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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.