Curved Girder Behavior & Design - H-B-S.org · Curved Steel Girder Design L1 L2 OUTSIDE GIRDER L A...
Transcript of Curved Girder Behavior & Design - H-B-S.org · Curved Steel Girder Design L1 L2 OUTSIDE GIRDER L A...
Curved Girder
Behavior & Design
Cur
ved
Ste
el G
irder
Brid
ges
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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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Curved Steel Girder Design
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
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Cur
ved
Ste
el G
irder
Des
ign
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Cur
ved
Ste
el G
irder
Des
ign
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Cur
ved
Ste
el G
irder
Des
ign
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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
Curved Steel Girder Bridges
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The V-Load Method
(Analysis)
Cur
ved
Ste
el G
irder
Brid
ges
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Cur
ved
Ste
el G
irder
Des
ign
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Cur
ved
Ste
el G
irder
Des
ign
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Curved Steel Girder Design
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
θθθθθθθθ
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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
ls o
f Ana
lysi
s
•In
fluen
ce S
urfa
ce E
xam
ples
BSDI, Ltd.
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Leve
ls o
f Ana
lysi
s
•In
fluen
ce S
urfa
ce E
xam
ples
BSDI, Ltd.
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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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Levels of Analysis –Approximate Analysis
• 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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Levels of Analysis –Approximate Analysis
• 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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Levels of Analysis –Approximate Analysis
• 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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Levels of Analysis – 2D “Grid”Analysis
• Grid Analysis Computer Tools– MDX– DESCUS I & II– General FEM programs – Others?
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Levels of Analysis – 2D “Grid”Analysis
• 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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Levels of Analysis – 2D “Grid”Analysis
• Disadvantages of Grid Analysis– Diaphragm modeling – Deck modeling – Load Distribution – In sum: Accuracy questions?
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Levels of Analysis – 2D “Grid”Analysis
• 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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Levels of Analysis – 3D Analysis
• 3D Analysis Computer Tools– BSDI 3D System (limited LRFD capabilities)– General FEM programs – Others?
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Levels of Analysis – 3D Analysis
• 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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Levels of Analysis – 3D Analysis
• 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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Levels of Analysis – 3D Analysis
• 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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Curved Steel Girder Design
� 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
Curved Steel Girder Bridges
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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!
Curved Steel Girder Bridges
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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
der
1
3/4"
3/8"
Max
imu
m V
erti
cal D
isp
lace
men
t
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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
te)
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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.
Curved Steel Girder Bridges
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Bearing OrientationBearing OrientationBearing Orientation
Curved Steel Girder Bridges
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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
Curved Steel Girder Bridges
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Cut
Cur
ving
Cut
Cur
ving
Cut
Cur
ving
Cur
ved
Ste
el G
irder
Brid
ges
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Hea
t Cur
ving
Hea
t Cur
ving
Hea
t Cur
ving
Cur
ved
Ste
el G
irder
Brid
ges
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FHWA/NCHRP Documents
•FHWA-IF-99-004
•NCHRP Report 271
FHWA/NCHRP Documents
•FHWA-IF-99-004
•NCHRP Report 271
Curved Steel Girder Bridges
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
ved
Ste
el G
irder
Brid
ges
Clo
sing
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