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Structural Engineering International

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Design of Haunched Single Span Bridges

Kenneth W. Shushkewich (Principal)

To cite this article: Kenneth W. Shushkewich (Principal) (2020) Design of HaunchedSingle Span Bridges, Structural Engineering International, 30:4, 580-591, DOI:10.1080/10168664.2020.1801368

To link to this article: https://doi.org/10.1080/10168664.2020.1801368

Published online: 25 Sep 2020.

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Design of Haunched Single Span BridgesKenneth W. Shushkewich, Principal, KSI Bridge Engineers, San Francisco, CA, USA.

Contact: kenshushkewich@hotmail.com

DOI: 10.1080/10168664.2020.1801368

Abstract

A novel method for the design of variable depth single span bridges havingmaximum depth at the ends and minimum depth at midspan is presented.These bridges are intended to be used for long span river crossings or highwayoverpasses, where only a single span is required, and the vertical clearancebelow needs to be maximized, and/or an aesthetically pleasing graceful shape isdesired. The design is made possible by “fixing” the ends to “lock-in” negativemoments, so that the positive moments at midspan are greatly reduced, and ashallow section may to be used. The method is developed and presented in twoparts. The first part discusses and unifies the behavior of three very famousbridges (the Luzancy Bridge in France designed by Eugène Freyssinet, theGänstor Bridge in Germany designed by Ulrich Finsterwalder, and the PinzanoBridge in Italy designed by Silvano Zorzi). The second part describes themethod in detail by virtue of a complete design example. Application of themethod to other bridges is included, and abutment treatments to enhance thevisual qualities are presented. This innovative bridge type will be of interest tothose looking for a practical and elegant new bridge solution for long spanbridges.

Keywords: behavior; design; inclined leg bridge; rigid frame bridge; shallow archbridge; Luzancy Bridge; Gänstor Bridge

Introduction

The design of variable depth singlespan bridges having maximum depthat the ends and minimum depth atmidspan is presented. The design ofthese bridges is made possible by“fixing” the ends to “lock-in” negativemoments, so that the positive momentsat midspan are greatly reduced, thusallowing a shallow section to be usedat midspan.

Although haunched single spanbridges have been designed and con-structed for a great many years, noattempt to unify the behavior of thesebridges has been made, and no sys-tematic approach for the design ofthese bridges has ever been presented.This paper fills this void by presenting adesign method that can be used for awide variety of prestressed concreteand structural steel bridges.

In general, three types of haunchedsingle span bridges have been built:

(1) Rigid frame bridges—The bridgesuperstructure is made monolithicwith the substructure (abutments).

(2) Bridges with ballast—The bridgehas short cantilever extensions atthe ends where ballasted material(weight) is added.

(3) Bridges with tie-downs—The bridgehas short cantilever extensions atthe ends where tie-downs (rock/soil anchors) are activated.

Only bridges with tie-downs will beconsidered here, as these bridges areeconomical and may be presented asa general design method.

The first half of this paper providesinsightful observations and commentsabout the behavior of haunchedsingle span bridges with historicalreference to three very famousbridges, while the second half presentsa methodical design approach for thedesign of these bridges.

Historical reference is made to theLuzancy Bridge in France designedby Eugène Freyssinet, the GänstorBridge in Germany designed byUlrich Finsterwalder, and the PinzanoBridge in Italy designed by SilvanoZorzi.

A complete design example for acast-in-place segmental bridge withtie-downs is presented, after whicha variety of applications of thisdesign method are discussed, andabutment treatments that enhancethe visual qualities of this bridgetype are presented.

These bridges can be used for longspan river crossings or highway over-passes, where only a single span isrequired, and the vertical clearancebelow needs to be maximized, and/oran aesthetically pleasing gracefulshape is desired.

This innovative bridge type will be ofinterest to owner agencies, bridgedesigners, and design/build contractorslooking for a practical and elegant newbridge solution for long span bridges.

Bridges with Tie-Downs

Consider a simply supported variabledepth box girder bridge with spanlength “L” having short cantileverextensions at the ends of length “a”(Fig. 1). Vertical supports carry thereactions R for this simply supportedbridge. Since the maximum positivebending moment occurs at midspan, itwill not be possible to have the shal-lowest section at midspan as shown.

Let us now apply downward verticaltie-down forces F at the ends of eachcantilever extension. These forces“lock-in” a negative moment at eachend (M− = F × a), which reduces thepositive moment at midspan to allowthe very shallow section to be used asshown.

Now, instead of looking at vertical sup-ports and tie-downs, let us look atinclined supports and tie-downs. Thevertical component of the tie-downforces FV “lock-in” a negativemoment at each end (M− = FV × a) toreduce the positive moment atmidspan, while the horizontal com-ponent of the tie-down forces FH addscompression to the deck (the horizon-tal component of the support reactionsRH also adds compression to the deck—these will be discussed later).

Note that inclined supports reduce theoverall span length required for themain span, and inclined tie-downsallow the same foundation to be usedfor both the support and the tie-down. In fact, the self-weight of thebridge can resist the tie-down force sothat soil/rock anchors will not be

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required, and only inclined prestres-sing tendons will be needed to transferthe tie-down force from the deck to thefoundations.

The required negative moment M−

can be provided by having a short can-tilever extension “a” with a large tie-down force “F”, or a long cantileverextension with a small tie-downforce. Clearly, a short cantileverextension is desirable, as the totalstructure length will be a minimum.However, a short cantilever extensionneeds to transmit a large shear force

(equaling the tie-down force)through the length of the cantileverextension to the abutment. If the can-tilever extension is too short, verticalprestressing will be required to trans-mit the shear force in the deck, andif is much too short the section willnot work. Thus, an optimum cantile-ver extension length needs to befound.

Also, the force in the tie-downs may beadjusted or “tuned” in order to havethe desired distribution of positiveand negative moment. Figure 2 shows

a haunched single span box girderbridge having a main span of 82.0 mand cantilever extensions of 6.1 m oneach side. The cross section for thisbridge is the same as that used laterin the design example as shown inFig. 7.

The seven self-weight bending momentdiagrams shown are for different tie-down forces, which yield differentdegrees of fixity going from 0% fixityto 120% fixity in increments of 20%.(100% fixity is the condition whererotation is restrained at the abut-ments.) What is interesting to see isthe distribution of positive and nega-tive moments that can be attained byvarying the fixity force in the tie-downs.

With 0% fixity (simply supported)most of the moment is positivemoment (97%), whereas with 120%fixity most of the moment is negativemoment (97%). With 60% fixity halfthe moment is positive moment andhalf the moment is negative.

The case of 100% fixity gives 81%negative moment and 19% positivemoment for this variable depthbridge, and not 66% negativemoment and 33% positive moment aswould be expected for a constantdepth bridge (ie. wL2/12 and wL2/24).This case is represented by 80% fixityfor this variable depth bridge.

In general, the negative moment is acombination of the moment due tothe self weight of the cantileverextension as well as the moment dueto the tie-down force. This is whythe simply supported case (no tie-down force) has 3% negativemoment. As the cantilever extensionsbecome longer, a larger portion ofnegative moment is carried by theself weight. For this type of example,a cantilever extension length of8.20 m (0.10 L) carries 5% of thenegative moment, while a length of16.40 m (0.20 L) carries 21% of thenegative moment.

It may be noted that If the tie-downwas a reaction (support) instead of anaction (force), then the bridge wouldbe a three span continuous bridge,and there would be unfavorable sec-ondary moments. These would causeadditional secondary stresses due tothermal gradient, diminish the primaryeffects of the prestressing, and causemoment redistribution under theeffects of creep and shrinkage.

Fig. 1: Single span haunched bridges

Fig. 2: Tie-down force study

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Three Famous Bridges

Three historically significant and beau-tiful bridges with three different vari-ations of vertical / inclined supportsand vertical / inclined tie-downs aredescribed here.

Luzancy Bridge

The Luzancy Bridge1–5 in France is avery slender bridge over the MarneRiver (Fig. 3). It was designed byEugène Freyssinet and is a veryspecial bridge (see Appendix A). It isthe first precast segmental bridge everbuilt. It has a main span length of55 m. Construction started in 1941(shortly after Freyssinet patented thevery first post-tensioning anchorage in1939), but because of the war was notcompleted until 1946.

Freyssinet designed this bridge toreplace a suspension bridge. Therequirements were that this girderbridge span from shore to shore,while maintaining both the roadwayprofile and the navigation channel.Thus, he could only have a sectiondepth of 1.27 m at midspan for a spanof 55 m, and this is why the resulting

bridge is very light in appearance,having a remarkable span to depthratio of 43. The bridge has beendescribed as a two-hinge portal frame.

Note the red arrows in the linediagram. The upward red arrowshows an inclined support, while thedownward red arrow shows an almostvertical tie-down. The vertical com-ponent of the tie-down force actingon the short cantilever extension“locks-in” a negative moment at eachend, which reduces the positivemoment at midspan, thus allowing thevery shallow 1.27 m deep section tobe used.

The cross section of the bridge is com-prised of three box girders that wereindividually cast and erected, and inter-connected to give a five cell box girderhaving a deck width of 8.00 m. Theroadway consists of two 3.00 m lanesand 1.00 m sidewalks.

The bridge is post-tensioned longitud-inally, transversely, and vertically with12 × 5 mm diameter wire tendons. Thelongitudinal post-tensioning consistsof 8 cantilever tendons at the top thatdrape down and anchor at thebottom, and 16 continuity tendons at

the bottom that drape up and anchorat the top. The tie-down (tension tie)is also post-tensioned. It has an ancho-rage at the top and a loop at thebottom. Flat jacks and reinforced con-crete shims are located where thelower inclined element frames intothe abutments. They have been usedto further compress the bridge as wellas to make adjustments for the effectsof creep.

With the great success of the LuzancyBridge, Freyssinet used this same sol-ution to build five similar bridgeshaving spans of 74 m on the MarneRiver between 1947 and 1951. Thesefive bridges are the Ussy, Annet, Tri-bardou, Changis, and Esbly bridges.The span to depth ratio for thesebridges is 86, which is double thevalue of 43 for the Luzancy Bridge.These are extremely slender bridges!

Gänstor Bridge

The Gänstor Bridge6 in Germany is avery elegant bridge over the DanubeRiver in Ulm (Fig. 4). It was designedby Ulrich Finsterwalder and has amain span length of 82.4 m.

Fig. 3: Luzancy bridge (55 m span)

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Construction was completed in 1950.The bridge replaced a three-archbridge that was destroyed in the war.

The red arrows in the line diagramshow that the bridge has vertical sup-ports and inclined tie-downs, featuresthat are hidden by the abutment wallsin the photo.

The section depth for this 82.4 m spanvaries parabolically from 4.282 m at theabutments to an amazing 1.20 m atmidspan. This 1.20 m depth allows thevertical clearance requirement for thenavigation channel to be maintained(without having to raise the road). Thespan to depth ratio is thus 19 at the abut-ments and an amazing 69 at midspan.

The cross section of the bridge is com-prised of four girders, and these girdersnot only have a parabolic variation indepth, but they also have a parabolicvariation in width from 1.40 m to0.70 m. This has been done to minimizethe self weight as much as possible.This reduction in girder width occurson the inside faces only, so that theoutside faces of the bridge are

uniform as can be seen in the photo.The overall deck width is 18.60 m.

As mentioned, the bridge replaced athree-arch bridge. The abandonedabutment and pier foundations can beseen in the line diagram. The aban-doned abutment foundations havelimited the cantilever extensions to alength of 6.85 m, which is quite shortfor a 82.4 m span (a ratio of 0.083 L).This means that large tie-down forcesare required to provide the large nega-tive moments required at the ends, tooffset the small positive moment thatcan be tolerated at midspan. Eachlarge tie-down force is transferred asa large constant shear force throughthe end cantilever to the abutment.Vertical prestressing bars have beenprovided to carry these large shearforces. The longitudinal prestressingconsists primarily of top tendons overthe abutments with only a few continu-ity tendons that travel the length of thebridge.

At the same time that Finsterwalderwas constructing the Gänstor Bridge6

over the Danube River (82.4 m span),he was also constructing the Balduin-stein Bridge7 over the Lahn River(62.1 m span). Both of these bridgesare haunched single span river cross-ings, and they look quite similar.However, the Gänstor Bridge usestie-downs to achieve the hauncheddesign, while the Balduinstein Bridgeuses ballasted ends to achieve thesame result. More importantly,whereas the Gänstor Bridge was con-structed on falsework, the BalduinsteinBridge was the first bridge ever to beconstructed by cantilevering segmentsover the river. This is the first cast-in-place segmental bridge, and itssuccess allowed Finsterwalder to con-struct the Rhine River Bridge7 atWorms (101.65–114.20–104.20 m spans),which became the first cast-in-placesegmental bridge constructed in truebalanced cantilever fashion.

Whereas Eugène Freyssinet was thefirst to use precast segments for the con-struction of the Luzancy Bridge, UlrichFinsterwalder was the first to use cast-in-place cantilever construction for the

Fig. 4: Ganstor bridge (82.4 m span)

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segments of the Balduinstein Bridge,and then cast-in-place balanced cantile-ver construction for the Rhine RiverBridge at Worms. The circle was thencompleted by Jean Muller (a discipleof Eugène Freyssinet), who combinedthe precast segments of Freyssinetwith the balanced cantilever construc-tion of Finsterwalder on the Choisy-le-Roi Bridge8 over the Seine River nearParis in 1962. This was the first match-cast precast segmental bridge built inbalanced cantilever.

Pinzano Bridge

The Pinzano Bridge9 in Italy is a verybeautiful bridge over the TagliamentoRiver (Fig. 5). It was designed bySilvano Zorzi. It has a main spanlength of 163 m and an overall lengthof 185 m. Construction was completedin 1969. The bridge replaced a three-arch bridge that was damaged byfloods in 1966.

The red arrows in the line diagramshow that the bridge has inclined sup-ports and inclined tie-downs, featuresthat are hidden by the abutment walls

in the photo. It can be noted that theline diagram for this bridge has beenused as the basis of Fig. 1 in this paper.

The section depth varies parabolicallyfrom 7.00 m at the abutments to anextremely slender 2.50 m at midspan.The span to depth ratio is thus 23 atthe abutments and an amazing 65 atmidspan. There is a hinge at midspan.The bridge has been described byZorzi as a three-hinge portal arch.

The cross section of the bridge is a singlecell box girder whose deck width is9.60 m, and whose roadway consists oftwo 3.50 m lanes and 1.30 m sidewalks.

The inclined supports reduce the mainspan from 163 m to 147.3 m (and not135 m as given on the line diagram ie.184.0–18.35–18.35 = 147.3 m). The18.35 m long cantilever extensions area ratio of 18.35/147.3 = 0.125 L of the147.3 m reduced main span, which isagain quite short.

The triangulated abutment portionswere cast on falsework after which can-tilever construction with form travelerswas used to cast 3.50 m long segments.Each cantilever is prestressed

longitudinally with 80 × 32 mm diam-eter Dywidag bars, and vertically with28 mm diameter Dywidag bars spacedat 0.70 m. Each inclined tie-down isprestressed with 36 to 42 × 32 mmdiameter Dywidag bars that carry thetie-down force from the cantileverextension to the common foundationthat is shared with the inclinedsupport. Here, the tie-down force isresisted by the self-weight of thebridge. Therefore, rock anchors(below the foundation) were onlyused during cantilever construction,and they were removed once the struc-ture was made continuous.

Compression Forces Actingon These Bridges

It is interesting to note that bridgeswith inclined support reactions R /tie-down forces F, as given in Figs. 3–5, have the added advantage that thehorizontal component of the supportreaction / tie-down force adds com-pression to the bridge deck. The threediagrams in Fig. 6 show the com-pression forces added to the deck for

Fig. 5: Pinzano bridge (163 m span)

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bridges of the Luzancy, Gänstor, andPinzano type respectively.

The horizontal dimensions for thisexample are shown in the figure, whilethe vertical dimension is such that thebridge has equilateral triangularelements at each end (60 degreeangles). The cross section of the bridgeis the same as that shown in Fig. 7.

The Luzancy type bridge has inclinedsupports and vertical tie-down forces.The combined vertical reaction of theself weight and tie-down force is 589+ 484 = 1073 kN. This creates a com-pression of 1240 kN in each of theinclined supports. The horizontal com-ponent of these reactions adds a com-pression of 620 kN to the deck. Thisbridge thus behaves like a threemember arch (with respect to com-pression). The vertical tie-down forceof 484 kN has no component in thehorizontal direction and therefore hasno effect on the compression.

The Gänstor type bridge has verticalsupports and inclined tie-down forces.The vertical component of the 559 kN

tie-down force is 484 kN, while thehorizontal component is 280 kN. Thisadds a compression of 280 kN to theentire bridge deck.

The Pinzano type bridge has inclinedsupports and inclined tie-down forces.The compression forces for thisbridge are the superposition of thecompression forces of the Luzancytype and Gänstor type bridges. Theresulting compression in the deck is620 + 280 = 900 kN between theinclined supports and 280 kN for theremainder of the deck.

As far as structural efficiency is con-cerned, the Pinzano type bridgeappears to be the most efficient, as theinclined supports reduce the main spanlength while introducing the greatestamount of compression into the deck.The Gänstor type bridge appears to bethe least efficient in that the main spanlength is not reduced and the smallestamount of compression is introducedinto the deck.

Despite all of these advantages ofinclined supports / inclined tie-down

forces, this paper will proceed with ver-tical supports / vertical tie-down forces,as it is believed in general that con-struction will be easier. However, ifadditional main span length or deckcompression is desired, one of thesethree solutions may be used toachieve this result.

Design Example

Figure 7 shows the elevation and crosssection for a proposed 82.00 m longvariable depth cast-in-place segmentalriver crossing. The end cantilevershave a length of 13.67 m, which is aratio of L/6 of the span length.(Shorter end cantilevers may be used,but the shear forces in them will bequite high and they will require verticalprestressing. The present examplekeeps the shear forces in the end canti-levers to within the same range asthose for the main span.) The lengthof the bridge is 4/3 L or 109.34 m,which is significantly less than that ofa three-span continuous bridge, whichwould be a minimum of 2 L to nothave uplift at the ends, and mostlikely would be quite a bit longer (say2.30 L = 0.65 + 1.00 + 0.65 L). The tie-down forces are applied at a distanceof 0.60 m from the ends, giving anoverall bridge length of 110.54 m.

The abutments shown are founded ondriven piles, but they can also be onspread footings or drilled shafts(depending on the soil conditions).The tie-downs are rock/soil anchors,and the force in the tie-downs can bespecified as some percent of the fixityforce as discussed in Fig. 2.

The bridge has two 3.66 m traffic lanesand two 3.05 m shoulders, giving aclear roadway width of 13.42 m andan overall width of 14.33 m. Thebridge depth is 4.10 m at the abutments(and the ends) and 2.05 m at midspan,which gives span to depth ratios of 20and 40 respectively. Key dimensionsof the box girder cross section areshown in the figure.

Figure 8 shows the segment layout andconstruction sequence for this cast-in-place segmental bridge. The bridgeconsists of 17.77 m long end portionsthat are cast on falsework, seven5.00 m long cantilever segments oneach side, and a 5.00 m long closuresegment. There are 0.60 m thick dia-phragms at the abutment and tie-down locations. The abutment dia-phragms transfer the bearing reactionsFig. 6: Compression forces acting on three bridges

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from the webs, while the tie-down dia-phragms transfer the rock/soil anchorforces distributed across the width ofthe box girder to the webs.

The construction sequence consists ofcasting the end segments on falseworkand then activating the tie-downs.Form travelers are then used to cantile-ver out segment by segment untilmidspan is reached, whereupon theclosure segment is cast. The form tra-veler has been assumed to weigh 45tonnes (50 tons). Top cantilevertendons are stressed as each segmentis erected, while bottom continuitytendons are stressed after continuityis established. The articulation is suchthat the pot bearings at both abutmentsare locked against longitudinal move-ment during construction, and one ofthe bearings is freed after closure, soas not to lock-in stresses in the mainspan. (An alternative design might beto have the superstructure monolithicwith the abutments—this may be amore efficient design—but many ofthe generalizations made here wouldbe difficult to describe as this designwould be more site specific).

Figure 9 shows three bending momentdiagrams for this bridge. The firstshows that a tie-down force of 9817kN acting over an arm of 13.67 mcreates a negative moment of 134200 kN-m. This negative momentshifts the self-weight positive moment

of 143 200 kN-m down to 9000 kN-m,while also shifting the negativemoment down to 159 200 kN-m.

The second diagram shows the positivemoments at midspan and the negativemoments at the abutments for superim-posed dead load (barriers and overlay)and live load (AASHTO HS25 andHL93 loading). The third diagramshows that the combination of selfweight, superimposed dead load, andHL93 live load gives positive and nega-tive design moments of 71 100 kN-mand 177 100 kN-m respectively.

Actually, two different tie-down forceshave been considered in this design.The first is a tie-down force of 9817kN which gives the bridge a smallreserve of positive moment under selfweight (as shown in Fig. 9), while thesecond is a tie-down force of 11450 kN which gives the bridge a smallreserve of positive moment under per-manent load (self weight and superim-posed dead load). (These tie-downforces represent 120% and 140%fixity.) A reserve is necessary so as tonot have a stress reversal at midspanwhen the transient live load acts onthe bridge.

This second tie-down force gives posi-tive and negative design moments of48 800 kN-m and 199 500 kN-mrespectively. This is actually morefavorable, as this negative moment isessentially the same as the 199

900 kN-m that occurs during cantileverconstruction (with the 45 tonne formtraveler), while the positive momentis reduced. However, as the shearforces in the cantilever extensions arebecoming larger, and the net result ofthis second solution is a minimalreduction in the bottom continuitytendons, the first solution is maintained.

The prestressing tendon layout isshown in Fig. 10. There are 16 cantile-ver tendons (two for each segment)that are stressed as each segment iserected, and 9 continuity tendons(anchored in pairs at five segments)that are stressed after continuity isestablished and carry the serviceloads. Each tendon consists of 15 × 15mm diameter strands (although a fewof the cantilever tendons have only 12strands in a 15 strand anchorage).

One end of each cantilever tendon isanchored at the face of a segmentafter it is cast, while the other end isanchored at the ends near the tie-down diaphragms. Here, twelvetendons are anchored at the top,while four tendons drape down andare anchored in the webs (so as not tohave tension at the bottom of thesection). The continuity tendons areanchored in bottom slab anchor blocks.

The tie-downs consist of a row of rock/soil anchors across the width of the boxgirder. Each rock/soil anchor is a highstrength steel tendon with a stressinghead at one end, and a transferdevice at the other end to allow forcetransfer to the rock or soil.

It is imperative that these rock/soilanchors be adequately protected toprevent corrosion. The integrity ofthe bridge relies on these rock/soilanchors to provide a prescribed force,and even the partial loss of some ofthis force might prove disastrous andcause the bridge to collapse.

The rock/soil anchors need to beinstalled and grouted correctly usingthe latest technology. They should havemultiple levels of protection in thesame way as stay-cables have multiplelevels of protection. Also, provisionshould be made during design to accom-modate future contingency tie-downsthat may be installed and stressed atany time during the life of the structure.This would be similar to future externalpost-tensioning tendons on segmentalbridges that are designed to have theiranchorage / deviation devices installedduring construction.

Fig. 7: Design example (units: mm)

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Finally, just as health monitoringsystems are being used for stay-cablesand post-tensioning tendons, it maybe prudent to consider somethingsimilar for tie-downs. Ensuring thedurability of the tie-downs is a veryimportant and serious subject, thatmay give significant opportunities foradditional research and technicalpapers in this area.

Selected Applications

Four different bridge types that canreadily be designed and constructedusing the method described here areshown in Fig. 11. These bridges havethe same span lengths and deck dimen-sions as the design example.

The steel I-girder bridge has five girderswith a spacing of 2.90 m. The girder

depth varies from 4.56 m at the abut-ments to 1.64 m at midspan, whichgives span to depth ratios of 18 and 50respectively. A similar steel box girderbridge with the same girder depthswould have two box girders with a3.60 m wide bottom flange and a spaceof 3.60 m between the girders.

Both of these bridges are built by firsterecting the 30.67 m long abutment

Fig. 8: Segment layout and construction sequence

Fig. 9: Bending moment diagrams

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portions that have their tie-downs acti-vated, and then dropping in the49.20 m long main span portion ofeach girder. The deck is cast after allof the steel has been erected.

The precast spliced I-girder bridge hasfive girders with a spacing of 2.90 m.The girder depth varies from 4.56 mat the abutments to 2.28 m atmidspan, giving span to depth ratiosof 18 and 36 respectively.

Each of the five 110.54 m long girdersis cast in three pieces, a “standard”constant depth 45.70 m long drop-ingirder, and two “specialty made”variable depth 31.82 m longhaunched girders (constant depth atthe end and variable depth in themain span).

The haunched girders are erected first,after which the tie-downs are activated.The drop-in girder is then supportedfrom hangers until the 0.60 m longclosure pours are made at each endand the post-tensioning tendons areinstalled and stressed.

The drop-in and haunched girders arepretensioned, and the entire girderlength is post-tensioned in two stages.The first is after the girders are con-tinuous, while the second is after thedeck is placed.

The cast-in-place concrete box girderbridge is similar to the cast-in-placesegmental bridge, but has two cellsinstead of one cell. The girderdepths are the same, varying from4.10 m at the abutments to 2.05 m at

midspan, again giving span to depthratios of 20 and 40. This bridgehas the same weight as the cast-in-place segmental bridge, since it hasthree 305 mm webs rather than two455 mm webs.

This bridge is constructed entirely onfalsework (with access openings asrequired). After the post-tensioningtendons have been stressed, the false-work is removed. By virtue of theextensive falsework required, appli-cation of this bridge type will mostlikely be limited to road crossings andnot river crossings.

The precast segmental box girder bridgeis similar to the cast-in-place segmentalbridge given in the design example,with the only significant difference

Fig. 10: Prestressing tendon layout

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being the segment layout. Rather thanhaving seven 5.00 m long cast-in-placesegments, this bridge would havefifteen 2.68 m long precast segments, inorder to keep the maximum segmentweight to under 68 tonnes (75 tons).

Abutment Treatments

Figure 12 shows two types of abut-ments that can be used to hide the can-tilever extensions, and enhance thevisual qualities of haunched singlespan bridges. Abutment type 1 has itswingwalls at the location of the boxgirder webs, while abutment type 2has its wingwalls at the location of thebarriers. Abutment type 1 is shownfor a river crossing, whereas abutmenttype 2 is shown for a roadway crossing,but these are interchangeable depend-ing on the site conditions.

With respect to the three famous his-torical bridges discussed here, the

Luzancy Bridge has a type 2 abutmentwhere the superstructure frames intomasked abutments, while the GänstorBridge and Pinzano Bridge have type1 abutments, where the superstructureand abutment wingwall appear as asingle surface in elevation. Also,whereas the supports / tie-downs arehidden for Gänstor Bridge andPinzano Bridge, they are clearlyvisible for the Luzancy Bridge.

Conclusions

This paper has presented a systematicmethod for the design of haunchedsingle span bridges.

This design method uses short cantile-ver extensions with tie-downs, and dis-cusses the use of various combinationsof vertical / inclined support reactionsand tie-down forces. Various degreesof fixity provided by the tie-downforces are also discussed.

Historical reference has been made tothree very famous bridges withrespect to vertical / inclined supportreactions and tie-down forces.Additional compression forces addedto the deck for each of these threetypes of bridges has been discussed.

A complete design example for a cast-in-place segmental bridge has beenpresented. The length of the cantileverextensions (to transmit the shearforces) and the degree of fixity (tocarry negative and positive moment)have been discussed.

The design of the prestressing is veryefficient, as the cantilever tendons pro-vided to construct the bridge are morethan adequate to carry the negativeservice load moments, and the require-ment for bottom continuity tendons isgreatly reduced.

Selected applications of the method toother bridge types have been

Fig. 11: Selected applications (units: mm)

Fig. 12: Abutment treatments

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discussed. Suitable abutment treat-ments for the application of themethod to river crossings and roadcrossings have been presented.

Finally, an explanation of the behaviorof Eugène Freyssinet’s very famousand often misunderstood LuzancyBridge has been presented.

References

[1] Freyssinet E. Une révolution dans l’art debâtir: les constructions précontraintes. Travaux.novembre 1941; 101: 335–359 (in French).

[2] Lalande M. L’emploi du béton précontraintdans la préfabrication des ouvrages d’art: lePont de Luzancy sur la Marne. Travaux. août1946; 142: 281–298 (in French).

[3] Ordonez JAF. Eugène Freyssinet. EditionsEyrolles: Paris, 1979; 444 pages (in English andFrench).

[4] Shushkewich KW. Eugène freyssinet – inven-tion of prestressed concrete and precast segmen-tal construction. Struct. Eng. Int. J. IABSE.August 2012; 22(3): 415–420.

[5] Godart B. La Pérennité du BétonPrécontraint. Presses de l’Ecole National desPonts et Chaussees: Paris, 2014, 443 pages (inFrench).

[6] Finsterwalder U, Konig H. Die Donaubrückebeim Gänstor in Ulm. Bauingenieur. October1951; 26(10): 289–292 (in German).

[7] Finsterwalder U, Schambeck H. Von derLahnbrücke Balduinstein bis zur RheinbrückeBendorf. Bauingenieur. March 1965; 40(3): 85–91 (in German).

[8] Podolny Jr W, Muller JM. Construction andDesign of Prestressed Concrete SegmentalBridges. John Wiley & Sons: New York, 1982,561 pages.

[9] Zorzi S, Cortiana F. Bridge on theTagliamento river at Pinzano (Udine).Realizzazioni Italiane in Cemento ArmatoPrecompresso 1966/70; ANICAP: 174–179 (inEnglish, French, and Italian).

[10] Esquillan N. Prestressed concrete in civiland industrial buildings and religious edifices.Travaux April–May 1966; 375–376: 399–428(special English Edition).

Appendix A: Some Notes onthe Luzancy Bridge

The Luzancy Bridge1–5 designed byEugène Freyssinet (Figure 3) over theMarne River in France is a veryspecial bridge. It is the first precast seg-mental bridge ever built. The bridge

was post-tensioned in all three direc-tions, and flat jacks were activated atthe abutments to increase the level ofcompression in the bridge (and theseflat jacks were reactivated later tocounteract any unforeseen losses dueto creep or abutment movement).

There has been some confusion aboutthe structural behavior of this bridge,first because of the appearance of anupper compression strut in addition tothe lower compression strut (inclinedsupport), and second because of theappearance of a void above thisupper compression strut in the linediagram (but not in the photo).

Let us discuss the void first. Carefulinspection of the line diagram (byblowing it up) reveals that this is some-what of an optical illusion. The upperopening appears only because there isno prestressing (or any other featurethat needs to be shown or labeled) atthis location. In fact, the right side atthis location reveals a 20 mm segmentjoint, which is similar to the segmentjoints between all the other segments.

Now let us look at the upper com-pression strut. It is because the upperinclined element extends past the webof the box girder that additional linesoutline this element in the linediagram and can be seen in the photo.What appears to be an upper com-pression strut is in fact the bottomflange of the cantilever extension,where the tie-down force creates nega-tive moment with tension at the topand compression at the bottom (atthis bottom flange).

To summarize, what appears as anupper compression strut is simply thebottom flange of the cantilever exten-sion, and there is no void above thisbottom flange. These two featuresmay have contributed to the lack ofunderstanding of this bridge andbridge type through the years. Thedefinitive biography of Eugène Freys-sinet has been written by Ordonez,3

and many other works have beenbased on this material. With respectto the Luzancy Bridge, Ordonez haswritten:

The slimness of the beams is possiblethanks to the end cantilevers formedby a triangular cell, whose two inclined

elements work in compression and thevertical prestressed one works intension (Pl. 323). The cantilever pro-duces an oblique thrust which acts onthe existing pillars some three metersbelow ground (Plates 315 and 316).The triangular cell is supported on thepillar by a Freyssinet hinge and severalflat jacks, placed so as to regulate thethrust upon the pillars and thus the com-pression in the concrete. The jacks alsoenable the shrinkage losses and theeventual movements of the pillars to becompensated for.

Everything stated in this explanation istrue, but it is hardly a clear explanationof the structural behavior, and norshould it be expected to be. Ordonezhas written the only extensive volumeon the life of Eugène Freyssinet, andit cannot also be a structural analysistextbook.

Freyssinet also used this solution forthe Underground Basilica atLourdes10 (Figure A1). The structurewas conceived by him in only fifteenminutes, and constructed from 1956 to1958. It consists of 29 portal frameswith tie-downs and can accommodate20 000 people.

Figure A1 clearly shows the inclinedsupports and almost vertical tie-downs. The 12 cantilever tendons, 8continuity tendons, and 3 tie-downtendons are also clearly shown andlabeled. Each tendon consists of 12prestressing wires each having a diam-eter of 7 mm.

The short cantilever extensions areextended further to the perimeter ofthe enclosed structure, where the 12cantilever tendons are anchored.These carry the negative moment,while the 8 continuity tendons atmidspan carry the positive moment.The dead end anchorage loops for 4cantilever tendons can also be seen.

It should be noted that Freyssinetinvented a new type of structuralform with the Luzancy Bridge, MarneBridges, and Lourdes Basilica; that isto say, a haunched single span bridge(or structure) having short cantileverextensions with tie-downs at the ends(and that form is precisely what thispaper is about).

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Figure A1. Underground Basilica at Lourdes.

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