Structural Analysis and Design of Steel Railway Bridges - Design of Modern Steel Railway Bridges - page 210

S

S remax

Δ S re

S remean

S remin

t

FIGURE 5.33 Constant amplitude cyclical loading.

Mid-span flexure (KN -m ) on 7.6 m span (wheel load)

900

E80

800

700

600

500

400

300

200

100

0

Time

FIGURE 5.34 Mid-span bending moment for Cooper's E80 load traversing a 25 ft simply
supported bridge span.

traces in elastic structures. Areas near the 1/4 span length ∗ and locations of change
in section may also be important for the determination of the maximum number of
stress cycles and their magnitude.
The effective stress cycles must accumulate the same damage as the variable
amplitude stress cycles over the total number of stress cycles to failure. Therefore, a
damage accumulation rule is required. There are many damage accumulation rules,
but it is usual to apply the Palmgren-Miner (Miner, 1945) linear damage accumu-
lation rule because, even though the sequence and interaction of load cycle effects
are not accounted for, the linear damage rule provides good agreement with test
results (Stephens et al., 2001). The rule is also independent of the stress magnitude.
Also, where residual stresses are high † (typical of modern steel railway bridge fab-
rications), mean stress effects are negligible ‡ and the stress range magnitude is of

∗ Because of the relationship between span length and car length during the cycling of spans, locations
around the 1/4 point may govern the maximum number of stress range cycles and magnitude (Dick,
2002).
† Typically at yield stress level.
‡ Dead load is unimportant since mean stress effects are negligible.