Resea ch A icle
S eng hening and Rehabili a ion o U-Shaped RC B idges Using
Subs i u e Cable Duc s
Adam S oboda , Ladisla Klus´
aˇ
cek, and Ma in Olˇ
s´
ak
Ins i u e o Conc e e and Mason y S uc u es, B no Uni e si y o Technology, Ve eˇ
´
ı331/95, 602 00 B no, Czech Republic
Co espondence should be add essed o Adam S oboda; [email p o ec ed]
Recei ed 23 July 2019; Re ised 20 Sep embe 2019; Accep ed 23 Oc obe 2019; Published 30 No embe 2019
Academic Edi o : Mohammad A. Ha i i-A debili
Copy igh ©2019 Adam S oboda e al. This is an open access a icle dis ibu ed unde he C ea i e Commons A ibu ionLicense,
which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed.
The p esen ed pape deals wi h s eng hening and ehabili a ion o U-shaped ein o ced conc e e b idges om he pe iod o
1905–1930 using pos - ensioning, which is a sui able, eliable, and du able me hod. These b idges ha e wo main beams pulled
o e he b idge deck, which is suppo ed by c oss gi de s. The c oss gi de s connec he wo main beams o ming a hal - ame in
he ans e se di ec ion, which p o ides spa ial igidi y o he s uc u e. The spans o hese b idges a e usually be ween 15 and
25 m. The high efficiency o pos - ensioning can be seen on many implemen ed applica ions o b idge econs uc ions wo ldwide.
Howe e , in his pape , he pos - ensioning me hod is ex ended by a unique s uc u al sys em o subs i u e cable duc s ha allows
o significan ly expanding applicabili y o his me hod on exis ing conc e e b idges. This me hod is highly ecommended due o
minimiza ion o in e en ions in o he cons uc ions, unseen me hod o cable a angemen , and hence he absence o impac on
appea ance, which is app ecia ed no only in case o aluable his o ical s uc u es bu in gene al as well. In conclusion, he pos -
ensioning by monos ands in subs i u e cable duc s is a highly efficien me hod o s eng hening o exis ing b idges in o de o
inc ease hei load-bea ing capaci ies in e ms o cu en affic load and o ex end hei se ice li e. This me hod was also e ified
by moni o ing he beha io o ehabili a ed b idges be o e and a e s eng hening.
1. In oduc ion
Rein o ced conc e e beam b idges ha e been buil since he
e y beginnings o ein o ced conc e e. Bo h simple and
con inuous pa ape b idges ep esen a sui able s uc u al
op ion o beam b idges because o hei small cons uc ion
heigh (U-shaped b idges, camelback b idges, and ough
gi de b idges). These s uc u es ha e been de eloped nea
Michigan, USA, and soon hey ha e sp ead in Eu ope as well
[1]. The e is s ill a couple o hund ed o hese s uc u es
a ound he oadways in he Czech Republic [2].
The oldes U-shaped b idges we e buil be ween 1905
and 1915, and hey we e designed in acco dance wi h he
Aus ian Minis y o Railways B idge S anda d o Augus
1904 [3]. A ha ime, he la ges load he oad b idges had
o endu e on he p ima y oads was an 18 (180 kN)
s eam olle o a uni o mly dis ibu ed load o 460 kg/m2
(4.6 kN/m2) o e he su ace o he b idge [4]. This b idge
ype was e y popula up un il 1930, bu om he s andpoin
o cu en affic demands upon b idge s uc u es, i usually
does no comply because o i s load-bea ing capabili y and
an efficien s eng hening and o al econs uc ion has o be
pe o med upon b idge s uc u e [5]. These conc e e b idges
a e also aluable om he his o ical s andpoin because hey
ep esen a legacy o he fi s gene a ion o ein o ced
conc e e b idge enginee s.
1.1. Rein o ced Conc e e B idge S eng hening Using he
Subs i u e Cable Duc Me hod. Pos - ensioning is a sui able,
eliable, and du able me hod o ein o ced conc e e b idge
s eng hening. A s eng hening sys em using pos - ensioning
effec s has also been discussed in p e ious s udies and ap-
plica ions; o example, Recupe o e al. [6, 7] p esen ed an
applica ion o ex e nal p es essing echnique o s eng h-
ening a single-span conc e e ailway b idge in I aly. The effec
o s eng hening was also esea ched wi h he help o nu-
me ical simula ions. Nilimaa e al. [8] ocused on
Hindawi
Ad ances in Ma e ials Science and Enginee ing
Volume 2019, A icle ID 8920718, 21 pages
h ps://doi.o g/10.1155/2019/8920718
s eng hening o conc e e ailway b idges (in Sweden) in he
ans e se di ec ion using p es essed ba s ins alled in ad-
di ionally d illed holes in he exis ing conc e e. Pe angeli
e al. [9] published a pape ocused on s eng hening o he
con inuous ein o ced conc e e b idge in 1976 in E hiopia
ac oss he Gibe i e using ex e nal p es essing endons. Daly
and Wi a nawan in a icles [10, 11] p esen ed wo applica-
ions o s eng hening composi e (s eel-conc e e) b idges in
Indonesia using ex e nal p es essing and also discussed key
pa ame e s o designing such a sys em. Woodwa d and Daly
[12] examined he effec o ex e nal p es essed endons
wi hin an expe imen on a b idge model o a 1 : 4 scale. The
expe imen al load es s ha e shown ha he pos - ensioning
me hod p o ides a sa e and s able me hod o s eng hening.
Dai e al. [13] examined he s eng hening echnique wi h
double-laye p es essed s eel wi e opes (PSWRs) o enhance
he se iceabili y o an exis ing conc e e box gi de . Miya-
mo o e al. [14] s udied he beha io o p es essed beams
s eng hened wi h ex e nal endons. In he p esen ed pape ,
simply suppo ed p es essed composi e gi de s wi h al e -
na ing p es essing le els, eccen ici y o endons, and endon
p ope ies a e examined. Mimo o e al. [15] de eloped a
s eng hening sys em using pos - ensioned endons wi h
in e nal ancho ages in he exis ing conc e e. The in e nal
ancho age hole is made using a special d illing machine, and
he sys em p o ides join s be ween he exis ing and addi-
ionally cas conc e e pa s. O he esea che s ocused on
pos - ensioning o conc e e using FRP elemen s; o example,
Lee e al. [16] and Jung e al. [17] p esen ed a pos - ensioned
FRP nea -su ace moun ed sys em o s eng hening o
exis ing s uc u es wi hou changing i s dimensions. The
s eng hening effec was in es iga ed bo h expe imen ally and
nume ically. A a in han and Heid [18] s udied inno a i e
me hods o s eng hening o b idge heads ocks using pos -
ensioned fib e composi e w aps as an al e na i e o s eel
p es essing endons. Some scien is s deal wi h he compa -
ison o p es essing me hods using s eel endons o FRP
elemen s; o example, Choi [19] examined effec i e s esses o
conc e e beams s eng hened using CFRP and ex e nal p e-
s essing endons. The s eng hening effec o ex e nal en-
dons was ound o be significan ly g ea e in compa ison wi h
CFRP. Also, RC beams s eng hened wi h ex e nal endons
showed small diffe ence be ween he analysis and expe i-
men al esul s compa ed o beams s eng hened by he CFRP
me hod.
Howe e , none o he ci ed au ho s applied he pos -
ensioning me hod o s eng hening he desc ibed U-sha-
ped RC b idges. Resea che s a he B no Uni e si y o
Technology (Czech Republic) ha e de eloped he subs i u e
cable duc me hod, whose s uc u al design pushes he
limi a ions o his o ical s uc u e p es essing.
Basic s uc u al a angemen o p es essing cables in
beam b idge s eng hening using he me hod o subs i u e
cable duc s is shown in Figu e 1. A e a p e ious de ailed
diagnos ics, usable spaces be ween ein o cemen a e de-
e mined and subs i u e cable duc s a e d illed h ough he
beams. The di ec ion and dis ibu ion o duc s is in-
en ionally selec ed so ha he ancho age a ea could be
c ea ed abo e o behind he bea ing axis, and he
dis ibu ion o saddles was selec ed a 1/5 o 1/4 om he
heo e ical suppo in compliance wi h he s a ic calcula ion.
P epa a o y wo ks o cables a e finished by c ea ing he
saddles in such a manne ha he adial o ces o he cables
a e di ec ed s aigh in o he conc e e o he e ofi ed
s uc u e, and he complex and unclea ans o ma ion o
o ces is no pe o med. A e p es essing, he ancho ing
a eas a e filled wi h conc e e and he cables (monos ands)
on he bo om side o he beams a e co e ed wi h an ad-
di ional conc e e co e ing laye , o hey a e hidden in he
econs uc ed o iginal co e ing laye . The sui abili y o he
me hod was confi med o bo h simple and con inuous
U-shaped b idges wi h span leng hs om 8 o 25 m [20].
1.2. Cables in Subs i u e Duc s in O iginal Beams. Using he
subs i u e cable duc me hod leads o a placemen o pos -
ensioning cables and monos ands di ec ly in o he con-
c e e o he o iginal beams. The essen ial equi emen o his
me hod is a a ou able dis ibu ion o he o iginal main
load-bea ing ein o cemen , which p o ides abundan space
o sui able d illing o subs i u e duc s in he a ailable spaces
be ween he o iginal ein o cemen s wi hou i s in-
e up ion, o wi h jus a small dec ease in s eng h, which
can be included in he s eng hening design calcula ions and
which can be compensa ed by he pos - ensioning effec s.
This equi emen is me ela i ely o en (in mos cases e-
sol ed by pos - ensioning, sui able spaces could be ound
be ween he o iginal ein o cemen s), which is gi en by he
design cus oms om he ime o cons uc ion. Use o he
subs i u e cable duc me hod hen p o ides significan
ad an ages:
(1) Th ough saddles, he cables lean di ec ly on he
conc e e o he beams, and he e o e, he adial e -
ec s o cables di ec ly affec he o iginal s uc u e
(p ac ically in he e ical axis o he beams).
The e o e, hey do no ha e o be a he in ica ely
ans o med by weldmen s placed on beam sides, o
wi h sepa a ely cas blocks wi h duc saddles.
(2) The saddles can be c ea ed e y simply as s eel shee s
(s ap s eel) ben in o he p esc ibed adius o 1.2 m
o 1.5 m, which a e moun ed in o high-s eng h
mic oconc e e wi h a ull-a ea ancho ed saddle.
(3) The p es essing ein o cemen (cables composed o
monos ands) is comple ely p o ec ed agains me-
chanical damage a e subsequen filling o duc s wi h
injec ion. I his p o ec ion is u he complemen ed
wi h addi ionally ancho ed cable shea hing in a
s aigh sec ion be ween saddles on he bo om su -
ace o beams, hen he en i e p es essing se is
hidden in he o iginal conc e e and in he newly
cons uc ed co e . The e o e, he equi emen s o
pe ec mechanical p o ec ion o he plas ic shea hs o
indi idual monos ands a e me . I he s able con-
di ions o p ima y and seconda y p o ec ion o
p es essing ein o cemen a e obse ed, long li e ime
(long- e m eliabili y) o his ype o s eng hening is
gua an eed.
2Ad ances in Ma e ials Science and Enginee ing
Subs i u e cable duc s equi e d illing o holes in o
conc e e and mason y in leng hs mul iple imes longe han
he commonly manu ac u ed machines and ools allow. A
special posi ioning d illing de ice—a d illing suppo —was
designed and manu ac u ed o his pu pose. The main pa s
o he de ice a e guiding ba s and a d illing ca .
The ca allows defined clamping o d illing machines and
a ans e o o ce o p o ision o he necessa y d illing h us .
Toge he wi h he ca , he guiding ba allows p olonga ion o
d illing sha s. This de ice (Figu e 2) composed o he ca and
he guiding ba s p o ides machine guidance o he d illing
machine and dec eases s ain o he ope a o s o he d illing
machine o an accep able le el. Secondly, i also inc eases he
accu acy o d illed cable duc ajec o y o he highes deg ee
possible. Thi dly, i allows he ope a o s o se a comple ely
a bi a y ajec o y because hey can se any angle in bo h he
ho izon al plane and he e ical plane (usually an angle o-
wa ds he longi udinal axis o he load-bea ing s uc u e). The
d illing suppo can be axially equipped wi h bo h diamond
and impac d illing echnology, and hese can be swapped e en
du ing he d illing o a single cable duc . Ano he ad an age o
he d illing suppo is ha i can be a ached o he e ofi ed
s uc u e i sel . Figu e 3 shows a deploymen o he d illing
suppo wi h diamond d illing echnique.
Bo h simple and con inuous ein o ced conc e e beam
s uc u es can be s eng hened using cables in subs i u e
duc s. In he case o simple s uc u es (usually simply sup-
po ed beams), he duc s and p es essing ein o cemen s a e
a anged in acco dance wi h Figu e 1; in he case o con-
inuous s uc u es, hey a e a anged in acco dance wi h
Figu e 4. Con inuous s uc u es can be efficien ly ensioned
wi h con inuous aised cables, ensioned om bo h sides. In
acco dance wi h s a ic equi emen s, hese cables can be
complemen ed wi h noncon inuous cables, ancho ed in a
composi e slab o in ancho ing blocks (ex ensions), which will
be placed be ween he o iginal beams.
In monos and p es essing, he coefficien o ic ion μ,
which is used only in saddles in his dis ibu ion, has he
alue o 0.06 o 0.10, which was epea edly e ified du ing
p es essing o s uc u es s eng hened in his manne by
compa ing he calcula ed and he achie ed monos and
ex ension sizes. The ic ion does no apply in di ec sec ions
o cable ajec o ies (in such case, monos ands mos ly lead
almos linea ly om saddle o saddle, h ough ai and
wi hou ic ion).
Subs i u e cable duc s can be d illed in o he s uc u e
e y accu a ely and wi h e y li le damage o he o iginal
beam ein o cemen . Si e diagnos ic o beam ein o cemen ,
which p o ides in o ma ion on he mos sui able space o duc
d illing, is necessa y o d illing he cable duc . The designe
defines he posi ion o heo e ical poin s (TP) only in he
longi udinal di ec ion, and hey le he exac ou le s o duc s in
he ans e se di ec ion o he beams up o he cons uc ion
p ocess. In many cases, he conc e e o he s eng hened
s uc u e is mo e damaged by co osion in he a ea o he
bo om ace o he beams ha he conc e e co e laye has
al eady allen off and he dis ibu ion o ein o cemen s is
5.0°
15.0°
Figu e 2: Scheme o he d illing suppo o d illing subs i u e
cable duc s o ela i ely small diame e s (ϕ�35 ∼52 mm) in o he
conc e e o he exis ing b idge s uc u e. I allows adjus men o
bo h e ical and ho izon al d illing angles. The pic u e shows a
suppo fi ed wi h a d ill using he impac echnology.
Longi udinal sec ion
A-A
C oss sec ion
B-B A
A
B
B
L/4~L/5 L
Figu e 1: The basic scheme o cable a angemen in he case o s eng hening a simple span b idge by pos - ensioning using he subs i u e
cable duc me hod.
Figu e 3: A ealiza ion o d illing subs i u e cable duc s on he
bo om side o a U-shaped b idge using a d illing suppo [21]. The
pho o shows he use o in en ed d illing suppo equipped wi h a
d illing machine wi h he diamond d illing echnology. The d illing
machine, clamped in o a ca , is led by guiding ba s in he equi ed
angle (bo h e ical and ho izon al) ela i e o he bo om ace o
he s uc u e while d illing a duc .
Ad ances in Ma e ials Science and Enginee ing 3
clea ly isible. In o he cases, in he a ea o u u e saddles, he
o iginal co e can be emo ed because a e p es essing, he
cables will be p o ec ed by he ancho ed co e and he su aces
o he en i e s uc u e a e usually e ofi ed wi h a special laye .
Figu e 5 shows an example o a duc ou le be ween beam
ein o cemen s o a s eng hened con inuous beam s uc u e in
acco dance wi h p ojec documen a ion. I shows ha sui able
space could always ha e been ound and ha he subs i u e
duc s could ha e been p epa ed wi hou o wi h minimum
damage o he o iginal p ofiles o he main load-bea ing
ein o cemen .
2. S eng hening o U-Shaped B idges
U-shaped b idges ha e wo main gi de s ex ending abo e
he oadway, and he b idge deck is suppo ed by c oss
gi de s. The c oss gi de s connec bo h main gi de s, and
oge he wi h hem, hey o m a hal - ame in he ans e se
di ec ion; he hal - ame p o ides spa ial igidi y o he
s uc u e. These b idges can also be efficien ly s eng hened
using he subs i u e cable duc me hod bo h in he longi-
udinal and ans e se di ec ions [22]. The spans o hese
s uc u es a e be ween 15 and 25 mm, and he desc ibed
s eng hening was used in he ealized designs, e.g., [21, 23].
The main gi de s a e usually ein o ced wi h he o iginal
ein o cemen in he amoun o 8 o 12 pieces wi h ϕo 35 o
50 mm in wo o h ee ows. This p o ides enough space o
subs i u e duc s. The main gi de s o U-shaped b idges a e
egula ly s eng hened wi h wo o ou cables wi h h ee o
ou monos ands in e e y cable. Simila ly o main beams,
he ans e se gi de s can be s eng hened wi h cables in
subs i u e duc s ancho ed on side a eas o main gi de s.
Basic dis ibu ion o pos - ensioning cables is shown in
Figu es 6 and 7.
U-shaped b idges, buil be ween 1905 and 1930, a e
sui able s uc u es o s eng hening using he subs i u e
cable duc me hod, which is gi en by he ollowing s uc u al
pa icula i ies:
(1) Gi de on sides a e a ailable o cable ancho ing in
he main gi de s (U-shaped). Cable lines can be
designed wi h ze o end eccen ici y abo e he sup-
po s. The ensioning se can be bes ancho ed in he
cen e o g a i y o gi de s, which con ibu es o high
efficiency o pos - ensioning and o a good dis i-
bu ion o o ces in ancho s in o he conc e e o he
o iginal gi de s.
(2) Comple ely ee side a eas o main gi de s a e
a ailable o ancho ing o ans e se cables (cables
s eng hening he ans e se beams). On he ee side
a eas, he ancho ing a eas can be c ea ed ei he wi h
cu bea ing su ace (olde sys em) o in he o m o
cas conc e e ex ension (cu en ly used sys em,
which gua an ees bo h p ima y and seconda y
p o ec ion o he en i e leng hs o cables including
ancho s).
In he U-shaped gi de , cables a e led h ough space
c ossways wi h ega d o bo h he ho izon al and he e ical
planes so ha he ancho s would ac in he icini y o he
cen e o g a i y o he end c oss sec ion (in he c oss-
sec ional co e). The loca ion o c oss gi de ancho s has o be
selec ed ca e ully because he p es essing o ces affec he
ans e se semi ame; he ancho s ha e o be placed in he
cen e o g a i y o p ojec ion o he c oss gi de in o he
main beam o sligh ly below i . Then he addi ional se o
o ces will be balanced wi h ega d o he semi ame, and i
will no s ess i ad e sely in he ans e se di ec ion.
P es essing will efficien ly c ea e condi ions o he
addi ionally cas composi e slab, which, in acco dance wi h
he equi emen s o he in es o , s eng hens he o iginal
b idge deck o as high a load as he U-shaped gi de s and
c oss gi de s can be s eng hened.
Figu e 6 shows he shape and a angemen o he
p es essing sys em o s eng hening he U-shaped b idge
wi h a span leng h o l�16.4 m on a seconda y oad o
load-bea ing class B in acco dance wi h ˇ
CSN 73 6203 [24].
The main gi de s we e sufficien ly p es essed wi h ou
cables; c oss gi de s we e p es essed wi h wo cables.
The e o e, condi ions ha e been c ea ed o ca y he weigh
o an addi ionally cas composi e slab, which s eng hened
he o iginal b idge deck. This case is also an example o
L1L2L3
Figu e 4: The basic scheme o cable a angemen in he case o s eng hening a con inuous span b idge by pos - ensioning using he
subs i u e cable duc me hod. Also, i is an example o he usage o mul iple phases o pos - ensioning. The fi s phase (on he pic u e
desc ibed by ed dashed lines) c ea es a possibili y o cas ing an addi ional conc e e composi e slab o slab s eng hening. The second phase
(on he pic u e desc ibed by blue dashed lines) inc eases he o e all load-bea ing capaci y o he c i ical middle span.
Figu e 5: An example o a subs i u e cable duc (ϕ52 mm) ou le a
he bo om side o he beam in a sui able posi ion in a gap be ween
he exis ing ein o cemen .
4Ad ances in Ma e ials Science and Enginee ing
ancho ing using he single-s and wedge wi h bea ing
pla es wi hou obse ing he p ima y p o ec ion in ancho s
(olde way). The seconda y p o ec ion was gua an eed by
he usual cas ing o ancho holes. Figu es 8 and 9 show he
cha ac e is ic de ails o his s eng hening: cable saddles in
U-shaped beams and he ancho s a he end o hese beams
[21].
Figu e 7 shows he shape and dis ibu ion o he p e-
s essing sys em in s eng hening o a U-shaped b idge wi h
a iable heigh o he main beam and a leng h span o l�
14.1 m on a e ia y oad also o he load-bea ing class B [24].
The main gi de s we e pos - ensioned wi h wo cables o
ou monos ands, he c oss gi de s we e pos - ensioned
wi h one cable o monos ands. Once again, condi ions o
ca y he weigh o an addi ionally cas composi e slab we e
c ea ed. Howe e , his is an example o ancho ing using he
encapsula ed ancho sys em wi h an obse ance o p ima y
p o ec ion in ancho s (newe , egula ly used b idge an-
cho ing sys em). The seconda y p o ec ion was once again
gua an eed by he usual cas ing o ancho a eas in conc e e.
Figu e 10 shows cha ac e is ic de ails o cable ancho s in he
main gi de and he c oss gi de ancho s a he sides o he
main gi de [23].
S eng hening o he U-shaped b idges wi h pos - en-
sioning using he subs i u e cable duc sys em gene ally
b ings many ad an ages:
(1) In con as o he glued ein o cemen , which is
ac i a ed only a e load, and he e o e does no
con ibu e o he ans e o o ces om he pe -
manen load, ans e o p es essing in o he
s uc u e balances a significan po ion o in e nal
o ces c ea ed by he pe manen load; his efficien ly
imp o es he condi ion, in which he s uc u e is no
s essed by li e load and a necessa y ese e is
c ea ed o he ans e o effec s o li e load.
(2) The inc ease o load-bea ing capaci y by his
me hod is significan , egula ly 200%–300%, which
is an effec , highe almos by an o de han he use
o glued ein o cemen , o which gene al expe i-
ence speaks on an achie able inc ease o app oxi-
ma ely 30% [19].
(3) C acks c ea ed by s a ic o dynamic load in he
ension flanges o ein o ced conc e e beams sig-
nifican ly accele a e he p ocess o ein o ced
conc e e co osion significan ly. The ans e o
p essu e o ces by p es essing leads om a pa ial
o a comple e closu e o c acks and a subsequen
Longi udinal sec ion
A-A
C oss sec ion
B-B
B
B
A
A
16.25m 9.45m
7.95m
2.45m
Figu e 6: Cable a angemen in he longi udinal and ans e se di ec ions o s eng hening o a U-shaped b idge wi h s aigh gi de s, buil
in Tˇ
ebecho ice in 1932, acco ding o p ojec documen a ion [21].
Longi udinal sec ion
A-A
C oss sec ion
B-B
B
B
A
A
14.15m 7.50m
5.98m
2.59m
Figu e 7: Ano he example o cable a angemen in he longi udinal and ans e se di ec ions o s eng hening he U-shaped b idge wi h
cu ed gi de s which was buil in V aˇ
zn´
e in 1928 acco ding o p ojec documen a ion [23].
Figu e 8: An example o he ancho age a eas made di ec ly in he
exis ing conc e e o he main gi de s o U-shaped b idge. The
s eng hening was implemen ed in 2002, so he old ype o ancho s
was used [21].
Ad ances in Ma e ials Science and Enginee ing 5

p olonga ion o he conc e e s uc u e esis ance
agains co osion.
(4) Mos cons uc ion wo ks connec ed o his ech-
nology can be c ea ed wi hou in e up ion o he
affic on he b idge o only wi h a pa ial limi a ion.
(5) When we s eng hen b idges by p es essing, we use
he en i e p es ess le el in e al. In he case o beam
b idge s eng hening, he in e al usually achie es
alues o λ�0.15∼0.25 (in acco dance wi h Bach-
mann [25]).
(6) Fo b idges seemingly i epa able due o hei s a ic
condi ion, o i he eques ed load-bea ing capaci y
canno be achie ed wi h o he me hods, and when
he b idges a e usually demolished and a new
s uc u e is buil , he equi ed pa ame e s can be
achie ed using his e y me hod o load-bea ing
capaci y inc ease o a me e hi d o hal o he p ice
o he new s uc u e [26].
The ac ual design and pe o mance o s eng hening
mus emphasize he ac ha he s a ic s eng hening is
usually a pa o a o al econs uc ion and o e ofi ing o
he b idge. I mus c ea e p e equisi es o eliabili y and
du abili y o he selec ed design. Tha is why he below
men ioned measu es ha e o be conside ed and p oposed:
(1) A ho ough ea men o he deg aded conc e e o
he en i e b idge (su ace a eas including he plas e ),
fi s mechanically and hen using a o a ing high-
p essu e wa e je .
(2) Ca e ul cleaning o he exposed and co oded s eel
ein o cing ba s in he en i e b idge s uc u e, fi s
mechanically and hen wi h a high-p essu e wa e
single-je ool.
(3) P o ec ion o he s eel ein o cing ba s wi h silica e
ma e ials.
(4) The ac ual pos - ensioning o he b idge s uc u e by
bo h ans e o p es essing and by he composi e
slab.
(5) Applica ion o he adhesion p ime coa on he
whole su ace o he e ofi ed conc e e o he
b idge.
(6) Rough and finish ep ofiling o he b idge load-
bea ing s uc u e.
(7) Applica ion o a p o ec i e and uni ying coa ing on
he inne and uppe a eas o he U-shaped gi de s.
3. S a ic E ec o P es essing Cables in
S eng hening by Pos -Tensioning
S a ic effec o p es essing cables, addi ionally buil in o he
o iginal ein o ced conc e e s uc u es, is basically he same
as he effec o a p es essing ein o cemen in egula
p es essed conc e e [27]. This is achie ed because he
pos - ensioned cables a e buil in o he c oss sec ion o
s eng hened s uc u es using he subs i u e cable duc s in a
manne simila o he new, mos ly ully p es essed s uc-
u es. The e a e almos no diffe ences in he se ice s age; in
his case, adial effec s o he addi ionally buil -in p e-
s essing se mani es hemsel es posi i ely, while he a-
o able effec o he ac ual p es essing o ce mani es s i sel
as well, bu no so clea ly. This is gi en by small, bu su -
ficien p es essing deg ees λ�0.12∼0.25 [25]. In he s age
o ul ima e limi s a e, he main diffe ence lies in he ac ha
cables composed o monos ands appea o be ee (wi hou
cohesion wi h conc e e), e en i buil -in and injec ed in a
c oss sec ion. Howe e , he ul ima e limi s a es inc ease as
well by he e y addi ional effec o p es essing o ces,
which ans e he o me sec ions in pu e bending o
sec ions in eccen ic comp ession [28].
3.1. Dec ease o Dead Weigh Effec s. The basic s a ic
unc ion o hus designed beam b idge s eng hening is
shown in Figu e 11. I is depic ed on a simple s uc u e, and
he used app oach can be analogically ex ended o a
con inuous s uc u e as well. The adial effec o addi ional
Figu e 10: Realiza ion o he addi ional ancho age a eas o bo h
main gi de s and c oss gi de s. In his implemen a ion, a new ype
o encapsula ed single-s and ancho s was used (2008). The an-
cho s a e co e ed and p o ec ed in conc e e ex ensions [23].
Figu e 9: P es essing endons composed o indi idual mono-
s ands (black HDPE shea hs) on he bo om side o he gi de a e
cu a u e o hei ajec o ies in saddles [21]. A e he p es essing
o endons, he bo om side o he gi de is p o ided wi h he
ancho ed p o ec i e conc e e co e laye ( he second co osion
p o ec ion). The appea ance and he conc e e cha ac e o he
b idge a e hen p ese ed.
6Ad ances in Ma e ials Science and Enginee ing
cables leads o a dec ease in he effec o he dead weigh .
The e o e, he LBM (load balancing me hod) is sub-
sequen ly applied [27].
The beam b idge s uc u e is loaded by i s own weigh g0,
o he pe manen load g1(long- e m li e load, he weigh o
all laye s o he oadway wi h possible addi ional load by he
aised and o e -laye ed oadway), and li e load q. The li e
load is usually de e mined as he load-bea ing capaci y o he
b idge in acco dance wi h he ele an echnical s anda d
be o e he beginning o he e ofi ing p epa a ions [29].
The load-bea ing capaci y o a b idge is defined he e; i is
de e mined by he ollowing alues: no mal load-bea ing
capaci y Vn, ese ed load-bea ing capaci y V , and an ex-
cep ional load-bea ing capaci y Ve. In acco dance wi h he
espec i e echnical s anda d, a bending momen o ul ima e
limi s a e can be de e mined o he c i ical sec ions o he
s uc u e (i.e., he limi , o which he sec ion can be loaded in
o de no o exceed he maximum load on conc e e and s eel,
se by he s anda d) [30].
Figu e 11 shows which pa o he bending momen o
he ul ima e limi s a e can be used o he momen o
de e mining he load-bea ing capaci y o he b idge. The
load decisi e o he load-bea ing capaci y o he b idge
be o e s eng hening can cause he highes bending momen
Mq, and i s o al effec is inc eased by he dynamic co-
efficien o a mo ing load δ. In acco dance wi h calcula ions
and s udies o se e al dozens o beam b idges buil be ween
1915 and 1950, he load-bea ing capaci ies o he o iginal
b idges come ou o be e y low. No mal load-bea ing ca-
paci ies Vna e be ween 8 and 15 , and ese ed load-bea ing
capaci ies V usually cons i u e 15 o 30 , exp essed wi h
ega d o he momen o bending momen o ul ima e limi
s a e; 1/4 o 1/3 o a bending momen o an ul ima e limi
s a e o a sec ion can be used o he load-bea ing capaci y. In
he case o o e filled b idges, i.e., b idges, whose oadway
was simply aised wi h o he laye s o asphal conc e e in he
pas , his numbe can be e en lowe , o en 1/10 o 1/4 o he
bending momen o ul ima e limi s a e. We can o en en-
coun e pa adoxic si ua ions, in which he en i e momen o
ul ima e limi s a e can be consumed by he weigh o he
b idge i sel , o he limi can be e en lowe . In e ms o
calcula ions, such a s uc u e canno e en ca y i s own
weigh . I is clea ha a collapse will no occu because o he
in e nal ese es in he ma e ials and sec ions, bu he
s uc u es exploi ed in his way hen lack he sa e ies
gua an eed by s anda ds and e en a egula affic o e loads
hem and all he ela ed nega i es ensue (sagging, c acks, and
ib a ion). This leads o a dec ease o li e ime o such
o e loaded s uc u es.
As shown in Figu e 11, bending momen effec s o sui ably
designed pos - ensioning efficien ly dec ease bending momen s
om pe manen load. The ollowing in e se p opo ion applies
o he bending momen s ess de e mining he load-bea ing
capaci y o he b idge: he dec ease o bending momen effec s o
pe manen loads (g0, g1) caused by bending momen s since
p es essing MPis in e sely p opo ional o he po ion o he
o al bending momen o he ul ima e limi s a e which can be
used. E en wi h a small le el o p es essing, he bending
momen gain o hus-s eng hened s uc u es is significan and
many imes la ge po ion o he bending momen o ul ima e
limi s a e han be o e s eng hening can be used o he de-
e mining bending momen s o he ul ima e limi s a e a e
s uc u e p es essing. I can be s a ed ha
MRd,new �(2∼3)MRd,old,(1)
whe e MRd,new is he la ges momen de e mining he
load-bea ing capaci y o s uc u es s eng hened wi h
p es essing, MRd,old is he la ges momen de e mining
load-bea ing capaci y on he o iginal, nonp es essed
s uc u e.
I he usable momen s MRd,new a e s eng hening a e
mul iple imes la ge han momen s MRd,old be o e
s eng hening, he load-bea ing capaci y o hus-s eng h-
ened beam b idges inc eases as well. The load-bea ing ca-
paci y can commonly be inc eased by 200 o 300% in
compa ison wi h he o iginal alues be o e s eng hening.
Slab b idges we e also s eng hened, and in hei case, 10
imes highe no mal load-bea ing capaci y alues and 6
imes highe ese ed load-bea ing capaci y ha e been
achie ed.
PP
PP
P
P
Mg0+g1
Mg0+g1 + MP
Mg0+g1 + MP
MRd,new
MRd,new
MRd,old
MP
MPMRd,old
Mg0+g1
+
=
δMq
δMq
q
q
g0 + g1
A e s eng hening
Be o e s eng hening
Figu e 11: The basic scheme o p es essing s a ic effec on he
simple span b idge ( educ ion o dead load bending
momen s—applica ion o LBM). P es essing c ea es a much bigge
ese e o bea ing capaci y which can be used o affic load, and
he e o e, he load-bea ing capaci y is inc eased. The efficiency o
his me hod is up o 300%.
Ad ances in Ma e ials Science and Enginee ing 7
3.2. Sec ion Load-Bea ing Capaci y Inc ease. Axial compo-
nen o p es essing o ce has a mino effec upon eal
sec ion s eng hening and he e o e on he inc ease o he
bending momen o he ul ima e limi s a e. In acco dance
wi h Figu e 12, he sec ion o iginally in pu e bending
changes o a sec ion in eccen ic comp ession, which is
accompanied by an expansion o he comp essed a ea o
conc e e sec ion x. This ac causes a mino inc ease in he
bending momen o ul ima e limi s a e in acco dance wi h
Figu e 13.
P io o s eng hening, he ben b idge beam sec ion is
cha ac e ized by a pai o in e nal o ces N�0;M�MRd,old.
In acco dance wi h he size o he momen Min effec , i s
cu en s ess can be exp essed only on he ho izon al axis o
he ailu e unc ion π. A e s eng hening, s essing o ce Pis
ans e ed in o he sec ion. In acco dance wi h he achie ed
deg ee o p es essing λ,any ho izon al line in he ma ked
a ea inside he ailu e unc ion πapplies o he s eng hened
sec ion. The in e sec ion o his line and he ailu e unc ion π
is gi en by he pai N�P;M�MRd,new. The ollowing
s a emen mus apply o e e y ho izon al line in he ma ked
a ea ( hus o e e y nonze o P) on he basis o shape o he
ailu e unc ion π:
MRd,new >MRd,old,(2)
whe e Pis a p es essing o ce ans e ed by pos - ensioning
du ing s eng hening, MRd,old is he sec ion bending mo-
men o ul ima e limi s a e p io o s eng hening, and
MRd,new is he sec ion bending momen o ul ima e limi
s a e a e s eng hening wi h p es essing o ce P.
Inc ease o heigh o he comp essed a ea xo he
s eng hened sec ion inc eased he ideal momen o ine ia
a ound he mos s essed sec ions. Theo e ically, his leads
o a dec ease in s uc u e sagging ( he s uc u e becomes
s iffe ), which was also expe imen ally measu ed and
confi med (pa ag aphs 5.1 and 5.2 o his a icle). A en ion
should be paid o he ac ha , o he used low le els o
p es essing, he mo emen o he neu al axis is ela i ely
small and he co esponding inc ease o he ideal momen
o sec ion ine ia is only 10 o 15% in compa ison wi h he
o iginal. We can ne e expec ull p es essing o he
sec ions. Thei de o ma ion beha io a e s eng hening is
basically he same as be o e (c ack openings occu again in
he ensioned flange because o he o he , nonbalanced
po ion o pe manen loads and li e loads), bu hei wid hs
will dec ease and sagging will sligh ly dec ease because o
he effec o he li e loads.
I is clea ha e en in low le els o p es essing, he effec s
o beam b idge s eng hening a e significan . The load-bea ing
capaci y alues inc ease o mul iples o he o iginal alues a e
s eng hening. E en he me e dec ease o influence o he dead
weigh o he s uc u e ( o example, by emo ing he o e -
filled laye s o oadway), which also eleases a pa o he
bending momen o ul ima e limi s a e, can be su p isingly
used e y sca cely. The e ical alignmen o he oadway is
mos ly he decisi e ac o because i is gi en by he connec ion
be o e and a e he b idge. I s dec ease on he b idge causes
la ge and he e o e financially demanding modifica ions o
long s e ches o he oad. Alongside he beam s eng hening,
he b idge deck o en has o be s eng hened as well so ha i
could wi hs and he wheel p essu e o he ca s. Addi ionally
cas slabs, which can be efficien ly designed o he e y
s uc u e s eng hened by p es essing, can be used o his
pu pose because he inc ease o he dead weigh wi h an
addi ionally cas slab can be elimina ed by he e y pos -
ensioning.
The in en s o only inc ease he load-bea ing capaci y o
a b idge wi h minimum cos s because o he limi ed financial
means a e also equen . In such cases, his is a e y efficien
me hod because all he laye s o he o iginal oadway can be
kep on he s uc u e. The ac ha his s eng hening can be
pe o med unde almos no mal ope a ion o he b idge wi h
minimum demands upon affic limi a ion is also wo h
men ioning. Subs i u e cable duc s as well as saddles a e
mos ly c ea ed om he bo om pa o he s uc u e, usually
wi h no in e up ion o ope a ion o he b idge. The pe -
o mance o he ancho ing a eas and p es essing can be
pe o med g adually (one hal o he b idge a e ano he )
because he cha ac e o pos - ensioning using he sub-
sequen cable duc me hod is s uc u ally simila o he
assembled s uc u e.
3.3. Shea Fo ces Reduc ion. Simila ly, he shea o ces a e
efficien ly educed by p es essing. The educ ion is
depic ed in Figu e 14. The sec ion abo e includes an
example o a ypical basic cou se o shea o ces o
pe manen loads and a load co esponding wi h he Vn
se . The middle sec ion desc ibes a cou se o shea o ces
om p es essing which has he opposi e sign. The
esul ing educed cou se o he shea o ces is s a ed in
he sec ion below. The la ge is he dis ance be ween he
saddle and he suppo , he smalle is he angle o he
cable agains he axis o he beam and he smalle a e he
shea o ces, which a e able o educe he o iginal shea
o ces and which a e affec ed by he p es essing cable.
F om he s andpoin o he shea o ces, i would be
be e o c ea e saddles close o he suppo ; om he
s andpoin o bending momen , i would be be e o he
saddles o be as a away om he suppo as possible.
E en hough he specific design depends on many o he
ac o s o s uc u es gene ally e y di e se in e ms o
dimensions and composi ion, he esul s o as-ye
designed and ealized s eng henings lead o a disco e y
ha he ideal dis ance o dis ibu ion o saddles in a
leng h is in he in e al om 1/5 o 1/4. This applies o
bo h simple and con inuous s uc u es [31].
S uc u es wi h haunches equi e special a en ion. I he
haunches a e linea , hen he beginnings o haunches mos ly
co espond o he abo emen ioned ecommenda ion. In he
subs i u e cable duc me hod, he saddles can be placed in
he haunch ends. I he haunches a e longe ( o example,
pa abolic haunches o en each l/3), i is necessa y o use
sepa a ely cas blocks be ween beams and place hose in he
ecommended spaces.
8Ad ances in Ma e ials Science and Enginee ing
4. Diagnos ics, Design, and S eng hening
Pe o mance P ocess
4.1. Diagnos ics o he Cu en B idge S uc u e. In he di-
agnos ics o b idge s eng hening, i is necessa y o de-
e mine he ollowing:
(i) Rein o cemen o he cu en sec ions o beams,
c oss gi de s, and slabs in he cen e o hei leng h,
o abo e he suppo s o he con inuous s uc u e.
I is necessa y o de e mine he amoun , diame e ,
and loca ions o he indi idual ein o cemen
p ofiles including spaces be ween hem as he
sou ce da a o decision whe he he subs i u e
cable duc me hod can be used.
(ii) Rein o cemen o he cu en sec ions o beams,
c oss gi de s, and slab in suppo s. I is necessa y o
de e mine he amoun , diame e , and loca ions o
he indi idual ein o cing p ofiles in o de o de-
e mine he numbe o aised shea ein o cemen .
The aised shea ein o cemen (ben p ofiles) can
be swung ou om he e ical plane, and hey can
pa ially in e sec wi h he ajec o y o he sub-
s i u e cable duc . Tha is why i is be e o selec
hose spaces be ween ein o cemen s which a e no
immed wi h bends. In b idge slabs, i is necessa y
o de e mine how much ein o cemen is aised in
he suppo ; his usually cons i u es 1/3 o 1/2 o he
o al amoun o p ofiles.
(iii) S eng h o he conc e e o he load-bea ing
s uc u e a leas wi h nondes uc i e impac
me hod (Schmid ) wi h specifica ion using es co e
d illing. The NDT i sel is no sufficien because, in
olde s uc u es, i usually p o ides conc e e
s eng hs o one o wo classes highe han he final
ones a e specifica ion. The pe missible s ess o
conc e e unde ancho s has o be de i ed om he
de e mined s eng hs. The conc e e s eng h sig-
nifican ly code e mines he bending momen o
ul ima e limi s a e o he cu en sec ion.
(i ) The conc e e elas ic modulus has o be de e mined
i a e ifica ion o beha io o he b idge s uc u e
a e s eng hening wi h a s ess es can be ex-
pec ed. In he case o his o ical b idge cons uc-
ions, he modulus o elas ici y a ies depending on
he possibili ies o conc e e p oduc ion a ha ime
and especially on he placing, p ocessing, and
compac ing o he conc e e mix u e. In p ac ice o
+
=
A e s eng hening
Be o e s eng hening
Vg0+g1 + VP
Vg0+g1
VP
Figu e 14: The basic scheme o educ ion o shea o ces due o he
adial effec s o p es essing cables in polygonal ajec o y in he
case o s eng hening he simply suppo ed beam acco ding o
Figu e 11.
Mg0+g1 + δMq
Xold
MRd,old
Cg
(a)
Mg0+g1 + δMq
P
MRd,new
Xnew
MP
Cg
(b)
Figu e 12: Exp ession o he p es essing effec on he beam s uc u e c oss sec ion. The beam c oss sec ion and i s in e nal o ces (pu e
bending) (a) be o e and (b) a e applica ion o p es essing o ce. The c oss sec ion is now eccen ically in comp ession (a combina ion o
bending momen s and axial o ce), hus inc easing he load-bea ing capaci y o he c oss sec ion.
P
N (kN)
M (kNm)
λ = 0.10~0.25
[N = P; MRd,new]
∏ = [NRd; MRd]
[N = 0; MRd,old]
Figu e 13: Inc ease o he load-bea ing capaci y o he c oss sec ion
in he in e al o pa ially p es essed conc e e λ�0.12∼0.25
exp essed by he in e ac ion diag am ( ailu e unc ion π[25]).
Ad ances in Ma e ials Science and Enginee ing 9
(a)
(b) (c)
Figu e 21: S a ic load es o he U-shaped b idge buil in 1928 a e s eng hening [23]. The posi ion o hea y ehicles ( ehicles on and
ea axles) in he longi udinal and ans e se di ec ions is desc ibed on he pic u es.
0.5 1 1.5 20
Time (hou )
–1
–0.5
0
0.5
1
De o ma ion (mm)
1s es 2nd es
Tes load: 2 × 20 onnes
Figu e 25
T2- igh gi de
(a)
−4
−2
0
2
4
De o ma ion (mm)
02468
Time (hou )
P es essing o he igh gi de
Sign con en ion:
+ = sag, − = hog
To al o ce = 784kN
T2- igh gi de
(b)
Figu e 22: Con inued.
16 Ad ances in Ma e ials Science and Enginee ing

0.5 1 1.5 20
Time (hou )
–1
–0.5
0
0.5
1
De o ma ion (mm)
1s es 2nd es
Tes load: 2 × 20 onnes
Figu e 25
T2- igh gi de
(c)
Figu e 22: G aphs o he igh gi de (see senso T2 in Figu e 20) deflec ions (a) be o e s eng hening (s a ic load es wi h wo load
cases—hea y ehicles), (b) du ing p es essing, and (c) a e s eng hening (s a ic load es wi h an iden ical load be o e s eng hening).
0.5 1 1.5 20
Time (hou )
1
0
–1
2
De o ma ion (mm)
1s es 2nd es
Tes load: 2 × 20 onnes
Figu e 26
T3-c oss gi de
(a)
24680
Time (hou )
−4
−2
0
2
4
De o ma ion (mm)
P es essing o he c oss gi de
Sign con en ion:
+ = sag, − = hog
To al o ce = 392kN
T3-c oss gi de
(b)
Figu e 23: Con inued.
Ad ances in Ma e ials Science and Enginee ing 17
show examples om an ex ensi e se o measu ed saggings
and hoggings du ing p es essing and du ing he load es
using he wo es ehicles [23].
Wi hin he e alua ion o he s eng hening effec , he
measu ed alues we e a e aged. The summa y o he
esul ing alues is s a ed in Figu e 24. On he basis o he
measu ed da a, s eng hening o he load-bea ing elemen s
o he U-shaped b idge can be e alua ed as ollows:
(1) Main gi de s s eng hening: he change o in e nal
o ces, which led o an inc ease o load-bea ing
capaci y o he main gi de s, and he e o e he
en i e b idge, will mani es i sel in he hogging o
he main gi de s and in he a io o he measu ed
sagging be o e and a e s eng hening. Du ing
p es essing, he main gi de s ha e hogged (ben
upwa d) by 2.4 mm. In he absolu e alue, his alue
is a 4.6x highe posi i e de o ma ion effec han he
effec caused by wo Ta a ehicles weighing 2 ×22 .
This p o es he high efficiency o he pe o med
s eng hening.
(i) A e s eng hening, he measu ed sagging o he
main gi de s loaded by iden ical ehicles has de-
c eased o 86% o sagging be o e s eng hening
(Figu e 25). This p o es he ein o cemen o he
main gi de s achie ed by he pe o med s eng h-
ening. This is he p oo o inc ease o de o ma ion
s iffness o main gi de s, e en i a a low le el o
p es essing (λ�0.14)[25].
(2) C oss gi de s eng hening: he change in in e nal
o ces has also mani es ed i sel in he a io o
measu ed sagging be o e and a e c oss gi de
s eng hening. The c oss gi de s hogged (ben
upwa ds) by 3.0 mm du ing he p es essing. In he
absolu e alue, his alue is a 2.4x highe posi i e
de o ma ion effec han he effec caused by wo
Ta a ehicles weighing 2 ×22 . This is also an
example o he high s a ic efficiency o he pe -
o med s eng hening.
A e s eng hening, he measu ed sagging o he c oss
gi de s loaded by iden ical ehicles has dec eased o 91% o
sagging be o e s eng hening (Figu e 26). This once again
p o es he c oss gi de ein o cemen achie ed by he
pe o med s eng hening. This is he p oo o inc ease o
de o ma ion s iffness o c oss gi de s, e en i a a low le el o
p es essing (λ�0.12)[25].
Deflec ions o he U-shaped b idge s uc u e (mm)
Pa o he s uc u e
Be o e s eng hening
Du ing s eng hening
A e s eng hening
Ra io o a e age
deflec ions
a e /be o e
s eng hening
Main gi de T1 0.50 –2.60 –0.47 0.86
Main gi de T2 0.54 –2.20 –0.43
C oss gi de T3 1.75 –5.60 1.50 0.91
C oss gi de T4 1.78 –5.20 1.70
Figu e 24: Assessmen o deflec ions be o e and a e he
s eng hening o he U-shaped b idge in V aˇ
zn´
e, buil in 1928 [23].
No e: downwa ds +; upwa ds −.
0.5 1 1.5 20
Time (hou )
1
0
–1
2
De o ma ion (mm)
1s es 2nd es
Tes load: 2 × 20 onnes
Figu e 26
T3-c oss gi de
(c)
Figu e 23: G aphs o c oss gi de (see senso T3 in Figu e 20) deflec ions (a) be o e s eng hening (s a ic load es wi h wo load
cases—hea y ehicles), (b) du ing p es essing, and (c) a e s eng hening (s a ic load es wi h exac he same loading like be o e
s eng hening).
18 Ad ances in Ma e ials Science and Enginee ing
6. Recommenda ions o Design and
Pe o mance o S eng hening by Pos -
Tensioning
On he basis o al eady designed and ealized s uc u es and
on he basis o measu emen s pe o med du ing p es essing
and subsequen ly du ing s uc u e loading, he below
men ioned ecommenda ions ega ding design and he
ac ual pe o mance o he pos - ensioning using he sub-
s i u e cable duc me hod can be p o ided.
6.1. Values o P es essing Losses. I he cables used a e
composed o monos ands, he coefficien o ic ion de-
c eases significan ly. This is caused by he lowe ic ion o
he plas ic p o ec i e shea hs and he me al componen s o
he saddle and also by he g easing effec o he an ico osi e
passi a ing filling be ween he monos and wi es and he
p o ec i e shea h. The passi a ing filling con ains g ease o
pa affin wax, which limi s ic ion efficien ly. E en hough
he s anda d documen s s a e he alue o he coefficien o
ic ion in a bend o be 0.06 o cables composed in his way,
du ing p ac ical es s pe o med du ing ensioning o he
s eng hened b idges, he alue o 0.10 was de e mined. This
alue can be ecommended o his pos - ensioning sys em,
in which he monos ands indi idually lean on he saddle
ein o cemen [31].
Single-s and encapsula ed ancho sys ems a e used
egula ly in b idge s eng hening (e.g., [34]). The ancho ing
is pe o med using sel -locking h ee-jaw wedges in he
conical opening o he ancho . Du ing hei use, hei
slipping was measu ed a 2.60 mm o 2.90 mm while en-
sioning wi h he maximum o ces o 200 kN. In conside -
a ion o slipping losses, 3.0 mm can be conside ed a sa e
alue. In such a small size, he slipping each is no sig-
nifican and he slipping usually disappea s al eady a ound
he loca ion o he fi s saddle. This allows a design o
con inuous cables o e h ee o e en ou span leng hs o
con inuous s uc u es. Tensioning om bo h sides is used
o hese cables ( espec i ely, ensioning om one side o he
cable, and a e ancho ing, he cable is ensioned om he
p e iously non ensioned end), and in such case, ic ion
losses emain accep ably low a he cen e o he cable
(usually wi hin 15%).
The losses caused by he elas ic sho ening o conc e e
losses a e negligible. This is gi en by he low le el o p e-
s essing (a e age p es essing in he sec ion achie es 1.5 o
3.0 MPa) and he e o e also by he e y small elas ic de-
o ma ion o he conc e e and he en i e s uc u e du ing
p es essing. Because he numbe o ensioned cables is no
la ge, epea ed ensioning o al eady ancho ed monos ands
can comple ely exclude his loss e en in cases in which he
exclusion is no ad isable. Relaxa ion losses can be de-
e mined he same in a new s uc u e as om p es essed
conc e e. In egula cases, in which low elaxa ion mono-
s ands a e used almos exclusi ely, he losses can be dis-
ega ded [27].
Losses caused by conc e e sh inking can be comple ely
dis ega ded because du ing s eng hening, he p es essing
is being used on conc e e s uc u es 80 o 100 yea s old.
Only in he case o s eng hening o a combina ion o pos -
ensioning and an addi ionally cas composi e slab, he load
om p e en ed conc e e sh inking o a new slab should be
included in he calcula ion. Losses caused by conc e e
c eeping can be dis ega ded in mos cases as well. This is
Time
Be o e s eng hening
A e s eng hening
0
0.2
0.4
0.6
De o ma ion (mm)
Figu e 25: A compa ison o he measu ed deflec ions o he main
gi de be o e and a e he s eng hening wi h he same es
ehicles in he same posi ion on he U-shaped b idge buil in
V aˇ
zn´
ein 1928 [23].
Time
Be o e s eng hening
A e s eng hening
0
0.5
1
1.5
De o ma ion (mm)
Figu e 26: A compa ison o he measu ed deflec ions o he c oss
gi de be o e and a e he s eng hening wi h he same es
ehicles in he same posi ion on he U-shaped b idge buil in
V aˇ
zn´
ein 1928 [23].
Ad ances in Ma e ials Science and Enginee ing 19
caused by he low le el o ans e ed p es essing and he
dec ease o comp essi e s ess in he comp essed a ea o
he o iginal sec ions, which is achie ed by he e y bal-
ancing o a pa o pe manen load o he s uc u e. Al-
e na i ely, hey can be quan ified mo e specifically using
c eeping models used by sepa a ely de eloped compu e
p og ams o ime-dependen analysis o conc e e s uc u e
c eeping [36].
6.2. Recommenda ions o S uc u al De ails. As ega ds he
saddle adii, we ecommend obse a ion o he minimum
adius o �1.2 m and a c ea ion o haunches on he s eel
s ap wi h a minimum leng h o 150 mm and a adius o
� /4. Regula shee s eel saddles can ans e adial o ces
om one o ou monos ands wi hou la ge s uc u al
issues. The saddle shape should be adap ed wid h-wise o
he inse ion in o he cable duc . Saddle leng h should no be
smalle han 400 mm (wi hou haunches) o p ac ical
easons so ha i could e en be moun ed including he
equi ed ole ances. The same adii a e applied o ube
saddles. Tube saddles should be equipped wi h haunches in
he shape o a hollow cone [31].
The diame e s o d illed duc s a e supposed o be as small
as possible, e.g., ϕo 35 mm is sufficien o single-s and
cables and ϕo 52 mm is sufficien o mul is and cables up
o ou monos ands. In beam s uc u e s eng hening, i is
sui able o allow o weakening by in e up ion o one o wo
p ofiles o he o iginal ein o cemen in he s a ic design.
Cables wi h e en la ge numbe o monos ands a e used
a ely, and in such case, hey mus be placed ou side o he
sec ion (e.g., [6, 9]). De ia ions ha e o be p esc ibed o
duc d illing and o saddle moun ing, and he de ia ions
mus be ulfilled.
The design o addi ional conc e e co e s always has o
include ancho ing in o he o iginal s uc u e. Ancho ing
wi h me e cohesion canno be conside ed sufficien because
o empe a u e changes o he cables, elas ic sagging o he
s uc u e, e c. The co e ing laye also has o be ein o ced
wi h welded wi e mesh so ha he o ces would be dis-
ibu ed om he ancho s o he en i e co e ing laye .
7. Conclusion
The desc ibed me hod is sui able o ehabili a ion (inc ease
o load-bea ing capaci y, econs uc ion, and p olonga ion
o du abili y) o ein o ced conc e e U-shaped b idges,
which we e buil be ween 1905 and 1930 and he o iginal
s uc u e o which almos ende s o he s eng hening
me hods impossible. Efficien ly, he main beams and c oss
gi de s can be s eng hened, and in ha manne , he inc ease
o he dead weigh connec ed o he use o a composi e slab
o s eng hen he b idge deck can be balanced. The s a ic
s eng hening is significan , and i is accompanied wi h
inc ease o de o ma ion s iffness, which was p o en by he
pe o med load es s. In he case o U-shaped b idges, he e
is no o he op ion o effec i ely imp o e hei s uc u al
beha io wi hou affec ing appea ances o hese unique
his o ical conc e e s uc u es.
The p esen ed me hod o subs i u e cable duc s can also
be used o s eng hen o he ypes o conc e e b idges wi h
diffe en s a ic schemes and c oss-sec ional shapes. I can be
used o s uc u al secu ing o he p es essed b idges and
mason y aul s.
Da a A ailabili y
The da a used o suppo he findings o his s udy a e
a ailable om he co esponding au ho upon eques .
Disclosu e
This pape has been wo ked wi h he suppo o he p og am
Compe ence o Technology Agency o he Czech Republic
(TAˇ
CR) wi hin he Cen e o Effec i e and Sus ainable
T anspo In as uc u e (CESTI), P ojec No. TE01020168.
This pape has been c ea ed du ing he solu ion o Specific
Junio Resea ch FAST-J-19-5989 Analysis o e ifica ion
s a ic loading es s o ein o ced conc e e b idges
s eng hened by pos - ensioning.
Con lic s o In e es
The au ho s decla e ha hey ha e no conflic s o in e es .
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