FATIGUE
OF
CONCRETE UNDER RANDOM LOADINGS
By Young
J.
Park,
1
Associate Member, ASCE
INTRODUCTION
Traditionally,
the
fatigue
of
concrete
has
been analyzed using
S-N
rela-
tionships.
The
most recent
and
frequently cited equation
may be the one
proposed
by
Aas-Jakobsen
and
Lenschow (1973)
and
modified
by
Tepfers
and Kutti (1979)
as
follows:
^ -
x
= l - 0 ( l - f ^ ) log*
(1)
J
c
\
J
max/
in which/
min
and/
max
=
minimum
and
maximum stress levels;/^
=
concrete
strength;
and p =
0.0685, according
to
Tepfers
and
Kutti (1979). This equa-
tion
was
examined using fatigue test data having various combinations
of
/
min
and /
mM
(Antrim
and
McLaughlin
1959;
Assimacopoulos
et al. 1959;
Bennett
and
Muir
1967;
El-Jandali
1978;
Holmen
1979;
Karsan
and
Jirsa
1969).
The
results
of
Fig.
1
appear
to
indicate
a
relatively poor correlation,
especially
at low
cycle range. Moreover,
a
difficulty arises
in
applying
the
formulation when loadings
are
defined
in
probabilistic terms, such
as a
power
spectrum density function
or
RMS
statistics.
In
this paper,
a
fatigue model
is presented
for a
plain concrete subjected
to
random loadings
in
compres-
sion.
The
nonlinear hysteretic behavior
of
concrete
is
idealized
and
incor-
porated
in a
mathematical formulation
of
fatigue progress under random loading
condition.
NONLINEAR FATIGUE MODEL
The large prediction error
in
Fig.
1
seems
to
indicate
the
limitation
in the
use
of
S-N
relationship
for
concrete material. Since
the
fatigue life
of
con-
crete,
unlike metallic material,
is
affected
by
many loading parameters, such
as/
m i
„//
m a
x,/mean//max,/n
K
a
n
//c,/max//'c,
and
(/
malt
-f
min
)/f'
c
,
e t C , it is
difficult
to define
a
single
S-N
relationship when
all the
loading parameters
are
var-
ied.
To
reduce
the
prediction error
in
fatigue life, especially
at low
cycle
range,
it
may
be
more appropriate
to
incorporate
the
highly nonlinear char-
acteristics
of
concrete than
to
manipulate existing
S-N
relationships.
As the
basis
for
fatigue model development,
the
stress-strain relationship
of
con-
crete
is
idealized
to
trace
the
hysteretic behavior
and
stiffness degradation
process
to a
failure point.
A
dual-coordinate system
is
used
to
model
the
envelope curve
in
compression
and the
hysteresis loops within
the
envelope
curve,
as
shown
in
Fig.
2. A
simplified degradation rule
is
adopted herein
by assuming
the
centerline
of
hysteresis loops always passes through
the
'Struct. Engr., Dept.
of
Nuclear Energy, Brookhaven
Nat. Lab.,
Upton,
NY
11973.
Note.
Discussion open until April
1,
1991.
To
extend
the
closing date
one
month,
a written request must
be
filed with
the
ASCE Manager
of
Journals.
The
manuscript
for this paper
was
submitted
for
review
and
possible publication
on
February
15,
1989.
This paper
is
part
of
the
Journal
of
Structural Engineering,
Vol. 116,
No.
11,
November,
1990.
©ASCE, ISSN 0733-9445/90/0011-3228/S1.00
+ $.15 per
page.
Paper
No.
25224.