ranges and RR for mean life for Category A: σ = +( ) = +( ) =ln cov ln . .1 1 0 217 0 21452 2 µ = ln(SrMean) = ln(33) = 3.4965 95th Percentile for Standard distribution with Mean µ and Standard Deviation s = 3.144 95th Percentile Sr = e3.144 = 23.2 2 Standard Deviation Shift for Standard distribution with Mean µ and Standard Deviation s = µ - 2s = 3.4965 - 2x0.2145 = 3.0675 2 Standard Deviation Shift Sr = e3.0675 = 21.5 Constant A for Design Stress Range = (SrDESIGN) 3x(2x106) = 23.23x(2x106) = 2.5x1010 Constant A for Mean Stress Range = (SrMEAN) 3x(2x106) = 333x(2x106) = 7.19x1010 RR for Category A Detail for Mean Life = 7 19 10 2 5 10 10 10 . . × × = 2.9 As can be seen from Table 5, a 95th percentile line matches the design stress ranges currently used in the AASHTO LRFD Specifications (2010), whereas a two standard deviation shift gives lower stress range values. Hence, the data provided in NCHRP Report 299 seem to indicate that the design fatigue curves are indeed based on a 95% lower confidence limit and Detail Category Sr at 2 x 106 cycles SrD at 2 x 106 cycles Intercept on the nominal S-N curves COV A 33.0 23.2 2.500E+10 21.7% B 22.8 18.1 1.191E+10 14.1% B' 18.0 14.5 6.109E+09 13.2% C 16.7 13.0 4.446E+09 15.3% D 13.0 10.3 2.183E+09 14.2% E 9.5 8.1 1.072E+09 9.7% E' 7.2 5.8 3.908E+08 13.2% Average 14.5% Table 4. Fatigue data reported in NCHRP Report 299. (a) (b) Figure 27. Standard normal distribution (two standard deviation shift vs. 95% lower confidence limit).

32 not on a two standard deviation shift which would give lower stress range values. Based on this, using the 95th percentile line as minimum life, the resistance factor RR was recalculated for mean life. Table 6 compares the RR values given in Section 7 with the recalculated RR values. As can be seen from the table, the recalculated RR values are generally higher than the cur- rent Section 7 values, except for fatigue categories B′ and E′. Hence, the recalculated RR values will provide a higher finite fatigue life for mean life (50% probability of failure). Similar RR values were recalculated for different levels of probability of failure from 5% to 50%. The values are given in Table 7. These values are plotted in the graph shown in Figure 28. As can be seen from the figure, the relationship between probability of failure and RR seems to be approximately lin- ear. Table 8 provides the linearly interpolated values of RR between minimum and mean fatigue lives. Comparing tables 7 and 8, the maximum difference between the values of RR is about 0.1. Hence, a linear approximation between the mean and minimum finite fatigue life levels can be used to arrive at approximate values of RR for different levels of probabilities of failure. Thus, this can be used to easily extend the finite fatigue life of the detail if the user is willing to accept a higher level of probability of failure. Instead of providing multiple values of RR for probabilities of failure, another solution would be to provide two differ- ent levels of safety besides the minimum and mean fatigue life. These would be Evaluation Life 1 and Evaluation Life 2 for probabilities of failure of 15.9% and 32.9% respectively. Evaluation Life 1 will correspond to the level of safety associ- ated with one standard deviation shift from the mean. This is what is currently provided as “Evaluation Life” safety level in Section 7. Evaluation Life 2 will be halfway between Evalua- tion Life 1 and Mean Life. This level of safety will correspond to a probability of failure of 32.9%. The calculated values of RR for these levels of safety are as shown in Table 9. Fatigue Serviceability Index The FSI, Q, is a method for providing a relative evaluation of the fatigue serviceability of a structural detail. The index itself is dimensionless, but it is expected that engineers can make planning decisions regarding bridge viability based on the quantitative value of the FSI and the overall qualitative assessment. The expression for the FSI is given as follows: Q Y a N GRI= −  ( )19 where: N = Greater of Y or 100 years G = Load Path Factor, as given in Table 10 R = Redundancy Factor, as given in Table 11 I = Importance Factor, as given in Table 12 Y = Calculated total fatigue life of the detail The load path, redundancy, and importance factors are risk factors that modify the FSI. They reduce the index from its Detail Category Sr (Mean) at 2 million cycles Sr (Design) at 2 million cycles COV (Std. Deviation) µ (Mean) 95th Percentile 95th Percentile Sr Two Standard Deviation Shift Two Standard Deviation Shift Sr A 33 23.2 21.70% 0.2145 3.4965 3.144 23.2 3.067 21.5 B 22.8 18.1 14.10% 0.1403 3.1268 2.896 18.1 2.846 17.2 B' 18 14.5 13.20% 0.1314 2.8904 2.674 14.5 2.628 13.8 C 16.7 13 15.30% 0.1521 2.8154 2.565 13.0 2.511 12.3 D 13 10.3 14.20% 0.1413 2.5649 2.333 10.3 2.282 9.8 E 9.5 8.1 9.70% 0.0968 2.2513 2.092 8.1 2.058 7.8 E' 7.2 5.8 13.20% 0.1314 1.9741 1.758 5.8 1.711 5.5 Table 5. Calculations for 95th percentile stress range vs. two standard deviation shift stress range. Detail Category Mean Life (50% Pf) Section 7 Values Recalculated Values A 2.8 2.9 B 2.0 2.0 B' 2.4 1.9 C 1.3 2.1 C' 1.3 2.1 D 1.6 2.0 E 1.6 1.6 E' 2.5 1.9 Table 6. Comparison between Section 7 and recalculated RR values for mean life.

33 Fatigue Category A B B' C D E E' Probability of Failure 5% 1.0 1.0 1.0 1.0 1.0 1.0 1.0 10% 1.3 1.2 1.2 1.2 1.2 1.1 1.2 15% 1.5 1.3 1.3 1.3 1.3 1.2 1.3 20% 1.7 1.4 1.4 1.4 1.4 1.3 1.4 25% 1.9 1.5 1.5 1.6 1.5 1.3 1.5 30% 2.1 1.6 1.6 1.7 1.6 1.4 1.6 35% 2.2 1.7 1.6 1.8 1.7 1.4 1.6 40% 2.4 1.8 1.7 1.9 1.8 1.5 1.7 45% 2.7 1.9 1.8 2.0 1.9 1.6 1.8 50% 2.9 2.0 1.9 2.1 2.0 1.6 1.9 Table 7. Variation of RR with probability of failure. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0% 5% 50% 40% 55% 30% 35% 20% 25% 10% 15% 45% R R Probability of Failure A B B' C D E E' Figure 28. Variation of RR with probability of failure. Fatigue Category A B B' C D E E' Probability of Failure 5% 1.0 1.0 1.0 1.0 1.0 1.0 1.0 10% 1.2 1.1 1.1 1.1 1.1 1.1 1.1 15% 1.4 1.2 1.2 1.2 1.2 1.1 1.2 20% 1.6 1.3 1.3 1.4 1.3 1.2 1.3 25% 1.8 1.4 1.4 1.5 1.4 1.3 1.4 30% 2.0 1.6 1.5 1.6 1.6 1.3 1.5 35% 2.3 1.7 1.6 1.7 1.7 1.4 1.6 40% 2.5 1.8 1.7 1.9 1.8 1.5 1.7 45% 2.7 1.9 1.8 2.0 1.9 1.5 1.8 50% 2.9 2.0 1.9 2.1 2.0 1.6 1.9 Table 8. Linear interpolation of RR between minimum and mean fatigue lives.

34 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 fac- tor). The net effect of a reduction in the index will be to move the composite index value to a lower value that may result in 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. The fatigue rating and assessment outcomes are given in Table 13. These values and outcomes were selected based on several different fatigue assessment trials. While not exact, they can be used to provide some guidance in deci- sion making. In order to illustrate the behavior of the FSI, consider a hypothetical bridge. There can be various details on the bridge experiencing different stress ranges and thus having varying total fatigue lives. For the time being, neglect the load path factor, redundancy factor, and the importance fac- tor, since these are penalizing factors that account for higher risk. Consider the variation of (Y-a)/N with the remain- ing life as shown in Figure 27. It can be seen that the curve remains bounded between zero and one for positive remain- ing lives. The curve follows a linear trend for fatigue lives less than 100 years. For fatigue lives less than 100 years, there is a direct linear correlation between remaining life and the FSI. For example, an FSI of 0.2 corresponds to remaining life of about 20 years, and an FSI of 0.1 indicates a remaining life of about 10 years. Also, a linear relationship helps define the boundaries for the FSI to which a fatigue rating can be assigned. From the assessment outcomes noted, it is likely that only the last two assessment outcomes of ‘Increase Inspection Fre- quency’ and ‘Assess Frequently’ are significant from the Bridge Owner’s point of view. The decision to monitor the bridge periodically or frequently is presently made by the owners based on the remaining life, which is in absolute years. Since the FSI is expected to provide an approximate guideline to the bridge owners for making this decision, the FSI should also vary linearly with the remaining life, at least when the FSI starts dropping into these last two assessment outcome ranges. Also, as can be seen from Figure 29, for bridge ages up to 80 years, the FSI still maintains a linear relationship below a value of 0.2. Hence the linear correlation between FSI and remaining life is maintained below 0.2 for bridge ages up to 80 years. This is advantageous as the fatigue engineer now has an approximate judgment of the remaining life in years left for the detail from the value of FSI. The three additional factors—load path factor, redun- dancy factor, and the importance factor—lead to a reduc- tion in the value of the FSI. A four-girder continuous span rural bridge is an example of a best possible condition of the bridge with respect to these risk factors, where all the fac- tors have a value of 1.0. A two-girder simple span interstate bridge is an example of the worst condition. Various bridge conditions have been examined in Figure 30 for a bridge age of 35 years. The worst possible reduction in the value of FSI due to these risk factors is 35.2% (1-0.8 × 0.9 × 0.9). Hence, an FSI of 0.2 for the best condition gets reduced to 0.13 for the worst condition. Or said another way, a bridge detail with Detail Category Minimum Life (5% Pf) (Design) Evaluation Life 1 (15.9% Pf) Evaluation Life 2 (32.9% Pf) Mean Life (50% Pf) 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 Table 9. Values of RR for different levels of safety. 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 Table 12. Importance factor I. Type of Span R Simple 0.9 Continuous 1 Table 11. Redundancy factor R. Number of Load Path Members G 1 or 2 members 0.8 3 members 0.9 4 or more members 1 Table 10. Load path factor G.

35 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 Table 13. Fatigue rating and assessment outcomes. Bridge Age 0 years Bridge Age 10 years Bridge Age 20 years Bridge Age 30 years Bridge Age 40 years Bridge Age 50 years Bridge Age 60 years Bridge Age 70 years Bridge Age 80 years Bridge Age 90 years Bridge Age 100 years 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 70 80 90 110 120 100 (Y -a) /N Remaining Life (years) Figure 29. Variation of (Y-a)/N with remaining life for various bridge ages. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 70 80 90 110 120 100 FS I Remaining Life (years) 4 Girder, Continuous Span, Rural Bridge 4 Girder, Continuous Span, Interstate Bridge 3 Girder, Continuous Span, Interstate Bridge 2 Girder, Continuous Span, Interstate Bridge 4 Girder, Simple Span, Interstate Bridge 3 Girder, Simple Span, Interstate Bridge 2 Girder, Simple Span, Interstate Bridge Figure 30. Variation of FSI for different bridge parameters (bridge age 35 years).

36 an approximate remaining life of 20 years gets reduced to a life of approximately 13 years for the worst possible bridge condition. The FSI can also become negative if negative remaining lives are obtained. For negative FSI values, strategies that can be adopted to ameliorate the unsatisfactory condition include refinements to the analysis procedure for estimat- ing the stress range, field stress measurements, and use of the truncated fatigue life distribution methodology. More Accurate Estimation for Truck Traffic The AASHTO MBE (2011) recommends an approximation to estimate the remaining fatigue life of a detail in Figure C7-1. This approximation may cause significant under- and over- estimation of the remaining life. This approximation has been eliminated in the proposed revisions to Section 7 of the specifications using a closed form solution for Y. This solution was completed in conjunction with NCHRP Project 12-51 (Fu et al., 2003) and has been implemented in a computer program Carris as a product of that research effort. Using the analytical sum of the truck traffic, the finite fatigue life is revised as follows: Y R A n ADTT f R SL PRESENT eff = ( )  ( )  log 365 3 ∆ g g g a 1 1 1 20 1 +( ) +       +( ) − log ( ) which eliminates the need for Figure C7-1. In Equation 20, a is the present age of the detail, g is the estimated annual traf- fic volume growth rate, and [(ADTT)SL]PRESENT is the present average number of trucks per day in a single lane, as defined in the AASHTO MBE (2011). As a result, iteration for an accu- rate ADTTSL has become unnecessary. Consequently, it is sug- gested that the updated Equation 20 be used for estimating the finite fatigue life in the revised Section 7 of AASHTO MBE (2011) to reflect this knowledge advancement. Two examples of an E′ detail (from bridges in New York and Maryland) have been examined regarding this issue. For these two examples and the range of present age and traffic growth rate covered in Figure C7-1, it has been found that the maximum over-estimation is 37% and the maximum under- estimation is 183%. Under-estimation over 100% means a supposedly positive remaining life is approximated as a nega- tive one. For example, in the Maryland example, a supposedly 18-year remaining life is approximated as -15 years, resulting in a 183% under-estimation. More details on this subject are described herein. For an illustration of Equation 20 and demonstration of the approximation involved in using Figure C7-1 in current Section 7 of the specifications, the following two examples are considered. Example 1 This example considers a cover plate weld detail in New York State belonging to Category E′ (Cohen et al., 2003). The situation is summarized as having the following char- acteristic parameters for Figure C7-1 in current Section 7 and Equation 20: RR = 1.0 for minimum life, A = 3.9′108 ksi3, [(ADTT)SL]PRESENT = 1896 trucks / day, Dfeff = 1.817 ksi, and n = 1 for a simple span longer than 40 ft. Conceptually, this case may occur with different growth rates and present ages. Accordingly, Table 14 shows a comparison between the closed form solution of Equation 20 and the Manual recom- a (yr) Minimum Remaining Life Using Manual Recommended Approach (yr) Minimum Remaining Life Using Exact Approach (yr) Manual Recommended Minimum Remaining Life/ Exact Approach Minimum Remaining Life 5 67 51 1.32 10 66 49 1.33 15 65 48 1.35 20 62 47 1.34 25 62 45 1.37 30 59 44 1.33 35 55 43 1.29 40 52 42 1.24 45 48 41 1.17 50 44 40 1.10 Table 14. Example 1—Comparison of Manual recommended approximation and exact solution Equation 20 for g  0.02.

37 a (yr) Minimum Remaining Life Using Manual Recommended Approach (yr) Minimum Remaining Life Using Exact Approach (yr) Manual Recommended Minimum Remaining Life/ Exact Approach Minimum Remaining Life 5 34 31 1.11 10 33 30 1.10 15 33 30 1.10 20 32 30 1.09 25 32 29 1.07 30 30 29 1.03 35 31 29 1.07 40 31 29 1.08 45 31 29 1.06 50 28 29 0.98 Table 16. Example 1—comparison of Manual recommended approximation and exact solution Equation 20 for g  0.06. a (yr) Minimum Remaining Life Using Manual Recommended Approach (yr) Minimum Remaining Life Using Exact Approach (yr) Manual Recommended Minimum Remaining Life/ Exact Approach Minimum Remaining Life 5 50 38 1.31 10 49 37 1.31 15 48 36 1.33 20 48 36 1.34 25 48 35 1.37 30 47 35 1.35 35 47 34 1.37 40 47 34 1.37 45 47 34 1.34 50 43 34 1.30 Table 15. Example 1—comparison of Manual recommended approximation and exact solution Equation 20 for g  0.04. mended approximation approach, for a range of a values and g = 0.02. The last column in the Table displays the ratio of two remaining minimum lives, using the closed form solu- tion as the reference. It is seen that the Manual-recommended approach produces approximation results all with an error larger than 10% except one case when a = 50 years. Tables 15 through 17 continue the comparison of the two approaches for g = 0.04, 0.06, and 0.08, to cover the range of the chart in AASHTO MBE (2011) (Figure C7-1). In Tables 16 and 17, the approximate approach generates cases of under-estimation, with the ratio in the last column less than 1. The worst case is 0.37 indicating a 63% under-estimation of the remaining life. Apparently, if the stress range Dfeff is large enough, this could cause a negative remaining life, while the closed form solution still produces a positive one. In addi- tion, Table 17 does not include the case a = 5 years because the chart in AASHTO MBE (2011) (Figure C7-1) does not include that case, while Equation 20 could still produce an exact solution. Example 2 This example considers a cover plate weld detail with a fatigue strength of Category E′ as well. The following param- eters for Figure C7-1 in current Section 7 and Equation 20 are identified: RR = 1.0 for minimum life; A = 3.9 x108 ksi3; [(ADTT)SL]PRESENT = 1081 trucks/day; Dfeff = 2.62 ksi; and n = 1 for a simple span longer than 40 ft. Again, this case may occur for different growth rates and present ages. Tables 18 to 21 show comparisons between the closed form solution Equation 20 and the Manual recommended approximation approach, for different average traffic growth rates g and a range of present life a. The last column in the Tables displays the ratio of two remaining minimum lives,

38 a (yr) Minimum Remaining Life Using Manual Recommended Approach (yr) Minimum Remaining Life Using Exact Approach (yr) Manual Recommended Minimum Remaining Life/ Exact Approach Minimum Remaining Life 5 27 27 0.98 10 24 26 0.93 15 22 25 0.88 20 20 24 0.82 25 18 23 0.77 30 15 23 0.67 35 13 22 0.60 40 11 21 0.51 45 9 21 0.42 50 5 21 0.24 Table 19. Example 2—comparison of Manual recommended approximation and exact solution Equation 20 for g  0.04. a (yr) Minimum Remaining Life Using Manual Recommended Approach (yr) Minimum Remaining Life Using Exact Approach (yr) Manual Recommended Minimum Remaining Life/ Exact Approach Minimum Remaining Life 5 37 35 1.08 10 34 32 1.06 15 32 30 1.04 20 28 28 1.00 25 26 26 0.98 30 22 25 0.89 35 17 23 0.75 40 14 21 0.65 45 10 20 0.50 50 5 19 0.26 Table 18. Example 2—comparison of Manual recommended approximation and exact solution Equation 20 for g  0.02. a (yr) Minimum Remaining Life Using Manual Recommended Approach (yr) Minimum Remaining Life Using Exact Approach (yr) Manual Recommended Minimum Remaining Life/ Exact Approach Minimum Remaining Life 10 21 26 0.82 15 20 26 0.78 20 18 26 0.71 25 17 25 0.66 30 15 25 0.60 35 14 25 0.55 40 13 25 0.51 45 12 25 0.46 50 9 25 0.37 Table 17. Example 1—comparison of Manual recommended approximation and exact solution Equation 20 for g  0.08.

39 a (yr) Minimum Remaining Life Using Manual Recommended Approach (yr) Minimum Remaining Life Using Exact Approach (yr) Manual Recommended Minimum Remaining Life/ Exact Approach Minimum Remaining Life 5 18 23 0.78 10 15 22 0.69 15 13 22 0.60 20 11 21 0.50 25 8 21 0.39 30 5 20 0.26 35 4 20 0.18 40 2 20 0.08 45 -1 20 -0.03 50 -4 20 -0.21 Table 20. Example 2—comparison of Manual recommended approximation and exact solution Equation 20 for g  0.06. a (yr) Minimum Remaining Life Using Manual Recommended Approach (yr) Minimum Remaining Life Using Exact Approach (yr) Manual Recommended Minimum Remaining Life/ Exact Approach Minimum Remaining Life 10 8 20 0.42 15 6 19 0.29 20 2 19 0.12 25 0 19 -0.02 30 -4 19 -0.19 35 -6 18 -0.35 40 -9 18 -0.50 45 -12 18 -0.65 50 -15 18 -0.83 Table 21. Example 2—comparison of Manual recommended approximation and exact solution Equation 20 for g  0.08. using the closed form solution as the reference. It is seen in Tables 18 and 19 for g = 0.02 and 0.04 that the Manual recommended approach may produce over- and underesti- mates, respectively, with values larger and smaller than 1.0. The maximum is 1.08 (8% over estimate) and the minimum is 0.24 (78% under-estimate). Tables 20 and 21 continue the comparison for g = 0.06 and 0.08, where negative values are seen in the last column, indicating that the Manual recom- mended approximate approach produces negative remain- ing life, but not the closed form solution Equation 20. Due to the change of sign for the ratio in the last column, these values should be so interpreted with a negative 1 added. For example, the last row of Table 20 for a = 50 years, a ratio value of -0.21 is shown. It should be interpreted as -0.21-1 = -1.21 or 121% under-estimated from the closed form solution of 20 years, resulting in -4 years as the minimum remaining life. Note also that the ratio in the last column is calculated before the remaining lives are rounded so that (-4)/20 is not exactly -0.21. In summary, Tables 18 to 21 show that the Manual recommended approximation may over-estimate by 8% and under-estimate by 183% for this example. In conclusion, it has been seen that the approximation recommended in the Manual may lead to significant errors. Note also that since the closed form solution in Equation 20 is easy to apply, the fatigue rating engineers can use it for their own comparison and check. Tack Weld Tests The tack weld tests involve a pair of lap plates attached to a middle main plate with tack welds attached on the sides. Rivets, simulated by bolts, hold the plates together. The assembly is subjected to a range of constant amplitude lon- gitudinal tensile stress to examine the fatigue susceptibility of the tack welds. An important part of the test procedure

40 involves determining how much the bolts need to be tight- ened in order to have the same clamping effect as a rivet. Bolt Tightening Procedure Need for Developing Procedures Tack welds have been used frequently in bridge structures to temporarily hold members in place before riveting. Some bridge structures can have hundreds of such tack welds that have been left in place. Most of these riveted bridges have already accumulated a significant fatigue life. Since riveting is a procedure that is rarely performed nowadays, bolts were used instead of rivets for the tack weld tests. In order to have the same effect as a rivet, it is essential to emulate the clamping force that a rivet would develop upon placement and subsequent cooling. A bolt tightening procedure was developed for this purpose. Photographs and Descriptions of Calibration Methodology The turn-of-nut method of tightening bolts, together with a Skidmore-Wilhelm bolt load indicator, was used to develop the bolt tightening procedure. The Skidmore-Wilhelm bolt load indicator is shown in Figure 31. A bolt has been fitted into the center of the indicator and made snug-tight. The dial gage at the top of the indicator displays the mea- sured bolt tension in pounds. The bolt head is held in posi- tion in a wedge present on the opposite side of the indicator. Since the length of the bolt used is less than four times the diameter of the bolt, the bolt has to be turned up to 1⁄3 of a turn or 120 degrees in order to fully tighten the bolt as per the AISC Steel Construction Manual (AISC 2010). After snug-tightening the bolt, angular lines were marked on the bolt load indicator as shown in the figure, such that the angle in between adjacent lines is approximately 1⁄12 of a turn or 30 degrees. The snap-on torqometer shown in Figure 32 was used to measure the torque needed while turning the bolt. The torque is measured in foot-pounds. Three ASTM A325 7⁄8-in. diam- eter bolts were tested. The bolts were initially made snug-tight by manually tightening them using a hand wrench. The bolts were then tightened using the torqometer in increments of 1⁄12 of a turn (30 degrees) up to 1⁄3 of a turn (120 degrees) in order to achieve the minimum bolt pretension of 39 kips for a 7⁄8-in. Figure 31. Skidmore-Wilhelm bolt load indicator. Figure 32. Turn-of-nut calibration.

41 0 10 0 20 0 30 0 40 0 50 0 60 0 0 1 0 2 0 3 0 4 0 5 0 6 0 To rq ue (l b- ft) Tension (kip) Bolt 1 Bolt 2 Bolt 3 Fit Figure 34. Torque required vs. bolt tension. 0 10 0 20 0 30 0 40 0 50 0 60 0 0 2 0 4 0 6 0 8 0 1 00 12 0 1 40 To rq ue (l b- ft) Turn (Degrees ) Bolt 1 Bolt 2 Bolt 3 Fit Figure 33. Torque required vs. turn-of-nut. diameter A325 bolt. The turn angle, bolt pretension, and torque needed were recorded for different turns of each bolt. Results of Calibration The measured values for turn angle, bolt pretension, and torque were plotted, and straight lines were fitted for the vari- ous plots. Figure 33 shows the plot of the torque needed for turning the bolt against the turn of the nut. Figure 34 shows the plot of the torque vs. the bolt tension, as measured by the Skidmore-Wilhelm bolt load indicator. Lastly, Figure 35 shows the plot of bolt tension vs. turn-of-nut. It can be seen that all the bolts tested gave very consistent values of torque and tension for a given turn-of-nut. The bolt tension, torque required, and the turn-of-nut all have linear relationships with respect to each other. The bolt pretension for snug-tight varied from about 5 to 8 kip force in these tests. From the plot of tension against turn, it can be seen that the pretension in the bolt exceeds the minimum required preten- sion of 39 kips for a 1⁄3 turn of the nut. Zhou (1994) tested nine specimens with rivets to examine the magnitude of residual clamping stress. The specimens had been cut from riveted girders removed from demolished bridges that were about sixty years old. The measured clamp- ing stress varied from 5 to 24 ksi, with an average of about 12 ksi with a standard deviation of 6 ksi. The force corresponding to the average clamping stress of 12 ksi stress for a 7⁄8-in. diameter bolt is 7.2 kips. It can be seen from the plot of tension against turn that this force can be easily achieved by simply snug-tightening the bolt with an ordinary wrench. Hence, the bolts on all speci- mens were simply snug-tightened to simulate the clamp- ing stress of a rivet, except for the specimens with fully tightened bolts.

42 Finite Element Analysis of Tack Weld Specimen Motivation for Analysis It is important to know how the stress will flow in the tack weld specimen. Knowledge of the stress distribution is useful for finding the locations where stress concentration occurs during the cyclic loading. The points at which stress concen- tration occurs will be where the fatigue cracks are most likely to initiate in the tack weld specimen. In order to determine the stress flow in the tack weld specimen, a non-linear three dimensional finite element model of the tack weld specimen was developed. This model was used to examine the effect of various parameters, such as the number and position of the tack welds or different stress ranges on the stress distribution in the tack weld specimen. Description of Model Parameters and Load Conditions The finite element model of the tack weld specimen is shown in Figure 36. The finite element model simulates friction contact between the plates. The friction coefficient has been taken as 0.35. The tack welds have a yield strength of 70 ksi while the plates are 36 ksi. The model also incor- porates the pretension force in the bolts and the normal contact between the bolt shanks and plates. The model was analyzed for 12 and 20 ksi stress ranges on the net section using an R ratio of 0.1 and for configurations with three, two, and zero tack welds along each side of the splice plate as shown in Figure 37. The stress range distributions at points along two sections, which are shown in Figure 38, were determined. Results of Analysis The measured stress ranges are compared in Figures 39 and 40. Figure 39 shows the measured stress ranges through the net section. Note that since the net section passes through the bolt holes, no stress range can be measured where the bolt holes are located. Figure 40 shows the measured stress ranges through the gross section. It was observed that the stress ranges in the net section of the splice plates are lesser than intended. For example, when loads required for pro- ducing a nominal 12 ksi stress range in the net section were imposed on the model with 3 tack welds on each side of the splice plate, the calculated average stress range in the net section was found to be of a lower value of 9 ksi. This calculated average stress range of 9 ksi across the net sec- tion was obtained by summing up the force across small discrete cross-sectional areas, obtained from the stress ranges shown in Figure 39, and then dividing it by the total Figure 36. Finite element model of the tack weld specimen. 0 5 10 15 20 25 30 35 40 45 50 0 2 0 4 0 6 0 8 0 1 00 12 0 1 40 Te ns io n (k ip) Turn (Degrees ) Bolt 1 Bolt 2 Bolt 3 Fit Figure 35. Bolt tension vs. turn-of-nut.

43 0 5 10 15 20 25 30 St re ss R an ge (k si) 0 6 5 4 3 2 1 Distance from plate edge (inch) 12 ksi Stress Range, 3 Welds 20 ksi Stress Range, 3 Welds 12 ksi Stress Range, 2 Welds 20 ksi Stress Range, 2 Welds 12 ksi Stress Range, No Welds 20 ksi Stress Range, No Welds Figure 39. Stress range across section through center of lower tack weld. Figure 38. Sections along which stresses are measured. Figure 37. Stress distribution in specimen for 3, 2 and 0 tack welds, respectively.

44 area of the net section. The reduced 9 ksi stress range in the net section indicates that some of the stress range has been transferred into the base plate through the tack weld toes which lie ahead of the net section. However, the stress range distribution in the gross section of the splice plates is comparatively more uniform, as seen in Figure 40, and the calculated average stress range of 8.25 ksi is comparable with the corresponding expected gross section stress value of 8 ksi. An analysis was also performed to observe the effect on the stress distribution after removing the leading line of tack welds with the specimen having three tack welds along each side of the splice plate. It was found that the stress at the toe of the weld in the direction of the applied load reduced from 4.2 ksi at the toe of the leading line of tack welds to 3.1 ksi at the toe of the second line of tack welds after the leading line of tack welds was removed. Conclusions The difference between the nominal stress range on the net section and the stress ranges determined by analysis occurs because of the bolts and the tack welds. A portion of the stress, however, flows through the tack welds, which are much stiffer than the bolts. This can be seen in the stress contours on the model in the figures. As a result, the actual stress flowing through the net section of the splice plates is lower. Hence, during the fatigue testing, it is expected that the most probable location where fatigue cracking will initi- ate is the toe of the lower tack welds. It can also be observed that there is not much change in the stress range distribution when the number of tack welds is reduced from three to two, as the first line of tack welds, which are mainly responsible for the change in stress flow, still remain in place. There is an appreciable increase in the stress range when all the tack welds are removed. Hence, the number of tack welds prob- ably does not appreciably affect the stress range at the weld toe of the first line of welds, and hence should not appre- ciably affect the fatigue life of the tack welds. Also, although the stress at the toe of the tack welds does reduce after the leading line of tack welds is removed, this is not enough to conclusively state that the second line of tack welds will not be susceptible to fatigue cracking after the leading line of tack welds is removed. Test Results A total of seventeen specimens were tested. Typically, cracks initiated at the toes of the lower tack welds spread lat- erally across the splice plates. Every specimen of the tack weld tests was run continuously at least until 5 million cycles were completed or until failure had occurred. In this case, failure is defined as the point at which a crack beginning at the toe of a tack weld spreads laterally across the splice plate into the adjacent bolt hole. Other than the specimens tested at a stress range of 20 ksi, most of the specimens were run well beyond 5 million cycles, mostly averaging about 7 million cycles. There were a total of 6 “run-outs” or specimens that did not show any evidence of fatigue cracking when the cyclic testing was stopped. 0 2 4 6 8 10 12 14 16 18 0 6 5 4 3 2 1 St re ss R an ge (k si) Distance from plate edge (inch) 12 ksi Stress Range, 3 Welds 20 ksi Stress Range, 3 Welds 12 ksi Stress Range, 2 Welds 20 ksi Stress Range, 2 Welds 12 ksi Stress Range, No Welds 20 ksi Stress Range, No Welds Figure 40. Stress range across section at level of strain gages.

45 Most of the specimens which experienced fatigue cracks had only one weld which cracked. Some specimens experi- enced crack initiation at multiple tack welds and simulta- neous crack growth. Typical fatigue cracks that occurred in the specimens are shown in Figure 41. All fatigue cracks that occurred initiated at the toe of the lower line of tack welds, the location of maximum stress concentration as predicted by the finite element analysis. The cracks then propagated through the splice plates laterally into the adjacent bolt hole depending on how long the crack was allowed to grow. Details of the tack weld specimens, weld parameters, and test results as well as photographs of fatigue cracks for all tack weld specimens are provided in Appendix C. Comparison of Test Results Table 22 shows the number of loading cycles at the end of testing for all 17 test specimens and the different parameters for the specimens. An asterisk after the cyclic life indicates a runout test with the number of cycles applied to the specimen when cyclic loading was halted. The net section stress range across the center of the bolt holes versus the number of cycles was plotted for the specimens. The net section stress was selected because it is commonly used for riveted connections. The results were compared to the AASHTO mean fatigue curves for catego- ries B, C, and D. As can be seen from Figure 42, the test results clearly lie above the category D mean curve and near Figure 41. Typical tack weld cracks. No. of Tack Welds Tack Weld Position Tack Weld Length No. of Specimens Tested at Sr Value (Sr on net section) 20 ksi 12 ksi 12 ksi 2 L <1-in 8,324,000 8,259,000 3 L <1-in 1,066,000 843,000 1,294,000 5,253,000* 5,103,000* 6,316,000 7,667,000* (FT) 7,546,000* (FT) 2 L <1-in 7,061,000 (MP) 6,507,000 (MP) 7,400,000 (MP) 2 T <1-in 5,513,000 7,570,000* 3 L >1-in 6,223,000* 6,243,000 Table 22. Cycles at end of testing (* indicates runout).

46 Category B Design Curve Category C Design Curve Test Results Test Results (Runouts) 1 10 100 1.00E+05 1.00E+06 1.00E+07 1.00E+08 St re ss R an ge (k si) Number of Loading Cycles Figure 43. Comparison of test results with AASHTO design fatigue curves (for Net Section Stress). 1 10 100 1.00E+05 1.00E+06 1.00E+07 1.00E+08 St re ss R an ge (k si) Number of Loading Cycles Category B Mean Curve Category C Mean Curve Category D Mean Curve Test Results Figure 42. Comparison of test results with AASHTO mean fatigue curves (for Net Section Stress). the category C mean curve. When comparing the test results with the AASHTO Design Fatigue Curves in Figure 43, it is evident that all the test results lie above the Category C curve. Distortion-Induced Fatigue Tests A number of cyclic tests were conducted to provide additional information and understanding of the behavior and performance of retrofits used to mitigate distortion- induced fatigue cracking. The purpose of the testing was to study the effectiveness of retrofit geometrical parameters in slowing or halting distortion-induced fatigue cracking. Finite element modeling was used to evaluate the response of retrofit elements as well as full connection models of bridge structures. The results of the finite element models and the experimental test results are summarized in the following sections. Finite Element Analysis for Distortion-Induced Fatigue Tests Finite Element Analysis of Retrofit Behavior Under Applied Loads in Distortion-Induced Fatigue Tests WT-, single-, and double-angle retrofit elements were evaluated in the distortion-induced fatigue tests. As noted

47 earlier, Connor and Fisher (2006) describe a situation where a retrofit detail with a small thickness was not fully effective in preventing further crack growth at a detail with distortion-induced fatigue cracking, while a thicker detail used elsewhere on the same bridge was effective in halting further crack growth. Clearly, the stiffness of the detail is quite important. Finite element analysis was carried out for the WT retrofit in order to determine the relative influence of flange thickness and web thickness on the stiffness of the retrofit. In this finite element analysis, the retrofit was modeled with restraint conditions similar to what it will have when attached to the stiffener plate and girder flange. The analysis was carried out for different combinations of the flange and web thickness of the retrofit to evaluate the load deformation behavior of the various retrofits. The thicknesses of the web and flange used are shown in Table 23. A total of 20 possible combinations of the web and flange thicknesses were used in the analysis. A typical finite element retrofit model is shown in Fig- ure 44. The model has four 0.9375-in. diameter bolt holes in both the flange and the web, the standard hole size to accommodate 7⁄8-in diameter bolts. The length of the web is 6.625 in., and the length of the flange is 12 in. The bolt hole spacing is shown in Figure 45. The retrofit was fixed on the inner surface of the bolt holes in the flange, while the load was applied on the web as a pressure load on the upper semicircular areas of the inner bolt hole surfaces. The deformation of the retrofit is measured as the verti- cal deflection of the corner of the web of the retrofit. The restraint conditions and load applied on the model are shown in Figure 46. The results obtained from the finite element analysis are shown in Figures 47 through 55. Figures 47 through 51 are plotted such that the flange thickness remains constant, while Figures 52 through 55 show the effect of variation of flange thickness when the web thickness is kept constant. The plots show the variation in maximum load capacity before failure and the type of failure of the retrofit for dif- ferent web-flange thickness combinations. It was observed that the retrofit exhibits two different fail- ure modes—failure in shear and failure in flexure. Shear fail- ure is primarily observed when the flange thickness is much larger than the web thickness, while flexural failure occurs when flange and web are of comparable thicknesses or if the web thickness exceeds the flange thickness. A shear failure and flexural failure are shown in Figures 56 and 57, respec- tively. A shear failure can also be pinpointed from the load deformation plots. Wherever the plot has a sharp corner and the deformation suddenly increases very rapidly with the load, that thickness combination has had a shear failure. When the curve slopes gradually and smoothly toward the plastic region, the failure for that particular thickness combi- nation is a flexural failure. Figure 44. Dimensions of retrofit model. Figure 45. Spacing of bolt holes. Flange Thickness (in.) Web Thickness (in.) 3/8 3/8 1/2 1/2 5/8 5/8 3/4 3/4 1 Table 23. Thicknesses of flange and web of retrofit detail.

48 F 0.500 W 0.375 F 0.500 W 0.500 F 0.500 W 0.625 F 0.500 W 0.750 0 2 4 6 8 10 12 14 16 0 0.1 0.15 0.05 0.2 0.25 0.3 Lo ad (k ip) Deformation (in) Figure 48. Load vs. deformation for constant 1⁄2” flange thickness. F 0.375 W 0.375 F 0.375 W 0.500 F 0.375 W 0.625 F 0.375 W 0.750 0 1 2 3 4 5 6 7 8 0 0.1 0.15 0.05 0.2 0.25 0.3 Lo ad (k ip) Deformation (in) Figure 47. Load vs. deformation for constant 3⁄8” flange thickness. Figure 46. Restraints and loading on retrofit model.

49 F 0.750 W 0.375 F 0.750 W 0.500 F 0.750 W 0.625 F 0.750 W 0.750 0 5 10 15 20 25 30 35 0 0.1 0.15 0.05 0.2 0.25 0.3 Lo ad (k ip) Deformation (in) Figure 50. Load vs. deformation for constant 3⁄4” flange thickness. F 0.625 W 0.375 F 0.625 W 0.500 F 0.625 W 0.625 F 0.625 W 0.750 0 5 10 15 20 25 0 0.1 0.15 0.05 0.2 0.25 0.3 Lo ad (k ip) Deformation (in) Figure 49. Load vs. deformation for constant 5⁄8” flange thickness. 0 5 10 15 20 25 30 35 40 45 50 0 0.1 0.15 0.05 0.2 0.25 0.3 Lo ad (k ip) Deformation (in) F 1.000 W 0.375 F 1.000 W 0.500 F 1.000 W 0.625 F 1.000 W 0.750 Figure 51. Load vs. deformation for constant 1” flange thickness.

50 F 0.375 W 0.625 F 0.500 W 0.625 F 0.625 W 0.625 F 0.750 W 0.625 F 1.000 W 0.625 0 5 10 15 20 25 30 35 40 0 0.1 0.15 0.05 0.2 0.25 0.3 Lo ad (k ip) Deformation (in) Figure 54. Load vs. deformation for constant 5⁄8” web thickness. F 0.375 W 0.500 F 0.500 W 0.500 F 0.625 W 0.500 F 0.750 W 0.500 F 1.000 W 0.500 0 5 10 15 20 25 30 35 0 0.1 0.15 0.05 0.2 0.25 0.3 Lo ad (k ip) Deformation (in) Figure 53. Load vs. deformation for constant 1⁄2” web thickness. F 0.375 W 0.375 F 0.500 W 0.375 F 0.625 W 0.375 F 0.750 W 0.375 F 1.000 W 0.375 0 5 10 15 20 25 0 0.1 0.15 0.05 0.2 0.25 0.3 Lo ad (k ip) Deformation (in) Figure 52. Load vs. deformation for constant 3⁄8” web thickness.

51 It can be observed from these plots that in general, as both web and flange thicknesses are increased, the maximum load capacity of the retrofit before failure increases. From the plots where the flange thickness of the retrofit is kept constant, it can be seen that changing the web thickness has compara- tively little effect on the maximum load capacity of the ret- rofit as well as the stiffness of the retrofit which is given by the elastic slope of the load vs. deformation plots. However, as the flange thickness becomes much greater than the web thickness, the effect of the web thickness starts becoming evi- dent. Thinner webs fail in shear, while as the web gets thicker, the retrofit starts transitioning to failure in flexure, which causes changes in the load capacity of the retrofit. This can be seen in Figures 50 and 51. When the web thickness is kept constant, and the flange thickness is varied, the flange thickness has a significant effect on the load capacity of the retrofit as well as the stiffness of the WT retrofit. Generally, as the flange thick- ness is increased, the load capacity and the stiffness of the retrofit increases; however, when the flange becomes too thick, the retrofit starts failing in shear after which a further increase in flange thickness has little effect on the load capacity of the retrofit. This can be seen in Figures 52 through 55. Figure 56. Shear failure of retrofit (deformations are exaggerated). F 0.375 W 0.750 F 0.500 W 0.750 F 0.625 W 0.750 F 0.750 W 0.750 F 1.000 W 0.750 0 5 10 15 20 25 30 45 50 35 40 0 0.1 0.15 0.05 0.2 0.25 0.3 Lo ad (k ip) Deformation (in) Figure 55. Load vs. deformation for constant 3⁄4” web thickness. Figure 57. Flexural failure of retrofit (deformations are exaggerated).

52 Clearly from the previous analysis, the flange thickness is a governing variable influencing the stiffness as well as the maximum load carrying capacity for the WT retrofit. Hence for the WT retrofits, the primary variable that will be changed for observing the behavior of the retrofit will be the flange thickness. Finite Element Analysis for Determining Typical Web Gap Distortions and Member Forces Before and After Retrofit A finite element model of a few typical bridges with cross frames was created from available bridge design plans. One bridge (Bridge A) is a continuous composite plate girder built in 1969 over SR 31 in St. Joseph County, Indiana. The bridge has X-type cross frames. Another bridge (Bridge B) has K-type cross frames and is a continuous welded steel plate girder and continuous steel beam bridge built in 1972 over SR 63 in Vigo County, Indiana. It should be noted that these structures were selected for typical sizes and dimen- sions for the girders and cross frames. They were then ana- lyzed to examine cross frame behavior before and after retrofit. However, neither bridge was retrofitted as noted herein. A finite element model of one entire bridge span of Bridge B was created, as shown in Figure 58. The ends of the girders were simply supported. The large model was used to estimate the amount of relative distortion that occurs between bridge girders when an HS20 truck is placed over the midspan of the bridge. This distortion was then used to estimate the increase in the force applied by the cross frames on the stiff- ener, perpendicular to the girder web, before and after the stiffener detail was retrofitted. To evaluate an upper bound behavior, the full weight of 72 kips of an HS20 Truck was applied as a single concentrated load on one interior girder at the center of the span. The deflections of the girders were measured, and the maximum inter-girder displacement was found to be about 0.2 in. In real- ity, the girders will be continuous over the supports instead of simply supported. Also, an HS15 fatigue truck load would be applied with corresponding distributed axle weights and not as a single concentrated load. The bridge deck was not modeled which would have redistributed the HS15 fatigue truck load to adjacent girders. Hence, the model created here will overestimate the real distortions of the bridge and thus provide an approximate upper bound. This means that for this bridge, inter-girder vertical displacement will most likely not exceed 0.2 inches. Figure 58. Bridge B—finite element model of single span with exaggerated displacements.

53 For the Bridge B and Bridge A models shown in Figures 59 and 60, the upper flanges of the exterior girders were fixed in place while the middle girder was displaced downward. The web gap distortion was measured. The forces in the angles of the cross frames were calculated and components taken to calculate the horizontal force exerted by the angles on the stiffener near the top flange of the exterior girder. This was done again for the model after retrofitting the stiffener con- nections with WT sections with flange and web thicknesses of 0.75-in. Two web gaps between the stiffener and the girder flange in the bridge models were used: 0.5 in. and 1.75 in. Also, the angle thickness in the cross bracing was varied from 0.5 in. to 0.75 in. The force and web gap distortions were measured before and after retrofitting. The stress distribution in the two bridge models is shown in Figures 61 and 62, and the results of the analysis are given in Tables 24 through 27. From the results obtained, it can be seen that the web gap distortion decreases significantly after the retrofit is in place while the force applied on the stiffener by the cross braces increases. The distortions after retrofit reduce by a factor that ranged from 6 to 64. Generally, larger displacements of the middle girder produced larger reductions in the web gap distortion after retrofitting. This is primarily because of the increase in the web gap distortion before retrofit with increase in the girder displacement. A thickness increase in cross-brace angles produced a greater jump in cross-brace force after retrofit. Similarly, a greater reduction in web gap distortion after retrofit was Figure 59. Bridge B—K-type cross frame. Figure 60. Bridge A—X cross frame. Figure 61. Bridge B—stress distribution before and after retrofit.

54 Figure 62. Bridge A—stress distribution before and after retrofit. Web Gap - 0.5" Angles - 0.5" Web Gap - 0.5" Angles - 0.75" Displacement 0.5 Distortion (inch) Before/After Ratio Displacement 0.5 Distortion (inch) Before/After Ratio Before Retrofit 0.00340 6.1 Before Retrofit 0.00488 5.9 After Retrofit 0.00056 After Retrofit 0.00083 Displacement 1.0 Distortion (inch) Before/After Ratio Displacement 1.0 Distortion (inch) Before/After Ratio Before Retrofit 0.00415 6.8 Before Retrofit 0.00662 7.0 After Retrofit 0.00061 After Retrofit 0.00095 Displacement 1.5 Distortion (inch) Before/After Ratio Displacement 1.5 Distortion (inch) Before/After Ratio Before Retrofit 0.00448 7.3 Before Retrofit 0.00744 7.6 After Retrofit 0.00062 After Retrofit 0.00098 Web Gap - 1.75" Angles - 0.5" Web Gap - 1.75" Angles - 0.75" Displacement 0.5 Distortion (inch) Before/After Ratio Displacement 0.5 Distortion (inch) Before/After Ratio Before Retrofit 0.01642 14.7 Before Retrofit 0.02309 13.3 After Retrofit 0.00111 After Retrofit 0.00173 Displacement 1.0 Distortion (inch) Before/After Ratio Displacement 1.0 Distortion (inch) Before/After Ratio Before Retrofit 0.02111 19.9 Before Retrofit 0.03211 17.8 After Retrofit 0.00106 After Retrofit 0.00181 Displacement 1.5 Distortion (inch) Before/After Ratio Displacement 1.5 Distortion (inch) Before/After Ratio Before Retrofit 0.02333 25.7 Before Retrofit 0.03620 20.9 After Retrofit 0.00091 After Retrofit 0.00173 Table 24. Bridge B web gap distortions before and after retrofit.

Web Gap - 0.5" Angles - 0.5" Web Gap - 0.5" Angles - 0.75" Displacement 0.5 Distortion (inch) Before/After Ratio Displacement 0.5 Distortion (inch) Before/After Ratio Before Retrofit 0.00827 10.1 Before Retrofit 0.01071 12.1 After Retrofit 0.00082 After Retrofit 0.00088 Displacement 1.0 Distortion (inch) Before/After Ratio Displacement 1.0 Distortion (inch) Before/After Ratio Before Retrofit 0.01155 13.9 Before Retrofit 0.01942 21.0 After Retrofit 0.00083 After Retrofit 0.00093 Displacement 1.5 Distortion (inch) Before/After Ratio Displacement 1.5 Distortion (inch) Before/After Ratio Before Retrofit 0.01518 18.2 Before Retrofit 0.02813 29.8 After Retrofit 0.00083 After Retrofit 0.00094 Web Gap - 1.75" Angles - 0.5" Web Gap - 1.75" Angles - 0.75" Displacement 0.5 Distortion (inch) Before/After Ratio Displacement 0.5 Distortion (inch) Before/After Ratio Before Retrofit 0.04368 17.7 Before Retrofit 0.05609 21.7 After Retrofit 0.00247 After Retrofit 0.00259 Displacement 1.0 Distortion (inch) Before/After Ratio Displacement 1.0 Distortion (inch) Before/After Ratio Before Retrofit 0.07184 32.0 Before Retrofit 0.11279 41.7 After Retrofit 0.00225 After Retrofit 0.00270 Displacement 1.5 Distortion (inch) Before/After Ratio Displacement 1.5 Distortion (inch) Before/After Ratio Before Retrofit 0.09857 44.1 Before Retrofit 0.17132 64.3 After Retrofit 0.00223 After Retrofit 0.00266 Table 26. Bridge A web gap distortions before and after retrofit. Web Gap - 0.5" Angles - 0.5" Web Gap - 0.5" Angles - 0.75" Displacement 0.5 Force (kip) After/Before Ratio Displacement 0.5 Force (kip) After/Before Ratio Before Retrofit 15.4 1.2 Before Retrofit 18.2 1.4 After Retrofit 18.0 After Retrofit 25.0 Displacement 1.0 Force (kip) After/Before Ratio Displacement 1.0 Force (kip) After/Before Ratio Before Retrofit 16.5 1.2 Before Retrofit 17.9 1.5 After Retrofit 19.6 After Retrofit 26.6 Displacement 1.5 Force (kip) After/Before Ratio Displacement 1.5 Force (kip) After/Before Ratio Before Retrofit 16.2 1.2 Before Retrofit 15.8 1.6 After Retrofit 19.2 After Retrofit 24.9 Web Gap - 1.75" Angles - 0.5" Web Gap - 1.75" Angles - 0.75" Displacement 0.5 Force (kip) After/Before Ratio Displacement 0.5 Force (kip) After/Before Ratio Before Retrofit 11.5 1.6 Before Retrofit 12.1 2.1 After Retrofit 18.0 After Retrofit 24.9 Displacement 1.0 Force (kip) After/Before Ratio Displacement 1.0 Force (kip) After/Before Ratio Before Retrofit 11.8 1.7 Before Retrofit 10.6 2.5 After Retrofit 19.5 After Retrofit 26.5 Displacement 1.5 Force (kip) After/Before Ratio Displacement 1.5 Force (kip) After/Before Ratio Before Retrofit 11.0 1.7 Before Retrofit 8.0 3.1 After Retrofit 19.1 After Retrofit 24.8 Table 25. Bridge B forces before and after retrofit.

56 Web Gap - 0.5" Angles - 0.5" Web Gap - 0.5" Angles - 0.75" Displacement 0.5 Force (kip) After/Before Ratio Displacement 0.5 Force (kip) After/Before Ratio Before Retrofit 16.9 2.7 Before Retrofit 15.9 3.0 After Retrofit 46.1 After Retrofit 48.3 Displacement 1.0 Force (kip) After/Before Ratio Displacement 1.0 Force (kip) After/Before Ratio Before Retrofit 20.9 2.4 Before Retrofit 19.1 2.7 After Retrofit 49.2 After Retrofit 51.3 Displacement 1.5 Force (kip) After/Before Ratio Displacement 1.5 Force (kip) After/Before Ratio Before Retrofit 23.7 2.1 Before Retrofit 20.9 2.6 After Retrofit 50.5 After Retrofit 54.3 Web Gap - 1.75" Angles - 0.5" Web Gap - 1.75" Angles - 0.75" Displacement 0.5 Force (kip) After/Before Ratio Displacement 0.5 Force (kip) After/Before Ratio Before Retrofit 8.9 4.7 Before Retrofit 7.2 6.1 After Retrofit 42.0 After Retrofit 43.7 Displacement 1.0 Force (kip) After/Before Ratio Displacement 1.0 Force (kip) After/Before Ratio Before Retrofit 12.2 3.5 Before Retrofit 10.0 4. 7 After Retrofit 42.4 After Retrofit 46.6 Displacement 1.5 Force (kip) After/Before Ratio Displacement 1.5 Force (kip) After/Before Ratio Before Retrofit 14.5 3.0 Before Retrofit 11.6 4.0 After Retrofit 43.5 After Retrofit 46.8 Table 27. Bridge A forces before and after retrofit. observed for larger web gaps. Also, the cross frame forces increase by greater amounts after retrofit for larger web gaps. Another factor is the type of cross frame. Larger distor- tion reductions and greater bracing forces were observed for X-type braces than for K-type braces. For K-type braces, the distortions reduce by a factor of 6 to 26, while the force jumps by a factor of 1.2 to 3.1. For the X-type braces, the distortions reduce by a factor of 10 to 64, while the force jumps by a factor of 2.1 to 4.7. This shows that the type of cross frame influ- ences the web gap distortions and cross frame forces before and after retrofitting. However, in the analysis, the girders are rigidly held, and the connections are all pinned over the over- lapping surfaces. Hence, the amount of rigidity in the models is larger than what it should be. Also the models are not able to simulate the effects of the presence of an existing fatigue crack at the stiffener ends. An existing fatigue crack would result in a more flexible girder web, which should increase the web gap distortion and reduce the forces in the cross bracings after retrofit. The displacements and forces for the two bridges when the displacement of the middle girder is 0.2 in. were also calcu- lated. The results are shown in Table 28. It can be seen here too that the web gap distortion reduces by a factor of about 10 and the force in the cross frames increases by a factor of 1.8 to 8.3, depending upon cross frame type. Based upon finite element analysis of the two bridge models, it can be observed that a wide range of angle brac- ing forces were developed before and after retrofit. Varia- tions occur due to changes in the cross frame type, angle bracing thickness and web gap size. No single value will be representative of the variation in brace force before and after retrofit. Nevertheless, a factor of two was selected as the multiplier for the force to be applied after retrofitting the test specimens compared to the initial force needed for pre-cracking the specimen. This value is at the lower end of the force ratio noted previously, but it is probably realistic when considering the softening effect of the web gap crack and associated drilled retrofit hole which was not consid- ered in the analysis. To verify if the load factor of two is also applicable to angle retrofits, finite element analysis was again performed for Bridge A that has an X-type bracing. The middle girder in the model was pushed downward, as shown in Figure 63, and the horizontal load in the cross bracings was measured. Three displacements of 0.5 in., 1.0 in., and 1.5 in. were induced in the middle girder. Also, two different web gap sizes of 0.5 in.

57 and 1.75 in. were used, and two different cross bracing thick- nesses of 0.5 in. and 0.75 in. were used. A single-angle retrofit of thickness 0.75 in. was used in the analysis. The results are given in Table 29. The factor for the forces varies from 2.1 to 5.2. Similar to the previous finite element model for the WTs, the current finite element model also has a greater stiffness than will be actually present. Hence, the factor of two that was used earlier for the WTs can also be used for the angle retrofits. Test Results As stated earlier, the purpose of the cyclic retrofit testing was to evaluate the effectiveness of the retrofit elements to mitigate distortion-induced fatigue cracking. The testing protocol involved application of a cyclic out-of-plane dis- tortion to pre-crack the specimen, followed by installation of the retrofit. After retrofit, the specimen was subjected to a constant amplitude load for 5,000,000 cycles minimum to evaluate the ability of the retrofit to halt or significantly decrease further growth of the distortion-induced fatigue cracks. After the retrofit is installed, it behaves like a fixed end for the stiffener. It was found that after the retrofit is installed, a force larger than 40 kips cannot be applied to the speci- men as it results in fatigue cracking occurring in the stiff- ener itself after about 2.5 million cycles of loading. Hence, in order to evaluate the fatigue behavior of the retrofit, and not the stiffener connection, the load that can be applied on the Bridge B Bridge A Web Gap - 1.75" Angles - 0.75" Web Gap - 1.75" Angles - 0.75" Displacement 0.2 Distortion (inch) Before/After Ratio Displacement 0.2 Distortion (inch) Before/After Ratio Before Retrofit 0.00869 10.9 Before Retrofit 0.02609 10.2 After Retrofit 0.00080 After Retrofit 0.00256 Displacement 0.2 Force (kip) After/Before Ratio Displacement 0.2 Force (kip) After/Before Ratio Before Retrofit 6.3 1.8 Before Retrofit 4.8 8.3 After Retrofit 11.3 After Retrofit 39.9 Table 28. Bridge A and B distortions and forces before and after retrofit for 0.2 inch displacement. Figure 63. X-brace type bridge A finite element model retrofitted with single-angle retrofit.

58 Web Gap - 0.5" Bracings - 0.5" Web Gap - 0.5" Bracings - 0.75" Displacement 0.5 Force (kip) After/Before Ratio Displacement 0.5 Force (kip) After/Before Ratio Before Retrofit 15.7 2.5 Before Retrofit 14.7 2.7 After Retrofit 39.2 After Retrofit 39.6 Displacement 1.0 Force (kip) After/Before Ratio Displacement 1.0 Force (kip) After/Before Ratio Before Retrofit 19.1 2.3 Before Retrofit 17.2 2. 6 After Retrofit 43.4 After Retrofit 44.0 Displacement 1.5 Force (kip) After/Before Ratio Displacement 1.5 Force (kip) After/Before Ratio Before Retrofit 21.3 2.1 Before Retrofit 18.6 2.5 After Retrofit 44.7 After Retrofit 47.1 Web Gap - 1.75” Bracings - 0.5” Web Gap - 1.75” Bracings - 0.75” Displacement 0.5 Force (kip) After/Before Ratio Displacement 0.5 Force (kip) After/Before Ratio Before Retrofit 8.8 4.3 Before Retrofit 7.3 5.2 After Retrofit 38.0 After Retrofit 38.1 Displacement 1.0 Force (kip) After/Before Ratio Displacement 1.0 Force (kip) After/Before Ratio Before Retrofit 11.4 3.7 Before Retrofit 9.4 4.5 After Retrofit 42.3 After Retrofit 42.4 Displacement 1.5 Force (kip) After/Before Ratio Displacement 1.5 Force (kip) After/Before Ratio Before Retrofit 13.2 3.3 Before Retrofit 10.7 4.3 After Retrofit 43.8 After Retrofit 45.5 Table 29. Cross bracing forces for bridge A (single-angle retrofit). specimen after the retrofit was subject to a maximum limit of about 40 kips. A total of thirteen test specimens were tested. Table 30 shows the specimen parameters, loading force, and distor- tion values and results of the experimental testing for all thir- teen specimens. Note that the pre-cracking force shown for every specimen in the Table is only the initial pre-cracking force needed at the beginning of cycling. As fatigue cracks develop in the specimen, the force needed to maintain a con- stant distortion starts reducing due to the increasing flexibil- ity of the cracked specimen. A more detailed description of the specimen tests, web gap distortions, and cyclic loads used before and after retrofit, along with photographs of retrofits and fatigue cracks are found in Appendix D. None of the WT retrofits experienced any fatigue cracking. Double-angle ret- rofits also did not experience any fatigue cracking. However, fatigue cracks did develop in the single-angle retrofits, except for the 1-in.-thick, single-angle retrofits. It is important to note that in all the tests performed, no retrofit holes were drilled to remove the crack tip after pre- cracking, except in case of the “RH” specimens. This was done to simulate the worst possible condition for the retro- fit. Ideally, a retrofit hole would also be drilled if a fatigue crack is present along with installing the retrofit. Since no retrofit holes were drilled for most of the specimens, more load was transferred to the retrofit from the specimen web as the distortion-induced fatigue cracks grew. This would effec- tively test the retrofit in the worst condition. Also, it allowed the research team to observe whether or not the retrofit was stiff enough to halt or notably slow fatigue crack growth. This was considered to be an indirect measure of the effectiveness of the retrofit. Most of the WT retrofits were installed with four bolts in the web and four bolts in the flange of the retrofit as shown in Figure 64. For one subassembly, retrofit holes of 1 in. diam- eter were drilled to remove the crack tip. For another subas- sembly, the WT retrofits were installed with only two bolts in the web and the flange of the retrofit to examine the influence of the reduced stiffness of the retrofit on the fatigue strength. These retrofits are shown in Figure 65. Figure 66 shows typical double-angle and single-angle ret- rofits installed. None of the double-angle retrofits showed any indications of fatigue cracking. Single-angle retrofits, on the other hand, did experience fatigue cracking as shown in Figure 67. Three of the four ¾-in.-thick, single-angle retrofits tested experienced fatigue cracks. However, none of the 1-in.- thick, single-angle retrofits tested experienced any fatigue cracking. Fatigue cracks in single-angle retrofits tended to

59 Specimen Web Gap Length (inch) Distortion (inch) Pre-cracking Force (kip) No. of Cycles for Pre- cracking Loading Force (kip) No. of Cycles after Retrofit Retrofit Type Retrofit Thickness (inch) Damage 1 1.5 0.01 9.6 3,066,000 20 10,479,000 WT 0.75 No new cracks or crack growth 2 1.5 0.01 13.1 2,395,000 20 5,356,000 WT 0.5 No new cracks or crack growth 3 1.5 0.02 24.7 710,000 40 5,129,000 WT 0.75 No new cracks, Little crack growth 4 1.5 0.02 24.9 970,000 40 5,049,000 WT 0.5 No new cracks, Little crack growth 5 1.5 0.01 8.75 3,770,000 20 5,039,000 WT (RH) 0.75 No new cracks or crack growth 6 0.75 0.01 20.4 1,996,000 40 5,113,000 WT 0.75 No new cracks, Little crack growth 7 1.5 0.01 9.8 3,403,000 20 10,327,000 WT (B) 0.75 No new cracks or crack growth 8 0.75 0.0075 14.7 12,676,000 30 5,254,000 DA 0.625 No new cracks or crack growth 9 0.75 0.01 29.6 5,955,000 40 4,345,000 DA 0.625 New crack initiation and growth in web-to- flange welds 10 0.75 0.0075 14.9 5,034,400 30 5,179,000 DA 0.75 No new cracks or crack growth 11 0.75 0.01 30 1,178,000 40 5,308,000 SA 0.75 New crack initiation in web-to-flange welds and crack in SA retrofit 12 0.75 0.0075 18.9 8,960,000 30 10,235,000 SA 0.75 New crack initiation and growth in web-to- flange welds and cracks in both SA retrofits 13 0.75 0.0075 27 925,000 30 5,153,000 SA 1 No new cracks or crack growth Table 30. Distortion-induced fatigue test results. Figure 64. Typical WT retrofits installed with and without retrofit hole.

60 Figure 66. Typical double-angle and single-angle retrofits. Figure 67. Typical fatigue cracks in single-angle retrofits (cracks marked with line). initiate on the top side of the flange of the retrofit away from the web of the specimen. The cracks traveled downwards and into the junction of the web and flange of the single angle. The fatigue cracks were initiated due to high stresses generated at the retrofit flange due to the asymmetry of the single-angle retrofit, which resulted in noticeable out-of-plane bending of the retrofit. Also, since the single-angle retrofit is consider- ably less stiff than a comparable double-angle or WT retrofit, the end of the stiffener plate at which the single-angle retrofit is installed behaves more like a pinned end connection than a fixed end connection. Hence, most of the tension force gets transferred from the stiffener into the retrofit through the top side of the retrofit, resulting in fatigue cracking at the top of the retrofit instead of what would be expected at the bottom side in the case of a fixed end connection. Figure 65. WT retrofit installed with reduced number of bolts.