Practical Design of Balanced Cantilever Bridges - Piyush Santhalia

Practical Design of Balanced Cantilever Bridges

Piyush Santhalia Project Engineer - AECOM

Image: Wikipedia

Piyush Santhalia

Contents

1. Introduction

2. Longitudinal Span Configuration 3. Construction Sequence 4. Cross Section 5. Support Conditions 6. Sub-Structure and Foundation 7. Prestressing Details 8. Design Check 9. Pre-Camber 10.Modelling & Other Suggestions

Piyush Santhalia

1. Introduction

• Cantilever construction method

– Very ancient technique

– Structure is built component by component above ground level.

– More recently: Construction of Cable Stayed Bridges, Extra-dosed Bridges etc.

– Prestressed Concrete Bridges

• Cast in situ Segments or Pre-cast segments

• Integral with Pier or On Bearings

• 60m – 300m span

Piyush Santhalia

1. Introduction

Balanced Cantilever Bridge : - Cast-in-Situ Segments - Integral with Pier

Image: Random Site in Delhi

Piyush Santhalia

2. Longitudinal Span Configuration

• Typical 3 Span system – Mid Span: L

– End Spans: 0.6L to 0.7L (to control uplift in bearing)

L 0.6 L to 0.7L 0.6 L to 0.7L

• Typical 4 or more Span (varying) system 0.6 L1 to 0.7L1 L1 (L1 + L2)/2 0.6 L2 to 0.7L2

Piyush Santhalia

2. Longitudinal Span Configuration

• No such luxury in today’s congested urban area

I. 34 + 60 + 34 m

II. 60 + 60 m

III. 37 + 70 + 67 + 55 + 34m

Piyush Santhalia

3. Construction Sequence • Pier head : On ground supported staging

• Most of Segments: – Erect/cast using Segment Lifter/Form Traveller

– Cantilevered out from preceding segment.

– Prestressing tendons running one of the cantilever to the other are stressed.

– Symmetrical construction to minimize unbalanced moment on sub-structure and foundation: Balanced Cantilever

– Cast portion (beyond 0.5 x L) of both End-spans Ground Supported staging.

– Cast Stitch segments • Stitch in the End – span

• Stitch in the Mid-span

• Levels of the Cantilever arms being stitched should be matched

• Segmentation: 2.5m to 4m or even 5m – Construction Cycle

– Capacity of Form Traveller/Segment Lifter

Piyush Santhalia

3. Construction Sequence

Balanced Cantilever Bridge : Delhi Metro Phase III 60 + 60m span

Piyush Santhalia

3. Construction Sequence

Casting of Stitch at Mid-span using suspender.

Balanced Cantilever Bridge : Delhi Metro Phase III (34 + 60 + 34m)

Piyush Santhalia

4. Cross-Section

L

H1 H2

• Highway Bridges – Depth at Face of Pier, H1 : L/15 – L/18 (roughly)

– Depth at Mid-Span, H2 : L/30 – L/35 (roughly)

• Highway vs Railway Bridge – 34+60+34m span CLC

Load Metro Highway

DL 463 463

SIDL 240 85

LL 262 134

Shear Force at Pier Face (ton)

Piyush Santhalia

4. Cross-Section

• Depth may vary – Parabolic

– Cubically: need to check for insufficient depth around L/4

– Linearly varying depth • Local thickening of soffit is required.

Piyush Santhalia

5. Support Conditions

• Box Girder – On simple bearing – Stability check during construction

– Minimal secondary effect of Creep, Shrinkage and Prestressing

• Box Girder Integral with Intermediate Piers – Check pier for un-balanced moment during construction.

– Pronounced secondary effect.

Piyush Santhalia

6. Sub-Structure and Foundation

• Flexibility – High time period (lesser seismic force)

– Lower force due to secondary effects of creep, shrinkage and Prestressing Tendons

– Twin Piers

𝐹 =3𝐸𝐼

𝐿δ

Piyush Santhalia

7. Prestressing Details • Cantilever Tendons

– For holding the segments added during cantilever construction

– To take up the negative moment due to SW of Segments, SIDL and/or Live Load

– At least 1 pair of tendon is anchored per segment.

• Continuity Tendons: – To take up the force due to effects after the cantilever have been

stitched.

Piyush Santhalia

7. Prestressing Details

• Top Tendons – Try to keep the web clear of the Tendons

• Bottom Tendons – Keep the webs clear of the tendons as much as possible

– Keep tendons nearer to the webs as much as possible

– Enough prestressing for sections at mid-span to hog.

– Blister Blocks for anchoring of tendons

Piyush Santhalia

8. Analysis

• Why Construction Stage Analysis

Bending Moment Diagram due to SW: Simultaneous Analysis

Bending Moment Diagram due to SW: Sequential Analysis

Piyush Santhalia

8. Analysis


– Time Dependent Effects of Creep and Shrinkage • No secondary effect of Creep and Shrinkage before stitching

Structure before casting of stitch segment

Deformation due to Shrinkage.

Residual Shrinkage Strain: i) After 3 days – 4.3 x 10-4

ii) After 14 days – 2.5 x 10-4

Piyush Santhalia

8. Analysis


– Time Dependent Effects of Creep and Shrinkage • Different age of concrete at different loading

– Modulus of Elasticity increases with time

Piyush Santhalia

9. Design Check

• Sub-structure & Foundation

– Regular Checks for Foundation & Piers

– Secondary effects of CR, SH & PS should be considered

– Check during construction (stability or adequacy) i) Imbalance of 1 segment ii) Accidental Fall of Empty Form Traveller

Imbalance of 1 Segment

Fall of empty FT

Piyush Santhalia

9. Design Check

• Super Structure

– Check during construction (ULS & SLS) • Maximum Compression at each stage

– Maximum compression: 0.48fck (IRC 112-2011)

• Maximum Tension at each stage – Minimum compression of 0.2fck - Precast segments (temporary Prestressing)

– Maximum tension of 1 MPa – Cast in situ segments.

• Loads – SW of Segments

– Form Traveller (usually half the weight of heaviest segment) + Shutter

– Weight of Green Concrete

– Construction Live Load

– Wind / EQ (cantilever)

Piyush Santhalia

9. Design Check Stress check during Construction: 37 + 70 + 67 + 55 + 34m

Stresses at Top Fibre due to DL + PS + CR + SH (N/mm2)

Piyush Santhalia

9. Design Check


Stress check during Construction: 37 + 70 + 67 + 55 + 34m

Piyush Santhalia

9. Design Check


Stresses at Bottom Fibre due to DL + PS + CR + SH (N/mm2)


Piyush Santhalia

9. Design Check




Piyush Santhalia

9. Design Check




Piyush Santhalia

9. Design Check




Piyush Santhalia

9. Design Check

• Super Structure

– Check during Service (0 - Design life) • Loads

– Regular Loads (SW, SIDL, LL)

– Prestressing

» Losses up to design life should be considered

» Secondary effects are usually significant

– CR & SH: Secondary effects are significant.

– Temperature Variation

• SLS Checks – Maximum Compression

» Maximum compression: 0.48fck (IRC 112-2011)

– Maximum Tension

Piyush Santhalia

9. Design Check

• Super Structure

– Check during Service (0 - Design life) • ULS Checks

– Moment at the intermediate support

» Hogging for Normal Case

» Reversible in Seismic case

– Shear Check

» Varying depth: Should be checked at regular interval

• Critical at locations with kink

Piyush Santhalia

9. Design Check

• Super Structure

– Check during Service (0 - Design life) • ULS Checks

– Shear Check

» Vertical component of Prestressing: reduces shear

» Resal Effect: Part of Shear is balanced by the component of Normal force in the soffit slab.

Piyush Santhalia

10. Pre-Camber

Piyush Santhalia

10. Pre-Camber

• Why pre-camber

– Under permanent loads the deck should have achieved the desired level.

• Desired Level at what time

– Concrete continues to sag/hog because of creep

– Achieving desired level at the end of design life: not logical

Piyush Santhalia

11. Modelling &other Suggestions

• For very wide or very deep section – Line Beam modelling: up to 20% error

• Shear Lag effect

• Difference in rates of shrinkage and drying creep because of different thicknesses of slabs.

• 3D model always yields larger deflections and larger Prestress losses

Ref: Excessive Long-Time Deflections of Prestressed Box Girders. I: Record-Span Bridge in Palau and Other Paradigms - Zdeněk P. Bažant, Qiang Yu and Guang-Hua Li

• Modelling of Piles

• Give concrete more time to gain strength before prestressing

Piyush Santhalia

THANK YOU Happy Designing

Documents

Practical Design of Balanced Cantilever Bridges - Piyush Santhalia