Chavel-Curved-Girders.pdf - Oregon.gov

6/23/2021

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Photo: 2020 Prize Bridge National Winner – Manning Crevice (Idaho) – Photo Credit: Ken Saindon

Primary Principles for Horizontally Curved Steel I-girder Bridges

Brandon Chavel, PhD, PE June 23, 2021

Director of Market Development, National Steel Bridge Alliance

Presentation Outline

• Structural Behavior

• Analysis Considerations

• Girder Design

• Cross-frame Design

• Fit Condition

• Summary

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• Girder Design


• Fit Condition

• Summary

Structural BehaviorL

OUTSIDEGIRDER

INSIDEGIRDER

CROSS-FRAME

RADIUS

SIMPLE SPAN CURVED BRIDGE - PLAN VIEW

Lb

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Structural Behavior

• Torsional Behavior

Chord line

eccentricity

X

Structural Behavior

• Torsional Behavior

G1

G3

G1 G1G1

G3G3

G3

* Superelevation & Camber not included in cross-section views!

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Structural Behavior

• Load Shifting

G1 G5

Structural Behavior

• Design Forces that need to be considered:• Major-axis bending moments

• Flange lateral bending moments from warping torsion

• Minor-axis bending moments from lateral loads (wind)

• Girder vertical web shear

• Cross-frame member forces

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Structural Behavior

• Girder Normal StressesMajor-Axis Bending

Minor-Axis Bending

Warping (source of lateral flange bending stresses)

• Cross-frames

• Lateral bending

Structural Behavior

Unrestrained by Cross Frame

Top Flange Cross Frame

CompressionCompression

TensionTension

Bottom Flange

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• Cross-frames

• Lateral bending

Structural Behavior

Restrained by Cross Frame

Top Flange Cross Frame

CompressionCompression

TensionTension

Bottom Flange

Structural Behavior

• Flange Lateral Bending Moments from Torsion• Generally, use absolute values in design

+ +-

Cross-Frame

Cross-Frame

MLML

Compression Flange

Tension Flange

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• Girder Design


• Fit Condition

• Summary

Analysis Considerations

• What is the appropriate level of Analysis?• 1D Line Girder with V-Load?

• 2D Grid or Plate and Eccentric Beam?

• 3D Finite Element Analysis?

• Remember: ALL ANALYSES ARE APPROXIMATE!• Some more approximate than others….

• “All models are wrong, but some are useful”• Quote by a wise bridge engineer!

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• 1D Line Girder Analysis• Analyze a single girder by itself

• Manual distribution of dead and live loads to each girder

• AASHTO LRFD Article 4.6.1.2.4b• Limits for a curved I-girder that can be designed neglecting curvature effects for major-axis

bending and shear.

• Flange lateral bending moment, approximated from V-load equation, C4.6.1.2.4b-1

• Stability still needs to be considered

• Cross-frames designed for wind and stability stiffness and forces

• Also good for preliminary design for bridges that need refined analysis!


• 2D Grid or Plate and Eccentric Beam• In-plane representation of the bridge structure

• Girders & cross-frames modeled with two-node/line elements with 3 DOFs per node

• IMPORTANT – Modeling of Cross-frames• AASHTO LRFD C4.6.3.3.4

• Use a shear-deformable (Timoshenko) beam element representation of cross-frames and for developing their stiffness and member area.

• AASHTO/NSBA Steel Bridge Collaboration Guidelines for Steel Girder Bridge Analysis G13.1 Article 3.11.3

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• 2D Grid or Plate and Eccentric Beam• Only considers St. Venant Torsional Stiffness, GJ/Lb.

• Can underestimate torsional stiffness

• IMPORTANT – Torsional Stiffness & Warping Rigidity• AASHTO LRFD C4.6.3.3.2

• NCHRP Report 725 and AASHTO/NSBA Steel Bridge Collaboration Guidelines for Steel Girder Bridge Analysis G13.1-2019 provide approximate method

• Equivalent Torsional Stiffness, Jeq:

• G13.1-2019: Section 3.12


• 3D Finite Element Analysis

Concrete Deck (not shown)

Flanges Cross-frame Struts

Web

Cross-frame Diagonals

Boundary conditions

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Analysis Guidance

• Where to get Guidance?

• Guidelines for Steel Girder Bridge Analysis (G13.1-2019)• Provides the most comprehensive presentation and discussion regarding analysis

techniques associated with steel girder bridges.

• Discussion about line girder (1D), 2D, and 3D analysis methods, while also helping engineers determine the appropriate level of analysis based on a bridge’s geometric aspects.

Analysis Guidance

• Guidelines for Steel Girder Bridge Analysis (G13.1-2019)• Table B.2-1 Matrix for Recommended Level of Analysis

Major Axis Bending Stress

Vertical Displacements

Cross Frame Forces

Flange Lateral Bending

Girder Layover at Bearings

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• Reduce individual member stiffness to 0.65AE• AASHTO LRFD Article C4.6.3.3.4

• Accounts for member end eccentricity

• Accounts for reduced stiffness at member end

• In model:• Use E_steel_CF = 0.65*29000 ksi


• Consider support stiffness in the analysis model• Transverse and Longitudinal

• Use spring elements to represent stiffness at bearing location

• Account for skew

Transverse Longitudinal

∆ =��

3��

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Dead Loads:Applied load = SReactions?


• Sanity Checks• Deflections

• Reactions

• Moments




• Girder Design


• Fit Condition

• Summary

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Girder Design

• Topics for consideration today:• Design of each girder

• Girder flange sizing for fabrication

• Flange lateral bending stresses

• Girder camber

• Girder shear & transverse stiffeners

Girder Design

• Load Shifting

G1 G5

MG5 >> MG1

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Girder Design

• Moment Comparison

Girder Design

• Girder with largest radius typically uses larger flanges

Larger Bottom Flange

Smaller Bottom Flange

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Girder Design

• Design Cycle• Iterative process between analysis and design

Preliminary Design

Create 2D or 3D Model

Analyze

Adjust Model

Design

STOP!Design Complete

Flange Sizing

• Fabricators cut multiple flanges from wide plates

• Try to limit the number of different plate thickness in a single job

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Flange Sizing

• Example• Try to use same flange thicknesses over all girders

• change the width over the adjacent field pieces

CL PierCL Pier

Flange Sizing

• Example• Try to use same flange thicknesses over all girders

• change the width over the adjacent field pieces

CL PierCL Pier

2.5” x 22”

2.5” x 28”

1.5” x 18”

1.5” x 24”

1.75” x 22”

1.75” x 28”

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Flange Sizing

• Example• Weld large plates together and cut the flanges

t = 2.5” t = 1.75”t = 1.75”

W1 = 28”

W2 = 22”

W2 = 22”

W1 = 28”

Keep a constant length for the thicker flange piece across all girders.

Flange Lateral Bending Stresses

• From warping torsion caused by the curvature and cross-frame restraint

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• How does AASHTO LRFD BDS consider flange lateral bending• On factored load (stress) side of equations

• Flange in Compression - Buckling

fbu fl

fbu + 1/3 fl


• How does AASHTO LRFD BDS consider flange lateral bending• On factored load (stress) side of equations

• Flange in Compression – Yielding

• Flange in Tension - Yieldingfbu fl

fbu + fl

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• Which stress (fl) should I use?• AASHTO LRFD BDS Article 6.10.1.6:

• Also note, lateral bending stress in continuously braced flanges shall be taken equal to zero.• Top Flange with hardened deck – lateral bending for DC2, DW, and LL+I all taken as zero.


• How do I get the flange lateral bending stress from my model?

• 1D line girder and 2D grid & PEB models• V-load equation for Mlat (C4.6.1.2.4b-1):

• 3D Finite Element Models• Flange modeled as beam elements

• Bending in the transverse direction of flange element

• Direct output

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Girder Camber

• What is needed?• Vertical Camber is only needed

• Lateral Deflection or rotation is not needed

• Steel Dead Load (A)

• Concrete Dead Load (B)

• Superimposed Dead Load (C)

• Geometric Camber (D)

• Different for each girder

Girder Shear

• Should I use Transverse Stiffeners?• Partially stiffened web is typically most economical

• Generally, additional transverse stiffeners in 1st and 2nd bay from support

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Girder Shear

• Cross-frame connection plates – can be used for a stiffened web panel• Interior bays - If spacing (Lb) is less than 3D (D = web depth)

• End support bay – If spacing (Lb) is less than 1.5D (D = web depth)

• AASHTO LRFD BDS Article 6.10.9.1




• Girder Design


• Fit Condition

• Summary

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Cross-frame Member Design

• Primary Members• AASHTO Table 6.6.2.1-1


• Introduction• Try to use angles first

• Only use a WT if an Angle will not work

• WTs are cut from WF beams – extra labor

• A note on Angles:• Avoid 1/16” gages

• These typically require a mill order

• Tonnage requirement is typically much greater than that required for the project

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Cross-frame Design Considerations

• Grouping of Cross-frames• Don’t just design members for all the Max/Min’s

• Low forces / fatigue range

• Medium forces / fatigue range

• High forces / fatigue rangeMedium

High


• Angles• Check Slenderness Requirements

• Tension (AASHTO LRFD Article 6.8.4)• primary members l /r ≤ 200

• Compression (AASHTO LRFD Article 6.9.3)• primary members K l /r ≤ 120

• Verify Resistance is Adequate for Applied Eccentric Tension Demands• AASHTO LRFD BDS 9th Edition Tension Checks (6.8.2.1)• Article C6.8.2.2 – moment due to eccentricities may be ignored, addressed through shear

lag factor, U.

• Verify Resistance is Adequate for Applied Eccentric Compression Demands• AASHTO LRFD BDS 9th Edition Compression Checks (6.9.2.1 & 6.9.4) • Article 6.9.4 – accounts for eccentric loading using (KL/r)eff

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• WTs• Check Slenderness Requirements

• Tension (AASHTO LRFD Article 6.8.4)• primary members l /r ≤ 200

• Compression (AASHTO LRFD Article 6.9.3)• primary members K l /r ≤ 120

• Generally, need to satisfy interaction equations:• Combined axial tension and flexure (AASHTO LRFD 6.8.2.3)

• Combined axial compression and flexure (AASHTO LRFD 6.9.2.2)


• WTs (continued)• Flexure: AASHTO LRFD 6.12.2.2.4 – Tees & Double Angles

• Yielding

• Lateral-Torsional Buckling

• Flange Local Buckling

• Local Buckling of Tee Stems

• Requires consideration of the whether WT flange or stem is in compression or tension

• Noncomposite Compressive Resistance AASHTO LRFD 6.9.4.1• Applicable buckling modes for singly symmetric members:

• Flexural buckling (6.9.4.1.2)

• Flexural-torsional buckling for open-section members. (6.9.4.1.3)

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• Girder Design


• Fit Condition

• Summary

Fit Condition

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Fit Condition

• Fit Condition – deflected girder geometry associated with a targeted dead load condition for which the cross-frames are detailed to connect to the girders.• A fit decision must always be made so the Fabricator/Detailer can complete the

shop drawings & successfully fabricate the bridge components – allows Erector/Contractor to assemble the steel & achieve the desired geometry in the field.

• The fit decision also affects design decisions regarding rotation demands on the bearings, and internal force effects for which the cross-frames and girders must be designed.

• The fit condition should ideally be selected by the Engineer.

Fit Condition

Loading Condition Fit Construction

Stage Fit

Description

No-Load Fit (NLF) Fully-Cambered

Fit

The cross-frames are detailed to fit to the

girders in their fabricated, plumb, fully-

cambered position under zero load.

Steel Dead Load Fit

(SDLF)

Erected Fit The cross-frames are detailed to fit to the

girders in their ideally plumb as-deflected

positions under the self-weight of the steel

at the completion of the erection.

Total Dead Load Fit

(TDLF)

Final Fit The cross-frames are detailed to fit to the

girders in their ideally plumb as-deflected

positions under the total dead load.

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Fit Condition

• NSBA White Papers - Skewed and Curved Steel I-Girder Bridge Fit• Standalone Summary (6 pages)• Full Document (47 pages)

• Explains Fit Conditions• No-Load Fit

• Steel Dead Load Fit

• Total Dead Load Fit

• Provides Recommended Fit Conditions for• Skewed Bridges

• Curved Bridges• Curved Bridges with Skewed Supports

Fit Condition

• Recommendations

• Avoid TDLF on Horizontally-Curved Bridges

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• Girder Design


• Fit Condition

• Summary

Summary

• Structural Behavior• Bridge acts as system

• Torsional behavior

• Warping and flange lateral bending

• Cross-frames

• Analysis Considerations• 1D, 2D, and 3D analysis methods

• 2D Model considerations

• Analysis Guidance

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Summary

• Girder Design• Individual girder design

• Minimize number of different flange thicknesses

• Flange lateral bending stresses – AASHTO LRFD

• Girder camber

• Girder shear and use of transverse stiffeners

• Cross-frame Design• Angles

• WTs

Summary

• Fit Condition• No Load Fit

• Steel Dead Load Fit

• Total Dead Load Fit AVOID

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More Information

• FHWA Steel Bridge Design Handbook• Design Examples:

• Vol. 23: 3-Span Continuous Horizontally Curved Composite Steel I-Girder Bridge

• Vol. 25: 3-Span Continuous Horizontally Curved Composite Steel Tub-Girder Bridge

• National Highway Institute• NHI Course 130095

• Analysis and Design of Skewed and Curved Steel Bridges with LRFD

• National Steel Bridge Alliance• Website, Education archive, and reach out with questions

Questions?

• Thank you for your time today!

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Photo: 2020 Prize Bridge National Winner – Manning Crevice (Idaho) – Photo Credit: Ken Saindon

Primary Principles for Horizontally Curved Steel I-girder Bridges

Brandon Chavel, PhD, PE

Director of Market Development, National Steel Bridge Alliance

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Structural Behavior

L1 L2 OUTSIDEGIRDER

L PIERC

INSIDEGIRDER

CROSSFRAME

RADIUS

CURVED BRIDGE - PLAN VIEW

d

L1 L2 OUTSIDEGIRDER

L PIERC

INSIDEGIRDER

CROSSFRAME

RADIUS

CURVED BRIDGE - PLAN VIEW

d

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Flange Sizing

• Example• Weld large plates together and cut the flanges

t = 2.5” t = 1.75”t = 1.75”

W1 = 28”

W2 = 22”

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Chavel-Curved-Girders.pdf - Oregon.gov

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Transcript of Chavel-Curved-Girders.pdf - Oregon.gov