This document provides guidance on designing balanced cantilever bridges. It discusses: 1) Typical span configurations including 3 or more spans of varying lengths. 2) Construction sequence where segments are cast and cantilevered out from the preceding segment to form balanced cantilevers on both sides. 3) Design checks that are required at various construction stages and during service life, accounting for time-dependent effects like creep and shrinkage.

1. Practical Design of Balanced
Cantilever Bridges
Piyush Santhalia
Project Engineer - AECOM
Image: Wikipedia

2. 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

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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

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1. Introduction
Balanced Cantilever Bridge :
- Cast-in-Situ Segments
- Integral with Pier
Image: Random Site in Delhi

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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 0.7L0.6 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

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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

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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

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3. Construction Sequence
Balanced Cantilever Bridge : Delhi Metro Phase III
60 + 60m span

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3. Construction Sequence
Casting of Stitch at Mid-
span using suspender.
Balanced Cantilever Bridge :
Delhi Metro Phase III
(34 + 60 + 34m)

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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)

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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.

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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.

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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
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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.

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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

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8. Analysis
• Why Construction Stage Analysis
Bending Moment Diagram due to SW: Simultaneous Analysis
Bending Moment Diagram due to SW: Sequential Analysis

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8. Analysis
• Why Construction Stage 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

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8. Analysis
• Why Construction Stage Analysis
– Time Dependent Effects of Creep and Shrinkage
• Different age of concrete at different loading
– Modulus of Elasticity increases with time

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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

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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)

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9. Design Check
Stress check during Construction:
37 + 70 + 67 + 55 + 34m
Stresses at Top Fibre due to DL + PS + CR + SH (N/mm2)

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9. Design Check
Stresses at Top Fibre due to DL + PS + CR + SH (N/mm2)
Stress check during Construction:
37 + 70 + 67 + 55 + 34m

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9. Design Check
Stresses at Top Fibre due to DL + PS + CR + SH (N/mm2)
Stresses at Bottom Fibre due to DL + PS + CR + SH (N/mm2)
Stress check during Construction:
37 + 70 + 67 + 55 + 34m

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9. Design Check
Stresses at Top Fibre due to DL + PS + CR + SH (N/mm2)
Stresses at Bottom Fibre due to DL + PS + CR + SH (N/mm2)
Stress check during Construction:
37 + 70 + 67 + 55 + 34m

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9. Design Check
Stresses at Top Fibre due to DL + PS + CR + SH (N/mm2)
Stresses at Bottom Fibre due to DL + PS + CR + SH (N/mm2)
Stress check during Construction:
37 + 70 + 67 + 55 + 34m

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9. Design Check
Stresses at Top Fibre due to DL + PS + CR + SH (N/mm2)
Stresses at Bottom Fibre due to DL + PS + CR + SH (N/mm2)
Stress check during Construction:
37 + 70 + 67 + 55 + 34m

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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

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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

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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.

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10. Pre-Camber

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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

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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

33. Piyush Santhalia
THANK YOU
Happy Designing