Understanding Skewed Bridge Behavior

8/8/2019 Understanding Skewed Bridge Behavior

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Understanding SkewedUnderstanding Skewed

Bridge Behavior Bridge Behavior Skewed Bridge Behavior

OutOut --of of --plane effects occur in skewed bridges that cannot beplane effects occur in skewed bridges that cannot bepredicted by onepredicted by one --dimensional (line girder) analysis methods.dimensional (line girder) analysis methods.

AASHTO/NSBA Guidelines for Design for Constructability identif AASHTO/NSBA Guidelines for Design for Constructability identif iesiestwo separate issues:two separate issues:

Intermediate Crossframe EffectsIntermediate Crossframe Effects

End Crossframe EffectsEnd Crossframe Effects

Both Intermediate and End Crossframe Effects will be examinedBoth Intermediate and End Crossframe Effects will be examinedusing a test case.using a test case.


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Test Case:60 Skew, 150 ft Span

FRAMING PLAN

TRANSVERSE SECTION

Analysis of Test Case, Line Girder Model:Analysis of Test Case, Line Girder Model:

We will conduct an initial analysis of the test structure using a LineGirder Model.

This is the most commonly used analysis method for non-complexbridges, and is used by many common software packages. (MDX,Merlin Dash, BARS-PC)

Each girder is modeled independently, with crossframe effectsignored .

Mz

Line Girder Model:


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0

1

2

3

4

5

6

0 25 50 75 100 125 150

Length (ft)

D e

f l e c

t i o n

( i n )

Exterior Girders(G1, G5)

Interior Girders(G2, G3, G4)

Test Structure, Deflection Due to Deck Weight

Line Girder Analysis ResultsCrossframe Effects Ignored

Line Girder Analysis ResultsCrossframe EffectsIgnored

0

1

2

3

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6

0.00 50.00 100.00 150.00 200.00

Length (ft)

D e

f l e c

t i o n

( i n

)

G2 G1G3G4G5

CrossframeLocations


Results Show:

Large differentialdeflections betweeninterior and exterior girders

Abrupt changes indifferentialdeflection acrossthe width of thebridge


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Line Girder Analysis ResultsLine Girder Analysis Results

Crossframe Effects IgnoredCrossframe Effects IgnoredTest Structure, Differential Deflections at Crossf rame Locations:

DD

DD

Section D-D

Differential Deflection (in)

Girder Deflection (in)

Deflections Exaggerated x 12Deflections Exaggerated x 12

Framing Plan



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Problem:Problem: If the girders are assumed to stay vertical, theIf the girders are assumed to stay vertical, thecrossframes will not permit differential deflections of thiscrossframes will not permit differential deflections of thismagnitude.magnitude.

Conclusion:Conclusion: Crossframe interaction needs to be included toCrossframe interaction needs to be included toaccurately model structure behavior.accurately model structure behavior.

Line Girder Analysis ResultsLine Girder Analysis Results

Crossframe Effects IgnoredCrossframe Effects Ignored

Section A-A


Girder Deflection (in)DeflectionsDeflections

Exaggerated x 12Exaggerated x 12

We will now use a refined method to analyze the test structurewith crossframe effects included.

All intermediate crossframes are fully connected during the deckpour (no slotted holes).

The end crossframes will be removed in order to isolateintermediate crossframe effects.

The behavior of the bridge will be examined under wet concreteload only.

FRAMING PLAN

Intermediate Crossframe Effects


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Twisting of the girders allows differential deflection to occur Twisting of the girders allows differential deflection to occur without deforming the crossframe.without deforming the crossframe.

Generally, the torsional stiffness of the girders is low compareGenerally, the torsional stiffness of the girders is low compare ddto the stiffness of the crossframes, so this behavior is dominanto the stiffness of the crossframes, so this behavior is dominan t.t.

UndeformedUndeformed


Analysis of Test Case, Refined Model:Analysis of Test Case, Refined Model:

In order to include crossframe effects in the analysis, we will need touse a Refined Model.

Refined Model is a general term we will use to refer to any analysisthat includes both the girders and the crossframes.

Refined Models will be discussed in more detail in another presentation.

Refined Model:


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Refined AnalysisResultsIntermediateCrossframe EffectsIncluded

Results Show:

More uniformdifferential deflectionacross the width of the bridge at

crossframe locations(compared to linegirder analysis)


0

1

2

3

4

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6

0.00 50.00 100.00 150.00 200.00

Length (ft)

D e f l e c t i o n

( i n )

G2 G1G3G4G5

Crossframe

Locations Refined AnalysisResultsIntermediateCrossframe EffectsIncluded

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1

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0.00 50.00 100.00 150.00 200.00

Length (ft)

D e f l e c t i o n ( i n )

G2 G1G3G4G5

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1

2

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5

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0.00 50.00 100.00 150.00 200.00

Length (ft)

D e f l e c t i o n

( i n )

G2 G1G3G4G5




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Refined Analysis

ResultsIntermediateCrossframe EffectsIncluded

Section D-D



DeflectionsDeflectionsExaggerated x 12Exaggerated x 12

Section D-D




The analysis results show that intermediate crossframe effectsThe analysis results show that intermediate crossframe effectscause girder twist in skewed structures.cause girder twist in skewed structures.

The next several slides will step though the deflection of the tThe next several slides will step though the deflection of the t esteststructure at each crossframe location.structure at each crossframe location.

Deflected Shape Due to Intermediate Crossframe EffectsDeflected Shape Due to Intermediate Crossframe Effects


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Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis):

AA

AA


Section A-A

DifferentialVerticalDeflection(inches)

BB

BB



Section B-B



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Section C-C

CC

CC



DD

DD


Section D-D




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EE

EE


Section E-E



FF

FF


Section F-F




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Section G-G

GG

GG


Differential

Vertica lDeflection(inches)

HH

HH


Section H-H


Differ ential

VerticalDeflection(inches)


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JJ

JJ



Section J-J

DifferentialVertical

Deflection(inches)

KK

KK



Section K-K



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LL

LL


Section L-L


Differential

Vertic alDeflection(inches)

MM

MM


Section M-M


DifferentialVerti calDeflection(inches)


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Animation of Deflection Under Wet Concrete Load withAnimation of Deflection Under Wet Concrete Load with

Intermediate Crossframe Effects Included (Exaggerated Scale):Intermediate Crossframe Effects Included (Exaggerated Scale):

Deflected Shape Under Wet Concrete Load with IntermediateDeflected Shape Under Wet Concrete Load with Intermediate

Crossframe Effects Included (Exaggerated Scale):Crossframe Effects Included (Exaggerated Scale):


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Test Structure, Refined Analysis, Intermediate Crossframes Only:Test Structure, Refined Analysis, Intermediate Crossframes Only:

In a single span skewed structure, twist is generally highest atIn a single span skewed structure, twist is generally highest at the supports.the supports.

End twist for the test case is shown below.End twist for the test case is shown below.

Definition of Girder TwistDefinition of Girder Twist ::

Girder Twist due to Intermediate Crossframe EffectsGirder Twist due to Intermediate Crossframe Effects

Sign Convention: (+ Clockwise, Looking ForwardSign Convention: (+ Clockwise, Looking Forward -- Counterclockwise, Looking Forward)Counterclockwise, Looking Forward)

ForwardForward

Support Reactions due to Intermediate Crossframe EffectsSupport Reactions due to Intermediate Crossframe Effects

HIGH REACTIONS

Intermediate crossframe effects cause vertical supportIntermediate crossframe effects cause vertical supportreactions to be concentrated at the obtuse corners of areactions to be concentrated at the obtuse corners of askewed structure.skewed structure.

Significant redistribution of reactions occurs throughoutSignificant redistribution of reactions occurs throughoutthe structure.the structure.


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Support Reactions Due to Wet Concrete Weight, Refined Analysis:

Rear Bearings(Fixed)

Forward Bearings(Exp.)

Rear Bearings(Fixed)

ForwardBearings(Exp.)

There are natural differences in dead load deflections atThere are natural differences in dead load deflections atopposite ends of intermediate crossframes in skewedopposite ends of intermediate crossframes in skewedstructures.structures.

Differential deflections occurring at intermediate crossframeDifferential deflections occurring at intermediate crossframelocations cause girders to twist.locations cause girders to twist.

Intermediate crossframe effects must be included in analysis of Intermediate crossframe effects must be included in analysis of highly skewed structures in order to accurately predict behavior highly skewed structures in order to accurately predict behavior ..

Conclusions for Intermediate Crossframe Effects:Conclusions for Intermediate Crossframe Effects:




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End crossframes produce twisting effects that are independent of End crossframes produce twisting effects that are independent of the intermediate crossframe behavior.the intermediate crossframe behavior.

End Armor

Bottom Chord

Diagonals

EndCrossframe

End Crossframe:


To illustrate end crossframe behavior, we will examine a 2-girder structure with end crossframes only (no intermediate bracing).

PLAN VIEWPLAN VIEW


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PLAN VIEW (PARTIAL)PLAN VIEW (PARTIAL)

ISOMETRIC VIEW (PARTIAL)ISOMETRIC VIEW (PARTIAL)

2-Girder Structure:The end crossframe isoriented on the skewand connects thebearing points of theadjacent girders.

The end diaphragm can be thought of as a pair of rigid linksThe end diaphragm can be thought of as a pair of rigid linksconnecting the top flange of one girder to the bottom flange of connecting the top flange of one girder to the bottom flange of thetheadjacent girders.adjacent girders.

2-Girder Structure:

ISOMETRIC VIEW (PARTIAL)ISOMETRIC VIEW (PARTIAL)


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Deflection of a Cambered Girder:Deflection of a Cambered Girder:

When a girder deflects, the top flange moves longitudinallyWhen a girder deflects, the top flange moves longitudinallyrelative to the bottom flange at the beam ends. We will definerelative to the bottom flange at the beam ends. We will definethis distance asthis distance as ..

The end crossframe of a skewed structure restrains theThe end crossframe of a skewed structure restrains thelongitudinal translation of the top flange.longitudinal translation of the top flange.

2-Girder Structure:


x

GIRDER AGIRDER A

GIRDER BGIRDER B


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The end crossframe forces the top flange to move radiallyThe end crossframe forces the top flange to move radiallyabout the adjacent bearing point. The resulting motionabout the adjacent bearing point. The resulting motionproduces twist in the girders.produces twist in the girders.

2-Girder Structure:


x y

GIRDER AGIRDER A

GIRDER BGIRDER B

A similar effect occurs in the adjacent girder A similar effect occurs in the adjacent girder

2-Girder Structure:


xx y y

GIRDER BGIRDER B

GIRDER AGIRDER A


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The movement of the top flange is approximatelyThe movement of the top flange is approximatelyperpendicular to the centerline of bearings.perpendicular to the centerline of bearings.

2-Girder Structure:


xx y y

xx y y

GIRDER BGIRDER B

GIRDER AGIRDER A

We will now perform a refined analysis of the test structure withend crossframe effects included.

All end crossframes are fully connected during the deck pour (noslotted holes).

The intermediate crossframes will be removed in order to isolateend crossframe effects.

The behavior of the bridge will be examined under wet concreteload only.

FRAMING PLAN

End Crossframe Effects


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By cutting sections along the length of the bridge it can be shownthat the twist caused by end crossframe effects is very similar tothat caused by intermediate crossframe effects.

Girder Twist Due to End Crossframe Effects:

DD

DDFraming Plan

Section D-D

By cutting sections along the length of the bridge it can be shownthat the twist caused by end crossframe effects is very similar tothat caused by intermediate crossframe effects.

Girder Twist Due to End Crossframe Effects:

JJ

JJFraming Plan

Section J-J


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Animation of Deflection Under Wet Concrete Load withAnimation of Deflection Under Wet Concrete Load with

End Crossframe Effects Only (Exaggerated Scale):End Crossframe Effects Only (Exaggerated Scale):

Deflected Shape Under Wet Concrete Load with EndDeflected Shape Under Wet Concrete Load with End

Crossframe Effects Only (Exaggerated Scale):Crossframe Effects Only (Exaggerated Scale):


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Test Structure, Girder End TwistTest Structure, Girder End Twist

End Crossframes Only:End Crossframes Only:

Intermediate Crossframes Only:Intermediate Crossframes Only:


ForwardForward


ForwardForward

End crossframe effects do not cause redistribution of vertical r End crossframe effects do not cause redistribution of vertical r eactions, buteactions, butthey do produce horizontal loads on restrained bearings.they do produce horizontal loads on restrained bearings.

For the test case, the rear abutment bearings are fully restrainFor the test case, the rear abutment bearings are fully restrain ed againsted againsttranslation, and the forward abutment bearings are free to movetranslation, and the forward abutment bearings are free to movelongitudinally but restrained laterally.longitudinally but restrained laterally.

The bearing restraints result in axial forces in the girders andThe bearing restraints result in axial forces in the girders and endendcrossframes due to differential movements caused by decrossframes due to differential movements caused by de --cambering of thecambering of thebeams (or differential lengthening of the bottom flanges).beams (or differential lengthening of the bottom flanges).

End Crossframe Support ReactionsEnd Crossframe Support Reactions

TEST CASE, MEMBER AXIAL FORCES:TEST CASE, MEMBER AXIAL FORCES:

6

T = 19 k

C = 11 k

T = 13 k

C = 9 k

C = 12 k

T = 22 k

T = 6 k

C = 1 k

C = 15 k


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Test Case, Support ReactionsTest Case, Support Reactions

The resulting horizontal components of the support reactionsThe resulting horizontal components of the support reactionsfor the test case are shown below.for the test case are shown below.

These forces need to be accounted for in the bearing design if These forces need to be accounted for in the bearing design if end crossframes are left connected during the deck pour.end crossframes are left connected during the deck pour.

TEST CASE, HORIZONTAL BEARING LOADS:TEST CASE, HORIZONTAL BEARING LOADS:

1 1

End crossframes in skewed structures cause girders to twist.End crossframes in skewed structures cause girders to twist.The magnitude of the twist is similar to that caused byThe magnitude of the twist is similar to that caused byintermediate crossframes.intermediate crossframes.

End crossframes in skewed structures produce longitudinal andEnd crossframes in skewed structures produce longitudinal andlateral forces at restrained bearing locations.lateral forces at restrained bearing locations.

If end crossframes are fully connected prior to the deck pour,If end crossframes are fully connected prior to the deck pour,end crossframe effects must be considered in the design.end crossframe effects must be considered in the design.

Conclusions for End Crossframe Effects:Conclusions for End Crossframe Effects:


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Combined Effects: Girder End TwistCombined Effects: Girder End Twist

End Crossframes Only / Intermediate Crossframes Only:End Crossframes Only / Intermediate Crossframes Only:

Combined effects:Combined effects:


ForwardForward


ForwardForward

Combined Effects: Girder End TwistCombined Effects: Girder End Twist

Conclusions:Conclusions:

Intermediate and end effects are not additive.Intermediate and end effects are not additive.

Interaction between effects redistributes twist slightly, but thInteraction between effects redistributes twist slightly, but th eeoverall magnitude remains about the same when effects areoverall magnitude remains about the same when effects arecombined.combined.


ForwardForward


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Q: Will using skewed intermediate crossframes prevent girder Q: Will using skewed intermediate crossframes prevent girder twisting?twisting?

Common Questions:Common Questions:

A: No. Skewed intermediate crossframes behave like endA: No. Skewed intermediate crossframes behave like endcrossframes. They will produce twist due to differentialcrossframes. They will produce twist due to differentialmovements between the bottom and top flanges of adjacentmovements between the bottom and top flanges of adjacentgirders.girders.

A: No. Tighter crossframe spacing does not address the basicproblem, which is differential movement between adjacentgirders. Adding crossframes may reduce crossframe member

forces and increase girder stability, but twisting will still occur.

Q: Will reducing crossframe spacing keep girders from twisting?Q: Will reducing crossframe spacing keep girders from twisting?

Common Questions:Common Questions:


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Both intermediate and end crossframes produce twist in skewedBoth intermediate and end crossframes produce twist in skewedbridges.bridges.

Intermediate crossframes cause significant redistribution of Intermediate crossframes cause significant redistribution of support reactions and girder forces (shear and moment) insupport reactions and girder forces (shear and moment) inheavily skewed structures.heavily skewed structures.

End crossframes may cause significant lateral and longitudinalEnd crossframes may cause significant lateral and longitudinal

reactions to occur at restrained bearingsreactions to occur at restrained bearings

Both intermediate and end crossframe effects need to beBoth intermediate and end crossframe effects need to beaccounted for in design of highly skewed bridges.accounted for in design of highly skewed bridges.

Summary:Summary:

QUESTIONS ?QUESTIONS ?

EE--mail questions to:mail questions to:

[email protected]@dot.state.oh.us

Understanding Skewed Bridge Behavior

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