an alternative proposal for the design of balanced cantilever bridges ...

IBSBI 2011, October 13-15, 2011, Athens, Greece
AN ALTERNATIVE PROPOSAL FOR THE DESIGN OF
BALANCED CANTILEVER BRIDGES WITH SMALL
SPAN LENGTHS
Ioannis A. Tegos 1 and Stergios A. Mitoulis 2
1,2 Aristotle University of Thessaloniki, Dept. of Civil Engineering, Greece
e-mail: itegos@civil.auth.gr, mitoulis@civil.auth.gr
ABSTRACT: In balanced cantilever structural method the prestressing is
utilised as means to control the strains and to reinforce the top flange of the
deck’s cross section at the supports. Ordinary strength reinforcements are
typically applied within the bottom flange of the deck, after accounting for the
unfavorable participation of the prestress. The last check is a critical one at the
balanced cantilever-method. Thus the use of ordinary reinforcements at the
bottom flange of balanced cantilevers, namely the avoidance of prestressing
tendons, seems to be an interesting design alternative which ensures a better
construction result. An analytical study on this design alternative had been
carried out for cantilever bridges of relatively small span lengths actually built
along the Egnatia Highway in Thrace.
KEY WORDS: Bridge; Balanced Cantilever; Small Span; Design; Ordinary
Strength Steel (OSS).
1 INTRODUCTION
Safety, serviceability, cost-effectiveness, aesthetics and particular technical
issues are typically the controlling factors in the selection of the proper bridge
type [1] [2] and construction method. In many cases, a prestressed bridge is a
cost-effective choice. Typically, segmental concrete bridge construction is
utilized, which is the most common method of bridge construction.
Segmental construction method typically introduces: (a) the conventional castin-situ
bridge construction, (b) the precast prestressed I-beam deck construction
with continuous cast-in-situ slab decks, (c) the balanced cantilever bridge
construction, which either utilises scaffolding or precast deck segments and (d)
the progressive and span by span incrementally launched bridge construction.
Segmental cast-in-situ bridge construction is preferable in case of straight and
curved in plan bridges with relatively small bent heights and when prestressing
is applied in the longitudinal direction of the superstructure, as shown in Figure
1. The formworks are typically supported directly to the ground or to a well
compacted temporary embankment. In most cases, the first span and a 15 to

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20% of the length of the second span are casted together. The construction of
the next bridge segment follows after the application of the prestressing force,
while keeping the immediate prestress losses within normal levels. The final
loading of the bridge due to the self-weight of the superstructure is varying with
time due to the influence of the creep effect [3] [4].
A new bridge construction method is investigated in this paper. The method has
similarities with the balanced cantilever method. The connection of the
cantilevers is achieved by the use of tendon couplers. The tendons are straight
and the scaffolding, which is used for the deck casting, is removed after the
application of the prestressing force. The applicability of the proposed
construction method has been attempted to a cast-in-situ benchmark bridge
actually built along a major motorway that runs across Northern Greece.
2 THE PROPOSED CONSTRUCTION METHOD
2.1 Structural assumptions
The proposed structural method, which can be utilised for the construction of
cast-in-situ bridges, is based on the following structural assumptions: (a) The
deck cross section has a variable height along the longitudinal direction of the
bridge with a symmetrical bottom flange, which is modulated by a polygonal
shape inscribed in a parabolic arch, as shown in Figure 1. The cross section of
the deck can be either a box girder or a voided slab. (b) The prestressing
tendons are straight and continuous in all the deck spans and they are installed
in the top flange of the deck. The appropriate concrete cover [5] [6] is provided
to protect the tendons against corrosion. Within the bottom flange of the deck
only ordinary strength steel is utilised. (c) The construction of the end spans can
follow two different design alternatives: (c1) The first alternative introduces the
construction of the end spans by maintaining the geometry of the intermediate
spans for reasons of aesthetics. In that case, the deck is chosen to be seated on a
wall-like abutment web, as shown in Figure 1 and 2. (c2) The second design
alternative introduces the construction of the end spans with lengths smaller
than the ones of the intermediate ones. Half of the length of the end span has a
deck cross section with variable height. This corresponds to the part of the deck
which extends from the end pier towards the abutment. The other part of the
span is seated through bearings to the abutment, as shown on the right abutment
of Figure 1. It extends from the abutment towards the pier and has a constant
cross section height. The need for the smaller length of the end spans was found
to be dictated by the relatively small height of the deck cross section that is 0,80
m and by the use of ordinary reinforcements in the bottom fibre of the deck.
It is noted that the use of prestressing within the bottom flange of the deck was
not deemed to be a rational design selection, as the tendons would induce a
large vertical load downwards, due to the variation of the height of the deck
cross section. This constraint loading, namely the one induced by possible

I.A. Tegos and S.A. Mitoulis 3
negative prestressing, would not be compatible with the rational use of tendons,
which are typically utilised in order to compensate for the vertical loading.
a-a
a
a
h2=0,80m
h1=2.20m
A1
bearing
b-b
a
a
P1
b
b
c-c
centre of gravity
of the deck
c
c
A2
h3=0,80m
Figure 1. The first stage of the proposed construction method with alternative abutment
configurations.
2.2 Particular design issues
Τhe rigid connection of the deck with the abutments was achieved by the
construction of a counterbalance that is a cantilever which extends from the
abutment towards the backfill soil, as shown in Figure 1 and 2. The length of
this cantilever is 5,0 m and its cross section height reduces from the abutment to
the backfill. The end cross section of the cantilever is utilised for the anchorage
of the tendons. The tendons are slightly lowered at their anchorages in order to
provide the appropriate cover for their anchoring devices, namely the bearing
plates. A structural tie, namely a reinforced concrete wall with a thickness of
0,30 m, is utilized in order to receive the bending moments of the
counterbalance-cantilever, which are developed due to the vertical loading of
the deck. In fact this wall, namely the structural tie, is under tension, while the
abutment web, which receives the vertical loading through the bearings, is
under compression. The structural tie has a transverse dimension equal to the
distance between the wing walls, with which it is in contact but not connected.
The reinforcement bars of the structural tie are anchored in the pile cap of the
abutment’s foundation. This pile cap has a relatively small thickness, as the
wing walls and the wall that retains the backfill soil formulate a stiff concrete
“box”, which increases the stiffness of the pile cap. In case the web is integral
with the deck, its in-service constrained movements can be accommodated by
subdividing it in walls.
c
c

4 Proceedings IBSBI 2011
backfill
inspection
opening
retaining
wall
lowered
tendons
counterbalance
cantilever
structural
tie
pile cap
(Detail)
straight
tendons
bearing
450mm
Detail
Figure 2. The abutment of the proposed construction method.
2,75
R=30m
2,75
R=30m
150mm
The minimum height of the deck cross section is proposed to be not smaller
than 0,80 m. After the curing of the casted cantilevers, the tendons are stressed.
The design of the prestressing force is based on the objective of the method that
is to provide a slight pre-cambering of the cantilevers that is a slight bending
deflection upwards. Therefore, at this stage the cantilevers of the deck are set
higher than the final design height of the bridge. After the application of
prestressing, the steel formwork is removed and the construction procedure is
repeated for the adjacent spans. The tendons of the subsequent spans are
coupled with the ones of the casted cantilever and the adjacent cantilever is
constructed. A detailed description of the prestressing application and the rebar
of the deck is given in section 3 of the paper.
After the completion of the deck construction and the application of the
prestressing force, positive bending moments, which are caused due to the
eccentricity of the straight tendons from the deck’s centre of gravity, are
induced along the deck. These positive bending moments overbalance the
negative ones that are imposed by the self-weight of the deck. Hence, the
aforementioned pre-cambering of the cantilevers is achieved. The precambering
was deemed necessary in order to compensate for the pre-determined
long-term prestress losses due to the creep and shrinkage of the deck and due to
the relaxation of prestressing steel. The rest of the vertical loads of the deck that
are the additional permanent and the variable loading [7] are imposed after the
completion of the total bridge system. Thus, the frame action of the total bridge
structure, in which the meeting cantilevers are connected, receives the
additional vertical loading. The final bridge system is then checked against the
resulting bending moments, the shear actions and the torsion effects after
considering the re-distribution of actions. In particular, the design of the deck
against shear actions is facilitated due to the beneficial inclination to the
horizontal of the compression zone of the deck in the critical section for shear,
namely where the maximum shear stress is acting. Possible deficiency of the
deck at the supports against the bending moments caused by either the ultimate
or the serviceability limit states [6] [8] shall be covered by additional

I.A. Tegos and S.A. Mitoulis 5
reinforcement bars of ordinary strength steel. The additional reinforcements
cover the safety criteria set by codes [6] [8] and the serviceability requirements
by limiting the crack width according to the code provisions [5] [6].
3 APPLICATION OF THE CONSTRUCTION METHOD TO A
CAST-IN-SITU BRIDGE
3.1 Description of the benchmark bridge
The bridge of Kleidi-Kouloura belongs to Egnatia Motorway that runs across
Northern Greece. It is a cast-in-situ structure with a total of three spans and a
total length equal to 135.8 m. More details on the bridge are given in an another
paper of IBSBI 2011 conference.
3.2 Results
The benchmark bridge was re-analysed and re-designed according to current
code provisions concerning serviceability [6] [8] and earthquake resistance [9].
The re-design took into account the construction phases of the proposed method
and the following predominant design parameters were revealed:
(1) The required number of straight tendons was less than the one needed in
case a classification category A or B was chosen, (table 4.118 in [6] [8]).
However, the total number of tendons ensures that the bridge is classified in
category C, when this requirement refers to the performance of the top fibre of
the deck, while the use of ordinary strength reinforcements in the bottom fibre
of the deck leads to the classification category D. It is noted that, the design of
the prestressing force and the resulting number of tendons aims at providing the
required pre-cambering of the cantilevers against the self weight of the bridge
deck, whose length was half of the total span length that is 45,60/2 = 22,80 m.
(2) The re-design of the prestressing showed that 15x19T15 (15 tendons of 19
wires with diameter 15mm each) of high strength steel St 1500/1770 are
adequate to receive the bending moment of the deck above its support.
Additionally, ordinary steel rebar 76Ø16 (76 bars with diameter 16mm each)
above the support were utilized, which gradually reduced to 28Ø16 at the bridge
mid-span. The tendons and the reinforcements needed in the top flange of the
deck are illustrated in Figure 3. The ordinary strength steel bars, which are also
required by the code [6], are the ones which allow the safe transition from the
uncracked to the cracked deck section and the avoidance of non-ductile failure
modes. The lengths of the steel bars were chosen to be sub-multiples, namely
half, of the conventionally produced ones by the steel manufactures in order to
avoid material waste. Figures 4 and 5 show in detail the reinforcement layout at
the support and at the mid-span. Figure 6 shows the steel rebar of the bottom
part of the deck. The bars are installed in couples that are 2x71Ø25 (71 couples
of bars with diameters 25mm each) at the mid-span, while 2x41Ø25 were found
to be required at the bottom flange of the deck at the supports. The

6 Proceedings IBSBI 2011
reinforcement splices were required to extend 2,15 m. The lengths of the bars
were selected to be 7,0 m and they were set parallel to the sides of the polygonal
shape of the bottom flange, as shown in Figure 6. (4) The thickness and the
reinforcement of the structural tie, that is the wall that restrains the vertical
movements of the counterbalance-cantilever at the abutment shown in Figure 1
and 2, were found to be 0,30m and 3xØ16/100 (3 lines of bars with diameter
16mm at a spacing 100 mm) correspondingly.
Y
X
28O16
L=14,0m
couplers
52O16
L=7,0m
Pier
76O16
L=14,0m
tendons 15x19T15 (St 1500/1770)
52O16
L=7,0m
28O16
L=14,0 m
lapping
3,50 m
Figure 3. The layout of the straight tendons and the ordinary strength steel bars of the deck’s top
flange at the support, (the scale is distorted: 1 unit at X equals 2 units at Y axis).
1,00
Pier
7,00 7,00
8,50 5,50
5,50 8,50
L=14,0 m
tendons
Figure 4. Detail of the straight tendons and the ordinary strength steel bars of the deck’s top
flange at the support.

I.A. Tegos and S.A. Mitoulis 7
7,00
14,00
couplers
tendons structural joint
Figure 5. Detail of the ordinary strength steel bars of the deck’s top flange at the mid-span and
coupling of the tendons.
2,0-2,50m
pier
top flange
7,0m
2X41Φ25
polygonal
bottom
flange
straight tendons
15x19T15 (St 1500/1770)
2,15m
7,0m
2X51Φ25
splicing
length
7,00
7,0m
lapping
3,52
~4,50m
corners of the polygon
d=150mm d>150mm
2X51Φ25
2X61Φ25
l=35,0-50,0m
Figure 6. Detail of the ordinary strength steel bars at the bottom flange of the deck.
2X71Φ25
mid-span
structural joint
4 CONCLUSIONS
This paper proposes a new bridge construction method, which can be used as a
design alternative to the conventional construction practices. The method has
many similarities with the balanced cantilever method. The prestressing tendons
are straight and installed within the top flange of the deck cross section, while
ordinary strength steel is utilized for the reinforcement within the bottom
flange. The deck has a variable cross section height along its longitudinal
direction. A benchmark bridge, actually built along the Egnatia Motorway by
the conventional segmental cast-in-situ method, was utilized to identify the
applicability of the proposed method. The bridge was checked according to the
current code provisions and the study came up with the following findings:
• The application of the proposed construction method revealed significant
structural benefits. The use of straight tendons for the prestressing of the
deck facilitates and accelerates the construction of the bridge. The tendons
are installed within the upper slab of the deck’s cross section, which is more
preferable than using tendons which are installed in the webs of the box
girder. It is noted that the use of tendons in the webs of the box-girder decks
is not allowed according to current code design, at least for bridges
constructed by the balanced cantilever method. Furthermore, the prestressing
losses due to friction are significantly reduced when the proposed

8 Proceedings IBSBI 2011
construction method is employed. The dead load of the bridge deck, which
typically constitutes the largest portion of the bridge’s vertical loading, is
decreased due to the reduction in the height of the deck cross section.
However, the variation of the deck cross section along the bridge deck
obstructs the falsework as the scaffolding is more demanding in terms of
geometry, compared to the conventional segmental bridge construction.
• The bridge aesthetics are significantly improved compared to the
conventional segmental bridge construction. This is due to the refined archtype
view of the bridge constructed by the proposed method and the reduced
deck cross section height.
• As far as it concerns the cracking of the deck, the proposed construction
method can be utilized for the construction of bridges with short to medium
spans up to 35 m. The check against cracking due to the short term vertical
loading of the deck, namely against the infrequent loading, showed that the
deck does not exhibit cracking. In case of bridges with longer spans up to
50m the use of partial prestress shall be used.
• The deflections of the deck were significantly reduced due to the objective
set during the design of the prestressing force, which ensured that the
cantilevers had a pre-cambering upwards, at least when the scaffolding was
removed.
• Possible differential settlements of the piers can be received by the resulting
bridge system without developing high bending loading to the deck, due to
flexibility of the arch-type superstructure.
REFERENCES
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[2] Chen WF and Duan L, Bridge Engineering Handbook, CRC Press Boca Raton London, New
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[3] Trost H., Lastverteilung bei Plattenbalkenbrucken, Werner Verlag, Dusseldorf, West
Germany, 1961.
[4] Kwak H-G and Son J-K, “Determination of design moments in bridges constructed with a
movable scaffolding system (MSS)”, Computers and Structures, Vol. 84, Issue 31-32, pp.
2141-2150, 2006.
[5] EN 1992-1-1:2004 Eurocode 2: Design of concrete structures, Part 1-1: General rules and
rules for buildings, 2004.
[6] DIN-Fachbericht 102, Betonbrücken, DIN Deutsches Institut fuer Normung e.V, 2003.
[7] EN 1991-2:2003 Eurocode 1: Actions on structures - Part 2: Traffic loads on bridges, 2003.
[8] EN 1992-2:2004 Eurocode 2: Design of concrete structures-Part 2: Bridges, 2004.
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2005.