fatigue and fracture of structures - umass · pdf filedesign for and assessment of fatigue and...
TRANSCRIPT
Des
ign
for a
nd A
sses
smen
t of
Fat
igue
and
Fra
ctur
e in
Ste
el S
truc
ture
s
Pres
ente
d by
R
ober
t J. D
exte
r, P.
E.
Ass
ocia
te P
rofe
ssor
of S
truc
tura
l Eng
inee
ring
Uni
vers
ity o
f Min
neso
ta
Stru
ctur
al E
ngin
eeri
ng S
emin
ar S
erie
s17
Mar
ch 2
004
Part
I: Fr
actu
re
•D
efin
ition
s•
Hoa
nB
ridge
frac
ture
•N
orth
ridge
mom
ent f
ram
e fr
actu
res
•C
harp
yte
st a
nd n
otch
toug
hnes
s (C
VN
)•
“k-li
ne”
prob
lem
•O
ther
infa
mou
s brit
tle fr
actu
res i
n st
ruct
ures
Hig
h-cy
cle
Fatig
ue
Def
initi
on:
Form
atio
n of
a c
rack
due
to c
yclic
el
astic
load
ing
belo
w d
esig
n st
ress
le
vels
Surf
ace
Appe
aran
ce o
f Fat
igue
C
rack
Is S
moo
th a
nd S
ilky
Frac
ture
Def
initi
on:
Rupt
ure
in te
nsio
n or
rapi
d ex
tens
ion
of
a cr
ack
lead
ing
to g
ross
def
orm
atio
n,
loss
of f
unct
ion
or se
rvic
eabi
lity,
or
com
plet
e se
para
tion
of th
e co
mpo
nent
Type
s of F
ract
ure
•B
rittle
frac
ture
–Li
near
Ela
stic
Fra
ctur
e M
ech.
(LEF
M)
•D
uctil
e fr
actu
re–
Net
-sec
tion
plas
tic c
olla
pse
load
•Tr
ansi
tion
–br
ittle
/duc
tile
Brit
tle F
ract
ure
Def
initi
on:
Sudd
en fa
ilure
in a
mat
eria
l tha
t us
ually
occ
urs w
ith n
eglig
ible
pl
astic
def
orm
atio
n
Surf
ace
Appe
aran
ce o
f Bri
ttle
Frac
ture
is
Rou
gh w
ith C
hevr
on M
arki
ngs
Bry
teB
end
Brid
ge, f
ract
ured
und
er c
onst
ruct
ion
in 1
970
Cha
ract
eris
tics o
f B
rittle
Fra
ctur
e
•A
pplie
d st
ress
≤yi
eld
stre
ss•
Frac
ture
surf
ace
appe
ars “
flat”
•Li
ttle
or n
o sh
ear
Brit
tle F
ract
ure
Due
to c
atas
trop
hic
natu
re o
f fai
lure
as
soci
ated
with
bri
ttle
frac
ture
W
e w
ant t
o en
sure
it d
oes n
ot o
ccur
This
is a
chie
ved
thro
ugh
the
prin
cipl
es o
f Fr
actu
re M
echa
nics
Frac
ture
Mec
hani
cs D
evel
oped
Afte
r Fr
actu
res o
f Wel
ded
Ship
s in
WW
II
•20
% o
f 470
0 m
erch
ant s
hips
suff
ered
brit
tle fr
actu
re
•145
bro
ke in
two
Fact
ors I
ncre
asin
g Po
tent
ial f
or
Brit
tle F
ract
ure
•St
ress
con
cent
ratio
ns (n
otch
es)
•M
inim
al n
otch
toug
hnes
s•
Low
tem
pera
ture
•C
onst
rain
t (th
ickn
ess)
•R
esid
ual s
tress
(thi
ckne
ss, w
elds
)•
Hig
h lo
ad ra
tes
Obj
ectiv
e of
frac
ture
mec
hani
cs•
To e
nsur
e, b
y m
ater
ial s
elec
tion
and
desi
gn,
that
brit
tle fr
actu
re d
oes n
ot o
ccur
, i.e
. if
frac
ture
doe
s occ
ur th
at it
be
duct
ile fr
actu
re
Hoa
n B
ridge
, fra
ctur
ed in
serv
ice
in 2
000
Unit S
2A N
orth
boun
d Tr
affic
Lan
esEa
st
24-6
24-6
10-0
12-0
12-0
12-0
6-0
Girde
r EGir
der F
Girde
r D
10-5
/16
Bot
tom
Fla
nge
Brit
tle
Frac
ture
in H
oan
Brid
ge
Bot
tom
Fl
ange
Web
WT
12x5
5
WT
12x5
5No
rth
1/2 45
deg.BT
C P4
E70x
x
7/8
A-32
5 Bo
lts 1
5/16
Hole
s (
typ.)
Loca
tion F
-28
2 1/
4 x 2
8 Fl
ange
Plat
e
Cra
ck-li
ke N
otch
at S
helf
Plat
eIn
ters
ectin
g / O
verla
ppin
gW
elds
Tem
pora
ry R
etro
fit a
t Eve
ry P
anel
Po
int o
f Ext
erio
r Gird
ers
Shel
f pla
te o
n op
posi
te fa
ce o
f web
(Ext
erio
r fac
e)
Fina
l Ret
rofit
of a
ll Sp
ans
Oth
er B
ridg
es H
ave
Sim
ilar D
etai
lsI-7
9In
ters
ectin
g w
elds
an
d la
ck o
f pos
itive
co
nnec
tion
SR 4
22
Inte
rsec
ting
wel
ds
and
poor
qua
lity
Shen
ango
R
iver
Brid
ge
Web
Fra
ctur
e
Cha
rpy
Test
ing
•N
ota
dire
ct m
easu
re o
f fra
ctur
e to
ughn
ess
•Ex
celle
nt fo
r mat
eria
l scr
eeni
ng•
Exce
llent
for q
ualit
y co
ntro
l•
Low
cos
t and
eas
y
Will
like
ly re
mai
n fa
vore
d m
etho
d
Cha
rpy
Test
ing
Cha
rpy
Test
ing
Exam
ple
Test
Tem
pera
ture
(de
g. F
)-1
20-1
00-8
0-6
0-4
0-2
00
2040
6080
100
120
CVN Energy (ft-lb)
020406080100
120
140
Test
Dat
aAA
SHTO
Non
-frac
ture
Crit
ical
AASH
TO F
ract
ure
Crit
ical
Step
1 –
Dev
elop
Cha
rpy
curv
e fr
om te
stin
gEf
fect
of T
empe
ratu
re o
n Fr
actu
re T
ough
ness
•Fr
actu
re to
ughn
ess d
ecre
ases
with
de
crea
sing
tem
pera
ture
•B
ridge
s are
subj
ecte
d to
larg
e te
mpe
ratu
re
varia
tions
•M
inim
um se
rvic
e te
mpe
ratu
re is
crit
ical
–R
elat
ed to
geo
grap
hic
loca
tion
How
doe
s Spe
cific
atio
n ad
dres
s eff
ect o
f te
mpe
ratu
re o
n fr
actu
re to
ughn
ess?
•R
equi
res m
inim
um C
VN
ene
rgy
at v
ario
us
serv
ice
tem
pera
ture
s•
Thre
e te
mpe
ratu
re “
zone
s” d
efin
ed a
s per
A
ASH
TO•
Sout
hern
Min
neso
ta is
Zon
e 2
Tem
pera
ture
Zon
e D
esig
natio
ns
3-3
1 F
to -6
0 F
2-1
F to
-30
F
10
F an
d ab
ove
Tem
pera
ture
Z
one
Min
Ser
vice
T
empe
ratu
re
Cha
rpy
Spec
ifica
tions
•To
ass
ure
duct
ile/b
rittle
tran
sitio
n te
mpe
ratu
re is
bel
ow m
inim
um se
rvic
e te
mpe
ratu
re•
Tem
pera
ture
shift
(38
C o
r 70
F)
allo
wed
bec
ause
Cha
rpy
test
has
muc
h hi
gher
stra
in ra
te th
an se
rvic
e lo
ads
K-li
ne P
robl
em
�� ��
k-lin
e
Area
of
redu
ced
toug
hnes
s
•R
otar
y st
raig
hten
ing
of
rolle
d sh
apes
redu
ces
toug
hnes
s and
duc
tility
in
“k-
area
” of
mem
bers
•W
eldi
ng o
f stif
fene
rs
in “
k-ar
ea”
may
lead
to
fabr
icat
ion
crac
ks
Att
achm
ent P
late
Ter
min
ated
in k
-are
aK
-are
a Fr
actu
re
Rot
ary
Stra
ight
enin
g –
Feed
ing
InR
otar
y St
raig
hten
ing
Side
Vie
wT
ensi
le S
peci
men
Tak
en F
rom
k-a
rea
Stra
in (i
n/in
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Stress (psi)
0
2000
0
4000
0
6000
0
8000
0
1000
00
As-R
olle
dG
ag S
traig
hten
edR
otar
y St
raig
hten
ed
W14
X 1
76R
otar
y St
raig
hten
ed
Dis
t. Fr
om O
utsi
de F
lang
e Fa
ce (i
n.)
01
23
45
K-area Hardness (HRB)
65707580859095100
CVN @ 72 F (ft-lbs)
0102030405060H
RB
CVN
W
14 X
176
Gag
Stra
ight
ened
Dis
t. Fr
om O
utsi
de F
lang
e Fa
ce (i
n.)
01
23
45
K-area Hardness (HRB)
65707580859095100
CVN @ 72 F (ft-lbs)
0102030405060
HR
BC
VN
W
14 X
176
A
s-ro
lled
Dis
t. Fr
om O
utsi
de F
lang
e Fa
ce (i
n.)
01
23
45
K-area Hardness (HRB)
65707580859095100
CVN @ 72 F (ft-lbs)
0102030405060H
RB
CVN
Insi
de F
lang
e Fa
ce
Insi
de F
lang
e Fa
ce
Insi
de F
lang
e Fa
ce
Har
dnes
s and
C
VN
for
Rot
ary
Stra
ight
ened
Gag
St
raig
hten
ed
As R
olle
d
Bri
ttle
Fra
ctur
es in
Tes
ts w
ith
Stiff
ener
Ter
min
atin
g in
k-a
rea
Det
ail s
tiffe
ner
with
1.5
in (3
8 m
m) c
utou
ts
to a
void
k-li
ne p
robl
em
Infa
mou
s Brit
tle F
ract
ures
fr
om th
e Pa
st•
Usi
ng ju
mbo
s as t
ensi
on c
hord
s in
truss
es•
Reb
ar a
nd a
ncho
r rod
s mad
e fr
om re
bar
•Fi
lene
Perf
orm
ing
Arts
Cen
ter,
Wol
f Tra
p•
All
had
sim
ilarly
low
toug
hnes
s
Mai
n Po
ints
•A
dequ
ate
CV
N is
crit
ical
•Fo
r exa
mpl
e, fo
r fra
ctur
e cr
itica
l brid
ges
–25
ft lb
s at –
20F
for w
eld
met
al–
25 ft
-lbs a
t 40F
stee
l pla
te fo
r Zon
e II
(-30
F)–
25 ft
-lbs a
t 10F
stee
l pla
te fo
r Zon
e II
I (-6
0F)
•G
ood
CV
N p
rovi
ded
in d
omes
tic st
eel s
hape
s w/o
ne
cess
ity fo
r sup
plem
enta
l CV
N sp
ecifi
catio
n (a
nd $
pr
emiu
m) —
avoi
d k-
area
•W
eld
met
al C
VN
is h
ighl
y va
riabl
e an
d no
t wel
l co
ntro
lled
by c
ertif
icat
ions
, so
pay
for h
igh-
toug
hnes
s w
eld
met
al•
Goo
d de
taili
ng, a
void
not
ches
, ess
entia
l
Type
s of F
atig
ue a
nd F
ract
ure
Prob
lem
s in
Min
neso
ta
•Po
or d
etai
ls u
sed
(< 1
975)
•O
ut-o
f-pl
ane
dist
ortio
n (<
1985
)•
Wel
ding
def
ects
(<19
75)
•Lo
w-to
ughn
ess m
ater
ial
(<19
75)
Thre
e M
ost I
mpo
rtant
Par
amet
ers
Rel
ated
to F
atig
ue D
amag
e C
alcu
latio
ns A
re:
•N
omin
al st
ress
rang
e (S
r)
•N
umbe
r of c
ycle
s (N
)
•D
etai
l cla
ssifi
catio
n (A
, B, C
, etc
.)
Nom
inal
Stre
ss
Stre
ss c
alcu
late
d in
des
ign
resu
lting
St
ress
cal
cula
ted
in d
esig
n re
sulti
ng
dire
ctly
from
the
desi
gn fo
rces
, di
rect
ly fr
om th
e de
sign
forc
es,
usua
lly in
the
long
itudi
nal d
irect
ion
of
usua
lly in
the
long
itudi
nal d
irect
ion
of
a m
embe
r, e.
g. P
/A, M
c/I
a m
embe
r, e.
g. P
/A, M
c/I
Tim
e
Stress (ksi)
S r=
9.0
ksi
1 C
ycle
(N
)
Def
initi
ons o
f Sran
d N
S-N
dat
a fr
om e
xist
ing
data
base
of C
-Mn
Stee
l fo
r lo
ngitu
dina
l fill
et w
elds
Yie
ld p
oint
rang
e: F
y=
248
to 6
90 M
pa (3
6 to
100
ksi
)
The
Bel
ief S
yste
m o
f M
echa
nica
l Eng
inee
rs•A
SME
Boi
ler a
nd P
ress
ure
Ves
sel C
ode
•Fat
igue
stre
ngth
is a
func
tion
of te
nsile
stre
ngth
•Fat
igue
lim
it is
app
roxi
mat
ely
half
the
ultim
ate
stre
ngth
•Geo
met
ric e
ffec
ts o
f wel
ds e
tc. c
an b
e ta
ken
into
ac
coun
t with
stre
ss a
naly
sis
•Mea
n st
ress
is im
porta
nt
Brid
gePr
essu
re v
esse
l•
Com
plex
con
figur
atio
n•
Hig
h cy
cle,
var
iabl
e•
Mat
eria
lunc
erta
in (v
aria
ble
thro
ugho
ut b
ridge
)•
Res
idua
l stre
sses
•W
eld
disc
ontin
uitie
s•
Mis
alig
nmen
t
•Si
mpl
e co
nfig
urat
ion
•Lo
w c
ycle
, con
stan
t•
Mat
eria
l wel
l cha
ract
eriz
ed
•St
ress
relie
f•
Strin
gent
ND
E•
Non
e
S-N
Cur
ves,
Det
ail C
ateg
orie
s
•D
esig
n fo
r spe
cific
num
ber o
f cyc
les
–e.
g. c
rane
ope
ratin
g <
30 c
ycle
s per
day
–50
0,00
0 cy
cles
for 5
0 ye
ar li
fe
•D
esig
n be
low
fatig
ue c
rack
ing
thre
shol
d–
cons
tant
-am
plitu
de fa
tigue
lim
it, C
AFL
–oc
curs
bet
wee
n 2
(for
Cat
egor
y B
) to
20 m
illio
n cy
cles
(f
or C
ateg
ory
E’)
–m
ost b
ridge
s exc
eed
this
num
ber o
f loa
d cy
cles
in
lifet
ime
Cat
egor
y E
or E
’
Ends
of W
elde
d C
over
Pla
teEn
ds o
f Wid
er C
over
Pla
te
Wak
ota
Bri
dge
Term
inat
ion
of C
over
Pla
tes
36 a
nd C
leve
land
36 a
nd C
leve
land
Cat
egor
y E
or E
’
Long
itudi
nal W
elde
d A
ttach
men
tLo
ngitu
dina
lly W
elde
d A
ttach
men
t (La
p Jo
ints
)
Exam
ple
of L
ongi
tudi
nal
Wel
ded
Flan
ge A
ttach
men
tEx
ampl
e C
ateg
ory
E Lo
ngitu
dina
l Wel
ded
Atta
chm
ent
Exam
ple
of a
Var
iabl
e A
mpl
itude
St
ress
Ran
ge H
isto
gram
Truc
k Lo
ads
App
rox.
A
ppro
x.
Mn/
DO
T M
n/D
OT
Truc
ksTr
ucks
15.5
15
.5
kips
kips
17.5
17
.5
kips
kips
10
10
ftft5
ft5
ft17
17
kips
kips
HS
HS --
2020
8 ki
ps8
kips
32 k
ips
32 k
ips
32 k
ips
32 k
ips
14
14
ftft14
14
--30
ft30
ft
Typi
cal 8
0 ki
p
Typi
cal 8
0 ki
p
Sem
iSe
mi -- T
ruck
Truc
k
12 k
ips
12 k
ips 14
.4 ft
14.4
ft4.
3 ft
4.3
ft
17
17
kips
kips
17
17
kips
kips
17
17
kips
kips
17
17
kips
kips
31 ft
31 ft
4.1
ft4.
1 ft
Perc
ent o
f Tru
ck T
raffi
c by
Con
figur
atio
n on
I-94
@ M
nRoa
d
0102030405060708090100
3axle
sin
gle
unit
4+ a
xle s
ingl
eun
it3&
4 ax
le s
emi
5 ax
le s
emi
6+ a
xle s
emi
5 ax
le tw
in6
axle
twin
7+ a
xle v
ehic
le
Truc
k C
onfig
urat
ion
Percent of Truck Traffic (%)
Wes
tbou
ndE
astb
ound
GVW
His
togr
am o
f All
Truc
k Ty
pes
on I-
94 @
MnR
oad
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0-44-88-1
2 12-16
16-20
20-24
24-28
28-32
32-36
36-40
40-44
44-48
48-52
52-56
56-60
60-64
64-68
68-72
72-76
76-80
80-84
84-88
88-92
92-96
96-10
0 100-1
04 104-1
08 108-1
12 112-1
1611
6+
GVW
Ran
ge (k
si)
Fraction of all Trucks
Wes
tbou
ndE
astb
ound
Furth
erm
ore,
nea
rly a
ll av
aila
ble
fatig
ue
test
dat
a w
ere
obta
ined
from
con
stan
t am
plitu
de te
stin
gC
onst
ant A
mpl
itude
La
bora
tory
Tes
t Dat
a
Varia
ble
Ampl
itude
St
ress
es In
-ser
vice
?
Hen
ce, w
e ne
ed a
met
hod
to re
late
:
S r v
arto
S rco
nst
In o
rder
to p
erfo
rm fa
tigue
des
ign
or
eval
uatio
n
Effe
ctiv
e St
ress
Ran
ge
•C
an u
se M
iner
’s ru
le to
cal
cula
te a
n ef
fect
ive
stre
ss ra
nge
from
a h
isto
gram
of v
aria
ble
stre
ss
rang
es.
•M
iner
’s ru
le 33
Re
)(
iri
iS
S Whe
re:
Whe
re:
ααi i
==#
of st
ress
cyc
les w
ith st
ress
rang
e S
# of
stre
ss c
ycle
s with
stre
ss ra
nge
S riridi
vide
d by
the
divi
ded
by th
e to
tal #
of s
tress
cyc
les.
tota
l # o
f stre
ss c
ycle
s.
Stre
ss-r
ange
Pro
babi
lity
Den
sity
Fun
ctio
n
Stre
ss o
r (G
VW )
% Occurrence
S ref
fS r
max
Sum
mar
y •
Con
vert
stre
ss-r
ange
his
togr
am in
to S
reff
of N
cyc
les o
f equ
ival
ent d
amag
e–
Usi
ng M
iner
’s ru
le
Cal
cula
te S
r eff
182.
250.
251
9.0
00
08.
00
00
7.0
00
06.
00
00
5.0
16.0
0.25
14.
00
00
3.0
4.0
0.5
22.
00
00
1.0
f i x
(Sri
3 )f i
(Ni/N
)N
iB
in(k
si)
SSre
ffre
ff=
(=
( ΣΣff i i xx
(S(Sriri33 )
)))1/
31/
3
Σff i i xx
(S(Sriri33 )
= 2
02.2
5) =
202
.25
SSre
ffre
ff=
5.9
ksi
= 5.
9 ks
iN
= 4
N =
4
Ope
n Tr
affic
Res
ults
, I-3
5W
Larg
e S
tres
s E
vent
In D
iago
nal o
f Flo
or T
russ
-20
-15
-10-5051015
01
23
45
6
Tim
e, s
ec
Stress, MPa
Stre
ss R
ange
s for
Flo
or T
russ
(I-3
5W)
S R(M
Pa)
Upp
er
Cho
rdD
iago
nal
Low
er
Cho
rd0-
3.5
13.3
36.8
3.0
3.5-
751
.130
.924
.5
7-10
.534
.225
.555
.0
10.5
-14
1.4
5.5
14.6
14-1
7.5
0.0
1.0
2.7
17.5
-21
0.0
0.2
0.3
21-2
4.5
0.0
0.04
0.01
S ref
f=
6.6
7.1
7.
3
Fatig
ue R
esis
tanc
e of
Cat
egor
y C
Det
ails
Stre
ss R
ange
Ver
sus N
umbe
r of C
ycle
s
Con
stan
t Am
plitu
de F
atig
ue
Lim
its (C
AFL
)
Des
ign
Bel
ow T
hres
hold
(CA
FL)
(infin
ite li
fe)
•Fi
nite
-life
onl
y us
eful
if A
DTT
less
than
550
(giv
es 1
0 m
illio
n cy
cles
in 5
0 ye
ars)
•D
esig
n so
that
fatig
ue li
mit-
stat
e st
ress
rang
e (S
rmax
) is
bel
ow th
e co
nsta
nt-a
mpl
itude
fatig
ue li
mit
(CA
FL)
•A
ISC
: Loa
ding
ass
umed
con
stan
t and
S rm
ax ta
ken
as
the
stre
ss ra
nge
due
toun
fact
ored
desi
gn li
ve lo
ad
•C
rack
s will
not
pro
paga
te si
gnifi
cant
ly in
the
life
of
the
stru
ctur
e
How
doe
s thi
s rel
ate
to v
aria
ble
live
load
spec
trum
?
GVW
% Occurrence
S ref
fS r
max
0.01
% p
rob.
of
exce
eden
ce
For D
esig
n B
elow
Thr
esho
ld•
Bas
ed o
n te
stin
g (N
CH
RP
Rep
ort 3
54)
-0.
05%
exc
eede
d C
AFL
, cra
ckin
g-
0.00
1% e
xcee
ded
the
CA
FL, n
o cr
acki
ng•
Con
clud
ed in
finite
life
if fe
wer
than
0.
01%
exc
eed
CA
FL•
Fatig
ue-li
mit-
stat
e st
ress
rang
e (S
rmax
) is
stre
ss ra
nge
with
0.0
1% e
xcee
denc
e
AA
SHTO
Des
ign
Bel
ow T
hres
hold
•A
ASH
TO L
RFD
cod
e us
es e
ffec
tive
fatig
ue
truck
= 0
.75
load
fact
or ti
mes
HS2
0 tru
ck, i
.e.
HS1
5 (2
40 k
N, 5
4 ki
ps)
•C
ompa
res t
his s
tress
rang
e to
hal
f the
CA
FL,
in
eff
ect t
he fa
tigue
lim
it-st
ate
load
rang
e is
2
x H
S15
or H
S30
(480
kN
, 108
kip
s)•
WIM
dat
a su
gges
t tha
t the
0.0
1% e
xcee
denc
etru
ck is
clo
ser t
o 66
7 kN
(150
kip
s)•
Rea
son
for d
iscr
epan
cy is
that
the
actu
al st
ress
ra
nges
in b
ridge
s are
alw
ays m
uch
less
than
pr
edic
ted
usin
g co
nser
vativ
e de
sign
equ
atio
ns
How
doe
s the
AA
SHTO
LR
FD
fatig
ue li
mit-
stat
e lo
ad re
late
to li
ve
load
spec
trum
?
GVW
% OccurrenceS r
eff
S rm
ax
0.01
% p
rob.
of
exce
eden
ce
S rm
ax
(LR
FD)
Two
App
roac
hes t
o Fa
tigue
D
esig
n fo
r Brid
ges
•Fi
nite
life
if:
–S r
efffr
om H
S15
> C
AFL
/ 2
–(r
eally
Srm
axfr
om H
S30
> C
AFL
)–
Def
ined
num
ber o
f cyc
les o
r yea
rs•
Infin
ite li
fe if
:–
S ref
ffr
om H
S15
< C
AFL
/ 2
–(r
eally
Sr m
axfr
om H
S30
< C
AFL
)–
Unl
imite
d cy
cles
Dam
age
Cal
cula
tions
Fal
l in
to T
hree
Cas
es:
•C
ase
I –
S r e
ff>
CA
FL &
Srm
ax >
CA
FL•
Cas
e II
–S r
eff
< C
AFL
& S
rmax
> C
AFL
•C
ase
III
–S r
eff
< C
AFL
& S
rmax
< C
AFL
Rel
atio
nshi
p B
etw
een
Stre
ss-R
ange
Spe
ctru
m a
nd
Fatig
ue R
esis
tanc
e -%
Exc
eede
nce
CA
FL
S re
Illus
tratio
n of
Stra
ight
-line
Ex
tens
ion
of S
-N C
urve
110100 1.E
+05
1.E
+06
1.E
+07
1.E
+08
Cat
D C
AFL
= 7
.0 k
si
Stra
ight
line
ex
tens
ion
of
S-N
cur
ve
Exam
ple:
Cas
e I
•G
iven
:–
Cat
egor
y E
deta
il (C
AFL
4.5
ksi
)–
S ref
f=
5.0
ksi
–S r
max
= 14
.5 k
si–
N =
1,7
55 c
ycle
s/da
y•
Wha
t is e
stim
ated
fatig
ue li
fe in
yea
rs?
Exam
ple:
Cas
e I
•S r
eff>
CA
FL &
Srm
ax >
CA
FL–
All
cycl
es g
reat
er th
an C
AFL
–Fi
nite
fatig
ue li
fe–
Cal
cula
te li
fe u
sing
equ
atio
ns fo
r S-N
cur
ve (N
=
A/S
reff
3 )
•Fo
r Cat
egor
y E
–A
= 1
1.0
x 10
8
Cal
cula
tion
of ‘N
’ yie
lds:
–N
= 8
,800
,000
Cyc
les
Exam
ple:
Cas
e I
•N
= 8
,800
,000
Cyc
les
•Li
fe c
alcu
latio
n in
yea
rs:
–R
ecal
l 1,7
55 c
ycle
s/da
y ar
e ap
plie
d–
8,80
0,00
0 ÷
1,75
5 cy
cles
/day
= 5
,014
day
s–
5,01
4 da
ys ÷
365
days
/yr =
13.
75 y
rs
110100 1.E
+05
1.E
+06
1.E
+07
1.E
+08
S rm
ax =
14.
5 ks
i
N =
8,8
00,0
00
S ref
f = 5
.0 k
si
Cat
E C
AFL
= 4
.5 k
si
Exam
ple:
Cas
e I
Exam
ple:
Cas
e II
I
•G
iven
:–
Cat
egor
y C
det
ail (
CA
FL 1
0 ks
i)–
S ref
f=
4.9
ksi
–S r
max
= 8.
5 ks
i–
N =
5,7
60 c
ycle
s/da
y•
Wha
t is e
stim
ated
fatig
ue li
fe in
yea
rs?
Exam
ple:
Cas
e II
I
•S r
eff<
CA
FL &
S rm
ax <
CA
FL•
Hen
ce:
–A
llcy
cles
less
than
CA
FL–
No
furth
er a
ctio
n re
quire
d–
Infin
ite fa
tigue
life
Exam
ple:
Cas
e II
I
110100 1.E
+05
1.E
+06
1.E
+07
1.E
+08
Cat
C
CA
FL =
10
ksi
S rm
ax =
8.5
ksi
S ref
f = 4
.9 k
si
Exam
ple:
Cas
e II
•G
iven
:–
Cat
egor
y D
det
ail (
CA
FL 7
.0 k
si)
–S r
eff=
4.7
ksi
–S r
max
= 13
.5 k
si (>
CA
FL!)
–N
= 2
,637
cyc
les/
day
•W
hat i
s est
imat
ed fa
tigue
life
in y
ears
?
Stre
ss-R
ange
His
togr
am
•Fr
om th
e hi
stog
ram
:–
S ref
f=
4.7
ksi
–S r
max
= 13
.5 k
si–
NTo
tal=
18,
462
(wee
kly)
•N
umbe
r cyc
les >
CAF
L–
Cat
D –
CA
FL =
7.0
ksi
–N
>CA
FL=
1,59
6–
% E
xcee
denc
e =
8.6
%–
8.6
% >
>> 0
.01%
S r m
inS r
max
S r A
vg
01
0.5
01
21.
552
362
32.
541
983
43.
532
054
54.
521
255
65.
512
136
76.
588
97
87.
565
38
98.
545
39
109.
529
610
1110
.512
511
1211
.555
1213
12.5
1213
1413
.52
Bins
N
Stre
ss-R
ange
His
togr
am
Exam
ple:
Cas
e II
•Si
nce
S rm
ax >
CA
FL–
Fatig
ue d
amag
e is
exp
ecte
d (i.
e., f
inite
life
)–
Cal
cula
te li
fe u
sing
stra
ight
line
ext
ensi
on o
f SN
cur
ve–
Proc
eed
with
cal
cula
tions
just
like
Cas
e I
Exam
ple:
Cas
e II
•C
alcu
late
safe
life
(N)
–Fo
r Cat
egor
y D
:•
A =
22.
0 x
108
•N
= A
/Sre
ff3
•C
alcu
latio
n of
‘N’ y
ield
s:–
N =
21,
189,
910
Cyc
les
Exam
ple:
Cas
e II
•N
= 2
1,18
9,91
0 C
ycle
s•
Cal
cula
tion
of li
fe in
yea
rs:
–R
ecal
l 2,6
37 c
ycle
s/da
y ar
e ap
plie
d–
21,1
89,9
10 ÷
2,63
7cy
cles
/day
= 8
,036
day
s–
8,03
6 da
ys ÷
365
days
/yr =
22.
0 yr
s
110100 1.E
+05
1.E
+06
1.E
+07
1.E
+08
S ref
f = 4
.7 k
si
Cat
D C
AFL
= 7
.0 k
si
S rm
ax =
13.
5 ks
i
N =
21,
189,
910
Exam
ple:
Cas
e II
Prim
ary
Nom
inal
Stre
sses
Stre
sses
cal
cula
ted
in d
esig
n St
ress
es c
alcu
late
d in
des
ign
resu
lting
dire
ctly
from
the
resu
lting
dire
ctly
from
the
desi
gn fo
rces
, usu
ally
in th
e de
sign
forc
es, u
sual
ly in
the
long
itudi
nal d
irect
ion
of a
lo
ngitu
dina
l dire
ctio
n of
a
mem
ber,
e.g.
P/A
, Mc/
Im
embe
r, e.
g. P
/A, M
c/I
Seco
ndar
y St
ress
esSt
ress
es in
duce
d in
a m
embe
r or
Stre
sses
indu
ced
in a
mem
ber o
r de
tail
from
def
orm
atio
ns, u
sual
ly in
de
tail
from
def
orm
atio
ns, u
sual
ly in
a
trans
vers
e di
rect
ion,
and
usu
ally
a
trans
vers
e di
rect
ion,
and
usu
ally
no
t acc
ount
ed fo
r or c
onsi
dere
d in
no
t acc
ount
ed fo
r or c
onsi
dere
d in
de
sign
de
sign
Exam
ples
of
Seco
ndar
y St
ress
es
•“O
il ca
nnin
g” o
r “pu
mpi
ng”
of fl
exib
le w
eb
plat
es in
ben
ding
–O
ccur
s with
no
late
ral f
orce
s app
lied
–So
met
imes
vis
ible
–N
o kn
own
in-s
ervi
ce fa
tigue
cra
cks e
ver o
bser
ved
–C
rack
ing
only
obs
erve
d in
labo
rato
ry a
t ele
vate
d st
ress
es &
at l
ocal
web
gap
def
orm
atio
ns–
Pres
ently
, the
re a
re d
esig
n ch
ecks
of s
hear
for
fatig
ue to
pre
vent
this
, may
not
be
nece
ssar
y
Exam
ple
of g
loba
l “O
il C
anni
ng”
Exam
ples
of C
rack
ing
from
Seco
ndar
y St
ress
es•
Out
-of-
plan
e di
stor
tion
due
to la
tera
l for
ces
–W
eb-g
ap c
rack
ing
at d
iaph
ragm
s and
floo
rbea
ms
–Sh
elf p
late
/con
nect
ion
plat
e de
tails
, Laf
ayet
te S
t. B
ridge
•D
eck
plat
e an
d di
aphr
agm
cra
ckin
g in
orth
otro
pic
brid
ge d
ecks
•Ti
e gi
rder
floo
rbea
m c
onne
ctio
ns–
Als
o in
trus
ses a
nd p
late
gird
er b
ridge
s
•C
antil
ever
bra
cket
cra
ckin
g
Web
Gap
Cra
ckin
gW
eb G
ap C
rack
ing
mos
t com
mon
type
of f
atig
ue c
rack
ing
in U
.S. b
ridge
sm
ost c
omm
on ty
pe o
f fat
igue
cra
ckin
g in
U.S
. brid
ges
Web
Flan
ge
Tran
s.
Con
n.
Plat
e
Term
inol
ogy
Dia
phra
gm
Web
Gap
G i r d e r
Dia
phra
gm
stiffener
Dis
tort
iona
l Str
ess M
echa
nism
��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ���
������������������������������������
������������������������������������
������������������������������������
��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ���
�����������������������������������
�����������������������������������
�����������������������������������
h
L
Diff
eren
tial
defle
ctio
n of
gi
rder
s
gW
eb-g
ap
dist
ortio
n
Fear
of W
eldi
ng to
Ten
sion
Fla
nge
Typi
cal “
mill
ed-to
-bea
r”
conn
ectio
n pl
ate
•O
nly
case
of p
robl
ems
was
brit
tle fr
actu
re o
f brid
ge
in B
elgi
um in
195
0’s
•D
ue to
low
qua
lity
stee
l use
d at
the
time
•N
o lo
nger
an
issu
e (to
ughn
ess
requ
irem
ents
)
Fini
te E
lem
ent S
tudy
Fini
te E
lem
ent S
tudy
Fini
te E
lem
ent S
tudy
Stre
ss (K
si)
Top
Flan
ge
Top
Flan
ge
Web
Gap
Cra
ckin
gW
eb G
ap C
rack
ing
(Stre
ss R
ever
sal)
(Stre
ss R
ever
sal)
Floo
r Bea
ms
Floo
r Bea
ms
Cra
ckin
g D
ue to
Out
-of-
Plan
e D
isto
rtio
n•
NC
HR
P 33
6: F
ishe
r, J.W
.,Ji
an, J
., W
agne
r, D
.C.,
and
Yen
, B.T
., D
isto
rtion
-indu
ced
fatig
ue c
rack
ing
in st
eel
brid
ges,
Nat
iona
l Coo
pera
tive
Hig
hway
Res
earc
h Pr
ogra
m (N
CH
RP)
Rep
ort 3
36, T
rans
porta
tion
Res
earc
h B
oard
, Was
hing
ton,
D.C
.,199
0•
Prob
lem
cor
rect
ed in
spec
ifica
tions
in 1
985,
requ
iring
co
nnec
tion
plat
es to
hav
e “a
pos
itive
atta
chm
ent t
o al
l el
emen
ts o
f the
cro
ss se
ctio
n”•
85%
of M
inne
sota
stee
l brid
ges b
uilt
prio
r to
1985
Rep
air a
nd R
etro
fit S
trat
egie
s•
Fatig
ue c
rack
s are
like
coc
kroa
ches
–Y
ou d
on’t
usua
lly se
e ju
st o
ne–
Insp
ectio
n an
d re
trofit
are
crit
ical
•R
epai
r exi
stin
g cr
acks
–H
ole
drill
ing
–D
oubl
erpl
ates
•R
etro
fit o
ther
sim
ilar c
onne
ctio
ns–
Red
uce
driv
ing
forc
e –
chea
p an
d ef
fect
ive
–M
ake
conn
ectio
n rig
id –
old
relia
ble
–M
ake
conn
ectio
n m
ore
flexi
ble
–so
mew
hat r
isky
Hol
e m
ust b
e 4
Hol
e m
ust b
e 4 --
inch
Dia
met
erin
ch D
iam
eter
only
use
ful i
f cra
ck is
less
than
6 in
ches
long
on
only
use
ful i
f cra
ck is
less
than
6 in
ches
long
on
each
sid
e, o
r tot
al 1
2 in
ches
long
each
sid
e, o
r tot
al 1
2 in
ches
long
Mus
t Loc
ate
Cra
ck T
ipM
ust L
ocat
e C
rack
Tip
use
Dye
use
Dye
-- pen
etra
nt
pene
tran
t or M
agne
ticor
Mag
netic
-- par
ticle
Tes
tpa
rtic
le T
est
Cra
cks
Will
Rei
nitia
te
Cra
cks
Will
Rei
nitia
te
at S
mal
l Hol
es
at S
mal
l Hol
es
Big
ger C
rack
s R
equi
re B
olte
dB
igge
r Cra
cks
Req
uire
Bol
ted
Dou
bler
Dou
bler
Plat
ePl
ate
I-35
WR
etro
fit
Ret
rofit
––R
educ
e D
rivin
g Fo
rce
Red
uce
Driv
ing
Forc
e •• R
emov
e di
aphr
agm
sR
emov
e di
aphr
agm
s––
not n
eede
d fo
r loa
d di
strib
utio
n no
t nee
ded
for l
oad
dist
ribut
ion
––on
ly n
eede
d du
ring
cons
truc
tion
only
nee
ded
durin
g co
nstr
uctio
n––
or in
ser
vice
at p
ier f
or c
ontin
uous
spa
nsor
in s
ervi
ce a
t pie
r for
con
tinuo
us s
pans
––fu
ture
fu
ture
red
ecki
ngre
deck
ing ?
acc
iden
tal l
oadi
ng?
? ac
cide
ntal
load
ing?
•• Nex
t bes
t thi
ng:
Nex
t bes
t thi
ng:
loos
en b
olts
loos
en b
olts
Effe
ctiv
enes
s of
Thi
s Ty
pe
Effe
ctiv
enes
s of
Thi
s Ty
pe
of R
etro
fit M
ust B
e of
Ret
rofit
Mus
t Be
Verif
edVe
rifed
Mag
netic
mou
nted
dis
plac
emen
t tra
nsdu
cer
Mag
netic
mou
nted
dis
plac
emen
t tra
nsdu
cer
chea
p, e
asy,
and
qui
ckch
eap,
eas
y, a
nd q
uick
Stra
in g
ages
use
d to
St
rain
gag
es u
sed
to
verif
y bo
lt lo
osen
ing
verif
y bo
lt lo
osen
ing
II -- 80
brid
ge in
Iow
a80
brid
ge in
Iow
a
Tigh
t bol
tsLo
ose
bolts -59
Strain, in/in
-241
Tim
e, se
cond
s
Fact
or o
f 4 d
ecre
ase
mea
ns 4
3 or
64
times
the
life
I-35
WII -- 3
5W o
ver M
issi
ssip
pi: S
trai
n ga
ges
show
ed
35W
ove
r Mis
siss
ippi
: Str
ain
gage
s sh
owed
fa
ctor
of t
wo
decr
ease
afte
r low
erin
g di
aphr
agm
fact
or o
f tw
o de
crea
se a
fter l
ower
ing
diap
hrag
m
I-35
WM
ake
Con
nect
ion
Rig
id:
Bolte
d D
etai
lR
igid
ity is
crit
ical
, ¾” t
hick
Oth
er D
isto
rtio
n-in
duce
d C
rack
ing
at S
helf-
plat
e D
etai
ls
Dfg
dg
Sche
mat
ic o
f dis
torti
on in
web
gap
at l
ater
al
guss
et p
late
Lafa
yette
Str
eet B
ridg
eLa
faye
tte C
hron
olog
y of
Eve
nts
•Fa
ll 19
68 -
Bri
dge
Ope
ned
•M
arch
20,
197
5 -2
1/2
” D
efle
ctio
n in
Med
ium
•A
pril
4, 1
975
-4”
Est
imat
ed D
efle
ctio
n•
Apr
il 28
, 197
5 -6
” M
easu
red
Def
lect
ion
•M
ay 5
, 197
5 -6
1/2
” M
easu
red
Def
lect
ion
•M
ay 7
, 197
5 -C
rack
ed G
irde
r D
isco
vere
d -C
lose
d B
ridg
e•
May
11,
197
5 -B
eam
Sup
port
ed b
y C
able
•M
ay 1
6, 1
975
-All
Supp
ort B
eam
s In
Plac
e•
May
21,
197
5 -J
acki
ng C
ompl
eted
•Ju
ne 2
, 197
5 -S
plic
e C
ompl
eted
Lafa
yette
Stre
et B
ridge
Rep
air S
plic
e
Sign
, Sig
nal,
and
Ligh
t Sup
port
Stru
ctur
es
Fatig
ue F
ailu
re o
f M
ast-A
rm S
truct
ure
Vis
ual C
rack
s
Exte
nt o
f Fat
igue
Pro
blem
•A
t lea
st 6
0% o
f sta
tes h
ave
had
exce
ssiv
e vi
brat
ion
or fa
tigue
, 42%
had
fatig
ue c
rack
s•
Abo
ut 3
3% o
f sig
nal s
uppo
rts in
spec
ted
in
Wyo
min
g fo
und
crac
ked
•A
bout
1%
of s
ign-
supp
ort s
truct
ures
in
spec
ted
in W
isco
nsin
foun
d cr
acke
d•
Six
rece
nt c
atas
troph
ic c
olla
pses
on
inte
rsta
te h
ighw
ays,
two
fata
litie
s
Fact
ors A
ffec
ting
Susc
eptib
ility
to
Vib
ratio
n fr
om W
ind
Load
s•
Hig
h fle
xibi
lity
–pa
rticu
larly
long
-spa
n m
onot
ube
cant
ileve
r stru
ctur
es
•Lo
w re
sona
nt fr
eque
ncie
s of a
bout
1 H
z –
in th
e ra
nge
of w
ind
gust
freq
uenc
ies
•Ex
trem
ely
low
dam
ping
–le
ss th
an 1
% o
f crit
ical
dam
ping
–am
plifi
es re
spon
se o
f the
stru
ctur
e to
smal
l cyc
lic fo
rces
22-m
eter
span
mas
t-arm
is e
xtre
mel
y fle
xibl
eB
RID
GE
SU
PPO
RT
S: F
ew F
atig
ue Is
sues
Als
o ca
lled
“spa
n-ty
pe”
supp
ort o
r “ov
erhe
ad”
supp
ort
Exam
ple
of E
ffec
t of L
ow D
ampi
ng(s
truct
ure
pulle
d fo
ur ti
mes
and
rele
ased
,cy
cles
con
tinue
with
littl
e de
crea
se in
am
plitu
de)
-150
.000
-100
.000
-50.
000
0.00
0
50.0
00
100.
000
150.
000 13:2
0:04
13:2
0:21
13:2
0:38
13:2
0:56
13:2
1:13
13:2
1:30
13:2
1:48
Tim
e (E
DT)
Strian (
AR
MTO
P
AL
UM
INU
M
•Fa
vore
d fo
r its
ligh
t wei
ght,
corr
osio
n re
sist
ance
•C
ost i
s gre
ater
•Fa
tigue
stre
ngth
is 1
/3 th
at o
f ste
el–
man
y fa
tigue
pro
blem
s–
not r
ecom
men
ded
for n
ew d
esig
ns–
mus
t ins
pect
freq
uent
ly b
ecau
se o
f lik
elih
ood
of fa
tigue
Fatig
ue C
rack
s in
Wel
ded
Alu
min
um T
russ
Fatig
ue C
rack
s in
Wel
ded
Alu
min
um T
russ
�ew
AA
��T�
�pe
cific
atio
n a
�es
ult o
f �re
viou
s �es
earc
h
Am
eric
an A
ssoc
iatio
n of
�ta
te �
ighw
ay a
nd
Tran
spor
tatio
n �
ffic
ials
�A
A��
T��
�tan
dard
�p
ecifi
catio
ns
for
�tru
ctur
al
�upp
orts
fo
r �
ighw
ay �
igns
,�um
inai
res
and
Traf
fic �
igna
ls�th
�diti
on, �
��1
�yn
amic
Win
d �o
ads
•A
eroe
last
ic �s
truct
ure
inte
ract
s with
win
d�–
�al
lopi
ng
–�
orte
� �h
eddi
ng
•A
erod
ynam
ic �l
oad
inde
pend
ent o
f stru
ctur
e�–
�at
ural
Win
d �
usts
–Tr
uck�
�ndu
ced
Win
d �
usts
Res
earc
h O
bjec
tives
Fatig
ue L
oadi
ngs
Truc
k G
ust
(in-p
lane
load
ing)
Gal
lopi
ng(in
-pla
ne lo
adin
g)
Nat
ural
Win
d G
ust
(out
-of-p
lane
load
ing)
9
Truc
k��n
duce
d W
ind
�us
ts
����
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antil
ever
ed �
igna
l
��
�igh
t �ol
e
��
��
ridge
�up
port
��ig
n or
�ig
nal�
��
Can
tilev
ered
�ig
n �f
our�
chor
d�
��
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antil
ever
ed �
ign
�on
e�or t
wo�
chor
d�
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�ot
e� �
indi
cate
s stru
ctur
e is
susc
eptib
le to
this
type
of l
oadi
ng�
�or
te�
shed
ding
has
occ
urre
d in
am
onot
ube
brid
ge su
ppor
ts a
nd c
an o
ccur
in
cant
ileve
red
stru
ctur
es if
the
sign
or s
igna
l atta
chm
ent i
s not
atta
ched
�
��
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IL��
A�
��I�
�N
�I�
I��
���
�M
��
�A
�IN
���
IN��
���
I�I�
A�
I�N
Figu
re �
����
�as
epla
te C
onne
ctio
n �
etai
ls�
�et
ail �
�
�et
ail 1
�
�et
ail �
3
�ock
et �o
int,
Cat
��
Term
inat
ion
of st
iffen
er, C
at C
, �, o
r �
�as
e of
stiff
ener
, C
at C
Fatig
ue P
rone
Det
ails
10
Fatig
ue P
rone
Det
ails
Box
to F
lang
eSt
ress
es in
box
(E)
σ R =
4.5
ksi
Mai
n M
embe
rSt
ress
es in
pol
e (E
)
σ R =
4.5
ksi
Mas
t Arm
Soc
ket
Stre
sses
in a
rm (E
’)
σ R =
2.6
ksi
Box
to M
ain
Stre
sses
in b
ox (E
T)
σ R =
1.2
ksi
Box
to M
ain
Stre
sses
in p
ole
(K2)
σ R =
1.0
ksi
11
�ow
to �
edes
ign
�tru
ctur
es th
at
�o
�ot
�ee
t Fat
igue
�eq
uire
men
ts
•�n
crea
se se
ctio
n si
�es
–in
crea
sed
mat
eria
l cos
ts a
s muc
h as
���
�•
�mpr
ove
conn
ectio
n de
tails
–in
crea
sed
fabr
icat
ion
cost
s abo
ut �
��
��
L�
��
���
IN�
��IN
���
�A
��A
��
��
A�
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IL�
MU
��
�M�
��
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U�
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AN
���
�A
N��
�L
��
�mpr
ove
Con
nect
ion
�et
ails
•�n
crea
ses a
llow
able
fatig
ue st
ress
es a
t con
nect
ion
–m
inor
det
ail m
odifi
catio
ns c
an si
gnifi
cant
ly in
crea
se
fatig
ue re
sist
ance
•
upgr
ade
from
Cat
egor
y ��
to �
� �
�� in
crea
se in
allo
wab
le
stre
ss ra
nge
from
1�
��a
����
ksi
� to
31 �
�a ��
�� k
si�
•up
grad
e fr
om C
ateg
ory
�� to
� �
1��
� in
crea
se fr
om
1�
��a
����
ksi
� to
�� �
�a ��
ksi
�
�ai
n �o
ints
•�
ood
deta
iling
, avo
id n
otch
es, e
ssen
tial
•��
� a
ppro
ach
easy
to u
se, s
uffic
ient
•�
sual
ly d
esig
n so
mos
t stre
ss ra
nges
are
bel
ow
thre
shol
d or
fatig
ue li
mit
•�o
or d
etai
ls m
ostly
on
brid
ges b
uilt
by 1
���
•W
eb g
ap c
rack
ing,
com
mon
pro
blem
, fi�
ed in
1��
�•
Fatig
ue c
rack
s in
brid
ges e
asily
repa
ired
and
prev
ente
d w
ith re
trofit
s•
�res
ent i
nven
tory
of s
ign,
sign
al, a
nd li
ght s
uppo
rts
very
poo
rly d
esig
ned
for v
ibra
tion
and
fatig
ue•
�ew
spec
ifica
tion
has f
atig
ue li
mit
stat
e de
sign
load
s, fa
tigue
resi
stan
ce o
f var
ious
det
ails