The fatigue reliability of steel-bridge components is evaluated. The m
ost commonly used S-N curve-based American Association of State Highwa
y and Transportation Officials (AASHTO) method is considered first. Th
e limit-state equation and the uncertainty associated with all the bas
ic random variables are quantified. Using the advanced first-order sec
ond-moment method, the corresponding probability of failure is calcula
ted in terms of the reliability index. It is observed that the reliabi
lity index is very similar to other design problems involving steel st
ructures. Since the AASHTO approach cannot incorporate the crack-size
information even if it is known at the time of evaluation, an alternat
ive linear-elastic fracture mechanics (LEFM) method is proposed. The c
orresponding limit-state equation and the basic variables are identifi
ed, and the uncertainties associated with them are quantified. The rel
iability index is calculated similarly. For comparison purposes, the r
eliability indexes according to the AASHTO and LEFM approaches are eva
luated for full-penetration butt welds in the tension flange of a stee
l-box girder used in a public-transportation system. The reliability i
ndexes are almost identical, at least around the design life of 50 yea
rs. The LEFM approach still retains the simplicity of the AASHTO metho
d, yet it is extremely powerful and efficient and can incorporate info
rmation on crack size as inspection results become available. It is pr
oposed that the LEFM can be used as an alternative to the AASHTO metho
d in the fatigue-damage evaluation of steel bridges. The LEFM method i
s extended in the companion paper to incorporate information from insp
ections and the corresponding updating of the underlying reliability.