Civil Engineering Reference
In-Depth Information
stress range cycles,
N
v
,
m
is a material constant established from regression analysis
of test data as
m
3 for structural steel,
C
is a
ma
terial constant established from
regression analysis of test data,
=
S
re
√
π
Δ
K
=
C
K
Δ
a
is the change in stress intensity
factor for effective stress range,
S
re
is the effective constant amplitude stress
range distribution that causes the same amount of fatigue damage as the variable
amplitudestressrangedistribution,and
C
K
istheconstantdependingonshapeandsize
of crack, edge conditions, stress concentration, and residual stresses (Pilkey, 1997).
Integration of Equation 5.48 yields
Δ
S
re
,
Δ
a
f
1
C
da
Δ
N
=
K
m
,
(5.49)
a
i
where
a
i
is the initial crack length a
nd
a
f
is the final crack length.
Substitution of
Δ
K
=
C
K
Δ
S
re
√
π
a
into Equation 5.49 yields
√
πΔ
S
re
−
m
C
a
f
da
C
K
√
a
m
.
N
=
(5.50)
a
i
Since
C
,
C
K
, and
a
=
a
i
(
a
f
a
i
, therefore neglect terms with
a
f
because of
−
m
power) are constant (Kulak and Smith, 1995),
S
−
m
re
N
=
A(
Δ
)
,
(5.51)
where
A
is a constant depending on detail and established from regression analysis
of test data (see
Section 5.3.2.2.2.2)
.
Equation 5.51 illustrates that the number of cycles to failure,
N
, for steel bridge
members or details is very sensitive to the effective stress range,
Δ
S
re
. Equation 5.51
also provides the number of cycles at failure at stress range level,
Δ
S
i
,as
S
−
m
i
N
i
=
A(
Δ
)
.
(5.52)
Substitution of Equation 5.52 into Equation 5.47 yields
n
i
N
i
=
n
i
λ
i
N
λ
i
N
)
=
)
=
)
=
1,
(5.53)
S
−
m
i
S
−
m
i
S
−
m
i
Δ
Δ
Δ
A(
A(
A(
where
n
i
n
i
=
n
i
N
λ
i
=
and substitution of Equation 5.51 into Equation 5.53 yields
λ
i
Δ
S
−
m
re
=
1
(5.54)
S
−
m
i
Δ
