Cantilever-constructed Bridges - ETH Z
Special girder bridgesCantilever-constructed bridges28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design1
Special girder bridgesCantilever-constructed bridgesIntroduction: First cantilever-constructed concrete bridges28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design2
Cantilever-constructed bridges – IntroductionPonte Emílio Baumgart, Herval-Joaçaba, Brasil (1930-1983) Brazilian Engineer Emílio Baumgart conceived the world’sfirst cantilever constructed concrete bridge, built in 1930 Cantilevering was chosen due to the frequent flood eventsat the site (Rio do Peixe rising by 10 m) The bridge had an open cross-section (two rectangularlongitudinal beams), with depths similar to modern cantileverconstructed bridges Passive reinforcing bars Ø38 mm were used, withoutprestressing Deformations during construction were controlled byrotations at the piers (“swing”), using counterweights at theabutments The bridge was destroyed in 1983 by a severe flood event4.10 23.6728.04.2020l171.70 l4068.0026.76ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design3
Cantilever-constructed bridges – IntroductionLahnbrücke Balduinstein, Germany (1951) – Why prestressing? It took another 20 years before the first prestressed concretecantilever-constructed bridge was built: The LahnbrückeBalduinstein (1951) in Germany, designed by UlrichFinsterwalder, with a span of 62 m. Obviously, passive reinforcement could be used forcantilever construction. However, deflections are hard tocontrol during construction (the method used by E. Baumgartis not applicable in most cases), and long-term deflectionsare hard to predict. As an order of magnitude, the followingdisplacements would be expected at midspan of theFelsenau Bridge (main span 156 m, see behind):Midspan deflection for different creep increments(effective creep during cantilever construction)Dj 0 Dj 1As built (full cantilever prestressing for dead load uncracked and bending moments partly compensated):120240Without cantilever prestressing, uncracked (EIII):2404801’2001’400Without cantilever prestressing, cracked (EIII):28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design4
Special girder bridgesCantilever-constructed bridgesRecapitulation of erection method(the following 5 slides are repeated from girder bridges – design and erection)28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design5
Cantilever-constructed bridges – ConstructionFree / balanced cantilevering (Freivorbau) Cast-In-Place The girder is segmentally cast on a movable formworkcantilevering from the previously built segments Before installing the travellers, a pier table (Grundetappe) mustbe built on separate falsework Usually, two cantilevers are built symmetrically, starting from apier ( balanced cantilevering) Free cantilevering (smaller spans) is possible in other cases(e.g. right end span in example below)28.04.2020(schedule assumes unbalanced moments of one element are admissible cantilevers with ½ element offset; fully balanced construction requirescasting of both cantilevers simultaneously)ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design6
Cantilever-constructed bridges – ConstructionFree / balanced cantilevering (Freivorbau) Cast-In-Place Cantilevers are often symmetrical ( cast both sidessimultaneously) or have ½ element offset ( faster, but unbalancedmoment) Economical for medium-large spans only (high initial cost for piertable and travellers) Suitable for high bridges crossing obstacles or soft soil, with spans70 m l 160 m (250 m in special cases)Inn Bridge Vulpera, Switzerland, 2010. dsp28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design7
Cantilever-constructed bridges – ConstructionFree / balanced cantilevering Precast segmental with cranes Suitable for sites with access for trucks andcranes over entire length of bridge Segment weight limited by transportation andcrane capacity Suitable for low-moderate height ( 10 m) Economic span ca. 45 m l 135 m High flexibility for curved alignments28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design8
Cantilever-constructed bridges – ConstructionFree / balanced cantilevering Precast segmental with lifting frames Suitable for sites with access for trucks overentire length of bridge High lifting capacity of frames largesegments possible Economic span ca. 45 m l 135 m High flexibility for curved alignments28.04.2020Vidin – Calafat Bridge over the Danube, RomaniaBulgaria, 2012. CFCSLETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design9
Cantilever-constructed bridges – ConstructionFree / balanced cantilevering Precast segmental with launching gantry Suitable for sites with access for trucksunless segments are delivered via bridge More efficient than erection on falsework,lighter gantry than for span-by-spanerection Limited flexibility for curved alignments Economic span about 25 m l 45 m28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design10
Special girder bridgesCantilever-constructed bridgesGeneral observations28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design11
Cantilever-constructed bridges – General observationsBasic principles of cantilever constructionClassic in-situ cantilever construction – also referred to a as“balanced cantilevering” – consists of the following steps:(i) Erection of pier and pier table (Grundetappe)(ii) Installation of formwork travellers (Vorbauwagen)(iii) Symmetrical cantilevering in segments ranging between3 5 m length(iv) Removal of travellers(v) Midspan closure (Fugenschluss)(i)(ii)(iii)(iv)Depending on site constraints and contractor preferences,different methods are used, which differ by the demand onmoment resistance at the starting pier:- Fully balanced, simultaneous casting of segments at bothcantilever ends (“1 crane bucket difference”)- Alternate casting, or installation of precast segments, atboth cantilever ends, with or without cantilever offsets ofhalf a segment length- Unidirectional free cantilevering (typically starting from apreviously erected part of the girder)28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design(v)12
Cantilever-constructed bridges – General observations28.04.2020Tarasp formwork travellerInn river236.00104.0073.0043.5059.00ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design8.5057.50Depending on site constraints and contractor preferences,different methods are used, which differ by the demand onmoment resistance at the starting pier:- Fully balanced, simultaneous casting of segments at bothcantilever ends (“1 crane bucket difference”)- Alternate casting, or installation of precast segments, atboth cantilever ends, with or without cantilever offsets ofhalf a segment length- Unidirectional free cantilevering (typically starting from apreviously erected part of the girder) Scuol4.70Classic in-situ cantilever construction – also referred to a as“balanced cantilevering” – consists of the following steps:(i) Erection of pier and pier table (Grundetappe)(ii) Installation of formwork travellers (Vorbauwagen)(iii) Symmetrical cantilevering in segments ranging between3 5 m length(iv) Removal of travellers(v) Midspan closure (Fugenschluss)Example (photos on previous slide)18.00Basic principles of cantilever constructionInn riverSurface layersBündner schist(fractured)Bündner schist13
Cantilever-constructed bridges – General observationsEconomy of cantilever-constructed bridgesCantilever-constructed bridges are suitable for sites whereconventional falsework is not feasible or would cause high cost due to height above ground access restrictions (rivers, soft soil, traffic)and if the spans exceed the economical span range of other girder bridge erectionmethods not requiring falsework (MSS, precast girders, ) but are below the economical span of cable stayed bridgesCantilever-constructed bridges are economical since only short, inexpensive, reusable formwork is needed, using thepreviously cast portions of the superstructure as support Identical tasks are repeated many times, enhancing productivityFor short spans, these advantages are less pronounced, andcantilever construction is less economical also due to the high initialcost of the pier table and travellers, see erection.Usually, the economical span range of cantilever-constructed bridgesis thus in the range of ca. 70 160 m.28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design14
Cantilever-constructed bridges – General observationsEconomy of cantilever-constructed bridgesThe design of cantilever-constructed bridges is governed by theconstruction process, which is decisive e.g. for span layout girder geometry (variable depth) prestressing layoutIf side spans are built by balanced cantilevering, they will be relativelyshort (side spans 50% of the interior span require special measures).Typically, a strongly variable girder depth is adopted for structuralefficiency and elegance. For prestressed concrete cantileverconstructed girders, the following span/depth ratios are typical: above piers: h/L 1/17 (large, limit cantilever deformations) at midspan: h/L 1/50Constant depth girders can also be cantilevered, but are structurallyinefficient due to the excessive weight at midspan, where the largedepth required to limit deformations during construction is not needed.Furthermore, they are subject to larger moment redistributions andlack a beneficial contribution of the bottom slab to the shear resistance,see dimensioning.28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design15
Special girder bridgesCantilever-constructed bridgesDesign28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design16
Cantilever-constructed bridges – DesignParticularities in design – OverviewThe design of cantilever-constructed bridges needs to accountfor their following particularities Change of static system from cantilever to continuous frame moment redistribution, affecting: prestressing concept / tendon layouts midspan moment Strongly variable girder depth choose statically optimised girder profile account for inclined chord forces in dimensioningThese particularities are further outlined on the following slides.28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design17
Cantilever-constructed bridges – DesignParticularities in design – Change of static systemSystem and moment line before midspan closurel 2The static system of cantilever-constructed bridges changesfundamentally when establishing continuity at midspan before midspan closure: cantilevers(hogging moments only) after midspan closure: continuous frame systemIf – as strongly recommended, see next slide – no hingesare provided at midspan, the change of the static systemthus causes a moment redistribution due to long-term effects(concrete creep and shrinkage, prestressing steelrelaxation).l 2l——— M g P t tcl M g( s )P t tcl System and moment line before midspan closurel 2l 2lThe redistribution is schematically illustrated in the figure: same difference in bending moments DMg P along theentire girder (or very similar in non-symmetrical cases)slightly favourable over piers (reducing the hoggingmoments by a small fraction of the initial value)very unfavourable in the span (causing a large portion ofthe moments at midspan, even if permanent loadsapplied after closure and traffic loads are considered)28.04.2020– – – – M g P t tcl ——— M g P t ETH Zürich Chair of Concrete Structures and Bridge Design Bridge DesignDM g PDM g P18
Cantilever-constructed bridges – DesignParticularities in design – Change of static systemHinge permitting rotation andlongitudinal movementHinge permitting rotation onlyResisting the same bending moment DMg P at the weakmidspan section requires much more reinforcement orprestressing than the corresponding moment reductionsaves in the strong the support region.Historically, hinges were therefore provided at midspan toavoid moment redistribution ( hinges permitting rotation).Hinges were sometimes also provided to prevent frameaction ( hinges permitting rotation and longitudinalmovements), i.e., provide horizontally statically determinatesupport.Balanced cantilevering from pier with bearings (temporary supports)However, such hinges cause many problems (durability,excessive deflections) and must be avoided: Bending moments at midspan can be covered indesign, see next slides. Longitudinal restraint may be problematic in case ofshort, stiff piers, but rather than hinges, bearings maybe provided on the piers (with temporary measures forstability in construction, see photo).28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design19
Cantilever-constructed bridges – DesignParticularities in design – Change of static systemMoment redistribution is caused by long-term stresses anddeformations, i.e., stresses due to all long-term actions: permanent load (self weight, superimposed dead load) prestressingThe moment redistribution DMg P can be determined using thetime dependent force method and Trost’s approximation (ageingfactor m 0.85, see Advanced Structural Concrete lecture): Application of time-dependent force method to determine DMg Pl 2l 2lsystem for t tclsystem for t tcl basic systemand redundant variableDM g Pone-casting system (subscript “OC”), compatibility:M g g x dx EI g m 10 M g P ,OC 11 0 M g P ,OC 10 11 M P P e p EI Pwith system change, compatibility at t tcl (midspan closure): m tcl 10M 0 EI 0DM g P (tcl ) 0 Mg MPwith system change, compatibility for t tcl :D m t 10 j t DM g P (t ) 11 1 mj t 0 mj t j t DM g P (t ) 10 M g P ,OC 11 1 mj t 1 mj t 28.04.2020permanent loads g prestressing PETH Zürich Chair of Concrete Structures and Bridge Design Bridge Designw M 0 10 0 M 1 dxM1M 12 11 dxEI DMg P 1 20
Cantilever-constructed bridges – DesignParticularities in design – Change of static systemEven if the system has already crept at midspan closure,such that a reduced creep coefficient can be used fordetermining DMg P , a pronounced moment redistributionoccurs, which is non-negligible particularly at midspan.Moment redistribution is caused by the total permanentcurvatures, i.e., only by the part of the permanent loads notcompensated by prestressing (using long-term values ofprestressing forces). If prestressing was neglected, DMwould be severely overestimated.For usual stiffness ratios EI(m) (0.05 0.10) EI(s)(correponding to common slendernesses h/l), DMg P canbe estimated as:DM g P (0.10 0.15) M g( s )P t tcl Estimation of moment redistribution for preliminary designl 2EI ( s )M g( s )P t tcl l 2lEI ( m ) 0.05– – – – M g P t tcl ——— M g P t DM g P (0.100.10 EI ( s )DM g P0.15) M g( s )P t tcl If furthermore, the cantilever tendons are designed to avoiddecompression during cantilevering as usual (seeprestressing concept), i.e., they compensate about 80% ofthe permanent loads, DMg P is approximately:DM g P (0.0228.04.20200.03) M g( s ) t tcl ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design21
Cantilever-constructed bridges – DesignParticularities in design – Prestressing conceptDuring cantilever construction, cracking must be avoided sinceit would lead to large deflections hard to predict (camber ?) due to largescatter of deflections (section might crack or not dependingon the concrete tensile strength) Typically, the cantilever tendons are designed to avoiddecompression during cantileveringMoment redistribution could be reduced (or even eliminated)by providing more cantilever prestressing. However, this is noteconomical since there are usually reserve capacities for ULSover piers anyways, due to minimum passive reinforcement low ratio of traffic loads to self-weightFurthermore, space requirements limit the number ofcantilever tendons, see figure: At the pier table, all tendonsmust be accommodated.28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design22
Cantilever-constructed bridges – DesignParticularities in design – Prestressing conceptlongitudinal sectionRather, additional tendons with differentlayouts are usually tensioned after midspanclosure (see cast in place girder erectionmethods and tendon layouts): cantilever tendons (essential) midspan tendons (usual today) continuity tendons (optional)anchorage blister formidspan tendonsMAs also mentioned there already, cantilevertendons are anchored near the webs space for anchorages longitudinal shear flowThe deck acts as tension chord, but thehorizontal shear transferred to the deckcannot be spread via compressive forces:plan (deck)cross-sectioncontinuity tendons(parabolic, in webs)tensioned in finalstagePconstruction jointsP28.04.2020cantilever tendonsmidspan tendons(curved in plan, in deck slab)(straight, in bottom slab)tensioned per construction stage tensioned after midspan closureETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design23
Cantilever-constructed bridges – Designcantilever tendons(curved in plan, in deck slab)tensioned per construction stagecontinuity tendons(parabolic, in webs)tensioned in final stagemidspan tendons(straight, in bottom slab)tensioned after midspan closure28.04.2020ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design24
Cantilever-constructed bridges – DesignParticularities in design – Midspan momentMidspan (Pmid) and continuity (Pcont) tendons causesignificant secondary moments, which need to beaccounted for in the design of the midspan section inaddition to DMg P (unless significant moment redistributionsare taken into account, which is unusual).Hence, the midspan cross-section needs to be designedfor the sum of the following bending moments: moment redistribution DMg P (long-term effects) secondary moment MPS due to midspan tendons Pmidand continuity tendons Pcont midspan moment due to permanent loads applied aftermidspan closure midspan moment due to traffic loads (envelope)Secondary moments due to continuity and midspan tendonsl 2lsystem for t tclMmDue to long-term losses of prestressing force, DMg Pincreases with time (resp. has a larger value), but MPSdecreases. If a strong continuity and midspan prestressingis provided, the permanent bending moment at midspan(DMg P MPS) may thus even slightly decrease with time.28.04.2020l 2ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Designbasic system andredundant variableM P , mid Pmid e p , mid EI P , midM P , cont Pcont e p , cont EI P , contM 0 EI 0 M P , mid M P , contM1 M m 1 M PS 10 0 M 1 dxM 12 11 dxEI 10 1125
Cantilever-constructed bridges – DesignParticularities in design – Strongly variable depth Usually, cantilever-constructed girders have a stronglyvariable depth girder axis (centroid) substantially inclined even if deck ishorizontal in elevationHowever, segment joints and stirrups are usually vertical internal actions obtained form global structural analysisusing a 2D or 3D frame model need to be transformed(see figures) the inclination d of the girder axis (centroid) is relevant here(inclinations dsup and dinf of top and bottom slab affect d viavariation of section properties)Internal actions obtainedfrom structural analysisInternal actions used instr
28.04.2020 ETH Zürich Chair of Concrete Structures and Bridge Design Bridge Design 15 Economy of cantilever-constructed bridges The design of cantilever-constructed bridges is governed by the construction process, which is decisive e.g. for span layout girder geometry (variable depth) prestressing layout
Fig. 3 (a): Mode 1 of cantilever beam (b) Mode 2 of cantilever beam (c) Mode 3 of cantilever beam III. MODAL ANALYSIS OF CANTILEVER BEAM (ANALYTICAL) For a cantilever beam Fig. (12), which is subjected to free vib
Cantilever Racking: Adjustable Long Goods Storage System Applications for Cantilever 08 Mobile Cantilever Racking Cantilever racking can also be installed on a MOVO heavy duty mobile carriage, helping to reduce costs for a new building or improving the efficiency of existing storage s
Anchored bulkheads and cantilever sheet pile walLs may be designed as described by Saczynski and Kulhawy 982!. Cantilever "L" Walls The cantilever "L" wall consists of a concrete stem and concrete base slab Figure 5.3!. Both the stem and slab are relatively thin and are steel reinforced to resist the moments and shears to which they are .
Types of sheet pile walls Sheet pile walls may be cantilever or anchored walls. Figure TS14R-6 illustrates both a cantilever sheet pile wall and an anchored sheet pile wall. Cantilever walls derive support from adequate embedment below the stream channel. Steel cantilever walls are limited to wall heights of 15 to 20 feet, while vinyl cantilever
The cantilever with a rectangular shaped SCR extended up to the edge of the cantilever width yields a maximum Mises stress of 0.73 kPa compares to the other designs. For the same design, the cantilever with minimum SCR thickness of 0.2 µm yields maximum stress which results in maximum sensitivity. I. cantilever sensitivity [11].
Cantilever Gate System Split Opening Cantilever Gate (9ft. to 27ft.) PRODUCT LITERATURE. The . Single Opening Cantilever Gate System. is a manual lift gate that can be used on loading docks, fall protection/railing openings, mezzanines, machine guarding, equipment protection, and more. The OSHA-compliant cantilever gate system reduces the .
As this thesis is a conceptual study of bridge design for cantilever constructed concrete bridges, we aim to get good design notions, that is, the guidelines we need to follow in order to project a pleasant looking bridge, and then evaluate this type of bridges throughout the world to see if what we have learned is what it is being made.
Accounting Standard (IAS) terminology and requiring pre sentation in International Standard format. Approach – These qualifications were designed using Pearson’s Efficacy Framework. They were developed in line with World-Class Design principles giving students who successfully complete the qualifications the opportunity to acquire a good knowledge and understanding of the principles .
