IBSBI 2011, October 13-15, 2011, Athens, Greece

 

AN ALTERNATIVE PROPOSAL FOR THE DESIGN OF BALANCED CANTILEVER BRIDGES WITH SMALL

SPAN LENGTHS

Ioannis A. Tegos1 and Stergios A. Mitoulis2 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 cast-in-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.

h1=2.20m

h2=0,80m

P1h3=0,80m

A1

centre of gravityof the deck

a

a-a

b

ba

aa

b-b

cc

c-c

bearing

A2cc

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.

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pile cap

structuraltie

retainingwall

counterbalancecantilever

straighttendons

loweredtendons

backfill

inspectionopening

(Detail)

Detail

2,752,75

R=30m

R=30m

150mm450mm

bearing

Figure 2. The abutment of the proposed construction method. 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 pre-cambering 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

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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.

tendons 15x19T15 (St 1500/1770)

Pier

52O16L=7,0m

76O16L=14,0m

lapping3,50 m

28O16L=14,0m

52O16L=7,0m

28O16L=14,0 m

couplers

YX

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).

tendons

Pier

5,50 8,508,50 5,50

7,00 7,00

L=14,0 m

1,00

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

tendons structural joint

7,007,00

14,00 3,52lapping

couplers

Figure 5. Detail of the ordinary strength steel bars of the deck’s top flange at the mid-span and coupling of the tendons.

15x19T15 (St 1500/1770)

2X71Φ252X61Φ252X51Φ252X51Φ252X41Φ25

top flange

polygonal

straight tendonsd=150mm d>150mm2,0-2,50m

bottom

7,0m7,0m 7,0m

pier

splicing mid-spanstructural joint

flange

length

2,15m

corners of the polygon

~4,50m

l=35,0-50,0m Figure 6. Detail of the ordinary strength steel bars at the bottom flange of the deck. 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

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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 arch-type 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.

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Sacramento, 1994. [2] Chen WF and Duan L, Bridge Engineering Handbook, CRC Press Boca Raton London, New

York Washington, D. C., 1999, Chapter 1. [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. [9] EN 1998-2:2005 Eurocode 8: Design of structures for earthquake resistance, Part 2: Bridges,

2005.