secondary effects in precast pre-stressed · pdf filepre-stressed w-girder integral and...

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Int. J. Struct. & Civil Engg. Res. 2015 Navin Kumar Chaudhary and S K Duggal, 2015

SECONDARY EFFECTS IN PRECASTPRE-STRESSED W-GIRDER INTEGRAL

AND CONTINUOUS BRIDGES

Navin Kumar Chaudhary1* and S K Duggal2

1 Design Manager, Transport Business Group, Ch2mHill, UAE.2 Professor, Department of Civil Engineering, MNNIT Allahabad, New Delhi.

*Corresponding author:Navin Kumar Chaudhary [email protected]

ISSN 2319 – 6009 www.ijscer.comVol. 4, No. 1, February 2015

© 2015 IJSCER. All Rights Reserved

Int. J. Struct. & Civil Engg. Res. 2015

Research Paper

INTRODUCTIONThe Continuous and Integral bridges are viableand economical alternatives to most of thebridges, if suitable foundation is available.Severe durability problems may emerge dueto penetration of water or/and de-icing salts(cold climates) in the expansion joints of decksof continuous bridge and its substructure.These problems can be overcome by makingthe bridge decks of < 60 m span and withskews < 300 integral with their supports (BA42/96, Amendment No. 1) , and are referred

Movement joints and bearings in concrete bridges can cause severe maintenance issues duringthe service life of a structure. A recent trend in bridge design has been towards integral typestructures. Durability of such bridges is greatly improved by removing or minimizing the movementjoints and bearings. Further, these structures offer better riding quality and a better distributionof horizontal loads. A simply supported pre-stressed girder deforms due to primary loads.However, secondary effects further affect the geometry, when these girders are made continuousover the supports or made integral with the supports. It is found that the secondary forces areimportant and must be considered in the design. This paper presents a comparison of primary,secondary and design forces in Integral and continuous bridges with open foundation, constructedusing W- type precast pre-stressed girders.

Keywords: Primary, Secondary, Design, Earth pressure, Creep, Shrinkage, Temperature

to as Integral bridge or rigid frame bridge. Thisconstruction leads to reduced forces anddeformation in the various components of thewhole bridge system comprising ofsuperstructure, substructure and foundation.Due to the movement restraints, the additionalstresses developed (referred to as secondaryeffects) may sometimes be comparable to theprimary effects due to Dead Load (DL), SuperImposed Dead Load (SIDL), Live Load (LL),and Impact Load (IL), etc. The secondaryeffects may also cause the stress reversals

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leading to the failure of the structure, if notaccounted for in the design. For the analysisand design of Integral bridges, the differentloads and their effects that need aconsideration, besides the primary loads, are:(i) Prestressing type (pre-tensioning/post-tensioning); (ii) Amount of prestress; (iii)Process of making the structure composite(girder-slab connection); (iv) Earth pressurevariation; (v) Differential settlement; (vi) Dailyand seasonal temperature variations on thestructures, (vii) Time dependent deformationof creep and shrinkage; and (viii) Sequenceof construction. A brief description of theseeffects follows.

The earth pressure is dependent onabutment height and longitudinal deckmovement and is highly dependent on thefriction coefficient. The abutments may bodilyslide (in case of bank seat) or may tilt (in caseof tall wall). The variable temperature effectsforce the structurally connected abutments tomove outwards/inwards during expansion/contraction of the bridge deck. The creep andshrinkage effects force the structurallyconnected abutments to move inwards. Themodes of abutment movement are primarilyrotation about its bottom and horizontaltranslation displacement. During expansion,large lateral earth pressure develops on theback of abutment, which may approach thetheoretical passive value. Further, the netinward movement of the abutments may causeafter a number of cycles of temperaturechanges a wedge slump in the adjacent soil.The upward/downward deflection and thecamber of a simple unloaded pre-stressedpre-tensioned beam depends upon themagnitude of pre-stressing force and its self

weight, which are modified by the Creep,Shrinkage and Relaxation with time. When twoadjacent beams are made continuous with arigid connection, a sagging restrained bendingmay develop over the supports. The fullcontinuity may be reduced due to developmentof tension in cross heads, which may crackunder action of the time dependent effects.Due to the load combinations, material andstructural properties, and the sequences ofconstruction, the levels of the hogging/saggingrestraint moment and their significance requirelengthy calculation for each combination.

Since bridge engineers are divided overthe importance of secondary effects and theirinclusion in the design, a proper study of sucheffects is required in the analysis and thedesign of integral and continuous bridges. Inview of the above, the primary, secondary anddesign forces were calculated in case ofcontinuous and Integral bridges with openfoundation using W-type precast pre-stressedgirders to establish the importance andinclusion of secondary effects in the design.

Analysis

The overall behavior of integral and continuousbridges is very complex as it depends onseveral parameters. The general problems thatrequire attention with regards to the modelingand design of these bridges are as follows: (i)Appropriate structural modeling of continuityconnections among structural members forestimating rigidity. (ii) Estimation of soilproperties and appropriate modeling of thesoil-structure interaction; (iii) Estimation of theeffects of daily and seasonal temperaturefluctuations on the structure; (iv) Determinationof the redistribution of time-dependent

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deformation of creep and shrinkage; and (v)Effects of construction sequence on thedistribution of primary and secondary forces.

The three dimensional effects of lateralloads on the piers, abutments, and wing wallsis not reflected by two dimensional modelingof the Integral bridge. This requires a threedimensional (3-D) model to analyze thestructure for the effect of lateral loads. Theweight of slab, girder, diaphragm,superimposed loads, live loads, earthpressure and effects of temperature variationneed a consideration for the design of thedeck-abutment and deck-pier joints. Further,for the soil-structure interaction correlationbetween the temperature variation and theeffects of earth pressure need a modeling. Theearth pressure coefficient is a function of thedisplacement of the earth retaining structure.Active earth pressure behind the abutment(Dicleli, 2000) is created even due to itsmeager displacement away from the backfillsoil. The coefficient of earth pressure K maychange between K

o(rest), K

a (active) and K

p

(passive). Its value depends upon the directionand displacement suffered.

Integral bridges are generally designed withstiffness and flexibility spread throughout thestructure-soil system. This results in all thesupports to accommodate the effects ofthermal and braking loads. The abutments andtheir foundations are so designed that they areflexible and less restraint to longitudinalmovement of the bridge deck. This minimizesthe effects of forces parallel to the bridge inlongitudinal direction.

The construction sequence of Integral/Continuous bridge affects the moments and

shears generated in the bridge elements andthis needs to be fully taken into account duringthe design. Stresses must be assessed ateach stage of construction with the finalmoments and shears derived to reflect theconstruction sequence. When the staticalsystem of a concrete structure is changedduring construction, creep of the concrete willmodify the as-built bending moments andshear forces towards the instantaneousmoment and shear distribution. The amountof the change is dependent on the creep factor (Ryal, 2000). Where the change to thestatistical system is sudden, such asconnection of precast girder to deck slabcreating continuity, the modification to themoments is through the following equation

Mfinal

= Ms + (1 – e-) (M

c – M

s) ...(1)

where, Mfinal

is final design moment, Mc is

moments if structure is constructed in one go,and M

s is simply supported moment.

The following construction sequences wereadopted for the analysis of superstructure ofIntegral and Continuous bridges.

Integral Bridge: (i) Construction of foundationand substructure. The dowel bars were keptat the top of pier/abutment for monolithicconstruction with deck; (ii) Erection of precastgirders on top of temporary supports near theabutment/pier; (iii) Casting of in-situ RCC deckslab and continuity diaphragms, which aremonolithic to abutment and pier top; (iv)Removal of temporary supports after in-situconcrete gains adequate strength; (v) Fixingof crash barriers/parapets and laying ofwearing course; (vi) Completion of otherfinishing works; and (vii) Opening of structureto traffic.

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Continuous bridge (diaphragm continuity):(i) Construction of foundation and substructure;(ii) Placement of bearings on top of pier andabutments; (iii) Erection of precast girders ontop of the bearings; (iv) Casting of in-situ RCCdeck slab and continuity diaphragms over thepier supports; (v) Fixing of crash barriers/expansion joints/parapets and laying ofwearing course; (vi) Completion of otherfinishing works; and (vii) Opening of structureto traffic.

In the present work, the bridges weremodeled as 3-D structure. The deck andgirders were modeled using beam element.The abutments and foundation were modeledas plate using 4-noded element. The 3-Dmodels of Integral and Continuous bridges areshown in Figures 1 and 2, respectively. Theearth pressure behind abutments is appliedusing spring stiffness (Hambly, 1991 andNicholson, 1998). The stipulated values of theparameters considered in the presentinvestigation are: differential settlement- 5 mm;

temperature fluctuation- +310C; differentialshrinkage strain- 100x10-6; long term creepcoefficient ( )-1.62; creep coefficient whengirder made continuous- 1.2 and shrinkagestrain- 130×10-6. The superstructure wasassumed to be made up of precast pre-stressed members. The loads and differenteffects considered were as given in BritishStandard. The live load considered were HA+ KEL for class 1 design and HA + HB-45 (BD37/01, 2001) for class 2 design (BS 5400 Part4, 1990).

MODELLING AND DESIGNFor comparison, a two span six lane bridge ofwidth 24.4 m was considered. Both theContinuous and Integral bridges weremodelled by using W-girders (Figures 1 to 4).The sections used were obtained after threecycle analysis and design iterations and wereused for the final analysis and design.Following stipulations were made: Thicknessof deck slab = 200 mm; Number of girders andspacing = 7 at 3.4 m center to center.

Figure 1: 3-D Model of Integral Bridge

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Figure 2: 3-D Model of Integral Bridge

Figure 3: W Type Girder

Figure 4: Typical Cross Section of Bridge Deck

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Span (depth) of girders considered forIntegral bridge were as under.

20 m (1200 mm), 30 m (1800 mm), 40 m(2400 mm), 50 m (3100 mm)

Span (depth) of girders considered forContinuous bridge were as under.

20 m (1000 mm), 30 m (1600 mm), 40 m(2200 mm), 50 m (2900 mm)

The properties of different materials usedin the present investigation were as under.

Concrete: (i) Characteristic strength of deckslab concrete = 50 MPa; (ii) Characteristicstrength of girder concrete = 70 MPa; (iii)Density of concrete,

c = 25 kN/m3; (iv)

Modulus of elasticity of deck slab = 34 GPa;(v) Modulus of elasticity of girder = 37 GPa;(vi) Age of Girder (at the continuity beingestablished) = 21 days.

Pre-stressing strand: (i) Characteristicstrength = 279 kN/strand; (ii) Area of strand =150 mm2; (iii) Modulus of elasticity = 200 GPa.

RESULTS AND DISCUSSIONThe primary, secondary and design resultsobtained from the analysis of Integral andContinuous bridges are presented in Figures5 to 9. The notations Ip, Is, Id, Idn, Idp, Cp, Cs,Cd ,Cdn and Cdp in the figures designateintegral primary, integral secondary, integraldesign, integral design negative, integraldesign posi tive, continuous primary,continuous secondary, continuous design,continuous design negative and continuousdesign positive values respectively. Thesagging moments are treated as positive andhogging moments are treated as negative.

The variations of girder depth, required for

primary and design BMs with span for Integraland Continuous bridges are shown in Figure5. From the figure, it is seen that when theprimary BMs are considered both the Integraland Continuous bridges require similar depths.When design BMs are considered the Integralbridges require higher depths than theContinuous bridges. The depths of girderrequired from design BM consideration are onan average 31 and 17% higher than thoserequired from primary BM consideration forIntegral and Continuous bridges respectively.

The variations of deck weight, required forprimary and design BMs, with span for Integraland Continuous bridges are shown in Figure6. From the figure, it is seen that when theprimary BMs are considered the weights ofconcrete for both Integral and Continuousbridges are similar. When design BMs areconsidered, the concrete weight for Integralbridge is higher than that of Continuous bridge.The concrete weights required from design BMconsideration are on an average 17 and 9%higher than those required from primary BMconsideration, for Integral and Continuousbridges respectively.

The variations of girder strand weight,required for primary and design BMs, withspan for Integral and Continuous bridges areshown in Figure 7. From the figure, it is seenthat when the primary BMs are consideredmore strand weight is required in case ofContinuous bridge. However, when designBMs are considered the strand weight ishigher in case of integral bridge. The strandweights required from design BMconsideration are on an average 39 and 12%higher than those required from primary BM

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Figure 5: Variation of Girder Depth for Primary and Design BM with Span

0

1000

2000

3000

4000

10 20 30 40 50

Span (m)

Dep

th (m

m) Ip

Id

Cp

Cd

Figure 6: Variation of Deck Weight for Primary and Design BM with Span

0.00

10000.00

20000.00

30000.00

40000.00

10 20 30 40 50

Span (m)

Wei

ght (

kN) Ip

Id

Cp

Cd

Figure 7: Variation of Girder Strand Weight for Primary and Design BM with Span

0

25

50

75

100

125

150

175

200

10 20 30 40 50

Span (m)

Wei

ght (

kN)

Ip

Id

Cp

Cd

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Figure 8: Variation of Primary, Secondary and Design BM with Span at Mid-Span

0

10000

20000

30000

40000

50000

10 20 30 40 50

Span (m)

BM

(kN

-m)

Ip

Is

Id

Cp

Cs

Cd

Figure 9: Variation of Primary, Secondary and Design BM with Span at Pier

-20000

-15000

-10000

-5000

0

5000

10000

15000

10 20 30 40 50

Span (m)

BM

(kN

-m)

Ip

Isn

Idn

Isp

Cp

Csn

Cdn

Csp

Idp

Cdp

consideration, for Integral and Continuousbridges respectively.

The variations of primary, secondary anddesign BMs (at mid-span) with span for Integraland Continuous bridges are shown in Figure8. From the figure, it is seen that the differencebetween primary BMs for Integral andContinuous bridges is not appreciable. Thesecondary BMs are on an average 62 and 34%of primary BMs for Integral and Continuousbridges respectively. The design BMs are onan average 62 and 34% higher than that of

primary BMs for Integral and Continuousbridges respectively.

The variations of primary, secondary anddesign BMs (at pier support) with span forIntegral and Continuous bridges are shown inFigure 9. From the figure, it is seen that thedifference between primary BMs for Integraland Continuous bridges is not appreciable.The secondary negative BMs are on anaverage 74 and 19% of primary BMs forIntegral and Continuous bridges respectively.There is a stress reversal at this location and

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the positive design BMs developed are on anaverage 1.18 times of primary BMs in case ofIntegral bridge. This positive BM varies from1.89 to 0.67 times of primary BM when spanis increased from 20 to 50 m. The BMs at pierlocation change sign in case of Continuousbridge also. The average positive BMsdeveloped are 0.77 times of primary BMs. Thepositive BMs range from 0.95 to 0.42 times ofprimary BMs when span is increased from 20to 50 m. The difference between the secondarypositive BMs of integral and continuous bridgeis not appreciable.

CONCLUSIONThe following conclusions are drawn in thepresent work.

1. In general, the primary BMs are larger incase of Continuous bridges as comparedto the Integral bridges.

2. The secondary BMs are larger in case ofIntegral bridges as compared to continuousbridges.

3. The design BMs are larger in case of Integralbridges as compared to continuousbridges.

4. The girder depths required for Integral andcontinuous bridges on primary BMconsideration are almost same.

5. When design BMs are considered, theIntegral bridge requires more depth than thecontinuous bridge.

6. The weight of concrete required for Integralbridge is higher than that of continuousbridge.

7. The strand weight calculated on primary BMconsideration is more for continuous bridge,whereas it is more for Integral bridges whendesign BMs are considered.

REFERENCES1. BA 42/96 (2003), “BA 42/96 Amendment

No. 1, The Design of Integral Bridges”,Department of Transportation UK.

2. BD 37/01 (2008), “Loads for HighwayBridges”, Department of TransportationUK.

3. BS 5400 (1990), “Steel, Concrete andComposite Bridges, Part 4: Code ofPractice for Design of ConcreteBridges”.

4. Dicleli M (2000), “A rational designapproach for prestressed-concrete-girder integral bridges”, EngineeringStructures 22, pp 230-245.

5. Hambly E C (1991), “Bridge DeckBehaviour”, E & FN Spon London.

6. Nicholson B (1998), “Integral abutmentsfor Prestressed beam bridges”, Pre-stressed Concrete Association.

7. Ryall M J, Parkee G A R and Harding J E(2000), The manual of BridgeEngineering, Thomas Telford Limited.

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