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27
number of loading cycles (N). The stress range is defined as tance. The resulting larger transient stresses in the steel may
the algebraic difference between the maximum and the min- adversely affect fatigue performance of the member. Specifi-
imum stress in a stress cycle: S = fmax - fmin (i.e., the transient cally, if designed efficiently, both the minimum and maxi-
stress). Most ferrous materials exhibit an "endurance limit" or mum stresses will increase coincident with the value of fy used
"fatigue limit" below which failure does not occur for an in design. However, the maximum stress may be increased to
unlimited number of cycles, N. In general, the concrete mate- a greater degree, resulting in a larger stress range under tran-
rial fatigue performance exceeds that of the steel and is not sient loads. For example, the value of fmin will generally be on
considered in design (Neville 1975). the order of 0.20fy. For Grade 60 A615 steel, the present
The AASHTO (2007) limit for fatigue-induced stress in AASHTO requirement (Equation 9) results in a fatigue limit
mild steel reinforcement is based on the outcome of NCHRP of 20 ksi. Applying the same equation to steel having a yield
Project 4-7 as reported by Helgason et al. (1976). The maxi- strength of 120 ksi, for instance, results in the unnecessary
mum permitted stress range ( ff) in straight reinforcement (and unwarranted) reduction of the permitted fatigue stress
resulting from the fatigue load combination is given in to 16 ksi. The lower fatigue limit implies that the higher
AASHTO LRFD (2007) §5.5.3.2 as follows: strength material has reduced fatigue performance, which is
contrary to all available data (Appendix E). The counterintu-
f f 21 - 0.33 fmin + 8 ( r h ) ( ksi units ) (Eq. 8) itive outcome, in terms of design, is that more of the higher
strength steel is required to carry the same transient loads.
Where:
Although some data suggest an improved fatigue limit for
fmin = algebraic minimum stress level (compression is neg-
higher strength bars (DeJong et al. 2006) may be permissible,
ative) and
there are insufficient data at this time to make any recom-
r/h = ratio of base radius to height of rolled-on transverse
mendation in the direction of changing the AASHTO fatigue
deformations; 0.3 may be used in the absence of actual
limit (Equation 9) and/or making the fatigue limit a function
values.
of yield (or tensile) capacity. Nonetheless, the impact of
Recent revisions to AASHTO LRFD §5.5.3.2 simply incor- applying Equation 9 to higher strength reinforcing steel is
porate the default r/h ratio as follows: that fmin may be increased by taking advantage of the higher
strength steel, but the increase results in an unwarranted
f f 24 - 0.33 fmin ( ksi units ) (Eq. 9) reduction in the fatigue limit. It is, therefore, proposed to
normalize fmin by the yield stress, fy. Calibrating this equation
The AASHTO-prescribed relationship is shown (see so that there is no effect for Grade 60 reinforcement, one
Appendix E) to represent the lower-bound results of many arrives at the following:
fatigue studies considering a range of bar sizes and is
reported applicable for Grades 40, 60, and 75 ASTM A615 f f 24 - 0.20 ( fmin f y ) ( ksi units ) (Eq. 10)
reinforcing bars (Corley et al. 1978). Corley et al. report that
"A No. 11 Grade 60 bar fractured in fatigue after 1,250,000 While still conservative, this equation recognizes that fatigue
cycles when subjected to a stress range of 21.3 ksi and a min- behavior of ferrous metals is largely unaffected by the yield
imum stress of 17.5 ksi tension. This is the lowest stress range strength of the material itself; thus, the baseline endurance
at which a fatigue fracture has been obtained in an undisturbed limit of 24 ksi is unchanged.
North American produced reinforcing bar" [emphasis added].
The fmin term is appropriate where fmin is positive (i.e., ten- 2.4.2 Effect of High-Strength Steel
sion, the usual case) but appears to be "calibrated" to result on the AASHTO Fatigue Provisions
in the same stress values as were used for working stress
In order to understand the role of fatigue in the design of
design using Grade 40 steel. Finally, bar size is not consid-
reinforced-concrete flexural members, the following approach
ered in the AASHTO-prescribed limit, although it is well
was taken.
established that larger bar sizes typically have lower fatigue
A simply supported beam having length L was considered.
limits (Tilly and Moss 1982).
Nominal moments are determined at the midspan using the
following loads:
2.4.1 AASHTO Fatigue Equation and Design
DL = dead load (self weight). This value is determined
with High-Strength Steel
for a range of values of DL/LLlane.
The use of high-strength reinforcement may permit a LLlane = specified lane load = 0.64 k/ft (AASHTO LRFD
reduction of the total area of steel required for flexural resis- §3.6.1.2.4).