Q-Bridge Transverse Analysis

Daniel Mariscal, P.E. AECOM - Tampa, Florida Project Location

United States of America Project Location

State of Connecticut Project Location

City of New Haven Project Location

Interchange: • Interstate I-95 • Interstate I-91 • CT Route 34 • Pearl Harbor Memorial Bridge, Over the Quinnipiac River (Q-Bridge) Existing Bridge: Steel Girder

• Bridge Owner: Connecticut Department of Transportation Existing Bridge: Steel Girder

• Plate Steel Girder, Opened in January 1958 • Main Span 118m, Once the Longest Plate Girder in Western Hemisphere • Functionally Obsolete, Carried Three Lanes in Each Direction Replacement Bridge: Extradosed Bridge

• Several Alternatives Studied • Concrete Extradosed Bridge Selected (First Extradosed Built in the USA) • New Bridge Carries Five Lanes in Each Direction. Economical Bridge Types

Sources: Podolny, Stroh

Steel Box 200 600 Q-Bridge = 515 ft. Segmental 200 600

Extradosed 400 800

Truss 500 1,200

Arch 500 1,200

Cable Stayed 600 1,800 2,800

1,500 Suspension

0 1,000 2,000 3,000 4,000 Span in Feet Girder Bridge

POSTENSIONING TENDONS

Girder Depth: 1:16 to 1:18 Cable-Stayed Bridge

Girder Depth:

STAY CABLES 5 to 6 ft. Tower Height:

V 0.25 Span

H Extradosed Bridge

STAY CABLES

Girder Depth: 1:30 to 1:35 Tower Height: 1:10 to 1:15 What is an Extradosed Bridge?

• Hybrid Bridge Type: – Cable-Stayed Bridge – Post-Tensioned Girder Bridge • Tower Height is Shorter than Cable Stayed Bridges • Girder Depth is Shallower than Girder Bridges, but Deeper than Cable- Stayed Bridges • Stay Cable Planes are Flatter than Cable-Stayed Bridges, and cover a Shorter Portion of the Span • Alternate Load Paths – Relatively Stiff Girder – Stay Cables – Primarily for Dead Loads • Stay Cables are Sized to Contribute to the Deck Prestressing • Low Fatigue Range for Stay Cables • Uniform Stress Range for Stay Cables Why an Extradosed Bridge?

• Falls Within Span Length Range – Longer Main Span Avoids Old Bridge Foundation • Under Clearance: Coast Guard – Shallower Girder – Lower Profile • Over Clearance: FAA – Shorter Towers – Airport Flight Path : Tweed New Haven Airport • Superior Aesthetics Project Description

FAA Clearance (2 Miles from Tweed Airport)

Coast Guard Clearance Project Description

• Northbound Bridge, Dedicated June, 2012 • Northbound Bridge Carried Both Northbound and Southbound Traffic • Southbound Bridge, Dedicated September, 2015 • Total Project Cost $2.0 Billion (approx.) • Main Span Cost $600 Million (approx.) Project Staging

Quinnipiac River

•• StageStage 3:2: DemolishBuild1: Existing NB Structure,Existing Bridge: Structure, NorthboundMove NB Build& SB(NB) SBTraffic & Structure Southbound (SB) Traffic Main Span Erection Sequence

Cast-in-Place, Balance Cantilever Erection

•• StageStage 7634251 -- FinishingClosureBalancedContinuationAssemblyConstruction atat Works Cantilever ofMainSide Travelingof- Cantilever SpanSubstructuresSpan Construction Forms Construction and and Pier Cable Tables Installation Project Design - Longitudinal

• Design Started in 2001 • Bentley’s RM Bridge (formerly TDV’s RM 2000) • Single Spine Model: Beam Elements Project Design - Longitudinal

• Stage Construction • Dead Loads • Post-Tensioning • Creep & Shrinkage • Thermal Loads • Live Loads Project Design - Longitudinal

Longitudinal Model, Erection Sequence Project Design - Longitudinal

Longitudinal Model, Stresses Summary Project Design - Longitudinal

Longitudinal Model, Stresses Summary Project Design - Transverse

• Intergraph’s GT STRUDL • 3-Dimensional Plate Element Model: – Dead Loads – Live Loads – Web Shear Distribution – Dishing Deformation at Cable Stay Locations • 2-Dimensional Frame Beam Element Model: – Interior Transverse Top Slab Post-Tensioning – Exterior Transverse Draped Post-Tensioning • Excel Spreadsheets Project Design - Transverse

3-Dimensional Plate Element Model

Stay Cables As Springs Project Design - Transverse

2-Dimensional Frame Beam Element Model

External PT Loading Project Design – Transverse Review

• New Software Available: Midas FEA • Increased Computing Power • As-Built Model • 3-Dimensional Model Using Solid Elements: 8-Node Hexahedron & 6-Node Wedge for the Superstructure • Linear Elastic Model • Creep & Shrinkage Not Implicitly Modeled • Construction Sequence • Superstructure & Substructure • Stay Cables, Longitudinal & Transverse Post-Tensioning Model Development – Cross Sections

• Multi-Cell Concrete Box • Variable Deck Width Along Length of Bridge • Variable Girder Depth At Towers • Variable Bottom Slab Thickness At Towers

• Variable Botom Slab Thickenes Model Development – Cross Sections

Variable Deck Width Along the Length of Bridge

BEGIN OF BRIDGE

END OF BRIDGE Model Development – Cross Sections

Variable Girder Depth At Towers Model Development – Cross Sections

Variable Bottom Slab Thickness At Towers Model Development – Cross Sections

Full Bridge Model: 57,094 Solid Elements, 2,688 Plate Elements, 14,639 Line Elements Model Development – Cross Sections

Close-Up At Bridge End Model Development – Cross Sections

• Cross Sections Drawn in Microstation • 40 Different Cross Sections Representing Entire Bridge Length Cross Section Variable Geometry • Cross Sections Exported to DXF • DXF Cross Sections Imported into Midas FEA Model Development – Cross Sections

Cross Sections Drawn in Microstation Model Development – Cross Sections

Cross Sections Imported to Midas FEA Model Development – Cross Sections

Cross Sections with “Mesh Control” Model Development – Cross Sections

Two Cross Sections Create Solid by “Lofting” Model Development – Cross Sections

Auto-Mesh Solid Model Development – Cross Sections

Solid Elements Created Model Development – Cross Sections

Close-Up At Tower

Variable Girder Depth and Bottom Slab Thickness Model Development - PT

• Variable Cross Section  Variable PT Geometry • 140 Different Top Transverse PT Geometries • 39 Different Transverse External PT Geometries • PT Geometry Developed In Excel, Points • PT Geometry Imported Into AutoCAD, Polylines • PT Geometry Exported To DXF • DXF Geometry Imported Into Midas FEA Model Development - PT

Variable PT Geometry Created Using Excel Model Development - PT

Geometry Imported Into AutoCAD Using Scripts Model Development - PT

Geometry Exported From AutoCAD to DXF Model Development - PT

DXF PT Geometry Lines Imported Into FEA Model Development - PT

Transverse Top Slab PT: “Bar In Solid”

T1 Tendons: 4 x 15.2mm Strands T2 Tendons: 2 x 15.2 mm Strands Model Development - PT

Transverse External PT Geometry Lines Model Development - PT

Transverse External PT: “Line Element”

T3 Tendons: 19 x 15.2mm Strands T4 Tendons: 7 x 15.2 mm Strands Model Development - PT

Top Cantilever PT Geometry Lines Model Development - PT

Longitudinal Cantilever PT: “Bar In Solid”

C1 Tendons: 27 x 15.2mm Strands C2 Tendons: 23 x 15.2 mm Strands C3 Tendons: 19 x 15.2mm Strands Model Development - PT

Bottom Continuity PT Geometry Lines Model Development - PT

Longitudinal Bottom Slab PT: “Bar In Solid”

B1 & B3 Tendons: 9 x 15.2mm Strands B2 Tendons: 12 x 15.2 mm Strands Model Development - PT

All Geometry Line, Including for Stay Cables Model Development - PT

Typical Stay Cable Segment With Diaphragm

Solid Elements

Plate Elements Model Development - PT

Typical Stay Cable Segment With Diaphragm Transverse Post-Tensioning

Top Slab PT

External PT Model Development - PT

Longitudinal Cantilever Post-Tensioning Model Development - Loads

Traveler Loads: Pressure Loads Model Development - Staging

Construction Sequence: Total 142 Steps, 2.1 Hours Model Development - Staging

Construction Sequence Model Development - Staging

Construction Sequence Model Development – Live Loads

Live Loads: Arbitrary Load/Vehicle Truck Load Model Development – Live Loads

Live Loads: 25 Positions Across Deck Model Development – Live Loads

Transverse Live Loads: 7 Locations Along Main Span Model Verification

• Model Verification Against RM Bridge Single Spine Model • Uniform 10kN/m2 Pressure Load Applied on Entire Deck Area Model Verification: Reactions

10kN/m2 Uniform Pressure Over Deck

Location RM Result FEA Result RM/FEA

Anchor Pier 1 3805 3941 0.97

Tower 2 12022 9935 1.21

21111 25300 0.83

11863 9797 1.21

Tower 3 11484 9475 1.21

19790 23800 0.83

11582 9585 1.21

Anchor Pier 4 4050 9816 1.06

TOTAL 95707 95649 1.00 Model Verification: Deflection

10kN/m2 Uniform Pressure Over Deck

Defelection Comparison - Uniform Load 10kN/m2 100 50 0 -50 0 50 100 150 200 250 300 -100 RM -150 FEA

-200 Defelction(mm) -250 -300 -350 Location (m) Model Verification: Top Deck Stresses

10kN/m2 Uniform Pressure Over Deck

Top Fiber Stress Comparison - Uniform Load 10kN/m2 10000 8000 6000 4000 2000 0 RM -2000 0 50 100 150 200 250 300 FEA

Stress (kN/m2) Stress -4000 -6000 -8000 -10000 Location (m) Model Verification: Top Slab Interior PT

Manual Verification Model Verification: Top Slab Interior PT

Manual Verification

HAND CALCULATIONS @ Midspan @ Web Outside cell Inside cell Outside cell b (mm) 4360 4360 4360 d (mm) 240 240 450 dp (mm) 167 198 80 e (mm) -47 -78 145 P (kN) -1360 -1360 -1360 M (kN-m) -63.92 -106.08 197.2 A (mm2) 1.04640 1.04640 1.96200 S (mm3) 0.04186 0.04186 0.14715 P/A (MPa) -1.300 -1.300 -0.693 M/S (MPa) 1.527 2.534 -1.340 Stop (MPa) 0.227 1.235 -2.033 Sbot (MPa) -2.827 -3.834 0.647

FEA RESULTS Stop (MPa) 0.220 0.962 -2.141 Sbot (MPa) -2.658 -3.384 0.799

RATIO FEA/HAND CALCULATIONS Stop 0.97 0.78 1.05 Sbot 0.94 0.88 1.24 Model Verification: Transverse Exterior PT

PT Forces Applied as Prestress Load Model Verification: Transverse Exterior PT

PT Forces Applied as External Forces Model Verification: Transverse Exterior PT

PT Forces Applied as Prestress Load Model Verification: Transverse Exterior PT

PT Forces Applied as External Forces Model Verification: Total Reactions

Dead Load Reactions Comparison

Location RM Result FEA Result RM/FEA

Anchor Pier 1 24176 8745* 0.36

Tower 2 40658 51330 1.26

71964 58760 0.82

40642 51310 1.26

Tower 3 39251 49520 1.26

67333 53870 0.80

39328 49440 1.26

Anchor Pier 4 23805 10138 0.43

TOTAL 347157 333113* 0.96

(*) Does not include anchor pier self weight. Model Results

• Web Shear Distribution • Multiple Dead Load Stress Checks • Service Stresses Load Rating: – Dead Load Stresses – Live Load Stresses • Flexural Strength Load Rating: – Dead Load Moments – Live Load Moments Model Results: Web Shear Distribution

Vertical Shear Distribution to Webs: Two Webs

V=Vertical Shear

50% V 50% V Model Results: Web Shear Distribution

Shear Distribution to Webs: Multiple Cells

V=Vertical Shear

?V ?V ?V ?V ?V ?V FEA Output: Local Direction Force Sum Model Results: Web Shear Distribution

LDFS: Total Cross Section Model Results: Web Shear Distribution

LDFS: Inclined Left Web Model Results: Web Shear Distribution

LDFS: Inclined Right Web Model Results: Web Shear Distribution

LDFS: Vertical Web 1 Model Results: Web Shear Distribution

LDFS: Vertical Web 2 Model Results: Web Shear Distribution

LDFS: Vertical Web 3 Model Results: Web Shear Distribution

LDFS: Vertical Web 4 Model Results: Web Shear Distribution

Tabulate Shear Distribution in Excel Model Results: Stay Cable Diaphragm

Stay Cable Segment: Diaphragm Model - Plates Model Results: Stay Cable Diaphragm

Stay Segment Diaphragm Max. Dead Load Principal Stresses Model Results: Stay Cable Diaphragm

Stay Segment Diaphragm Vertical Dead Load Stresses Model Results: Stay Cable Segment

Edge Beam Dead Load Stresses Model Results: Stay Cable Segment

Edge Beam Dead Load Stresses Model Results: Stay Segment TS2-11A

Bottom Slab, Segment Erection Model Results: Stay Segment TS2-11A

Bottom Slab, Stressing Top Slab Transverse PT Model Results: Stay Segment TS2-11A

Bottom Slab, Stay Cable Stressing Model Results: Stay Segment TS2-11A

Bottom Slab, Sidespan Closures Transverse PT Model Results: Stay Segment TS2-11A

Top Slab, Segment Erection Model Results: Stay Segment TS2-11A

Top Slab, Stressing Top Slab Transverse PT Model Results: Stay Segment TS2-11A

Top Slab, Stressing Stay Cables Model Results: Stay Segment TS2-11A

Top Slab, Sidespan Closures Transverse PT Model Results: Stay Segment TS2-11A

Top Slab, Sidespan Closures Transverse PT Model Results: Live Loads Deflections

Live Load HL-93 Truck Case 7A-#01 Model Results: Live Loads Deflections

Live Load HL-93 Truck Case 7A-#13 Model Results: Live Loads Deflections

Live Load HL-93 Truck Case 7A-#25 Model Results: Live Loads Deflections

Envelope of Load Cases 7A-#01 thru 7A-#25 Model Results: Live Loads Stresses

CLSR-3 Segment, Top Slab, Top & Bottom Transverse Stresses Envelope, Live Load 7A Model Results: Live Loads Stresses

CLSR-3 Segment, Bottom Slab, Top & Bottom Transverse Stresses Envelope, Live Load 7A Model Results: Live Loads Stresses

Maximum Transverse Stresses Envelope All Live Load Sets Model Results: Live Loads Stresses

Minimum Transverse Stresses Envelope All Live Load Sets Construction Pictures Construction Pictures Construction Pictures Construction Pictures Construction Pictures Construction Pictures Construction Pictures Construction Pictures Construction Pictures Construction Pictures Construction Pictures Construction Pictures Construction Pictures Pearl Harbor Memorial Bridge Pearl Harbor Memorial Bridge