8/11/2019 verification of Load deflection
1/15
V e r i fi c a t io n o f lo a d
d i s t r i b u t i o n a n d s t r e n g t h o f
s e g m e n t a l p o s t t e n s io n e d
c o n c r e t e b r i d g e s
J E B r e e n
Department of C ivil Engineering, U niversity of Texas at Austin, USA
S K a s h i m a
Honshu-Shikoku Bridge Authority , Japan
Th is paper ou t l i nes t he us e o f s ev era l c ompute r p rog rams o r i g i na l l y
dev e loped by P ro fes s or A . C . Sc orde l i s f o r p red i c t i on o f l oad d i s tr i bu -
t i on de f l ec t i ons and k ey i n t e rna l s t res s es i n s egm enta l l y c on-
s t ruc ted pos t - t ens ioned box g i rde r b r i dges . C ompar i s on w i t h ex per i -
men ta l res u l t s s ho w s genera l l y ex c e l l en t ag reem ent ev en fo r h i gh l y
non-s y mmet r i c a l l i v e l oad p lac ement . I n add i t i on p roc edures f o r
e s t im a t i n g t h e s tr e n g t h o f s u ch s t ru c t u r e s i n c lu d i n g m o m e n t
red i s t r i bu t i on a re i nc l uded .
Keywords pos t - t ens ion ed box g i rde r b r i dges l oad d i s t r i bu t i on
s t r e n g t h
Ove r t he l a s t 20 ye a r s , c ons ide r a b l e r e se a r c h on pos t -
t e ns ione d se gm e nta l l y c ons t r uc t e d box g i r de r b r idge s
ha s be e n c a r r i e d ou t a t T he Unive r s i t y o f T e xa s a t
Aus t i n . D ur ing t h i s pe riod e x t e ns ive use ha s be e n m a de
of se ve r a l box g i r de r a na lys is p r ogr a m s o r ig ina l l y de ve -
lope d a t t he Un ive r s i ty o f Ca l i f o r n i a a t B e r ke l e y by P r o-
fessor A. C. S corde l i s and severa l of his s tudents . W hi le
som e of t h i s m a te r i a l ha s be e n p r e v ious ly r e por t e d i n
l imi ted c i rcula t ion repor ts *'z and unpu bl ished disser ta -
t ions 3 4, the auth ors fe l t it w ould be e xt rem ely useful to
the de s ign p r of e ss ion t o p r e se n t a b r i e f sum m a r y i n a
m or e w ide ly a c c e ss ib l e j our na l . I n a dd i t ion , t he a u thor s
fee l it i s a f i tt ing t r ibute to Profe ssor Sco rde l i s wh o has
a lwa ys be e n m os t w i l l i ng t o sha r e h i s knowle dge a nd
ass is t other invest iga tors in any way poss ible .
T he m a jor phys i c a l i nve s t i ga t i on r e por t e d he r e t ook
place in the ear ly 1970s and has been a corners tone in
subse que n t use o f c a n t i le ve r se gm e nta l c ons t r uc t i on f o r
box girder br idges . The PrOtotype s t ruc ture which was
model led in the physica l tes t s was recent ly inspec ted by
the Cons t r uc t ion T e c hn ology L a bor a to r ie s a nd f ound to
be i n e xc e l l e n t sha pe 5 w i th no e v ide nc e o f j o in t ope n-
ings o r c or r os ion . T h i s a ga in i s a ve r y f a vour a b l e r e f l e c -
t i on on t he ove r a l l de s ign whic h be ne f i t t e d f r om the
c o m p r e h e n s i v e c o m p u t e r a n a l y s i s ( S I M P L A 2 ) d e v e l -
ope d by Br own 4 ( us ing a s a ba s i s P r of e s sor Sc or de l i s '
S I M P L A pr og r a m ) . T h i s p r ogr a m wa s use d to c he c k t he
or ig ina l de s ign be f or e c ons t r uc t i on . T he c ons t r uc t i on
0141 0296191/020113 15
1 9 91 B u t t e r w o r t h H e i n e m a n n L id
a nd the b e ha v iour o f t he b r idge g r e a t ly be ne f i t t ed f r om
the e xc e l l e n t m ode l s t udy by Ka sh im a 3 whic h ve r i f i e d
the a de qua c y o f t he de s ign unde r c ons t r uc t i on l oa ds ,
se r v i c e l oa ds , m o de r a t e ove r loa ds , a nd u l t im a te . T h i s
e xpe r im e nta l s t udy wa s he a v i ly de pe nd e n t on P r of e s sor
Sc or de l i s ' p r ogr a m M UPDI f o r t he i n t e r p r e t a t i on o f
be ha v iour .
I n t he pa s t two de c a de s , subs t a n ti a l use ha s be e n m a de
of p r e c a s t a nd c a s t - i n - p l a c e box g i r de r b r idge s e r e c t e d
us ing c a n t i l e ve r ing t e c hn ique s . I n t h i s c ons t r uc t i on
m e thod , p r e c a s t s e gm e nt s Figur e ] a) ) a r e c a s t a nd
t r a nspor t e d t o t he b r idge s i t e . Af t e r a pp l i ca t ion o f e poxy
jointin g ma terial the precast segments are erected as
shown in
F i g u r e l b ) ,
as balanced cantilevers from the
pier segment wh ich is rigidly connected o the pier either
temp orarily or perma nently. As ea ch pair o f segments is
positioned at the ends o f the balanced cantilever nega-
tive mo me nt tendon s are inserted and tensioned. These
tendons must provide moment capacity for the ful l
cant ilever m oment. E rect ion continues unt il the last
cantilevered sections are p laced at the ce ntre of the span
a nd a t t he e nd suppor t s , a s shown in Figure 1 c ) . T h e
pos i t ive m om e nt t endons i n t he e nd spa n a r e p r e s t r e s se d
a nd the e nd se gm e nt s a r e se a t e d on t he i r support s p r io r
to o r du r ing s t r e s s ing o f p r e s tr e s s ing c a b l e s i n t he m a in
spa n pos i t i ve m om e nt r e g ion . A t m idspa n , t he ga p
be twe e n the two c a n t i l e ve r a rm s i s c lose d w i th c a s t -i n -
place concre te . Pres t ress ing cables to res is t l ive load in
Eng. Struct . 199 1 Vol . 13 Apri l 113
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S e g m e n t a l p o s t t e n s i o n e d c o n c r e t e b r i d g e s : J . E . B r e e n a n d S . K a s h i m a
-_ - - . .+ -- ++ ~, ~ . . . . . . . . . ~:~-++=+.::Tr+ .u
a oint
P r e s t r e s s i n g c a b le
t o b a la n c e t h e w e i g h t
o f t h e s e g m e n t a n d
r e s i s t n e g a t i v e m o m e n t
I I
1 I \ e g o a r s
I I P i e r s e g m e n t
/ v
b M a i n p i e r - - I I B o l t s o r s t r e s s i n c c a b l e s
I I
m e r i t
C l o ad i n p o s i t i v e m o m e n t r e g i o n
F i g u r e
T y p i c a l b a l a n c e d c a n t i l e v e r c o n s t r u c t i o n . ( a) , t y p i c a l c r o s s s e c t i o n o f b o x g i r d e r; ( b ) , c a n t i le v e r e r e c t i o n o f p r e c e s t s e g m e n t s ;
( c) , c o m p l e t i o n o f c a n t i le v e r c o n s t r u c t i o n
t he c e n t r e span p os i ti ve m o m e n t r e g ion a r c i nse r t e d a nd
st ressed. Reac t ions in the end spans a re adjus ted as
r e qu i r e d .
Be c a use t h is t ype o f b r idge ha d ne ve r be e n bu i l t i n the
Uni t e d S t a te s a c oope r a t i ve r e se a r c h p r o j e c t w i th t he
T e x a s H i g h w a y D e p a r t m e n t a n d t h e F e d e r a l H i g h w a y
Adm in i s t r a t i on t o i nve s t i ga t e t he va r ious p r ob l e m s
a ssoc i a t e d w i th de s ign a nd c ons t r uc t i on p r oc e dur e s f o r
long spa n p r e c a s t p r e s t r e s se d c onc r e t e box g i r de r
br idge s o f s e gm e nta l c ons t r uc t i on we r e unde r t a ke n by
T h e U n i v e r s it y o f T e x a s a t A u s ti n C e n t e r f o r H i g h w a y
Re search in 1968.
T he T e xa s H ighwa y De pa r tm e nt u t i l i z e d a p r e l im in-
a r y de s ign de ve lope d a s pa r t o f t he p r o j e c t by t he
Un ivers i t y -o f Texas-at Aus tin- researchers in deve lop ing
p lans for a long spa n br idge o n the John F . Kennedy
Memor ia l Causeway , Corpus Chr i s t i , T exas . T he re -
qu i rem ent to main ta in nav igat iona l c learance dur in g
cons truc tion as we l l as the h igh ly cor ros ive env i ronm ent
on the Texas coa s t led to the cho ice o f a precast
pres t ressed concrete box g i rder br idge bu i l t in
cant i lever .
In orde r to s tudy the app l icab i l i t y and accuracy o f the
design cr i ter ia , analytical m ethods, construct ion tech-
n iques , and shear per formance of the epoxy res in jo in ts ,
an accurate one-s ixth scale mod el o f the three-span con-
t inuous br idge was bu i l t and tes ted a t the P . M.
Ferguson St ruc tura l Eng ineer ing Re search Lab oratory
o f T h e Un ive rs i t y o f T exas a t Aus t i n ' s Ba lcones
Resea rch Ce nter u '3.
This model of the three-span precast prest ressed con-
c re te segmenta l tw in box g i rder br idge was a or .c -s ix th
sca le d i r ec t ' mode l , and was bu i l t in f u l l con f o~ an ce
wi th pro to type cons t ruc t ion procedures . I t c lose ly
s im ula t e d t he be ha v iour o f t he p r o to type bo th i n t he
e las t ic and ine las t ic range .
T he ob j e c t i ve s o f t he m ode l s t udy i nc lude d t he
f o l l owing
De terminat ion o f s t ra in d is t r ibut ion due to pres tress-
ing and o f def lec t ions dur ing cant i lever cons t ruc t ion
and dur ing c losure operat ions
Documentat ion o f br idge I tmhav iour unde r service
leve l load ing for the var ious des ign load ing condi -
t ions
Com par ison o f ana ly t ica l resu lt s f rom beam theo ry
and fo lded p la te theory w i th the cons t ruc t ion and ser -
v ice level load ing exper imental resul ts
De t e rm ina t i on o f b r i dge bchav iou r under u lt ima t e
p r o o f l o a di n g ( 1 . 3 5 D L + 2 . 2 5 ( L L + I t , ) ) f o r th e
var ious des ign load ing condi t ions
Determinat ion o f f ina l fa i lu re mechanisms wi th
spec ia l a t tent ion to any adverse e f fec t o f the epoxy
res in on the shear or f lexura l capac it y o f thebr~dge.
De terminat ion o f the punc h ing shear capac it y o f the
top s lab and eva luation o f any adverse e f fec t o f the
epoxy res in o n suc h capac it y
Asses sme nt o f the app l icab i l i t y o f the u l t imate
s t rength des ign c r i te r ia proposed for th is t ype o f
br idge
D e t e r m i n a ti o n o f a n y i m p r o v e m e n t s o f d e s i g n d et a il s
whic h m igh t m in im iz e f i e ld c ons t r uc t i on p r ob l e m s
pr io r t o t he p r o to type b r idge c ons t r uc t i on
P r ov i s ion o f a m e a n ing f u l de m o ns t r a t i on t o p r ospe c -
t i ve c on t r a c to r s t o a s s i st t h e m in t he v i sua l i z at i on o f
the c ons t r uc t ion t e c hn ique so a s t o r e d uc e unc e r t a in ty
a n d e n c o u r a g e b i d d in g f o r t h e p r o t o ty p e c o n s t r u c t io n
1 1 4 E n g . S t r u c t . 1 9 9 1 , V o l . 1 3 , A p r i l
8/11/2019 verification of Load deflection
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Seg me ntal post tensione d con crete br idges: J. E. Bree n and S. Kashima
o d e l
T he 200 f t m a in spa n a nd ba l a nc ing 100 f t s i de spa ns o f
the p r o to type b r idge we r e m ode l l e d i n one - s ix th sc a l e .
De ta i ls a r e sho wn in Figure 2 . A m ic r o- c on c r e t e whic h
c lose ly e m ula t e d t he p r ope r t i e s o f t he p r o to type c onc r e t e
wa s use d . Conc r e t e c om pr e ss ive s t r e ng th a ve r a ge d
7100 ps i . T e ndon s a nd r e in f o r c ing ba r s we r e sc a l e d to
m a tc h t he p r o to type de s ign s . S t r a nd u l t im a te s t r e ng th
wa s a ppr ox im a te ly 260 ks i w hi l e r e in f o r c ing y i e ld
va r i e d f r om 71 ks i t o 79 ks i . E poxy r e s in j o in t ing
mater ia l had a f lexura l tens ion s t reng th of 733 ps i as
m e a su r e d w i th c on c r e t e spe c im e ns j o in t e d w i th the
e poxy . A l l s e gm e nt s ha d t he sa m e t r a nsve r se a nd
long i tud ina l m id s t e e l r e in f o r c e m e nt pa tt e r n a s d id t he
pr o to type s t r uc tu r e . A typ i c a l c a ge i s shown in Figure 3
Since i t was impossible to exac t ly model the mul t iple
s t rand commerc ia l tendons and anchor~Iges used in the
pr o to type , p r e s t r e s s ing c a b l e s w e r e m od e l l e d by se l e c t-
i ng f o r e a c h t e ndon a n e qu iva l e n t s i ng l e c a b l e whic h
c ou ld p r od uc e t he c or r e c t l y sc a l e d te ndon f o r c e . D ur ing
pre l im inary tes ts 6 , a tend ency for spl i t ting a long the
t e ndon wa s ob se r ve d , w hic h wa s r e s tr i c te d by use o f a
Figure 3 C a g e f o r a s e g m e n t
spi ra l in the model . Figures 4 a nd 5 show the p r o f i l e o f
the t e ndon duc t s i n t he m a in a nd s ide spa ns .
T o sa t i s f y s im i l i t ude r e qu i r e m e nt s a nd t o ob t a in t he
sa m e de a d l oa d s t re s s c ond i t i ons a s t he p r o to type b r idge ,
i t would be ne c e ssa r y t ha t t he de ns i t y o f a one - s ix th sc a l e
mod el mater ia l be s ix t imes tha t of the prototype br idge .
A B C D
S p a n A B B C C D
P r o t o t y p e 100' 200' 100 ~
M ode l 16 . 67 ' 33 . 33 ' 16 . 67 '
T 6
4
B I
B2
- I T
T 2
B 3
g
B
B5 t
v j C a s t i n p l a c e s t r i p
- - - . 2 v 2 / / /
T 3 ' : a t m a x. s e c t i o n ~
F i l l e t de t a i l
1
B B I B 2 B 3 B 5 B 7 T T 2 T 3 T 3 ' T q T 6 D H I V l H2 V 2 H3 V 3 Hq v 4
P r o t o t y p e 671 " 71 . 5 " 14 " 156" 80 " 24 " 8 " 7 " 6 " 10 " 12 " 6 " 96 " 8 " 6 " 8 " 6 " 8 " 6 " 4 " 4 "
M o d e l 1 1 2 " 1 1 . 9 " 2 . 3 " 2 6 " 1 3 . 3 " 4 " 1 . 3 3 " 1 . 1 7 " I " 1 . 6 7 " 2 " I " 1 6 " 1 . 3 3 " I " 1 . 3 3 " I " 1 . 3 3 " I " 0 . 6 7 " 0 . 6 7 "
F i gu re
B r i dge m ode l d i m ens i ons . ( a ) , l ong i t ud i na l d i m ens i ons o f b r i dge ; ( b ) , c r os s s ec t i on o f b r i dge
Eng. Struct . 199 1 Vol . 13 Apr i l 115
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S e g m e n t a l p o s t t e n s i o n e d c o n c r e t e b r id g e s : J . E. B r e e n a n d S . K a s h i m a
A i I
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1 I S e c ti o n A ~ A r o ~ A . S e c t io n B - B
I _ 1 A s l o o ~ l
L ~ I L A ~ \ I
A2 Bot tom s ldb
F i g u r e T e n d o n d u c t p r o f i le s i n m a i n s p a n
S 1 0 9
G r a d u a l t r a n s i t i o n o f c u r v e
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Main ier
F i g u r e 5 T e n d o n d u c t p r o f i l e s i n s i d e s p a n
This i s impract ica l to implement . Compensat ing dead
loads have been added in various wa ys for mod el s truc-
tures . In th is case , f ive t im es the weight o f the mod el
segm ent w as added to the segments us ing concrete
blocks . A l l dead load blocks were dis tr ibuted to repre-
sent the weigh t o f each port ion and to g ive reasonable
transverse as well as longitudinal d istribution. Loa d
cel l s , pressure gauges , s tra in gauges , surveyor s l eve l ,
and dia l gauges comprised the ins trumentat ion used for
the model study I .
C o n s t r u c t i o n m e a s u r e m e n t s
T h e fo l l o w i n g s t ep s w ere fo l l o w ed i n th e mo d e l b r i d g e
erec t i o n a n d c l o s u re
1 1 6 E n g . S t r u c t . 1 9 9 1 , V o l . 1 3 , A p r il
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Segmental post-tensioned conc rete bridges: J. E. Been and S. Kashima
1)
2)
3)
4)
5)
6)
7)
8)
9)
Pier segments were temporarily fixed to the piers
AII but the outer and the closure precast segments
were sequentially erected using the cantilever con-
struction method for epoxy joints
The bolts at the pier were temporarily slackened and
the vertical and horizontal alignment was adjusted.
The bolts were then re-torqued
The outer pier segments (SlO) were erected and the
positive moment tendons in the side spans were
prestressed
The half segments (MIO) in the main span were
erected. The longitudinal reinforcement extending
across the midspan gap from each of the half seg-
ments was jointed and the concrete closure seg-
ments were cast
The positive tendons in the main span were inserted
and tensioned after seven days of curing of the
closure segment. The bolts temporarily fixing the
segments to the main piers were released during the
positive tendon stressing operation
The bridge was lowered to final position on
neoprene pads on the piers
The correct reactions were jacked into the outer
piers
All tends were grouted
Friction test results indicated that tendon forces after
stressing were 94 to 97 of those predicted by
SIMPLA2 which considered friction losses assuming a
friction coefficient (w) of 0.23radian and a wobble coef-
ficient (A) of 0.000017 in-.
It was difficult to accurately measure the vertical
deflection during construction because the deflection
was so small in comparison to the span (L/1800).
Deflections were measured only to see the general trend
of cantilever section behaviour. Theoretical deflec-
tions were calculated using the computer program
SIMPLA2 which provides an analysis at each stage of
erection using the finite segment technique. The theore-
tical and experimental deflection profiles are shown in
Figures 6u
and
6b,
respectively, for all stages of erec-
tion. Relative deflections for one typical case are com-
pared in
Figure 7.
There are many factors which affect
the vertical deflections such as pier rotation, joint
thickness and casting soffit errors. Therefore, it is very
hard to determine the cause of errors in deflection. This
is especially difticult since the component of deflection
due to dead load is almost completely balanced by the
deflection due to the prestressing.
Figure 6
indicates that
the overall trend of the theoretical and experimental
results agreed fairly well except that the measured
results show a pronounced upward skew.
Experimental deflection measurements shown in
Figure 6 b)
are averages at each corresponding point to
eliminate the effect of load unbalance or bolt bending.
This figure readily indicates the jointing errors in the
initial stages of cantilever erection when temporary
tensile stresses at the bottom of initial joints were not
controlled and joints widened at the base, causing
upward deflections. During the positive tendon opera-
tions in the main span, Figure 8 indicates that the
experimental and theoretical deflections agreed well. An
additional theoretical procedure was used to calculate
these deflections using an elastic analysis program
BMCOLSO. Superimposing results from
Figures 6.
~~.S~ M~.S~~M~,S~M~.S~~MS,SS M~,S~,S~M~,S~M~,S~
0.10
m
t
a
I
o.oov
1
1
1 I I I
I
1
I
b
Figure 6 Cantilever deflections. a). deflection predicted by
SIMPLAZ for cantilever erection; lb), typical measured deflection
during cantilever erection
f igure 7 Deflection relative to the centre of 6th segment.
Assumes that the centre of the 6th segment is zero when 6th
segments are erected
-C- Experiment
--- BMCOL 50
-..- SIMPLA 2
A6 Raise 261100at
both end supports
Figure 6 Deflection at the centre in main span during positive
tendon operations
and 8 indicates that the relative displacement at the
centre in the main span should be almost zero upon
prestressing of all positive tendons (Al-A6). The centre
of the main span was subsequently lowered 0.08 in.
(0.48 in. in the prototype) by the jacking at the outer
supports.
Eng. Struct. 1991, Vol. 13, April 117
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Se gm enta l pos t tens ion ed c onc re te b r i dges : J . E . B reen and S . Kash ima
B ~ q F ~ A
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1 1 8 E n g . S t r u c t. 1 9 9 1 V o l . 1 3 A p r i l
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Seg me ntal post ten sioned cOncrete bridges: J. E. Breen and S. K ashima
Figure 9 show s tha t the exper im enta l s t ra ins in the top
s l ab o f t he M 1 and S 1 se gm e nt s va r i e d w ide ly a c r oss t he
c r oss se c t i on dur ing e r e c t i on o f s e ve r a l s e gm e nt s . T he
m e a sur e d r e su l t s a r e i n good a gr e e m e nt w i th t he
the or e ti c a l c a lc u l a ti ons f o r s t a ge 1 a nd a f t e r e r e c t i on o f
the 5 th se gm e nt . E xpe r im e nta l s t r a ins we r e un i f o r m
a c r oss t he c r oss se c t i on a nd c lose t o t he be a m a na lys i s
va lue s f o r t he e r e c t i on o f t he 6 th a nd subse que n t
segments . Al though the longi tudina l s t ra ins in the top
s l ab o f t he M I a nd S 1 se gm e nt s va r i e d a c r oss t he c r oss
sec t ions in ear ly e rec t ion s tages , i t is not a se r ious pro -
blem. Al l s t ra ins a re in compress ion across the c ross
se c t i on a nd a r e we l l be low the s t r a ins whic h would
a c c om pa ny the m a xim um a l lowa ble c om pr e ss ive s tr e s s.
T he non- un i f o r m i ty o f s t ra in i n t he t op s l a b ov e r t he we b
wa s p r oba b ly g r e a t l y i n f lue nc e d by t he l oc a l c on-
c e n t r a t e d t e ndon f o r c e s . As a dd i t i ona l t e ndons we r e
s t r e s se d dur ing t he e r e c t i on o f t he se c ond to f i f t h
se gm e n t s , t he se loca l e f f e c t s d i e d ou t . M e a su r e m e nt s
showe d m uc h be t t e r a g r e e m e nt dur ing c losur e ope r a -
t ions.
In genera l , both theore t ica l solut ions and the exper i -
m e nta l r e su l t s we r e i n r e a sona b le a gr e e m e nt whe n the
c ha nge o f s t r a in i n e a c h s t a ge wa s r e a sona b ly l a r ge ,
except for the local strains in the top slab during init ial
s t a ge s whe n the l a r ge l oca l c om pr e ss ive f o r c e s f r om the
tends seemed to a f fec t the s t ra in dis t r ibut ions .
Pr ior to posi t ive tendon pres t ress ing opera t ions in the
m a in spa n , t he end suppor t s we r e a d jus t e d t o j us t b e a r
on t he unde r s ide o f e ac h w e b a t t he e dge o f t he e nd p i e r
se gm e nt s . Re a c t ions at t he e nd suppor t s w e r e m e a sur e d
by ,sensi t ive load ce l l s dur ing each s tage . Compar ison
betw een theore t ica l and exp er imen ta l r esul t s i s show n in
Table .
A s im pl if i e d p r oc e dur e wa s use d t o c a l c u l a te t he e nd
reac t ion. Pres t ress ing forces were replaced by the ver -
t i c a l f o r c e s whic h would p r oduc e t he sa m e m om e nt
d i a gr a m a s t ha t p r oduc e d by p r e s t r e s s ing . T he se r e a c -
t ions w e r e c a l c u la t e d us ing t he BM COL 50 pr ogr a m 7.
E xpe r im e nta l r e a c t i ons a gr e e d ve r y we l l w i th t he
theore t ica l va lues for la rge va lues such as A I and A2
te ndons . A s t he r e a c t ion i nc r e m e n t be c a m e sm a l l e r , t he
e xpe r im e nta l r e a d ings be c a m e m uc h sm a l l e r t ha n t he
theore t ica l va lues . However , the tota l exper imenta l
reac t ion ( .69 8 kip) agreed very wel l wi th the tota l
theore t ica l va lue (1 .610 kip) .
e r v i c e l o a d t e s t s
The completed three-span four- lane box girder model
wa s loa d t e s t e d f o r t he gove r n ing AASHT O de s ign
loa d ing c ond i t ions show n in Figure I0. T r uc k loa d ings
u t il i ze d 1 /6 -sc a le m ode l s o f t he AAS HT O H S20- S16
trucks w i th tyre pressures assum ed a t 80 ps i in s iz ing
loa d ing pa ds . Uni f o r m l a ne l oa ds we r e s im ula t e d by a
ser ies of con cent ra te d loads a t 4 f t in te rva ls appl ied
a bove e a c h we b in t he m a in t e s t s e r i e s hu t va r i e d i n
t ransverse dis t r ibut ion ser ies . Comple te de ta i l s of
loa d ing a nd i ns t rum e nta t i on a r e p r e se n t e d e l se whe r e i j .
The resul t s of def lec t ion, s t ra in , and reac t ion
m e a sur e m e nt s we r e c om pa r e d w i th so lu t i ons o f
B M C O L 5 0 7 a n d M U P D I s p r o g ra m s .
BM COL 50 i s a be a m - type a na lys i s p r ogr a m whic h
so lve s t he l i ne a rly e la s t ic be a m or c o lu m n by a d i sc r e t e
e l e m e nt a na lys i s p r oc e dur e . T h i s p r ogr a m t a ke s i n to
a c c oun t va r i a b l e l oa ds a nd non l ine a r suppor t s . L oa d-
de f l e c t i on r e l a t i ons f o r e a c h ne opr e ne pa d we r e
m e a sur e d a nd t he se va lue s we r e i npu t t o BM COL 50 a s
the spr ing a t the suppor ts .
M UPDI i s a ve r sa t i l e ge ne r a l i z e d e l a s t i c p r ogr a m
whic h c a n a na lyse f o lde d p l a t e o r box s t r uc tu r e s w i th
inte r ior r igid diaphragms or suppor ts us ing folded pla te
the or ie s w hic h c ons ide r c r oss se c t ion w a r p ing .
A l though BM COL 50 c a n t r e a t va r i a b l e se c t i ons , t he
s e c t i o n f o r M U P D I h a s t o b e u n i f o r m . T h i s M U P D I
l imi ta t ion was not se r ious in this case because of the
smal l var ia t ions in the c ross sec t ions ( thickened bot tom
s la bs on ly a t m a in p i e r a nd a d j a c e n t s e gm e nt s ) .
BM COL 50 wa s use d t o a na lyse un i f o r m t r a nsve r se
ioa d ings ( f our l a ne l oa d ings ) whi l e M UPDI wa s use d
pr im a r i l y f o r non- un i f o r m t r a nsve r se l oa d ing a s i n t he
two- l a ne l oa d ing o r i n t he tr a nsve r se m om e nt s t udy . Fo r
a c h e c k a n d d i r e c t c o m p a r i s o n o f M U P D I a n d
BM CO L 50, bo th we r e r un f o r one un i f o r m loa d ing c a se .
A l l e x t e r na l a nd t h i c kne ss d im e ns ions f o r e a c h m e m be r
of t yp i c a l box se c t i ons we r e m e a sur e d f o r s e ve r a l
se gm e n t s a nd a ve r a ge d se c t ion p r ope r t i e s we r e use d i n
the pro gra m s *'3.
Only sa m ple t yp i c a l r e su l t s a r e p r ov ide d he r e . E x-
c e l l e n t a g r e e m e nt be twe e n c a l c u l a t e d a nd m e a sur e d
de f l e c t ions a nd r e a c ti ons we r e ob t a ine d f o r sym m e t r i c a l
lane loading as shown in Figure 11. The ful l usefulness
a n d a c c u r a c y o f M U P D I w a s s h o w n w i t h u n s y m m e t r i c a l
Ta b le I
Reaction at outer support during prestressing in main
span
Tendon Experimen t (kip) BMCOL 50 (kip)
A1 0.24 5 0.251
A2 0 .200 0 .213
A3 0 .115 0 .169
A4 0 .074 0 .131
A5 0 .012 0 .091
A6 0 .012 0 .055
a i s e
0.26 in at 1.04 0.70 0
o u t e r
supports
Total 1.698 1.610
Case Crit ical condition Loading condit ion
1 Maximum posi tiv e Lane loading .LP
moment
at the centre . ; . . . . . . r , - Jw
of the main span /x A A
SE SMI*= 0.15q NM NE
2 Maximum positiv e Tru ck loading
moment in tt t
the side span ~, A ~ A
SE SM NM NE
I = 0.222
3 Maximum negative Lane loading w /p /p
moment
at ...... J .... .... .... .... .
the main pie r ~, A A A
SE SM NM NE
1=0.182
q Maximum shear Lane loading IP ..
adjustment to
the main pier ,O, A ,x A
SE SM NM NE
I = 0.182
*1 = impact facto r
F i g u r e I Critical loading conditions in longitudinal direction
Eng. St ruct . 199 1 V ol . 13 Apr i l 11 9
8/11/2019 verification of Load deflection
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S e g m e n t a l p o s t t e n s i o n e d c o n c r e t e b r i d g e s : J. E . B r e e n a n d S . K a s h i m a
I w l
t t l
I
i w
F i g u r e
S E C ) O T o t a l
E x p e r i m e n t K ) - 0 . 5 8 3 - 0 . 6 7 0 - 1 . 2 5 3
B M C O L 5 0 - - - 1 . 2 4 0
E x p e r i m e n t / B M C O L 5 0 ~ ,} 1 01
N E T o ta l ]
x p e r i m e n t K ) - 0 , 6 5 8 - 0 . 67 2 - I . 3 3 0
B M C O L 5 0 - 1 . 2 4 0
E x p e r i m e n t I B M C O L 5 0 ~ ,) 1 07 I
R e a c t i o n s a t o u t e r s u p p o r t s f o r l a n e Io a d i n g s f o u r l an e s ) i n m a i n s p a n
l o a d i n g p a t t e r n s f o r w h i c h t h e b o x g i r d e r a n a l y s i s w a s
essen t i a l .
Figure 12
shows tha t t he exper imen ta l resu l t s
a n d MU PD I a n a l y s i s a g r e e d e x t r e me l y w e l l .
U l t i m a t e d e s i g n l o a d t e s t s
At the t ime o f th i s tes t , u l t imate load c r i te r i a we re no t
i n c l u d e d i n t h e A A SH T O s p e c i f i c a t i o n s . T h e Bu r e a u o f
Pub l i c R oads c r i t e r i a 9 we re used . Th i s requ i red 1 .35
d e a d l o a d s o e x t r a c o mp e n s a t i n g b l o c k s w e r e a d d e d t o
the model to b r ing i t t o tha t l eve l . L ive load ing was
i n c r e a se d t o t h e s p e c i f i e d 2 . 2 5 ( L i v e L o a d + I mp a c t
Load) l eve l i n s t ages . Crack ing was no ted a t [ 1 .35DL +
1 . 7 5 ( L L + I L ) ] ( s e e
Figure 13) .
Mi d s p a n d e f l e c t i o n s
b e c a m e m u c h l a r g e r th a n t h e e l a s t ic a n a l y s i s p r e d i c t io n s
o f p r o g r a m BM CO L 5 0 . A t d e s i g n ul ti ma t e , t h e s e g -
me n t s a t t h e o u t e r s u p p o r t s s u d d e n l y r a i s e d u p ( s e e
Figure 14) .
Cr a c k s e x t e n d e d t o t h e w e b mi d - h e i g h t a n d
w e r e i n o r n e a r t h e mi d s p a n c l o s u r e s e g me n t . C r a c k i n g
mo me n t s c a l c u l a t e d u s i n g t h e A CI b u i l d i n g c o d e i n -
d i c a t e d e x p e c t e d c r a c k i n g a t 1 . 3 5 D L + 1 . 9 0 ( L L + I L ) .
T h i s i s a v e r y g o o d p r e d i c t io n o f th e c r a c k i n g w h i c h w a s
a t a L L + I L f a c t o r o f 1 . 75 f o r o n e w e b a n d 1 . 8 8 f o r th e
o t h e r w e b . T h e c r a c k i n g mo m e n t i s v e r y s en s i ti v e t o t h e
ad jus t ing fo rce a t t he end suppor t s .
f - t h e r e a c t io n f o r c e p r o v i d e d a t t h e e n d s u p p o r t s i s
l a r g e , m i d s p a n c r a c k s w i l l a p p e a r a t l o w e r i n c r e me n t s o f
(LL + IL) . I f t he ad jus t ing fo rce p rov ided a t t he end i s
smal l , t he end segment s wi l l ra i se up f rom the neoprene
p a d s u n d e r v e r y s ma l l i n c r e me n t s o f ( L L + I L ) . T h e r e -
f o r e , w h e r e p o s s i b l e t h e e n d r e a c t i o n s f o r t h e b r i d g e
s h o u l d b e s e l e c t e d a t a n o p t i mu m p o i n t w h i c h b a l a n c e s
these two fac to rs .
S i mi l a r te s t s w e r e r u n f o r ma x i mu m n e g a t i v e mo me n t
a t t he main p ie r which opened up add i t iona l c racks near
the p ie r a long nega t ive moment t endon t ra j ec to r i es ,
p a r t ly b e c a u s e o f t h e l o w c o v e r s o v e r t h e l a r g e t e n d o n s .
Ma x i mu m s h e a r l o a d i n g a d j a c e n t t o t h e ma i n p i e r w a s
t h e n a p p l i e d . N o s l i p b e t w e e n s e g me n t s w a s f o u n d a n d
no add i t iona l f l exura l o r d i agonal t ens ion c racks were
o b s e r v e d . I n ma x i mu m p o s i t i v e mo me n t t e s t i n g i n t h e
s i d e s p a n , g e n e r a l l y l i n e a r b e h a v i o u r w a s n o t e d a n d n o
c r a c k in g w a s o b s e rv e d . M U P D I r e s u lt s s h o w e d
e x c e l l e n t a g r e e me n t w i t h me a s u r e d v a l u e s ( s e e
Figure
15 .
ai lure load te s t s
Si n c e t h e b r id g e mo d e l r e a d i ly c a r r i e d t h e B PR d e s i g n
u l t imate load fo r a l l c r i t i ca l f l exura l and shear load ing
cond i t ions , s evera l fa i lu re load t es t s were p l anned to
de te rmine u l t imate capac i ty . In the f i r s t t es t t o fa i lu re ,
f a c t o r e d A A SH T O t r u c k l o a d s w e r e a p p l i e d i n o n e s i d e
s p a n t o p r o d u c e a b e n d i n g f a i l u r e . T h i s l o a d i n g w a s
se lec ted even though the ca l cu la t ed fa i lu re l i ve load
fac to r fo r th i s case was l a rger than tha t wh ich was
c a l c u la t e d f o r ma x i mu m mo me n t l o ad i n g i n t h e ma i n
s p a n . S i n c e b o t h o f t h e s e t y p e f a i l u r e s w o u l d b e f l e x u r a l,
i t was fe l t t ha t a fa i lu re t es t i n the s ide span co u ld ver i fy
f l exura l u l t imate ca l cu la t ions . Such a t es t wou ld l eave
t h e s t r u c t u r e w i t h t w o r e l a t i v e l y u n d a ma g e d s p a n s s o
tha t a shear t es t t o fa i lu re cou ld a l so be run by app ly ing
lane load ings to the main and oppos i t e s ide span . Th i s
l o a d i n g w o u l d p r o d u c e ma x i mu m s h e a r a t t h e ma i n p i e r
a n d b e a n e f f e c t i v e t e st o f e p o x y j o i n t p e r f o r ma n c e .
Truck load ing on the s ide span was s topped af t e r d i s t inc t
y i e l d i n g h a d o c c u r r e d i n t h e s i d e s p a n a n d a t s u p p o r t
SM , a s j u d g e d b y t h e d e f le c t i o n ( s e e
Figure 16)
and
s tr a in r e a d i n g s , b u t b e f o r e c o m p l e t e c o l l a p s e o f t h e s id e
span . Al thoug h load s we re app l i ed in th i s tes t a f t e r fo r -
mat ion o f a p l as t i c h inge , t he e f fe c t o f th i s load ing on the
u l t imate ben d ing and shea r s t reng th o f the o ther spans
a n d d u r i n g t h e s e c o n d ( o r ma x i mu m s h e a r ) f a i l u r e
l o a d in g t e s t w a s j u d g e d n e g l i g ib l e . N o l iv e l o a d w o u l d
b e a p p l i e d o n t h e d a ma g e d s p a n a n d t h e e n d s e g me n t a t
SE w o u l d d e f l e c t u p w a r d .
T h e s c a l e d A A S H T O H S 2 0 - S 1 6 l o a d s w e r e ap p l ie d t o
a l l f o u r l a n e s o f t h e s i d e s p a n t o p r o d u c e ma x i mu m
mo me n t . T h e a l l o w a b l e l o a d r e d u c t i o n f o r a f o u r l a n e
br idge wa s ignored . The l ive loads app li ed" we re in
add i t ion to the a l ready app l i ed 1 .35 dead load . L ive and
impact loads were increased to the 5 .25 (LL + IL) l eve l .
A t t h e 2 . 8 8 ( L L + I L ) i n c r e me n t , a p p r e c i a b l e d e v i a -
t ions f rom the genera l ly l i near load vs def l ec t ion
d i a g r a m
Figure 16)
w e r e n o t e d . I t a p p e a r s a s t h o u g h
c r a c k i n g m a y h a v e s t a r t e d t o d e v e l o p in t h e i n n e r w e b s ,
a l t h o u g h n o c r a c k i n g w a s v i s i b l e i n t h e o u t e r w e b s . A t
the 3 .25 (LL + IL) increm ent , a f l exura l c rack on the
o u t e r w e b a r o u n d t h e c e n t r e o f t he S S 7 R s e g m e n t w a s
v i s ib l e a lmos t up to mid-he igh t and the s t ra in gauges in
the bo t tom s l ab showed a l a rge increase in s t ra in .
1 2 0 E n g . S t r u c t . 1 9 9 1 V o l . 1 3 A p r i l
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8/11/2019 verification of Load deflection
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S e g m e n t a l p o s t t e n s i o n e d c o n c r e t e b r i d g e s : J. E . B r e e n a n d S . K a s h i m a
Figure 3
~ 2 . 0 0
j . - ' ~
~
-~ 1.50 BMCOL 50 i
1.00
E
5
. ~ S E S I S M I O
1 . 3 5 D L 0 . 0 0 . / I I I I
0 . 0 . I 0 . 2 0 . 3 0 , 4
D e f l e c t i o n ( i n ]
D e f l e c t i o n s a t S M I O f o r l a n e l o a d i n g s ( f o u r l a n e s ) in m a i n s p a n ( d e s i g n u l t i m a t e
At the 4 .25 LL + IL) increment , a w id e crack mo re
than I /8 in v i sua l ly ) developed suddenly a t the SS6-7
jo int in the outer web o f the west s ide . At the 4 .38
LL + IL) increment a major crack form ed near the
S S 6 -7 jo in t i n th e o u ter w eb o f th e ea s t s id e . A f ter th e~
cra ck s d ev e l o p ed , d e fo rma t i o n s w ere co n cen tra ted i n
the v ic in i ty o f these large cracks . Stra ins w ere seen to
increase rapidly at the 4.8 LL + IL) increme nt and to
7 0 . 1 0 -
0 . 0 0 -
0 .10 -
0 . 2 0
0.30
0 . 4 0 -
2 . 0 0 ( L L + I L )
L o a d i n g c o n d i t io r ~ ( + 1 . 3 5 D L i
~ l l l l l l ~ l f i l l I I
/(~ SM NM ~'
1 . 0 0 ( L L + I L )
1 , 5 0 ( L L + I L )
- ' 0 - E x p e r i m e n t
2 . 1 2 5 ( L L + I L ]
r
. 2 5 ( L L + I L )
1 2 2 . 5
1 2 2 . 7
Figure 4
( L L + I L I SE SS4 SM SM5 SM I0 N M5
1 . 0 0 [ - 0 . 0 0 4 1 - 0 . 0 2 2 9 + 0 . 0 0 1 3 + 0 . 0 8 6 + 0 . 1 3 7 + 0 . 0 8 3
1 . 5 0 [ - 0 . 0 0 7 9 - 0 , 0 3 6 7 + 0 . 0 0 25 + 0 . 1 3 6 + 0 . 2 2 4 + 0 . 1 3 4
2 . 0 0 I - 0 . 0 1 5 5 - 0 , 0 5 5 3 + 0 . 0 0 q 8 + 0 . 2 0 3 + 0 . 3 4 8 + 0 . 2 0 2
2 . 1 2 5 I - 0 . 0 2 2 9 - 0 . 0 6 1 7 + 0 . 0 0 5 2 + 0 . 2 2 1 + 0 . 3 8 2 + 0 . 2 2 1
2 . 2 5 I - 0 . 1 0 1 0 - 0 . 0 9 4 8 + 0 . 0 0 5 9 + 0 . 2 7 1 + 0 . 4 6 9 + 0 . 2 7 2
D e f l e c t i o n s f o r la n e I o a d i n g s ( f o u r l a n e s ) in m a i n s p a n ( d e s i g n u l t i m a t e
N M N S4 N E
+ 0 . 0 0 1 4 - 0 . 0 2 3 9 - 0 . 0 0 4 9
+ 0 . 0 0 2 0 - 0 . 0 3 8 1 - 0 . 0 0 9 0
+ 0 . 0 0 32 - 0 . 0 5 6 3 - 0 . 0 1 7 5
+ 0 . 0 0 38 - 0 . 0 6 3 7 - 0 . 0 3 2 1
+ 0 . 0 0 4 0 - 0 . 1 0 3 8 - 0 . 1 2 8 0
1 2 2 E n g . S t r u c t . 1 9 9 1 V o l . 1 3 A p r i l
8/11/2019 verification of Load deflection
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Seg me ntal post tensioned concrete br idges: d. E. Bree n and S. Kashima
J
2 . 2 5
2 . 0 0
1 7 5
1 5 0
I 2 5
1 0 0
0 7 5
0 . 5 0
0 . 2 5
0 00
L o a d i n g c o n d i t i o n ( + 1 .3 S D L )
h lwl
S E S M NM NE
- 1 0 0
C o m p r e s s i o n
/ ' ~ O ~ O P o s i ti o n o f w h e e l s
. / ~ = ~ l q ' ~ l 2 i = ,1 2 = I / C B r i d g e
y ii ii
/ Y ~ 2 7. 5 ,J P o si ti on o t p a p er
s ~ i~ ~ I g a u g e ( t r a n s v e r s e l y )
~ / ~ ' X E x p e r i m e n t S S7
S E M _ _ _ INE
'~ 2 0 0 " - ' - L I0 0" " ' " 2 0 0 " " '
I I
- 2 0 0 - 3 0 0
S t r a i t . ( u i n / i n )
Figure 5 T r a n s v e r s e s t r a i n a t S S 7 R f o r t r u c k I o a d i n g s ( f o u r l a n e s ) in s i d e s p a n ( d e s i g n u l t i m a t e )
increas e l e s s rapidly a f ter that increm ent indicat ing that
a p l a st i c h i n g e w a s f o r m e d a t t h e S S 6 - 7 j o i n t . A f t e r
form ing the p las t i c h ing e the load s we re redis tr ibuted
a n d m o r e l o a d w a s c a r r i e d a t t h e S M p i e r r e g i o n . S i n c e
t he b r idge i s a th ree-span con t inuous beam, p las t i c
h inges have to be fo rmed a t A) and B) in Figure 7 to
have a comple te fa i lu re mechan i sm fo r load ing in the
s i d e s p a n . D u e t o t h e e x t r e m e w i d e n i n g o f t h e c r a c k a t
t h e S S 6 - 7 j o i n t a n u n e x p e c t e d h o r i z io n t a l f o r c e o c c u r -
r ed o n t h e t o p o f t h e S E p i e r . I t c o u l d b e v i s u a l l y
o b s e r v e d a t h i g h l o a d l e v e l s t h a t t h e S E p i e r w a s t i l t i n g
a n d i n c l i n i n g a f t e r t h e l a r g e c r a c k s o p e n e d a r o u n d t h e
S S 6 - 7 j o i n t . A p p a r e n t l y a si g n i f i c a n t h o r i z o n t a l f o r c e
d u e t o t h e d e f o r m a t i o n o f t h e b r i d g e w a s i n d u c e d a t t h e
t o p o f t h e S E p i e r. T h e m o m e n t c o n n e c t i o n b e t w e e n t h e
e n d p i e r a n d th e t es t f l o o r w a s n o t s t r o n g e n o u g h t o k e e p
the p ier from t i l t ing under th i s force .
Beca use i t was obv ious tha t a p l as t ic h inge had fo rm ed
n e a r th e 4 . 3 8 L L + IL ) i n c re me n t a n d b e c a u s e o f th e
inc lina tion o f the end p ie r , i t was dec ided m s top load ing
and rc l casc a ll l i ve load a t t he 5 .25 LL + IL) incremen t .
Th i s re p resen ted p rac t ica l fa i lu re o f the s ide span ,
a l though to t a l co l l apse d id no t occur . In th i s way fu r ther
load t es t ing cou ld be comple ted in the o ther two spans .
A l t e r c o mp l e t i o n o f th e s i d e sp a n t e s ts , f o u r A A S H T O
lane loads were app l i ed to the main span and one ad ja -
cen t s ide span to p roduce the c r i t i ca l shear cond i t ion a t
the f i rs t jo in t in the main span. I t wa s ant icipated fr om
com puta t ions that wi th fu ll deve lopm ent o f shear
s t reng th the b r idge would fa i l i n f l exure even though
u n d e r a ma x i mu m s h e a r l o a d i n g . H o w e v e r , i t w a s
dec ided to check the shear capac i ty s ince bas i c in fo rma-
t ion abou t f l exura l capac i ty w as ob ta ined by app ly ing the
t ruck loads to the s ide span . Lack o f pub l i shed in fo rma-
Figure 6
L o a d i n g c o n d i t i o n ( + 1 . 3 5 D L )
i n
s E ~ l , s M . M
N~
o ~
I E I
5.0 SS7
4 0
+ 3 .0
I I
_= ~ z= t =o 8
o
/ i.r
D f l e c t i o n : a v e r a g e o f 4 r e a d i n g s o n w e b s
1 0
0 0 I I I
0 .0 0 .1 0 .2 0 .3
D e f l e c t i o n ( i n )
D e f l e c t i o n s a t th e c e n t r e o f t h e S S 7 s e g m e n t i n s id e s p a n
I
0 . 4
E n g . S t ru c t . 1 9 9 1 V o l . 1 3 A p r il 1 2 3
8/11/2019 verification of Load deflection
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S e g m e n t a l p o s t t e n s i o n e d c o n c r e t e b r i d g e s : J . E . B r e e n a n d S . K a s h i m a
S E ( B } N M H E
S M
= s t p l a s t i c h i n g e
I_
'~ A I
( A ] ( B ]
M 0 1 ~ ( B )
Mo1,M02: plastic moment
2 n d p la s t i c h i n g e
( A ] _ I
U}
C
F i gu re 7
F a i lu r e m e c h a n i s m f o r t r u c k I o a d i n g s i n t h e s i d e s p a n
( a ), l o a d i n g c o n d i t i o n ( + 1 . 3 5 D L ) ; ( h i . f i r s t p l a s t i c h i n g e a n d
m o m e n t d i a g r a m ; ( c ), s e c o n d p la s t ic h i n g e a n d m o m e n t d i a g r a m
a t c o l l a D s e
tion made it very desirable to check the performance of
the epoxy joints under realistic high shear Ioadings.
In addition to the 1.35 dead load, AASHTO live and
impact lane loadings were applied by rams and increased
until failure. The position of the heavy concentrated load
could greatly affect the shear strength of the bridge. It
was considered that a direct shear failure might occur as
the effective depth decreased due to flexural cracks, so
concentrated loads were applied 10 in. outside but adja-
cent to the first joint in the main span.
After the load reached 2.25 LL + IL), the reaction at
the north end started to decrease and at higher loads the
north reaction was unloading the dead load effects. At
the 2.63 LL + IL) increment, the south end segment
SE) raised completely from the neoprene pad support.
At this load level the crack which had previously
developed at the joint of the main span closure segment
during the positive moment ultimate design load test
started to reopen. Strains in segments SS7, SS6, SS1 and
SM I increased almost linearly up to 2.63 LL + IL), but
remained constant after that increment because the south
end reaction became zero and no load was applied to the
unloaded side span. Strains at NS6 were very low until
the 2.5 LL + IL) increment, then increased steadily
until failure. This change was caused by the alteration in
structural configuration when the south side span
became a free cantilever.
At the 3.25 LL + IL) increment, the strain increase
at the NM6 segment stopped. This was due to the con-
centration of deformation in the crack around the centre
of the main span. The rate of deflection increase
changed substantially at 3.25 LL + IL) as shown in
Figure 18
Also, a diagonal tension crack started to
develop at the first segment in the main span outer web
on the west side). At the 3.75 LL + IL) increment, a
flexural crack at the joint of the closure segment
extended to near the top of the web and many cracks
started to develop in the region of segments SM6 to
SM9, as shown in Figu re 19
At the 4.25 LL + IL) increment, the diagonal tension
crack and the flexural crack around the NM pier joined
and a wide flexural crack developed about 1 in, away
from the first joint in the main span. At this stage, the
flexural crack on the top slab was only in the outer can-
tilever portion. At this loading the south end segment
raised up about I in. from the surface of the neoprene
pad support.
At the 4.25 LL + IL) increment in the east side and
the 4.75 LL + IL) increment in the west side, very wide
flexural cracks developed at the SM6-7, SM7-8 and
SM8-9 joints, as shown in
Figure 19
These cracks
F i gu re 8
7 . 0
6 . 0
0
~ 3 . 0 L o a d i n ~ c o n d i t i o n ( + 1 . 3 5 D L )
2 . 0 T S E S M N M N E
1 . 0
0. 0 I I I I I I I
0 . 0 I .0 2 . 0 3 . 0
D e f l e c ti o n a t c e n t r e o f m a i n s p a n i n)
D e f l e c t i o n s a t S M 1 0 d u r in g l o a d i n g t o f a i l u re
I
t l . 0
1 2 4 E n g . S t r u c t . 1 9 9 1 , V o l . 13 , A p r i l
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a
Segmental post-tensioned conc rete bridges: J. E. Breen and S. Kashima
A
0
C D
Lt
A
A
A
Span
AB
BC
CD
Prototype
100
200
100
Model
16.67
33.33
16.67
T3:
Fillet detail
B
B1 B2 83
05 87
Tl
T2 T3 T3' T4 T6 D Hl
Vl HZ V2 H3 V3 H4 V4
Prototype 671 71.5 14 156 80 24
8
7
6
10 12 6 96
8
6 8
6 8
6
4
4
Model
112 11 9 2 3.
26 13.3
4 1.33 1.17 1 1.67 2 1 16 1.33
1 1. 33 1 1.33 1 0.67 0.67
Figure 19 Development of cracks around the centre of main span during loading to failure
developed near the epoxy joints in the web portion in
the flexural tension zone) and about 1 in. away from the
joint in the bottom slab in the pure tension zone). The
cracks at these joints went nearly to the top of the web
with an increase of one increment of loading. The in-
crease of strain around the 4.09 to 4.75 (LL + IL)
increment range at NM9, NM I and NSI stopped
because of concentration of deformations at these joints
and at the first joints from the main pier. At the 5.0
LL + IL) increment. the crack on the top slab of seg-
ment NSI and the NM pier segment extended the full
width of the slab on the east side of the box).
At the 5.75 LL + IL) increment, the bridge looked
straight from the SE pier to the SM6-7 joint and all
major deformation was concentrated at the SM6-7 joint.
The NM pier segment on the neoprene pad support
started to crush on the east side. due to the high com-
pression force.
After taking the instrument readings at the 6.25
LL + IL) increment, the loads were being increased to
the 6.50 LL + IL) increment when a sudden rupture of
the positive moment prestressing cables occured at joint
SM6-7 on the west side. This failure occurred before
applying less than half of the planned increment and the
load dropped immediately after the failure. The load was
then brought back to the 6.25 LL + IL) increment and
rupture of the positive moment prestressed cables in the
east side box occurred after a small increase in load.
Even after rupture of the positive moment cables, the
bridge exhibited great toughness and continued to carry
1.35 DL as balanced cantilevers.
Ultimate capacity was computed recognizing that only
downward restraints existed at the piers. Under high
overload levels the bridge began to act as a two-span
continuous beam with an overhang. Ultimate moments
were computed for the various support conditions.3
and the redistribution of moments was followed through
the loading sequence.
The LF or level of LL + IL) which would form the
first plastic hinge for this loading was calculated for
each type structure. The first plastic hinge would form
at the joint of the closure segment at an increment of
1.35 DL + 5.21 LL + IL)) if the structure was ideally
supported by pins and there was no uplift possible at the
Eng. Struct. 1991, Vol. 13, April 125
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S e g m e n t a l p o s t t e n s i o n e d c o n c r e t e b r i d g e s : J. E . B r e e n a n d S . K a s h i m a
end supports. However, it is not proper to calculate the
LF for a three-span continuous beam since the SE sup-
port raised off its support pad at the (1.35 DL + 2.63
(LL + IL)) increment. Since the south end support
raised completely from the neoprene pad supports, all
forces applied at the time of construction (such as end
reaction due to positive tendon prestressing in the main
span or the jacking force at the end supports to adjust the
reaction) were erased and the structure became a two-
span continuous beam with an overhang. If the structure
were an ideal two-span continuous beam with an over-
hang, the reaction at the NE support would have to
increase as the load increased. But the reaction at the NE
support decreased after the (1.35 DL + 2.25 (LL + IL))
increment due to the appearance of cracks and concen-
tration of deformation around the centre of the main
span. Observations indicated that a plastic hinge was not
formed at the closure segment at (1.35 DL + 2.25
(LL + IL)) as would be indicated for a two-span con-
tinuous beam with an overhang. Since the calculation for
case (3) indicated that the minimum LF of 6,33
(LL + IL) for the first plastic hinge was at the SM6-7
joint for a simple beam with overhangs, it will be proper
to calculate the LF of (LL + IL) for the case and then
take into account the reaction left at the NE support. If
the structure is an ideal simple beam with overhangs, the
first plastic hinge would form at the 6.33 (LL + IL)
increment. The effect of the reaction left at the NE sup-
port was small _and 5.88 (LL + IL) is the calculated
increment to form the first plastic hinge when taking into
account the end reaction at the NE support. This value
agreed well with the 6.25 (LL + IL) experimental value.
I1" the AASHTO allowance for reduction on a four lane
bridge was considered, the bridge would withstand
(I.35 DL + 8.33 (LL + IL)) in this load configuration.
Alter demolishing the bridge, the joints where failure
occurred were carefully examined and it was found that
the five positive tendons in each web were completely
broken through. Although the side span positive tendons
were adequately proportioned by the design procedure
which assumed ideal three-span continuous beam action,
the positive moment reserve was reduced in the main
span because the design did not consider the upward
unrestrained end support condition. A check of the
loading condition which would produce maximum
moment at the centre of the main span indicated that the
main span maximum positive moment flexural capacity
is reduced to (1.35 D L+ 3. 13 (L L+ IL )) if the
AASHTO load reduction for multiple lanes is ignored.
This would be (1.35 DL + 4.17 (LL + IL)) if the nor-
nml design specifications are used for a four-lane bridge.
While this load case was not tested to failure, the good
agreement of other flexural test results and calculations
indicated that this value would undoubtedly have been
attained.
In order to match the test loading conditions, the
model's external dead load moment was computed with
1.0 DL acting on a balanced cantilever and 0.35 DL
acting on the_completed continuous structure. Becau~
of the construction sequence it is not logical to base the
analysis of the completed structure on fully continuous
beam load moments for 1.35 DL. A more rational load
factor procedure for computation of the ultimate design
moments in the completed structure should consider
possible uncertainty in the dead load at various stages of
construction. Based on experience in this program, the
following factors are suggested for analysis of the com-
pleted structure to check the negative moment and shear
capacity.
Load factors are chosen to conform to the BPR
general factor philosophy
U = 1.35 DL + 2.25 (LL + IL)
For a segmental bridge erected in cantilever, during
the construc tion phase M, - M,~ based on
U~ = .35 DL~ + 2.25 (LL~ + IL0 to be
computed for a balanced cantilever
Also, upon completion M, >-. M,_, + M, 3, where
U2 = .35 DLI to be computed for a balanced
cantilever
U3 = 1.35 DL3 +
2 25
(LL3 + IL0 + SL to be
computed for the completed continuous
structure
where
DL~ = dead load during cantilevering
DL~ = dead load applied after completion of
closure (topping, railing, etc.)
LLI = live load due to construction operations
LL3 = design live load
IL I = impact load o f construct ion operations
IL3 = design impact load
SL = resultant reactions due to prestressing of
of tendons and seating forces at outer
supports
Negative tendons can be designed by WSD or USD to
balance the dead load segments and the weight of con-
struction equipment on the segments during the balanced
cantilever stages. However, the ultimate negative
moment capacity of the cantilever structure should be
checked for Ui. The ultimate negative moment capacity
of the completed structure should be cheeked for
U=U,. U~.
In determining positive moment tendons it will be
unconservative to use U,, = i.35 DL~. A highly conser-
vative approach would be to use U, = 0.90 DL~ com-
puted for the balanced cantilever and the preceding
equations.
o n c l u s i o n s
Based on the experimental and analytical results
reported, the following conclusions were drawn.
The segmental bridge model safely carried the
ultimate design loads for all critical moment and shear
loading configurations on which its design had been
based.
The deflection under design live load in four lanes
(only three lanes required by live load reduction factors)
was approximately L/3200 in the main span. This is
much smaller than L/300 which is generally considered
as acceptable.
2 6
En g. Struct . 199 1 Vol . 13 Ap r i l
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Seg me ntal post tensione d conc rete br idges: J. E. Bre en and S. Kashima
Pos i t ive t e ndons i n t he m a in spa n we r e de s igne d a s i f
a n i de a l t h r e e - spa n c on t inuous be a m . S inc e t he c om -
p le t e d b r idge wa s suppor t e d on ne opr e ne pa ds whic h
have no ver t ica l r es t ra int aga ins t upl i f t , the outer ends
we re able to r i se of f the i r suppo r ts so tha t the s t ruc ture
d id no t a c t c on t inuous ly a t u l t im a te c ond i t i ons unde r
m a in spa n pos i t ive m om e nt loa d ing . E v e n so , t he r e wa s
suf f i c i e n t r e se r ve s t r e ng th i n t he m a in spa n t o c a r r y
design ul t imate load.
U n d e r v e r y h i g h c o m b i n e d m o m e n t a nd s h e a r l o a d in g ,
f l e xur al c r a c ks a ppe a r e d n e a r t he e pox y jo in t s i n t he t op
s l a b ne a r t he m a in p ie r . H ow e ve r , t he y j o ine d t he
d i a gona l t e ns ion c r a c ks a nd d id no t e x t e nd a long the
jo in t s . T he r e wa s no s ign o f a ny d i r e c t she a r f a il u r e at
the joints . In tes ts of the ful l br idge mo del , approx i -
m a te ly 75 o f t he t he or e ti c a l u l t im a te she a r l oa d wa s
a pp l i e d i n t he m a xim um she a r l oa d ing t e s t p r i o r t o
f a i lu r e o f t he b r idge dur ing t he t e s t by f l e xur e . N o s ign
of she a r d i s t r e s s wa s e v ide n t . ( Subse que n t t e s t s o f a
th r e e - se gm e nt m ode l unde r se ve r e she a r l oa d ing a s a
cant i lev er sec t ion indica ted tha t full shea r s t rength of the
uni t was deve loped~'3. Hen ce , the epoxy joint tech niqu e
use d d id no t r e duc e the de s ign sh e a r s t r e ng th ) .
Dur ing e r e c t i on o f t he f i r s t f e w se gm e nt s , t e ns i l e
s t ress occur red in the bot tom s lab as predic ted in the
de s ign . T e m por a r y p r e s t r e s s de v i c e s suc c e ss f u l l y c on-
t rol led the e f fec ts of these s t resses .
Theore t ica l ca lcula t ion of the load fac tor for l ive and
impact loads requi red to form the f i r s t p las t ic hinge
a gr e e d ve r y we l l w i th t he e xpe r im e nta l r e su l t s . T he se
tes ts provide the accuracy and appl icabi l i ty of the
ul t imate hind ca lcula t ion procedure consider ing redis t r i -
bu t ion o f m om e nt s .
Most of the theore t ica l ca lcula t ions were in good
a gr e e m e nt w i th t he e xpe r im e nta l r e su lt s , a l t hough the r e
we r e som e a ppr e c i a b l e de v i a t i ons be twe e n the e xpe r i -
menta l and theore t ica l va lues of s t ra in in the top s lab in
som e s t a ge s o f c a n t i l e ve r c ons t r uc ti on .
T he B M C OL 50 pr ogr a m wa s ve r y use f u l i n p r e d i c t i ng
the be ha v iou r o f t he b r idge d ur ing c on s t r uc ti on a nd f i~ r
un i f o r m loa d ing t e s t s . T he BM COL 50 r e su l t s a g r e e d
very wel l wi th the exper imenta l r esul t s for longi tudina l
s t ra ins and def lec t ions . The re la t ive ly s imple da ta input
f o r BM COL S0 i s a no the r a dva n ta ge whe n c om pa r e d t o
the f o lde d p l a te t he or y p r ogr a m s .
T he S I M PL A2 pr ogr a m r e a sona b ly p r e d i c t e d t he
var ia t ion of the longi tudina l s tra in un der very high s t ress
l e ve l s a c r oss t he t op s l a bs o f t he ne wly e r e c t e d se g-
ments .
T he M UPDI p r ogr a m , whic h c a n be use d on ly f o r a
constant c ross sec t ion, agreed very wel l wi th the exper i -
menta l r esul t s a t the se rvice load leve l . The var ia t ion of
c r oss se c t ion a long th is b r idge wa s ve r y sm a l l . M UP Di
c a n be use d t o de t e r m ine t he t r a nsve r se m om e nt s a nd
she a r s unde r unsym m e t r i c a l l oa d ing a nd c a n be use d
e f f e c t ive ly i n de s ign ing t he t r a nsve r se r e in f o r c e m e n t .
How e ve r , t he e f f e c ts o f c r e e p a nd sh r inka ge w e r e
minimal in this s tudy. M ul le r m points out for this c lass
of s t r uc tu r e .
T he e f f e c t o f s t e e l a nd c onc r e t e c r e e p m us t be c on-
s ide r e d w i th r e ga r d t o m om e nt d is t ri bu t ion , t oge the r
w i th t he poss ib l e e f f e c t o f m om e nt r e ve r sa l . F ina l
a d jus tm e nt a nd c om pe nsa t i on f o r sh r inka ge a nd c on-
c r e t e c r e e p m a y he lp t he s t r uc tu r e t o r e a c h t he
op t im um e qu i l i b r ium .
A c k n o w l e d g e m e n t s
This s tudy was par t of Research Projec t 3-5-69-121
sponsor e d by t he T e xa s S t a t e De pa r tm e nt o f H ighwa ys
a nd Pub l i c T r a nspor t a t i on a nd t he Fe de r a l H ighwa y
Adm in i s t ra t i on . T he op in ions e xpr e s se d a r e t hose o f t he
a u thor s a nd d o no t ne c e ssa r i l y r e f le c t those o f t he spon-
sor s . T he a u thor s a r e g r e a t l y i nde b t e d t o m a ny who
played key roles in this ambi t ious sca le model tes t .
L i a i son w i th t he T SDHPT wa s m a in t a ine d t h r ough the
c on ta c t r e pr e se n t a t i ve , M r . Robe r t L . Re e d , a nd t he
S ta t e Br idge E ngine e r , M r . Wa yne He nne be r ge r ; M r .
D . E . Ha r t l e y a nd M r . Robe r t E . S t a ndf or d we r e t he
c on ta c t r e pr e se n t a t i ve s f o r FHWA. Spe c i a l t ha nks a r e
due t o M e ss r s . T hom a s Ga l l a wa y , L a w r e nc e G . G r i f fi s
and John T . Wal l , a l l ass i s tant research engineers a t the
Fe r guson S t r uc tu r a l E ng ine e r ing Re se a r c h L a bor a to r y
a t T he Unive r s i t y o f T e xa s a t Aus t i n ' s Ba l c one s
Re se a r c h Ce n te r . T h e y p l a ye d ke y r o l e s i n t he de ve lop-
m e nt o f m o de l t e chn ique s , f a br i c a t ion p r oc e d ur e s , e r e c -
t i on m e thods , a nd i ns t r um e nta t i on sys t e m s , a nd we r e
r e spons ib l e f o r va r ious s t a ge s o f c ons t r uc t i on ope r a -
t i ons . T he L a bor a to r y s t a f f und e r t he i r supe r v i so r M r .
Ge o r ge M ode n , a l l c on t ri bu t e d s ign i f ic a n t ly to t h i s p r o -
j e c t w i th t he i r un t i r i ng w i l l i ngne ss t o wor k l ong hour s
a nd m a ke a n e x t r a e f f o r t t h r oughout t h i s p r o j e c t . D r .
Ne d H . Bur ns , P r of e s sor o f C iv il E ng ine e r ing a c te d a s
a n a dv i sor on m a ny que s t i ons c onc e r n ing p r e s t r e s s ing
sys t e m s .
Our l as t a c know le dge m e nt is t o t he t i n fe t te r e d ge ne r o-
s i t y o f P r of e s sor A . C . Sc or de l i s o f t he Unive r s i t y o f
Cal i fornia , Berke ley. Alex Scorde l i s wi l l ingly provided
c o m p u t e r p ro g r a m s M U P D I a n d S I M P L A f o r us e w i th
th i s p r o j e c t . He a nswe r e d ' dum b ' que s t i ons w i th h i s
c ha r a c t e ri s t ic g r a c e a nd p r ov ide d e nc o ur a ge m e nt a nd
advice to the authors . Without his he lp the ana lyt ica l
inte rpre ta t ions would have been very l imi ted.
R e f e r e n c e s
10
Kashima. S. and J. E. Breen. Const ruct ion and load tests o f segmen-
ta l p recas t box g i rde r b r idge mode l ' .
R e s . R e p . 1 2 1 - 5 .
Center fo r
H ighway Resea rch , The Un ive rs i t y o f Texas a t Aus t in , Feb rua ry
1975
Brown, R. C. , Burns, N. H. and Breen. J . E. C o m p u t e r analys is o f
segmenta l ly erec ted precast pres t ressed box g i rde r b r idges ' . Res .
Rep . 121 -4 . Cen ter I b r H ighw ay R esea rch . The U n ive rs i t y o f Texas
a t Aus l in , November , 1974
Kash ima. S. Const ruct ion and load tests o f a segmenta l p recast box
g i r d e r b r i d g e m o d e l ' . Ph.D . d i s s , . The Un ive rs i t y o f Texas at Aus t in ,
January 1974
Bro wn , R. C. 'C om pulc r ana lys is o f segmenta lly constructed
prest ressed bo x g i rders . PhD. d iss . . The Un ive rs i t y o f Texas a t
Aust in . 1972
V. Novokshchenov. Sa l t penet ra tion and corros ion in prest ressed
concre te members ' , Fede ra l H ighway Admin is t ra t ion Repo r t
RD-88-269. Ju ly 1989
Ga l lawa y . T .M . ' l ndus t ra l i za t ion and mo de l ing o f segmen ta ll y
p recas t box g i rde r b r idges ' . Ma s te r ' s t hes i s . The Un ive rs i t y o f Texas
at Aust in . 1971
Ma t tock . A . H . S t ruc tu ra l mode l t e~ t ing - - tbeo ry and app l i ca t ions ' ,
J PCA Res. Dev. I .~h. 1962 .4 (3 ) . 12 -22
Scordelis . A. C . 'Analysis of simply supported box girder brid ges ' .
Re p No
SESM 66-77. Depart .ment of Civil Engineering. Un ive~ ity
of Califiwnia. Berkeley, October 19(36
Bureau of Public Roads. Strength and serv iceabi/ iO. criteria rein-
forc e d c onc re te br idge me ntbe rs uhimate de s ign (2nd edn). Bureau
of Public Roads. U.S. Department of Transportation. Washington.
D.C. 1969
Muller. J. Long spa n precast prestressed
concrete
bridge built in
can t i leve r ' . Concrete Bridge Design. ACt Publication SP-23. 1969.
p p . 7 0 5 - 7 4 0
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