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28 LLtruck = greatest effect of design tandem (3.6.1.2.3) and AASHTO Equation 5.5.3.2-1 (Equation 9, above)] to deter- design truck (3.6.1.2.2). For truck on simple span, mine the ratio of transient (FATIGUE) stress to the calculated the minimum 32-kip axle spacing of 14 ft is used. fatigue stress limit. The results from this approach are shown LLfatigue = effect of single design truck having 32-kip axle in Figure 12 for simple spans L = 10 to 160 ft and DL/LLlane = spacing of 30 ft (3.6.1.4.1). 0.5, 1, 2, and 4. In this plot, the vertical axis reports the ratio ff /[24 - 20( fmin / fy)]. Based on this approach, it is not expected It is recognized that the maximum moment does not occur that the fatigue limits of 5.5.3.2 will affect design using fy = exactly at the midspan; however, the error in making this 60 ksi over the range considered since the ratio of stress assumption is quite small and becomes proportionally smaller range/fatigue limit is less than unity for all cases. The effects as the span length increases (Barker and Puckett 2007). From of using fy = 100 ksi in this simplified scenario include an these moments, the STRENGTH I and FATIGUE design expected increase in fmin and ff equal to the ratio of yield moments are determined (3.4.1) as follows: strengths = 100/60 = 1.67. As seen in Figure 12, however, the STRENGTH = 1.25 DL + 1.75 LLlane + (1.75 1.33) LLtruck calculated stress range remains below the fatigue limit given by Equation 5.5.3.2-1 for all but spans shorter than 20 ft hav- FATIGUE = ( 0.75 1.15 ) LL fatigue ing fy = 100 ksi. The effect of continuing to use the extant ver- sion of Equation 5.5.3.2-1: fr 24 0.33fmin, is relatively Where the 1.33 and 1.15 factors are for impact loading (IM) negligible, shifting the 100 ksi curves upward by less than 5% (3.6.2.1). in the scenario presented. In order to normalize for distribution, multiple lanes, etc., it Thus, despite the inherent conservativeness of the AASHTO is assumed that the STRENGTH design is optimized; therefore, LRFD 5.5.3.2 fatigue provisions, it is not believed that these the stress in the primary reinforcing steel under STRENGTH conditions is fy = 0.9fy regardless of bridge geometry. If this is will impact most rational designs for values of fy up to 100 ksi. the case, the reinforcing stress associated with the FATIGUE It has been shown that increasing the usable yield strength of load is as follows: steel decreases the margin of safety against fatigue. Only in the shortest of spans, where vehicular loads dominate behavior f f = 0.9 f y ( FATIGUE STRENGTH ) would the "fatigue check" fail and additional steel be required. Similarly, the minimum sustained load will result in a rein- forcing stress of 2.4.3 Fatigue of Slabs (AASHTO LRFD Section 9) f min = 0.9 f y ( DL STRENGTH ) Slabs, being shallower and having a proportionally greater The stress in the reinforcing steel under FATIGUE condi- LL/DL ratio, may be considered to be more fatigue sensi- tions is then normalized by the allowable stress [according to tive than the generic conditions described above. However, Figure 12. Transient stress-to-fatigue limit ratio for simple span bridges.