Curved Girder Behavior & Design - H-B-S.org · Curved Steel Girder Design L1 L2 OUTSIDE GIRDER L A...

Curved Girder

Behavior & Design

Cur

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Ste

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Brid

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Curved Steel Girder Design

L1 L2 OUTSIDEGIRDER

L ABUT

L PIER

L ABUT

C

CC

INSIDEGIRDER

CROSSFRAME

RADIUS

CURVED BRIDGE - PLAN VIEW

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25’R > 1000’

20’500’ < R < 1000’

17’200’< R < 500’

15’R < 200’

Max. Diaphragm SpacingCenterline Radius

Crossframe SpacingPD

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Design Forces (per specification)

� Primary Bending Forces

� Cross Frame Forces (Primary Members)

� Lateral Flange Moments

� Secondary Bending Forces

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Unrestrained by Cross Frame

Top Flange

Cross frame

CompressionCompression

TensionTension

Bottom Flange

Curved Steel Girder DesignPD

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CompressionCompression

TensionTension

Bottom Flange

Top Flange

Cross frame

Curved Steel Girder DesignPD

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Cur

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What Has Changed over the Years?

What Has Changed over What Has Changed over the Years?the Years?

Curved Steel Girder Bridges

�� Analysis MethodsAnalysis Methods

�� Yield StrengthsYield Strengths

�� Frequency of highly curved Frequency of highly curved and/or skewed bridgesand/or skewed bridges

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But there is still a key aspect of curved

girder behavior that an engineer must

understand

But there is still a key But there is still a key aspect of curved aspect of curved

girder behavior that girder behavior that an engineer must an engineer must

understandunderstand


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The V-Load Method

(Analysis)

Cur

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Central Angle Limit

� Primary Force

� Secondary Forces

� Lateral Flange Moments

Span X Span Y

Bridge Centerline

When Subtended Angle ( ) is Less Than Code Limit

Secondary Forces Neglected

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Behavior and Analysis of Curved and SkewedSteel Girder Bridges

Behavior and Analysis of Curved and SkewedSteel Girder BridgesDomenic Coletti, PE

John Yadlosky, PE

Domenic Coletti, PE

John Yadlosky, PE

World Steel Bridge Symposium 2005Orlando, FL

World Steel Bridge Symposium 2005Orlando, FL

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Levels of Analysis

• Three Levels of Analysis– Approximate Analysis– 2D (“Grid”) Analysis– 3D Analysis

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Levels of Analysis

• Issues– Level of modeling detail / accuracy– Level of modeling effort– Amount of output– Live load modeling

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Levels of Analysis

• Live Load Modeling– Multiple live load cases (“live load generator”)– Influence line approach– Influence surface approach

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Leve

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•In

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BSDI, Ltd.


Levels of Analysis –Approximate Analysis

• Approximate Analysis Methods– Line Girder + Factors– V-Load Method: I -Girders– M/R Method: Tub Girders

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• Line Girder + Factors– Any line girder analysis tool can be used– Factors from FHWA “Curved Girder Workshop”– Approximate! Good for preliminary design

FHWA Curved Girder Workshop

Manual, 1976

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• V-Load Method– For Curved I-Girders– Developed by USS in 1960s– “V-Loads” are the shears in diaphragms– Computer tools available

FHWA Curved Girder Workshop Manual, 1976

FHWA Curved Girder Workshop Manual, 1976

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• M/R Method– For Curved Tub Girders– Developed by Tung and Fountain in 1970– Analogous to V-Load– Very cumbersome for multiple girder systems

Tung and Fountain, 1970

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Levels of Analysis – 2D “Grid”Analysis

• What is a 2D “Grid” Analysis?– Girders modeled as line elements– Diaphragms modeled as line elements– Deck modeled in strips as line elements

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• Grid Analysis Computer Tools– MDX– DESCUS I & II– General FEM programs – Others?

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• Advantages of Grid Analysis– Simple modeling– Efficient (level of modeling effort)– Some find it easier to understand– Computer tools readily available

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• Disadvantages of Grid Analysis– Diaphragm modeling – Deck modeling – Load Distribution – In sum: Accuracy questions?

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• Grid Analysis is Not Recommended for…– Severe curvature and/or skew – Deep girders – Long spans – Variable depth girders

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Levels of Analysis – 3D Analysis

• What is a 3D Analysis?– Flanges: beam or plate elements– Webs: plate elements– Diaphragms, bracing: truss or plate elements– Deck: solid or plate elements

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• 3D Analysis Computer Tools– BSDI 3D System (limited LRFD capabilities)– General FEM programs – Others?

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• Advantages of 3D Analysis– All pieces and parts modeled - rigorous– Direct analysis results for all pieces and parts– Greater refinement– Greater accuracy (?)

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• Disadvantages of 3D Analysis– Greater modeling effort– More complicated model – Results less “intuitive”– In sum: Is the refinement

worth the effort?

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• Limitations of 3D Analysis– Virtually no limitations on type or complexity of

structures that can be modeled– Limitations come down to time and money

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� Lay out framing plan� Establish initial plate sizing philosophy� Run line Girder� Adjust plates for 3D Model� Run 3D Model� Resize plates� Rerun 3D Model� Design remaining girder elements

Design Process

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Detailing & ConstructionDetailing & Detailing &

ConstructionConstruction


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Construction Issues

• Horizontal, Vertical and Rotational Camber

• Single I Girder Stability

• Erecting Curved Girders

• Shipping and Handling

• Heat - Curving

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Say ‘No’ to

Oversized Holes in Main

(Geometry Controlling)Load Carrying Members!

Say Say ‘‘NoNo’’ toto

Oversized Holes in Oversized Holes in Main Main

(Geometry Controlling)(Geometry Controlling)Load Carrying Members!Load Carrying Members!


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Girder 3 Girder 2 Girder 1

3/4" 3/8"

Maximum Horizontal Displacement

3/8" : (1 1/16" - 7/8") 3/16" (1/2" Hole) x (4 Holes):

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Gir

der

3G

ird

er 2

Gir

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1

3/4"

3/8"

Max

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isp

lace

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Girder 3 Girder 2 Girder 1

See Detail 1 See Detail 2

See Detail 3

DWG. CT-010

See Detail 4

Maximum Displacement with Rotation

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Left Outside

Top Flange

(Detail 1)

Center Girder

Top Flange

(Detail 2)

Girder 3 Girder 2

0.371"

2.30

2 "

“Original” Location

of Girder

“Original” Location

of Bolt Holes

7/8" Dia. Bolt

Displaced & Rotated

Position

8'-9"

(Not to Scale) 0.191"

0.75

2 "

(See

No

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Consider Warping Stresses and Associated Deflections During Lifting

and Handling.

Consider Warping Consider Warping Stresses and Associated Stresses and Associated Deflections During Lifting Deflections During Lifting

and Handling.and Handling.


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Bearing OrientationBearing OrientationBearing Orientation


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Before Expansion

Tangent

Radial Line

After Expansion

Radial Line

Tangent

End

SupportEnd

Support

PierPier

DIRECTION OF MOVEMENT

Suggested Support Arrangement for Curved Girder Spans

• Minimize Number of Total Fixed Points

• Adjust for Longer Structures

A & C

B

All Other

Tangential

Radial

Any

Radially

Tangentially

Bearings Lineal in

Horizontal PlaneMovements

Arrested

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Bearing Design Tips

• Use multi-rotational bearings

• Pot/spherical bearings

• Round laminated neoprene pads

• Restrain as few bearings as possible

• Restraint costs more

• Minimizes bearings locking up

• Minimizes concern over lateral restraint forces

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Some Thoughts on Cut Curving &

Heat Curving

Some Thoughts Some Thoughts on Cut Curving & on Cut Curving &

Heat CurvingHeat Curving


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Cut

Cur

ving

Cut

Cur

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Cut

Cur

ving

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Hea

t Cur

ving

Hea

t Cur

ving

Hea

t Cur

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FHWA/NCHRP Documents

•FHWA-IF-99-004

•NCHRP Report 271

FHWA/NCHRP Documents

•FHWA-IF-99-004

•NCHRP Report 271


Heat-Straightening Repairs of Damaged Steel Bridges (A Technical Guide and Manual of Practice)

Guidelines for Evaluation and Repair of Damaged Steel Bridge Members

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Review - Parts I & II:Review Review -- Parts I & II:Parts I & II:Curved Steel Girder Bridges

�� Cross Frames are Primary MembersCross Frames are Primary Members

�� Lateral Flange Bending (Warping) / WindLateral Flange Bending (Warping) / Wind

�� Analysis MethodsAnalysis Methods

�� Holistic Approach Holistic Approach –– Consider Consider Construction During DesignConstruction During Design

�� Account for ROTATIONS and Account for ROTATIONS and Deflections Deflections –– ‘‘NoNo’’ Oversized HolesOversized Holes

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Cur

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Clo

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Curved Girder Behavior & Design - H-B-S.org · Curved Steel Girder Design L1 L2 OUTSIDE GIRDER L A...

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Transcript of Curved Girder Behavior & Design - H-B-S.org · Curved Steel Girder Design L1 L2 OUTSIDE GIRDER L A...